CST Studio Suite - FEST3D User Manual [PDF]

Zitiervorschau

User Manual 2021

Fest3D User Manual 1

1

Table of Contents

1.

Table of Contents

2.

Fest3D Online Help 2.1.

Fest3D Introduction

2.2.

Fest3D Tutorial

2.2.1. Tutorial 1: The First Circuit

1-4 5 5-8 8 8-15

2.2.2. Tutorial 2. Running the Simulation

15-19

2.2.3. Tutorial 3. Accuracy or speed?

19-22

2.2.4. Tutorial 4. Arbitrary Shape Editor

22-28

2.2.5. Tutorial 5. Optimizer 2.2.5.1. Tutorial 5.1. Optimizer: setup

28-38

2.2.5.2. Tutorial 5.2. Optimizer: run

38-41

2.2.6. High Power

2.3.

28

41

2.2.6.1. Tutorial 6: Electromagnetic field Analysis

41-50

2.2.6.2. Tutorial 7: Multipactor Analysis (single-carrier case)

50-64

2.2.6.3. Tutorial 7: Multipactor Analysis (multi-carrier case)

64-72

2.2.6.4. Tutorial 8: Corona Analysis

72-87

Fest3D Manual

87-88

2.3.1. Requirements

88

2.3.2. Graphical User Interface (GUI) 2.3.2.1. The Main Window 2.3.2.2. Elements bar 2.3.2.3. Frequency Specifications 2.3.2.4. The General Specifications Window

88-89 89-94 94 94-97 97-100

2.3.2.5. 3D Viewer

100-104

2.3.2.6. The Preferences Window

104-105

2.3.2.7. Parameters configuration

105-107

2.3.2.8. Compare Results tool

107-109

2.3.3. Analysis

109

2.3.3.1. ElectroMagnetic Computational Engine (EMCE)

109-111

2.3.3.2. Adaptive Frequency Sampling Method

111-115

2.3.3.3. Engineering tools

116-130

2.3.3.4. EM Field Analysis

130-133

2.3.3.5. Convergence Study

133-134

2.3.3.6. Fest3D Parallelization

134-137

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Fest3D User Manual 2.3.4. Design

2 137

2.3.4.1. Optimizer (OPT)

137-144

2.3.4.2. Tolerance Analysis (TOL)

144-148

2.3.5. Synthesis Tools

148

2.3.5.1. Synthesis Tools: Low-Pass Filter

148-157

2.3.5.2. Synthesis Tools: Band-Pass Filter

157-167

2.3.5.3. Synthesis Tools: Dual-Mode Filter

167-179

2.3.5.4. Synthesis Tools: Impedance Transformer

179-184

2.3.6. High Power Analysis: Multipactor and Corona.

184

2.3.6.1. Corona Discharge Analysis

184-195

2.3.6.2. Multipactor Analysis

195-211

2.3.6.2.1. Multipactor Practical Considerations

211-213

2.3.7. Export tools

213-216

2.3.8. CLI

216-220

2.4.

Elements Database

2.4.1. Waveguides 2.4.1.1. Basic Waveguides

220 220-225 225

2.4.1.1.1. Rectangular Waveguide

225-228

2.4.1.1.2. Circular Waveguide

228-230

2.4.1.1.3. Coaxial waveguide

230-232

2.4.1.2. Arbitrary Rectangular Waveguides

232

2.4.1.2.1. Arbitrary Rectangular (ARW)

232-236

2.4.1.2.2. Coaxial waveguide

236-239

2.4.1.2.3. Cross waveguide

239-242

2.4.1.2.4. Draft waveguide

242-245

2.4.1.2.5. Elliptic waveguide

245-248

2.4.1.2.6. Ridge waveguide

248-251

2.4.1.2.7. Lateral coupling circular waveguide

251-254

2.4.1.2.8. Ridge-gap waveguide

254-257

2.4.1.2.9. Square coaxial waveguide

257-260

2.4.1.2.10. Slot waveguide

260-263

2.4.1.2.11. Truncated waveguide

263-266

2.4.1.2.12. Waffle waveguide

266-269

2.4.1.3. Arbitrary Circular Waveguides

269

2.4.1.3.1. Circular Arbitrary (ACW)

269-275

2.4.1.3.2. ACW with an Ellipse

275-278

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2.4.1.3.3. ACW with a Cross

278-281

2.4.1.3.4. ACW with Screws

281-285

2.4.1.4. Other Waveguides

285

2.4.1.4.1. Curved waveguide

285-289

2.4.1.4.2. Circular-Elliptic Iris

289-290

2.4.1.4.3. Radiating Array

290-294

2.4.2. Discontinuities 2.4.2.1. Basic Discontinuities

294-298 298

2.4.2.1.1. Step

298-305

2.4.2.1.2. N-Step

305-308

2.4.2.1.3. N-Port User Defined

308-310

2.4.2.1.4. 1-Port User Defined

310-312

2.4.2.1.5. Lumped

312-314

2.4.2.1.6. Coupling Matrix

314-317

2.4.2.1.7. Touchstone

317-318

2.4.2.1.8. Rounded corner iris 3D

318-328

2.4.2.2. Junctions

328-329

2.4.2.2.1. Cubic Junction

329-331

2.4.2.2.2. T-Junction

331-332

2.4.2.2.3. Y-junction General with N screws

332-338

2.4.2.2.4. Y-Junction (60 deg)

339-340

2.4.2.2.5. 2D OMT

340-349

2.4.2.2.6. 2D Compensated Tee

349-355

2.4.2.3. Bends

355

2.4.2.3.1. Stepped Bend

356-361

2.4.2.3.2. Mitered Bend

361-367

2.4.2.3.3. 2D Curved

367-372

2.4.2.4. Const width/height discontinuities

372

2.4.2.4.1. Arbitrary shape

372-381

2.4.2.4.2. Waveguide step with N Metal inserts

381-389

2.4.2.4.3. Waveguide step with N Screws

389-396

2.4.2.4.4. Waveguide Step with rounded corners

396-400

2.4.2.4.5. Rounded corner iris

400-405

2.4.2.4.6. 2D Rounded short

405-410

2.4.2.5. Coaxial library 2.4.2.5.1. Cavity with posts

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411 411-424

Fest3D User Manual 2.4.2.5.2. Straight feed cavity

424-436

2.4.2.5.3. Mushroom feed cavity

436-449

2.4.2.5.4. Straight contact feed cavity

449-460

2.4.2.5.5. S-Shape contact feed cavity

460-471

2.4.2.5.6. Loop feed cavity

471-482

2.4.2.5.7. Magnetic feed cavity

482-493

2.4.2.5.8. Top contact feed cavity

493-504

2.4.2.5.9. General cavity

504-516

2.4.2.6. Helical resonators library

516-517

2.4.2.6.1. Helical resonator

517-528

2.4.2.6.2. Contact feed to helical resonator

528-540

2.4.2.7. CST solver library

3.

4

540

2.4.2.7.1. General rectangular cavity

540-558

2.4.2.7.2. General cylindrical cavity

558-577

2.4.2.7.3. Lateral couplings to cylindrical cavity

577-585

2.4.2.7.4. Circular to Rectangular T-Junction

585-593

2.4.2.7.5. Circular T-Junction

593-601

2.4.2.7.6. Ridge T-Junction

601-615

2.4.2.7.7. Coaxial T-Junction

615-630

2.4.2.7.8. Square coaxial T-Junction

630-644

2.4.2.7.9. General bend

644-654

2.4.3. Allowed Symmetries

654-656

Index

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Fest3D Online Help

The Fest3D help system is organized into the following main topics: Introduction

What is Fest3D.

Tutorial

Guided tour of Fest3D features. Recommended for new users.

Manual

Using Fest3D - reference manual.

Elements database

Description of the elements supported by Fest3D.

2.1 Fest3D Introduction The objective of this introduction is to explain the motivations behind Fest3D development and the target of Fest3D software, as well as the approach and basic concepts used by Fest3D. The introduction contains the following topics: Objective

The objective of Fest3D.

Features

Main Features in Fest3D.

Terms and Concepts

Terms and concepts widely used in Fest3D and in this documentation.

Features Fest3D is an efficient software tool for the accurate analysis of passive components based on waveguide technology. Fest3D is the first commercial software capable to integrate high power effects in the design process.

Analysis Fest3D is able to efficiently analyse different type of passive microwave structures in waveguide technology. Basically, Fest3D is based on an integral equation technique combined with the Method of Moments. Additionally, the Boundary Integral-Resonant Mode Expansion (BI-RME) method is employed for extracting the modal chart of waveguides with non-canonical shapes. These methods ensure a high degree of accuracy as well as reduced computational resources (in terms of CPU time and memory). On this basis, Fest3D is capable to simulate complex microwave devices in extremely short times (of the order of seconds or few minutes) whereas general purpose software (based on segmentation techniques such as finite elements or finite differences) can spend hours for the same calculation. Furthermore, unlike mode-matching techniques, the electromagnetic algorithms employed in Fest3D minimize the problems of relative convergence leading to more confident results. Moreover, the integral equation technique extracts part of the frequency dependent computations, allowing a faster computational time per frequency point when compared to mode-matching techniques. This benefit is more evident when many modes are required for an accurate analysis of the component. Based on these methods, the user can analyze a wide range of passive components with Fest3D: Filters (dual-mode, evanescent, bandstop, interdigital, waffle-iron...) Multiplexers Dual-mode filters Couplers Polarizers Waffle-iron filters

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Evanescent filters Power Dividers Bandstop filters Infinite phased array antennas

Synthesis Fest3D includes the possibility to automatically design several types of components from the user specifications making use of the so-called Synthesis Tools. Up to now, the user can easily design band-pass filters, low-pass filters, rectangular tapers, dual-mode filters in circular wavwguide. The synthesis stage performs full-wave simulations to consider higher waveguide modes. Thanks to this and to particular algorithms employed in each case, the synthesis process provides very good responses with respect to the user specifications. In particular, bandpass filters can be designed with up to 25-230 % of BW without the need of post-optimization, as well as dual-mode filters in circular waveguide with different order and making use of different resonant modes. Once the synthesis process is finished, the full structure is simulated and the full-wave result is shown.

Optimization Fest3D has an optimization tool (OPT) for the refinement of the component geometrical parameters to get the desired response. The OPT supports multiple optimisation algorithms such as: Downhill simplex method. Powell's direction set method. Gradient method. The OPT also supports weighted constraints in the form of equalities or inequalities between a left and a right expression of the parameters being optimised. This allows, for instance, controlling the maximum length of a filter or to ensure that an element length is larger than a particular value. The OPT progress can be monitored in real time, as well as stopped, reconfigured and resumed from the Graphical User Interface (GUI) at any time. Moreover, the results from the previous optimization iteration and the current one are shown, which allows identifying the source of the improvement in the response.

Tolerances Fest3D also allows performing tolerace analysis in the components by varying their dimensions according to a gaussian deviation. The different tries are shown altogether and the user can control the whole process.

High Power Fest3D can be easily used to analyse high-power breakdown phenomena in several type of components. In particular, multipactor and corona (arcing) modules are fully integrated into Fest3D which is capable to determine the breakdown level in complex passive components.

Export 3D geometry Fest3D can export the 3D geometry to SAT format. This allows an easy interaction with other EM tools and using Fest3D exported file in, e. g., milling machines.

Export Project to CST MWS® Copyright 2009-2019 Dassault Systemes Deutschland GmbH.

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Fest3D projects can be exported to a CST Microwave Studio® project.

Export Project to CST Design Studio® Fest3D projects can be exported to a CST Design Studio® project.

Terms and Concepts Several terms and concepts are used in Fest3D. Even though some of them may be well known to some users, these terms may have different meanings in Fest3D, or some users may not associate them to millimeter-wave and microwave circuits. Circuit

The kind of circuit currently supported by Fest3D: passive, linear millimeter-wave or microwave circuit composed on cascaded discontinuities based on rectangular and circular waveguides (and perturbed variants of them). The full list of the supported waveguides and discontinuities is available in the Elements Database.

Element

The term element is very generic. In Fest3D it indicates each elementary building block of a passive, linear millimeter-wave or microwave circuit. A synonym also used in Fest3D is component. The elements, or components, supported by Fest3D are divided in two classes: waveguides and discontinuities. See also the Elements Database.

Component

A synonym for element.

Waveguide

A classic microwave waveguide, optionally open-ended (I/O port) or closed on a load, and attached to something else (one or two discontinuities). A whole section of this manual is dedicated to the various waveguides supported by Fest3D.

Discontinuity A component connecting two or more waveguides. Discontinuities often have a non-uniform cross-section and may have non-trivial 3D geometry. In Fest3D you can only connect a waveguide to a discontinuity, and vice-versa. A whole section of this manual is dedicated to the various discontinuities supported by Fest3D. Port

Ports are used to connect elements together. Each element has a number of ports equal to the number of elements it is connected to. Each port of an element is connected to a port of another element. The connections between elements are represented as black lines in the GUI.

GUI

Graphical User Interface. The part of a program devoted to interaction with the user. The Fest3D GUI activates the other parts of Fest3D on user demand, by launching external executables.

EMCE

ElectroMagnetic Computational Engine. The part of Fest3D that actually performs the simulation of millimeter-wave and microwave circuits.

OPT

OPTimization service. The part of Fest3D devoted to optimization. In order to optimize a circuit, the OPT repeatedly invokes the EMCE. See the Optimizer section in this manual.

Synthesis Tools

Additional programs integrated in Fest3D, capable of performing microwave circuits synthesis from user specifications. See the Synthesis Tools section in this manual.

Engineering Tools

Additional programs integrated in Fest3D, used to perform unit conversions and small computations. See the Engineering Tools section in this manual.

Convergence Convergence Study is an essential technique to reasonably ensure the accuracy of EMCE results. Study A brief, but incomplete, summary is that the simulation must always start with low numeric accuracy parameters, continuously increasing them until the response converges. A single simulation with high numeric accuracy parameters is definitely not enough to ensure accuracy of

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the results. In Fest3D, numeric precision parameters include all the number of modes and also element-specific parameters. See also the tutorial section Accuracy or Speed? MoM

Method of Moments. A mathematical model of microwave propagation physics, used in Fest3D.

Integral Equation

A mathematical model of microwave propagation physics, used in Fest3D.

BI-RME

Boundary Integral - Resonant Mode Expansion. A very efficient electromagnetic model of microwave propagation physics, used in Fest3D.

2.2 Fest3D Tutorial The goal of the tutorials is to show you how to use the basic features of Fest3D to create, edit, analyze and optimize a millimeter-wave or microwave circuit. The first three tutorials are provided to familiarize you with the Fest3D user interface. Tutorials 4 and 5 treat more complex topics, like the Arbitrary Shape Editor and the Optimizer. Tutorial 6 shows how the EM field analysis tool works, and tutorials 7 and 8 cover high power issues, Multipactor and Corona, respectively. To learn the basic features of Fest3D, you are recommended to work through tutorials in the order they are presented. It is also essential to play around with the list of examples provided to you during the installation in the folder "Examples". 1. The First Circuit is a step by step guide to the creation of a simple microwave circuit. 2. Running the Simulation shows you how to configure and execute the analysis (simulation) of a microwave circuit. 3. Accuracy or Speed? introduces you in the world of numeric methods, where high accuracy often means long computation time. 4. The Arbitrary Shape Editor shows you how to create and edit the arbitrary shapes used by some elements. 5. Optimizer is a group of tutorials describing how use the Fest3D Optimizer: 5.1 Optimizer: setup describes how to prepare a circuit for optimization and how to configure Fest3D Optimizer. 5.2 Optimizer: run shows how to start an interactive optimization and what you can do during it. 6. EM field analysis is a step-by-step guide on how to use the EM field analysis module 7. Multipactor analysis is a step-by-step guide on how to use the Multipactor analysis module for single and multi-carrier signals. 8. Corona analysis is a step-by-step guide on how to use the Corona analysis module

2.2.1 Tutorial 1: The First Circuit In this tutorial, you will learn how to create and edit millimeter-wave and microwave circuits with Fest3D. Tutorial 1 is divided in four lessons. In order to get maximum benefit from the tutorial, you are recommended to work through the lessons in the order they are presented. 1. Important Concepts: waveguides, discontinuities, connections, coordinate systems gives an overview of the approach used by Fest3D to represent millimeter-wave and microwave circuits. 2. Creating elements gives a step-by-step guide on how to create the elements contained in a simple circuit. 3. Editing elements explains how to view and modify the properties of created elements. 4. Connecting Elements shows you how to connect the elements together.

Important Concepts: waveguides, discontinuities, connections,

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coordinate systems In Fest3D, circuit means a passive, linear millimeter-wave or microwave circuit. This is what Fest3D supports. In Fest3D, elements are the basic blocks used to build a circuit. They are represented by icons with a schematic picture of their 3D shape. A circuit is composed by a set of elements connected to each other, respecting certain connection rules. The connection between two elements goes through the ports of these elements. A port is where the modal expansion is defined according to a certain coordinate system. When connecting two elements through their ports, the coordinate systems should match each other. In most of the cases, Fest3D adjusts the coordinate systems of the elements automatically, but there are some exceptions that need user interaction. The situation of the coordinate system is defined in the documentation of each element. Elements are divided into two main groups: waveguides and discontinuities. Waveguides are the simplest elements. They usually have uniform cross-section, and they can be attached to other elements at both sides (front and back). Two simple examples are the rectangular waveguide and the circular waveguide. The complete list of supported waveguides is in the Waveguides section of this manual. Discontinuities are used to connect waveguides together. A discontinuity often has non-uniform cross-section and non-trivial 3D geometry. A discontinuity may have a 3D volume or may be a zero-thickness surface. Two simple examples are the step and the T-junction. In Fest3D you can only connect a waveguide to a discontinuity, and vice-versa. The complete list of discontinuities supported by Fest3D is in the Discontinuities section of this manual. The following figures show a simple circuit (an asymmetric one-pole cavity) in Fest3D main window and its 3D geometry:

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In order to interactively view the 3D geometry of the circuit, click on the

icon: the 3D Viewer window will open.

In this example, the circuit is composed by five rectangular waveguides ( represent the connections among them.

) and four steps (

). The black lines

As you can see, Fest3D main window is divided in three parts: 1. the menubar and toolbar at the top 2. the canvas in the center 3. the canvas in the bottom The menubar lets you access most Fest3D features, including the usual File Load and Save, cut-and-paste and Fest3D specific features. The complete description of menubar contents is in the Main Window Menubar section in this manual. The toolbar duplicates the most used features of the menubar for faster access. The canvas in the center contains the current circuit and lets you edit it. The canvas on the bottom is used to show the output information of a simulation. In the right side there is a bar containing the Fest3D elements (elements bar). This bar is used to select the element to be created in the main canvas. The elements bar can be hidden and pop-up by means of the rectangular icon in the toolbar.

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Creating elements In Fest3D, creating an element consists in two steps: 1. click on the icon of the element type you want from the elements bar. The icon will stay pressed. 2. click on the canvas. An element of that type will be added where you clicked. If you click again on the canvas background (not on an element or a connection) further elements of the same type will be added. Let's say you want to create the asymmetric one-pole filter seen above. For this purpose, create five rectangular waveguides and four steps. You should obtain something like the left figure:

Now click on the menubar command structure | show icons. The elements should change to something like the right figure. If the numbers are ordered differently, you can move the element around as explained below. This is not needed in general (there is no requirement that the elements you connect have any particular ordering), but you would better know how to perform such basic operations on elements. You can move elements on the icon button at the top of the elements bar, then press mouse left button on an element in the canvas and drag it. You can select more than one element by pressing mouse left button on the canvas background, then dragging the mouse. A rectangular selection area will be created, and all elements inside it will be selected. You can now move all selected elements at once by dragging them with the mouse. You can also cut, copy or delete all selected elements at once using the corresponding commands in the menubar or in the toolbar. After a cut or copy, you can undo the operation or you can paste the contents of the clipboard using the corresponding commands in the menubar or in the toolbar. Now that you have learned how to do it, order all the elements as shown in the right picture above and proceed with the next part of this tutorial.

Editing elements This part of the tutorial explains how to view and edit the properties of the created elements. Click with the right mouse button on the rectangular waveguide [1] you created in the canvas. The following

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Element Properties dialog box will appear:

Now you can enter the values for the geometric parameters A, B and L (in millimeters) of the rectangular waveguide. In this tutorial you are building the one-pole cavity seen above, so enter the following values then click on the OK button: A 22.86 B 10.16 L 10.0 Since these dimensions correspond to a standard waveguide, you could have clicked on the standard waveguide box, and select the WR-90. Doing this, the A and B dimensions (22.86, 10.16) are automatically obtained. The rectangular waveguide [2] of the circuit has different geometric parameters: A 8.0, B 10.16, L 2.0. The rectangular waveguide [3] has geometric parameters: A 22.86, B 10.16, L 15.0. The rectangular waveguide [4] has the same geometric parameters as [2]: A 8.0, B 10.16, L 2.0. The rectangular waveguide [5] has the same geometric parameters as [1]: A 22.86, B 10.16, L 10.0. In general you may also want to edit the waveguides Common Properties, but in this case you can leave them to the default values. You need instead to change the SubType of rectangular waveguides [1] and [5] to Input/Output Port, in order to inform Fest3D that they will be the external interfaces of the circuit. Set rectangular waveguide [1] to have I/O Port

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Number 1 and rectangular waveguide [2] to have I/O Port Number 2. It is now time to edit the four steps. Click with the right mouse button on the step [1]., then click on the Ports page. The following Element Properties dialog box will appear:

Enter the values for the geometric parameters: X offset (mm) of port 2 4.0 Y offset (mm) of port 2 0.0 Rotation (degrees) of port 2 0.0 The step [2] is identical to step [1] but of opposite sign, edit it too and enter the values: X -4.0, Y 0.0, Rot 0.0. The step [3] and step [4], have instead the following values: X 5.0, Y 0.0, Rot 0.0. and X -5.0, Y 0.0, Rot 0.0., respectively, That's all. In the next part of this tutorial you will connect the elements together.

Connecting elements This part of the tutorial explains how to create and edit the connections among elements. Click on the connect ( pencil.

) button at the top of the elements bar. The mouse pointer shape will change to a

Press and hold the left mouse button on the first rectangular waveguide. Drag the mouse to the first step: a black line connecting the two elements will appear. Release the left mouse button. Repeat the same procedure until you completed all the connections as in the left figure:

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Click again on the menubar structure -> show icons command, you will obtain the right figure. You can delete connections by clicking on the arrow ( ) button at the top of the elements bar, then press mouse left button on a connection in the canvas to select it, finally click on the menubar edit -> delete command or hit the delete key on the keyboard. In Fest3D there is a subtlety in definition of the connections. The reason is that for some discontinuities (Step, N-Step, T-Junction, Constant width/height arbitrary shape, Y-Junction) the various ports where you can connect waveguides are not equivalent. But when you connect two elements, you have no way to specify the ports to use... a simple firstfree first-used algorithm is used. In other words, the first element you connect is considered as port 1, the second element as port 2, and so on. In particular, you saw that a step has two ports but you can specify X offset, Y offset and Rotation only for the second port. The Edit Connections dialog exists for changing the port definition. Click on the move ( ) button at the top of the elements bar, then click with the right mouse button on one of the connections (the black lines) of the discontinuity. The Edit Connections dialog will appear. This dialogs allows the user to specify the ports of a discontinuity where each connected waveguide should be attached. For each connected element, a row of radio-buttons is available to specify which port it should use. Attaching more than one waveguide on the same port is not allowed.

2.2.2 Tutorial 2. Running the Simulation Tutorial 2 is divided in two parts. In order to get the maximum benefit from the tutorial, you are recommended to work through the lessons in the order they are presented. In particular, this tutorial assumes you have read, understood and practiced the topics treated in Tutorial 1 and you have a circuit already loaded in Fest3D (preferrably the circuit you created in the previous Tutorials). Configuring explains how to configure the frequency/angle sweeps and the global circuit parameters. These windows are explained in detail in the sections Frequency specifications and General Specifications. Running shows how to compute S parameters or multi-mode S, Z or Y matrices of a Fest3D circuit.

Configuring Once you have created a millimeter-wave or microwave circuit, there are two main things that must be configured before you run a simulation on it:

Frequency/angle sweeps configuration General modes/symmetries configuration

Frequency/angle sweeps configuration

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For this purpose, click on the Frequency Specifications command in the execute menu bar, or click on the Frequency Specifications ( appear:

) button in the toolbar. A dialog box, typically looking as the following figure, will

This window lets you edit the frequency range and points　where the circuit should be simulated as well as the method (discrete/adaptive) to be used. In case your circuit contains Radiating Array elements, you can also perform an angle sweep (theta or phi) instead of a frequency sweep. The frequency (or angle) sweep is specified by its start and end frequencies in GHz (or degrees for angles), and by the sampling. Fest3D supports three different sampling modes: 1. step lets you specify the distance between consecutive points to be sampled. 2. number of points lets you specify the total number of points to sample, including start and end points. 3. manual selection of points lets you manually edit each and every point you want to simulate. Only the last sampling mode allows non-uniformly distributed points. For further details, see the General Specifications section in this manual. In our case (the asymmetric one-pole cavity) you should enter the following values: Frequency Start 9.0 Frequency End 12.0 Frequency Step 0.001

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Once the frequencies/angle sweeps are defined. It is necessary to configure the global symmetries and the default waveguides parameters for the circuit.

General specifications For this purpose, click on the General Specifications command in the execute menu bar, or click on the General specifications button (

)

For a detailed explanation of the meaning of the various global symmetries and default waveguides parameters, see again the General Specifications section in this manual. The asymmetric one-pole cavity example you created, in particular, has constant height and is invariant under translations along the Y axis. So the Constant height (H plane) symmetry can be applied. Click on it. In this case no other symmetry is applicable. Since you are using symmetries, you can (and should) lower the various number of modes used in waveguides. Enter

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the following values: Number of accessible modes 4 Number of MoM basis functions 10 Number of Green function terms 100 The other parameters can stay at their default values: Dielectric Permittivity 1.0 Dielectric Permeability 1.0 Dielectric Conductivity 0.0 Metal Resistivity 0.0 Number of Taylor expansion terms 1

Running Computing the S parameters is really simple: click on the Analyze ( ) button in the toolbar and watch the progress messages produced by the Electromagnetic Engine (EMCE) integrated in Fest3D. If the Autoplot option in the graphics menu is active, or if you execute the Plot command (still in the graphics menu) at the end of the simulation, the S parameters graphical plot will be displayed. With Fest3D you can also compute the multi-mode S, Z or Y matrix of a circuit, to reuse it later as a single block in a bigger circuit. You can stop a running simulation at any moment by clicking on the stop (

) button.

The following figures show Fest3D main window during the simulation and the produced plot:

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2.2.3 Tutorial 3. Accuracy or speed? In this tutorial it is explained how to manage and balance for your purposes the tradeoffs between simulation accuracy and speed that is typical of Fest3D and other numerical simulation software. This tutorial assumes that you have a circuit already loaded in Fest3D (preferrably the circuit you created in the previous Tutorials). This tutorial is divided in two parts. 1. Accuracy Parameters explains which parameters control numeric accuracy in Fest3D, their meaning and the effect of changing them. 2. Balancing shows how to choose a trade-off between accuracy and speed in Fest3D.

Accuracy Parameters In Fest3D, each element (waveguide or discontinuity) can be configured independently from the others. Several elements also contain numeric accuracy parameters. To simplify the task of configuring manually the numeric accuracy (and other) parameters common to all waveguides, by default their Common page is set to Use General Specifications, i.e. to use the default values stored in the General Specifications dialog box you used in Tutorial 2. This allows configuring the parameters common to all waveguides at once, unless you manually set some waveguides not to use the default values.

Waveguides Common Parameters

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Let's start with the numerical parameters Number of accessible modes, Number of MoM basis functions and Number of Green function terms. Here we will not describe the electromagnetic theory and models behind Fest3D, which would be needed to understand the meaning of the above parameters. We will only say that Number of accessible modes is the number of modes in a waveguide that are treated as accessible or propagating by Fest3D i.e. only those modes are assumed to transport E.M. fields and energy across the whole length of a waveguide. Increasing these three parameters (Number of accessible modes, Number of MoM basis functions and Number of Green function terms) will yield more accurate results at the price of higher memory usage and longer computation time. Typical values are: Parameter

Low Accuracy

Medium Accuracy

High Accuracy

Number of accessible modes

10

20

40

Number of MoM basis functions

30

60

120

Number of Green function terms

300

600

1200

For simple circuits, starting with Low Accuracy (i.e. 10 accessible modes, 30 MoM basis functions and 300 Green function terms) is usually enough to deliver satisfactory results. Of course, this is true if no symmetries are considered. If symmetries are taken into account, the circuit parameters can be dramatically reduced, keeping accuracy but increasing speed. This is particularly important if the circuit is going to be optimized. Anyway, there is no guarantee that certain fixed values for numeric accuracy parameters will yield satisfactory results for your particular circuit. It is thus of critical importance to always perform a Convergence Study. Some elements contain also other numeric accuracy parameters, as explained in the following paragraphs.

Arbitrary Rectangular The Arbitrary Rectangular waveguide, which is also used as base for all waveguides in the RECT-CONTOUR BASED WG section in the palette of elements, contains the Number of reference box modes parameter:

The Number of reference box modes is the number of modes to be used in the rectangular cavity to compute the modes of the arbitrary rectangular waveguide. The required value for this parameter depends a lot on both the role of the arbitrary waveguide and the ratio between the reference box area and the arbitrary waveguide area. If the arbitrary rectangular waveguide is smaller than the surrounding waveguides to which it is connected, i.e. it is playing the role of an iris, the number of generated modes must be slightly higher than the number of the MoM basis functions of such an arbitrary waveguide. Therefore, the number of reference box modes has to be adjusted to reach this condition. If it is set to zero by the user, Fest3D will automatically calculate its value. On the other hand, if the arbitrary waveguide is larger than one of the waveguides to which it is connected, the number of generated modes has to be slightly larger than the number of Green function terms of the arbitrary waveguide. Therefore, the number of reference box modes has to be modified to accomplish such a rule. In order to get enough generated modes, this number of reference box modes will need to be increased if the area of the arbitrary waveguide is much smaller than the area of the reference box. By default, the number of reference box modes is set to the double of the number of Green function terms.

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The Number of reference box modes is also important for another reason: Fest3D can directly connect to each other two Arbitrary Rectangular waveguides or derivatives using a Step or N-Step. In this case, the coupling integrals between the two sets of modes are computed by convoluting two coupling integrals matrices. Since the matrices are only known numerically, in order to obtain accurate results Number of reference box modes and Number of terms in Green's function should be high enough. In case you have Arbitrary Rectangular waveguides with TEM modes (the cross section must be non-simply connected), which propagate even at zero frequency, the two numbers above become more and more important at frequencies much lower than the cutoff of the first non-TEM mode, since the circuit behaviour strongly depends on the exact couplings between TEM modes. With so low frequencies, the Number of accessible modes and Number of MoM basis function will have very little effect on the overall accuracy, since only the TEM modes will be accessible. Known accuracy limitations exist in Fest3D if you try to analyze a circuit with TEM modes at extremely low frequencies (< 0.2 GHz): due to the TEM-TEM couplings being computed numerically and not with analytical exactness, the results produced by Fest3D will be less and less accurate as frequency decreases. To solve this problem, you need to progressively increase the Number of reference box modes and Number of Green's function terms until you get convergence (see Convergence Study above) in the frequency range you are using.

Arbitrary Circular The Arbitrary Circular waveguide, which is also used as base for all waveguides in the CIRC-CONTOUR BASED WG section in the palette of elements, contains two basic precision parameters: the number of box modes and the Distance between points. The number of box modes (in this case, the box is a circle!) has the same meaning as for the ARW case, so the same can be said.

Balancing This section gives basic guidelines to the art of finding a compromise between accurate simulations and fast simulations. Due to the sheer size an complexity of the topic, only a brief explanation of high-level strategies can be summarized here. First of all you should understand which of your goals and needs are immediate, and which can be postponed. Accuracy issues can be usually postponed, while fatal errors reported by the EMCE should be addressed immediately. 1. Split large circuits and use the User Defined element to import generalized Z matrices generated from subcircuits. Apply the rest of this section on each subcircuit if appropriate (i.e. you often cannot optimize a subcircuit since you only know the results you want from the complete circuit). This divide-and-conquer strategy costs some time to set up, but can really make life easier when tackling very large circuits. 2. Once you have created a circuit in Fest3D, the next step should be to complete its simulation without errors. At this early stage accuracy has no importance at all, but rather can be an obstacle by slowing down each simulation you perform and halting the simulation due to accuracy errors. For this reason, you should usually stick down to the "Low Accuracy" values listed above in Accuracy Parameters section. Now continue retrying to simulate your circuit until you have solved all geometry and numerical errors that the EMCE may report. Depending on the errors you get, finding a solution may be tricky. It is possible that you tried to do something not supported by Fest3D, or maybe you made some mistakes and the geometry you created is not what you think it is. The 3D Viewer section may help you. 3. Ok, now the simulation completes successfully and produces a result. You can be confident that many times this result will be, at least, inaccurate. It's now time to think about the next step: Global Symmetries. Enable all the symmetries that apply to your

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circuit, since they will increase the accuracy. If you made mistakes and your circuit does not respect the symmetries you think it respects, Fest3D will report the error. As above, keep retrying until you have solved all errors. 4. Understand what is your final goal. If the geometry you are using is already fixed (i.e. you are only analyzing a pre-defined circuit and you are not planning to tune or optimize it), then skip all the rest of this section and immediately perform a Convergence Study. Otherwise, you should start tuning accuracy and speed together. 5. Tuning accuracy and speed together. You will need a lot of compromises, and only you can be the final judge. Some tips and tricks you may find useful are: each simulated frequency point costs time. Consider using the Adaptive Frequency Sampling to solve the frequency sweep, or in case of using the discrete solution, reduce the number of frequency points to the minimum you can live with. Consider editing manually the list of sampled frequencies. you don't need a complete Convergence Study, but a quick check that your results are not too far from convergence is necessary. At this point is very useful to employ the Comparing results tool available in Fest3D to compare the record of simulation results. If you use Fest3D optimizer: do not use too many parameters simultaneously, they slow down optimization and make more difficult for the algorithm to reach the target (your goal functions). remember that at any time you can stop the optimizer, manually change some parameters, then perform one-shot analysis and/or resume optimization. if possible, use formulas instead of constraints: formulas reduce the effective number of free parameters, speeding up the optimization. if a certain optimization algorithm does not reach the goal functions you want, try alternating among different algorithms and/or slightly change the parameters values manually. 6. Don't forget to perform a Convergence Study.

2.2.4 Tutorial 4. Arbitrary Shape Editor In this tutorial it is described how to use the Arbitrary Shape Editor to view and edit arbitrary shapes for the Fest3D elements Arbitrary Rectangular, Arbitrary Circular and Constant width/he¡ght discontinuity . This tutorial is divided in four parts: 1. 2. 3. 4. 5.

Introduction what is the Arbitrary Shape Editor. Terms and Concepts terms and concepts widely used in the Arbitrary Shape Editor and in this documentation. Contours and Region of Interest the high-level structure of an arbitrary shape: how to use them Points, Segments, Arcs, Elliptical Arcs the basic blocks of an arbitrary shape: how to use them Caveats and Differences between Arbitrary Rectangular, Arbitrary Circular and Constant width/height arbitrary shape discontinuity

Introduction Some elements supported by Fest3D (Arbitrary Rectangular, Arbitrary Circular and Constant width/height arbitrary shape discontinuity) do not have a predefined 3D geometry. They allow the user to arbitrarily define their shape or cross section in a 2D plane, and they are invariant under translations in the direction orthogonal to that plane. The Arbitrary Shape Editor is a 2D shape editor, allowing to view and edit the arbitrary shape of such elements. The different kinds of elements allowing arbitrary shapes have slightly different features and limitations. For this reason, the Arbitrary Shape Editor offers similar, but not identical, functionalities when editing the different arbitrary

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shapes corresponding to the Arbitrary Rectangular, Arbitrary Circular and Constant width/height arbitrary shape discontinuity elements. The following figure shows a typical Arbitrary Shape Editor window as it appears on the screen:

Terms and Concepts Several terms and concepts are used in Fest3D Arbitrary Shape Editor. Even though some of them may be well known to some users, these terms may have different meanings in Fest3D, or some users may not associate them to arbitrary shapes of millimeter-wave and microwave circuits. Contour

A planar, continuous, non self-intersecting and possibly closed curve composed by Segments, Arcs and Elliptic Arcs. An arbitrary shape is made of one or more contours (possibly enclosing one another, but not intersecting) plus some prescriptions to decide which connected area contains the electromagnetic fields.

Region of Interest

A user-specified Point which must be inside the area intended to contain the electromagnetic fields.

Point

The start or end point of a segment, arc or elliptic arc. If two Segments, Arcs and Elliptic Arcs arcs have a Point in common, they are consecutive and belong to the same contour. The user can modify the coordinates of a Point only if it is the start or end point of segments, not arcs or elliptic arcs.

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Segment

A normal, straight segment. In the Constant width/height arbitrary shape it is also possible to change a Segment into a Port.

Port

A Segment used to connect the arbitrary shape with other elements. Only supported by Constant width/height arbitrary Shape element. Drawn in pink.

Arc

A mathematical arc of circle.

Elliptic Arc

A mathematical arc of ellipse.

Contours and Region of Interest If an arbitrary shape contains multiple contours, the contours must not intersect to each another. A contour may completely contain other contours (again, contours must not intersect to each other). Using multiple contours also raises an ambiguity: if there are more than one connected areas, which one is intended to contain electromagnetic fields? The following example comes from the Arbitrary Rectangular waveguide:

The shape of the example defines the areas S,S1,S2 or S3 but only one of them can be simulated at once. The user needs a way to resolve this ambiguity, or at least know which area will be used by Fest3D to simulate the electromagnetic fields propagation. To do so, the user has to specify the coordinates of a Point (the Region of Interest): the area containing the Region of Interest will be the one used for the simulation. The Region of Interest is drawn as a blue cross (

).

Creating and Deleting Contours You can create a Contour from the Add Contour command in the Edit menu. The following dialog will appear:

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You can only create Contours with a standard shape (rectangular, circular, elliptical) but you are free to modify the Contours as you want after you created them. To delete a Contour, click on a part of it (Point, Segment, Arc, Elliptical Arc), then execute the Delete Contour command in the Contour menu. If you deleted something by mistake, use the Undo command in the Edit menu.

Editing Points, Segments, Arcs, Elliptical Arcs These are the building blocks of contours, and thus of arbitrary shapes. The basic idea behind the Arbitrary Shape Editor is that complicated Contours can be created incrementally, by progressively creating and editing its building blocks (Points, Segments, Arcs, Elliptical Arcs). Starting from a simple Contour, you can edit or split its Points, Segments, Arcs, Elliptical Arcs. If a Point is only connected to Segments, you can edit it and freely change its coordinates. To edit a Point, Arc or Elliptical Arc (Segments can only be viewed, not edited) do the following: Select the Point, Arc or Elliptical Arc you want to edit by clicking on it with the mouse left button. It will become red. Choose the command you want to perform from the menu bar, or from the popup menu that appear by pressing the mouse right button.

Editing Points By selecting a Point, the following Point menu will be accessible, either from the menu bar or pressing the mouse right button:

Delete Point: deletes the selected Point. The two adjacent Segments, Arcs or Elliptical Arcs are deleted and replaced by a single segment. Change corner to arc: changes the Point and the two adjacent Segments, Arcs or Elliptical Arcs into a single Arc. Smooth corner: smoothes the corner having the Point as vertex. The user has to define the Radius (value greater than zero). NOTE: the point must be adjacent to Segments (Arcs or Elliptical Arcs not allowed). Edit Point: opens a dialog showing Point X,Y coordinates and allowing the user to modify them. NOTE: the

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point must be adjacent to Segments (Arcs or Elliptical Arcs not allowed).

Editing Segments By selecting a Segment, the following Segment menu will be accessible, either from the menubar or pressing the mouse right button:

Delete Segment: deletes the selected Segment and extends the adjacent Segments until they converge. Split Segment: splits the selected Segment in 2 new Segment whose dimensions are defined by means the ‘Split percentage (%)’ value (specified by the user). Multi-split Segment: splits the selected Segment in N equal segments. The number N is specified by the user. Change to Arc: allows to change the Segment into an Arc. The user has to define the Radius. Using the default value the generated Arc will be 90° wide. Change to Port: allows to change the Segment into a Port. Available only for the Constant width/height arbitrary shape element. Toggle Invisible: makes the selected Segment Invisible allowing to create an Open Contour. Segment Properties: opens a dialog showing Segment properties: extrema coordinates and segment length.

Editing Arcs and Elliptical Arcs In the following paragraph, the term Arc means both circular Arcs and Elliptical Arcs, unless explicitly stated otherwise. By selecting an Arc or Elliptical Arc, the following Arc menu will be accessible, either from the menubar or pressing the mouse right button:

Delete Arc: deletes the selected Arc and extends the adjacent segments until they converge. Split Arc: splits the selected Arc in 2 new arcs whose dimensions are defined by means the ‘Split percentage (%)’ value (specified by the user). Multi-split Arc: splits the selected Arc in N homogeneous Arcs. The number N is specified by the user. Polygonize Arc: approximates the selected Arc by N homogeneous Segments. The number N is specified by the user. Change to Segment: changes the Arc into a Segment. Reverse Arc: changes the Arc orientation.

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Edit Arc: opens a dialog box allowing to view and edit Arc properties, as shown in the following figures:

In case the selected Arc is circular, both the Arc and Elliptical Arc pages are active. You can modify the Radius

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or Extent parameters on the Arc page or change the Arc from circular to elliptical modifying the Major Axis and Minor Axis parameters in the Elliptical Arc page. Otherwise if the selected Arc is elliptical, only the Elliptical Arc page is active. To transform an Elliptical Arc back into a circular Arc, set both Major Axis and Minor Axis parameters to the same value and click on the ‘OK’ button. It is also possible to apply a Rotation to an Elliptical Arc.

Caveats and Differences The elements Arbitrary Rectangular, Arbitrary Circular and Constant width/height discontinuity contain some differences and caveats the user should be aware of in order to use the arbitrary shape editor properly. Some differences have been already explained above, here they are only summarized: Constant width/height discontinuity has no Reference Cavity, the other elements have it and implicitly define it. Constant width/height discontinuity editor is the only one allowing ports.

2.2.5 Tutorial 5. Optimizer The goal of this tutorial is to show you how to use Fest3D Optimizer to tune a circuit. Tutorial 5 will guide new users through the procedure of optimizing (tuning) the circuit you created in the previous tutorials. Even though it is possible to execute this tutorial on a different circuit, this requires some practice and is not recommended for new users.

Concepts In Fest3D, optimization is performed by varying some (user-specified) parameters following an (user-specified) algorithm in order to minimize the difference between the circuit output and the target (user-specified) output. The rest of this tutorial explains how to specify the parameters, target and algorithm in Fest3D Optimizer, how to start and control the optimization, and finally some advanced techniques.

Index Tutorial 5 is divided in two parts: 5.1 Optimizer: setup describes how to prepare a circuit for optimization and how to configure Fest3D Optimizer. 5.2 Optimizer: run shows how to start an interactive optimization and what you can do during it.

2.2.5.1 Tutorial 5.1. Optimizer: setup This tutorial is the first of the two tutorials dedicated to Fest3D Optimizer. In this tutorial you will learn how to prepare a circuit for optimization and how to configure Fest3D Optimizer. Tutorial 5.1 will guide new users through the procedure of setting up an optimization for the circuit you created in the previous tutorials. Even though it is possible to execute this tutorial on a different circuit, this requires some practice and is not recommended for new users. Tutorial 5.1 is divided in three parts: 1. Choose which parameters to optimize explains how to prepare Fest3D to optimize the circuit parameters you

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want. 2. Define formulas, goal functions and constraints shows how to setup the target output you would want your circuit to produce. 3. Choose and configure the algorithm shows how to choose and configure one of the optimization algorithms supported by Fest3D.

Choose which parameters to optimize This part of the tutorial explains how to choose the circuit parameters that will be optimized (tuned).

By opening the Parameters window ( ) or Optimizer ( ) buttons in the Toolbar, you may introduce the parameters to be optimized. Remember to check the opt button to enable each of the parameters to be optimized (the opt button must be green). Choose the parameter names at your convenience, for instance: IrisW = 8.0 IrisL = 2.0 CavityL = 15.0 IrisOffset1 = 4.0 IrisOffset2 = 5.0 Once the parameters have been defined, open the element dialog windows to use the parameters to set the corresponding element properties: IrisW to set rectangular 2: A and rectangular 4: A IrisL to set rectangular 2: L and rectangular 4: L CavityL to set rectangular 3: L IrisOffset1 to set step 1: X offset -IrisOffset1 to set step 2: X offset IrisOffset2 to set step 3: X offset –IrisOffset2 to set step 4: X offset

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Define formulas, goal functions and constraints Open the Optimization Window from the Execute menu or from the corresponding button ( Toolbar. The following window should appear:

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Create the following constraints in the Constraints page with the Add Constraint button:

constraints are intended to keep the circuit total length (2*IrisL+CavityL) small, as well as to keep the irises (IrisL) narrow. The weights are determined empirically. Create Goal Functions with the Add Goal Functions button. In general, for each Goal Function you can either choose an existing goal file or enter a non-existing file name and create/edit its contents. In this case you are not expected to already have useful goal files available, so instructions will be given below to create them with the Goal Functions Editor. A common technique for circuits with only two I/O Ports is to create two Goal Functions, one to tune circuit's S11 and the other for S12. This is what you will be instructed to do. Now create the following Goal Functions:

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It's time to create the goal files. Click on the Edit button of the first Goal Function (near "goal11.out"). The Goal Functions Editor window will appear, as shown in the following left figure:

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Set the number of columns to 2 and click on Apply: column 1 will be frequency, column 2 will be the goal for S11. Set the number of rows to 21 and click on Apply: 21 frequency points will be used. The window will change to the right figure above. Enter the frequency points. As you have seen in Tutorial 2 this circuit has a resonance at about 11.1 GHz. We are interested in the frequencies near it, so enter 11.0 in row 1 of the value column and enter 11.5 in the row 21 of the same column. Entering all the intermediate frequency values would be tedious and error-prone, so Fest3D is designed to help you here. Select with the mouse (pressing the left button) all the cells in the value column. Those cells should now be hilighted (usually in blue) as shown in the following left figure:

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Click on the Linearize button. All the intermediate values will be created automatically, as shown in the right figure above. Enter the goal S11, in dB. Experiment with Linearize on the S11 dB column selecting only a subset of the rows to find the easiest way to obtain the following:

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All done, click on the OK button. It's now time to edit the second goal file, "goal12.out". Since you should have already learned how to use the Goal Functions Editor, we leave the procedure to you as an exercise and only present the final result:

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Choose and configure the algorithm The last step of Fest3D Optimizer setup is choosing and configuring the algorithm. Click on the Algorithm button on the bottom to select the algorithm among the allowed ones and configure it. Currently supported algorithms are Simplex, Powell, and Gradient. For this tutorial, you will use the Simplex algorithm. Click on the corresponding Simplex button, then click on OK:

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The default values for the algorithms configuration are good in most cases, no need to modify them here.

2.2.5.2 Tutorial 5.2. Optimizer: run This is the second of the two tutorials dedicated to Fest3D Optimizer. In this tutorial you will learn how to start, control, stop and resume the optimization of a circuit using Fest3D Optimizer. This tutorial supposes you have read, understood and practiced the topics treated in Tutorial 1, Tutorial 2, Tutorial 3 and Tutorial 5.1 and you have already completed the optimizer setup as explained in them. Tutorial 5.2 will guide new users through the procedure of interactively running an optimization for the circuit created in the previous tutorials. Tutorial 5.2 is divided in two parts: 1. Just Run and Watch explains how to start Fest3D Optimizer and observe its progress in real time. 2. Stop, Edit and Resume shows how to interact with setup the target output you would want your circuit to produce.

Just Run and Watch This section explains the minimal steps required to run Fest3D Optimizer. They reduce to: Ensure the Auto Plot button ( ) in the Toolbar is pressed and the corresponding Plot Window is visible. This will let you watch the circuit output (S parameters) as they evolve. Click on the Optimize button ( ) in the Optimization Window to start optimization. Beware that an identical button is present in the Main Window Toolbar, but has a completely different function (runs an Sparameter simulation). See the progress. You should see something analogous to the following figures:

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If the optimization succeeded (and it always should in this simple example), you now have a circuit whose resonance is approximately at 11.25 GHz, instead of the original 11.1 GHz. You can Stop the optimization when you think the result is good enough, or you can wait for it to stop either because the maximum number of iterations was reached or because a possible minimum was found. Click on "Apply Parameter changes" to save your tuned parameters into the file, or click on "Discard Parameter changes" if you are not satisfied with the results.

Note that if you close the Optimization Window, the Parameters labels and expressions, Goal Functions, Constraints and Algorithm configurations are not lost. Open again the Optimization Window and you will get them back.

Actions while using optimizer While using the optimizer you can discard, save or backup your current optimization status, these are the main differences:

Discard all optimization steps: This will replace all the current values with the initial values since the last time you saved your project. If you have not saved it, it will revert to the original status. Apply opt changes and save project. This will save your current optimization status to the current .fest3 project file. Save status into a backup file: This option lets you creating a clone of the current optimization status for future use. So you can keep optimizing and experimenting with new goals/constraints/algorithms and you will be always capable to revert to the status you had when you created the backup file. The backup file is just a .fest3 file so you can re-open it with the open button.

Stop, Edit and Resume You are recommended to experiment with parameters, goal files and their weights in order to learn how the optimizer reacts to changes and how to guide the optimization algorithms to your target. At any moment, you can Stop the Optimizer, edit the setup as you did in Tutorial 5.1 then restart the Optimizer. This allows changing the Parameters values, the Goal Functions, Constraints, Algorithm and every other aspect of optimization without losing the progress you already achieved in tuning the circuit. Try the following experiments: Change the value of one or more parameters, then restart optimization. Watch whether the algorithm is able to restore the parameters values to the ones before you modified them or not. Modify the goal functions to be centered at 11.35 GHz, then restart the optimization. With a little patience, by repeating this procedure you can move the resonating frequency even by large frequency intervals. Goal files. Learn by experiments that using goal files whose dB values are very far from circuit output can create local minima in the error function and prevent optimization from succeeding. You will recognize this case by observing that the optimizer is tuning the circuit to have maximums or minimums of the output exactly at one of the sampled frequencies, instead of moving them around. Change the expressions. Learn that the optimization algorithms do not touch or even know about parameters having an associated expression: they are simply set to whatever value their expression dictates, independently from the algorithm being used. Change the constraints. Learn that constraints are only used as additional terms to the error

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function, so they are soft constraints and they are not guaranteed to be exactly satisfied/respected. However, to mitigate this, one can set a very large weight to the constraint when a hard constraint is needed.

2.2.6 High Power 2.2.6.1 Tutorial 6: Electromagnetic field Analysis In this tutorial, you will learn how to configure and launch an electromagnetic (EM) field analysis in Fest3D. For detailed information on EM field analysis, visit EM Field Analysis section in the manual. Tutorial 6 presents a guided example in which the EM field analysis process is explained step-by-step. It is divided in 3 parts. 1. Preliminaries. We open an example and see what considerations should be taken prior to the EM field analysis. 2. Launching an EM Field Analysis. The main parameters are set and the analysis is launched. 3. Plotting the Fields It gives an overview of the visualization tool Paraview.

Preliminaries First we need a circuit for EM field analysis. In the tutorial 1 the main steps to create your own circuit are given. In this example we will open one of the circuits in the examples folder. Click on the examples icon ( ) and open HP/Multipactor/single_carrier/multipactor_lowpass/multipactor_lowpass.fest3 file.

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In order to increase the resolution of the simulations, increase the number of accessible modes and green functions. Click on the Global Specification window (

) and change the global parameters to:

Num. of accessible Modes: 10 Num. of MoM basis functions: 15 Num. of Green's function terms: 100 Num. of Taylor expansion terms: 1

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) to open the electromagnetic field analysis window.

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Click on the Specification button, then click again on the frequency button and set 9.5 GHz in the text box.

Click on the resolution button on the Specification window. The number inserted in this text box is the default characteristic length, in millimeters or inches, used to generate the mesh where the EM field will be evaluated. Set this value to 1.

Click on the resolution button on the electromagnetic field analysis window to perform the analysis. It is also possible to override the spatial resolution of an element by clicking on the EM Field folder on the element properties window. In the next figure is shown how to change the resolution

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Once, the specifications and the resolution have been set press "Run" button, and the EM field analysis starts.

Plotting the fields During the simulation, the calculated fields are written in ASCII files, in XML Paraview's vtk format. To visualize them it is necessary to use Kitware's Paraview Software, included with Fest3D distribution. When the simulation is over, Fest3D launches Paraview automatically for you, and asks which file should open. (The Paraview icon in Fest3D toolbar ( can be pressed at any time to launch Paraview.)

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Remember that the fields are given in peak values and correspond to an average input power of 1 W. In this case, the name of the simulation output file is "volume_vectorfield_9.5GHz_average.pvd". Click on it and press "open".

The Paraview main window looks like this

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With the left, right and center button of your mouse you can rotate, zoom and translate the camera view. In the menu bar there is a display list where the different fields (electric, magnetic, Poynting vector) can be selected.

Fest3D also includes predefined 2D cuts that allow visualizing the fields inside the structure. On the left side of the Paraview's window, the main object and the 2D cuts are shown in a tree-like distribution. You can show or hide any of them by simply clicking on their corresponding "eye" icons.

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Computing voltage with Paraview With Paraview it is also possible to compute the voltage as the integration of the electrical field between two points in the mesh. In Fest3D, the fields are defined for an input power of 1W, therefore the computed voltage is also at 1W, called V1W. This can be useful for multipactor to translate from breakdown power to breakdown voltage and compare results with theoretical parallel-plate predictions. The expression to convert from power to voltage is the following: V=V1W√P Be careful because the voltage computed this way depends on the selected path in the mesh. In order to have meaningful results, the device geometry and fields, should be similar to a parallel-plate case. The process is as follows: 1. Apply paraview filter "plot over line" 2. Specify the coordinates of the line 3. Apply paraview filter "Integrate variables". In this particular case we will compute the voltage in the center of the centre iris, where the maximum field is located. In order to do so, one has to select the "Plot Over Line" filter in Filters->Alphabetical->Plot Over Line menu.

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Select the line for displaying the data by either moving the start and end points with the mouse, or by inserting coordinates manually. In this case, just press "y axis" button to automatically orient the line properly. Then press "Apply" button. A 2D plot with the fields displayed along the selected line appears. Now, apply another filter called "Integrate Variables" in Filters->Alphabetical->Integrate Variables. This filter will integrate all quantities displayed in the 2D plot. In this case, we obtain a voltage at 1W of V1W= 17.8 V as shown below. Note: Line start and end points must be adjusted to be inside a valid data region. If any of the line nodes lies outside, NaN integration values may appear.

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More information on Kitware's Paraview can be found in https://www.paraview.org .

2.2.6.2 Tutorial 7: Multipactor Analysis (single-carrier case) In this tutorial, you will learn how to configure and launch a multipactor simulation for high power analysis in Fest3D. For detailed information on multipactor analysis, visit Multipactor Analysis section in the manual. Tutorial 7 presents guided examples in which the multipactor analysis process is explained step-by-step. It is divided in 2 parts, covering single-carrier and multi-carrier signals, respectively. This first part of the tutorial shows an example of multipactor with a single-carrier signal. It deals with the following topics: 1. Preliminaries. We open an example and see what considerations should be taken prior to the multipactor analysis. 2. Launching the simulation. The main parameters are set and the simulation is launched. 3. Interpreting the results It gives an overview of the simulation output. See the next part of the tutorial for a multi-carrier case example.

Preliminaries First we need a circuit for multipactor analysis. In the tutorial 1 the main steps to create your own circuit are given. In this example we will open one of the circuits in the examples folder. Click on the examples icon ( ) and open HP/Multipactor/single_carrier/multipactor_lowpass/multipactor_lowpass.fest3 file.

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In order to increase the resolution of the simulations, increase the number of accessible modes and green functions. Click on the Global Specification window (

) and change the global parameters to:

Num. of accessible Modes: 25 Num. of MoM basis functions: 100 Num. of Green's function terms: 500 Num. of Taylor expansion terms: 4

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For realistic results, the simulation should be done for frequencies in the transmission band of the circuit. Therefore, we will run first a circuit analysis to determine the right frequencies for the multipactor simulation. Press the analyze button (

) in the menu bar, the frequency response of the circuit is plotted.

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The frequency range depends also on the application, but for this particular example, we will analyze multipactor in the range from 8 to 11 GHz. We will then set 3 frequencies for simulation, the lowest the highest and the centre one. Multipactor analysis is done independently for each element in the circuit. Therefore, the elements can be selected or deselected for simulation. Remember that multipactor analysis is restricted to some kind of components (see Multipactor Analysis). Of course, if we do not know anything about the circuit, we could select all elements for the analysis, but this is a rather slow approach since an individual simulation would be launched for each element. A wiser approach consists on first calculating the fields along the whole circuit using the EM field analysis (see tutorial 6). Click on the EM field analysis button (

) and set:

1. Specifications -> resolution to 1.0 2. Specifications -> frequency to 9.5 GHz (with the override specifications option). 3. Click on Run button The EM field analysis shows the field strength along the whole circuit, which is very helpful to identify the "hot spots" for multipactor. The elements with short gaps and high field strengths are those with highest probability of multipactor. In the figure below we see that elements 4, 6 and 8 are the main candidates for multipactor simulation.

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Right-click on elements 4, 6 and 8 and select the multipactor analysis box.

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In order to compute the voltage at the critical gap, see corresponding section in EM field Tutorial. We are now ready to launch the simulation.

Launching the simulation Click on Execute -> High power analysis in the menu bar to open the high power analysis window. See Multipactor Analysis for a description of all the available options. First of all, you must set the operation mode to Multipactor. For this particular example, we will analyze multipactor in the range from 8 to 11 GHz. We will then set 3 frequencies for simulation, the lowest the highest and the centre one. In the input tab, select the option of Frequency loop and set the start and end frequencies to 8 and 11 GHz and the number of points to 3. Select 1. Single carrier mode 2. Frequency loop Frequency start: 8 GHz Frequency end: 11 GHz Num points: 3 3. Initial power (W): 500

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In the configuration tab, select 1. Material: Silver 2. Initial number of electrons: 500 3. Mesh size (mm): 0.3

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Press the "Run" button button . The simulation starts now. Once the simulation starts, an individual simulation is carried out for each element at each different frequency. The info console shows the current status of the simulation: the element, frequency, input power and the existence of multipactor or not. When the multipactor breakdown is found with the desired precision, the next simulation starts.

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Interpreting the results While simulation runs, it is possible to see the partial results that are being obtained in the results window.

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For each analyzed element, the results include: a table located in the left-side of the window, which shows the analyzed power levels in the process of searching the threshold breakdown power. For each power, depending on whether multipactor occurs or not, it appears either the order of multipactor or the message "No break", respectively. a graph, where for each analyzed power the electron population evolution is represented versus time. Multipactor output data also includes a table situated on the top of the window, where it is shown the threshold breakdown power for the elements under study. By clicking on a cell corresponding to a particular element both the graph and the left-side table update their values to the current element. Right-clicking on a cell will display a context menu in which a "show 3d statistics" button appears. This opens a Paraview window with 3D statistical information of the simulation for that specific element and frequency (see Output section in the manual). By clicking on the cell corresponding to the frequency value, a bar diagram appears in the graph comparing the threshold breakdown power for all regions. With this information it is easy to recognize which is the most critical element in the device for multipactor onset and the limiting power.

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In this example, the multipactor analysis shows that the element with lowest multipactor breakdown (critical element) is the element number 6, located in the center of the circuit and that it has a multipactor breakdown of 7250 W at the lowest frequency of the transmission band. That is, the maximum allowed power for this device is 7250 W.

Running Multipactor Video Alternatively to a multipactor analysis, it is possible to record a video of the electrons moving inside the 3D structure for a particular input power. Follow the provided steps for creating your circuit and setting the simulation parameters Now, press the record video button

. The following window will appear:

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Select: 1. 2. 3. 4. 5. 6. 7.

Video for element / region : Rectangular WG (W6) Number of Frames / period : 15 Maximum video size (MB) (0 = no limit) Start time (ns): 0 End time (ns): 20 Input Power (W): 10000 Frequency (GHz): 9

The remaining parameters, such as SEY properties, number of initial electrons, multipactor criterion, etc. are defined in the Configuration tab. Press Ok button and choose output file (*.v3d format). After that, video generation will start. Note that video is saved outside the project and will not erase previous simulation results. When the video simulation is finished, you can choose to immediately visualize it, or open it later by pressing the play video button

in the main window at any time.

The video is visualized with the 3D CAD viewer Paraview. 3D rotations, perspective customization and zoom are allowed on recorded animations. Play, pause, forward and backward buttons can be found on top. Animation parameters can be changed in the Animation View panel (View -> Animation View). Concretely, the video duration can be changed in the Duration textbox.

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Video can be exported using File -> Save Animation... The video size, duration and format can be chosen.

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2.2.6.3 Tutorial 7: Multipactor Analysis (multi-carrier case) The first part of this tutorial covered a multipactor analysis with a single carrier signal. In the second part of the tutorial, you will learn how to configure and launch a multipactor simulation exciting with a multi-carrier signal. The following topics are discussed: 1. Preliminaries. We open an example and see what considerations should be taken prior to the multipactor analysis. 2. Single-carrier analysis. We run first a single-carrier analysis to have an estimation of the breakdown in the multi-carrier case. 3. Multi-carrier analysis. The main parameters are set and the simulation is launched. 4. Interpreting the results It gives an overview of the simulation output. For this example, we propose a multi-carrier signal composed of 4 carriers with the following parameters: Carrier #

Frequency (GHz)

Phase (deg)

1

11.5

0

2

11.55

0

3

11.6

0

4

11.65

0

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Preliminaries First, we need a circuit for multipactor analysis. In the tutorial 1 the main steps to create your own circuit are given. In this example we will open one of the circuits in the examples folder. Click on the examples icon (

) and open HP/Multipactor/multi_carrier/multicarrier_transformer.fest3 file.

In order to change the resolution of the simulations, set the number of accessible modes and green functions. Click on the Global Specification window (

) and change the global parameters to:

Num. of accessible Modes: 5 Num. of MoM basis functions: 15 Num. of Green's function terms: 100 Num. of Taylor expansion terms: 4

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For realistic results, the carrier frequencies should be within the transmission band of the circuit. In order to check it, we will run first a circuit analysis. Press the analyze button (

) in the menu bar, the frequency response of the circuit is plotted.

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In this case, all carriers lie inside the pass band of the circuit. Multipactor analysis is done independently for each element in the circuit. Therefore, the elements can be selected or deselected for simulation. Remember that multipactor analysis is restricted to some kind of components (see Multipactor Analysis). Of course, if we do not know anything about the circuit, we could select all elements for the analysis, but this is a rather slow approach since an individual simulation would be launched for each element. A wiser approach consists on first calculating the fields along the whole circuit using the EM field analysis and selecting the elements with higher fields and shorter gaps (see tutorial 6 and tutorial 7 (single carrier)). In this case we will perform the analysis on the central element of the transformer (element number 5), since it has the lowest gap and the highest voltage. Right-click on element 5 and select the multipactor analysis box.

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Single-carrier analysis It is advisable to run a single-carrier simulation before the multi-carrier one. This is because, for a faster multi-carrier simulation, it is better to have a good initial guess of the breakdown power per carrier. One way to obtain it, is from the calculated single-carrier breakdown power. According to the multipactor theory, the breakdown power per carrier of a multicarrier signal composed of N carriers is expected to be greater than the single-carrier breakdown power at the lowest frequency divided by N squared. In other words, in order to estimate the breakdown power per carrier, we proceed as follows: 1. Run a single carrier simulation for the lowest frequency of all carriers (11.5 GHz). 2. Obtain the single carrier breakdown power, Psc. 3. In the multi-carrier simulation, set the initial power per carrier to Psc / 16 (4 carriers in this example). Alternatively, Psc can be obtained with other methods, such as the ECSS Multipactor tool, or with the classical multipactor theory. The steps to analyze the circuit with a single-carrier signal are similar to those given in the first part of this tutorial. Click on Execute -> High power analysis in the menu bar to open the multipactor analysis window. See Multipactor Analysis for a description of all the available options. For this particular example, we will analyze multipactor for the lowest frequency of the multi-carrier signal carriers, which is 11.5 GHz.

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Select 1. 2. 3. 4. 5. 6. 7. 8.

Single carrier mode Use single frequency (GHz): 11.5 Material: Silver Initial number of electrons: 200 Initial power (W): 500 Precision (dB): 0.1 Maximum power (W): 100000 Mesh size(mm): 0.5

Press the "Run" button. The simulation starts now. The results for all selected elements and frequencies can be seen directly in the output console.

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In this example, the multipactor analysis shows that the multipactor breakdown for the element number 5 at 11.5 GHz is 1164 W. Therefore, and according to the multipactor theory, the expected breakdown power per carrier for the multi-carrier signal must be greater or equal to 1164/16 W / carrier, which is approximately 73 W / carrier. A slightly lower number, for example 69 W / carrier, is a good starting point for the multi-carrier analysis.

Multi-carrier analysis Click again on Execute -> High power analysis in the menu bar to open the multipactor analysis window. Select multi-carrier mode and enter the signal parameters of this example 1. 2. 3. 4. 5. 6. 7. 8.

multicarrier mode Number of carriers: 4 Fill the table with the signal parameters (see figure) Material: Silver Initial number of electrons: 500 Precision (dB): 0.1 Maximum power per carrier (W): 100000 Mesh size (mm): 0.5

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Press the "Run" button. The simulation starts now.

Interpreting the results The output console shows the current status of the simulation: The element, frequency, input power per carrier and the existence of multipactor or not. When the multipactor breakdown is found with the desired precision, the simulation stops.

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While the simulation runs, a folder is created with the label "multipactor" and the mean frequency (average of all carriers) of the current simulation. Inside, the output files for each of the selected elements are stored, with information about the breakdown power and the charge growth with time for each of the tested input powers. Visit Multipactor Analysis for more information on output files. Finally, the results for all selected elements and frequencies can be seen directly in the output console. In this example, the multipactor analysis shows that the maximum allowed power per carrier for this device is 263 W / carrier. This result is highly dependent on the frequency scheme and the phase distribution of the carriers. Notice that this simulation does not give necessarily the lowest breakdown power for the circuit, because a different phase distribution could lead to a worse case. In order to determine which is such worst case, please refer to the ECSS standards or use specialized tools such as the ECSS Multipactor Tool.

2.2.6.4 Tutorial 8: Corona Analysis In this tutorial, you will learn how to configure and launch a Corona simulation for high power analysis in Fest3D. For detailed information about Corona analysis, visit Corona Analysis section in the manual. Tutorial 8 presents a guided example where the whole Corona analysis process is explained step-by-step. It is divided in 3 parts: 1. Preliminaries. We open an example and discuss which considerations should be taken prior to Corona analysis. 2. Launching the simulation. The main parameters are set and the simulation is launched. 3. Understanding the results. An overview of the simulation output is given.

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Preliminaries First, the circuit where Corona is being analyzed must be created. In the tutorial 1 the main steps for creating your own circuit are given. In this tutorial we will open one of the circuits in the examples folder. Click on the examples icon

and open HP-> Corona ->lowpass_air-> corona_lowpass.fest3 file.

In order to enhance the resolution of the simulations, increase the number of accessible modes and green functions. Click on the Global Specification window (

) and change the global parameters to:

Num. of accessible Modes: 5 Num. of MoM basis functions: 15 Num. of Green's function terms: 100 Num. of Taylor expansion terms: 4

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Then, we have to choose the frequencies for the simulation in the RF range. For realistic results, they should be in the transmission band of the circuit. Press the analyze button (

) in the menu bar, the frequency response of the circuit is plotted.

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The frequency range depends also on the application, but for this particular example, we will analyze Corona in the range from 8 to 11 GHz. We then choose 3 frequencies for simulation, the lowest, the highest and the centre ones. Corona analysis is independently done in each element of the circuit. Therefore, the elements can be selected or not for simulation. Remember that Corona analysis is restricted to some kind of components (see Corona Analysis Limitations) and that the simulation will involve not only the selected element but also its adjacent ones, whenever they are of a permitted type. Of course, if we do not know anything about the circuit, we could select all elements for the analysis, but this is a rather slow approach since an individual simulation would be launched for each element. A wiser approach consists on first calculating the fields along the whole circuit using the EM field analysis (see tutorial 6). Click on the EM field analysis button (

) and set:

1. Specifications -> resolution to 1.0 2. Specifications -> frequency to 9.5 GHz (with the override specifications option). 3. Click on Run button The EM field analysis shows the field strength along the whole circuit, which is very helpful to identify the "hot spots" for Corona, as a first approach. The elements with high field strengths are those with highest probability of Corona, although it is important to notice that Corona breakdown power highly depends on the range of pressures analyzed and on the geometry of the device. In the figure below we see that elements 4, 6 and 8 are the main candidates for Corona simulation.

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Right-click on elements 4, 6 and 8 and select the Corona analysis box.

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We are now ready to launch the simulation.

Launching the simulation Click on Execute -> High power analysis in the menu bar to open the High power analysis window. See Corona Analysis for a description of all the available options. First of all, you must set the operation mode to Corona. For this particular example, we will analyze corona in the range from 8 to 11 GHz. We will then set 3 frequencies for simulation, the lowest the highest and the centre one. In the input tab, select the option of Frequency loop and set the start and end frequencies to 8 and 11 GHz and the number of points to 3.

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In the configuration tab, select 1. 2. 3. 4. 5. 6. 7. 8.

Minimum pressure (mBar): 6 Maximum pressure (mBar): 18 Pressure sweep step (mBar): 3 Temperature (K): 293 Precision (dB): 0.1 Characteristic length (mm): 1 Gas: air Simulation type: numerical

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Press on the play button

79

. The simulation starts now.

Once the simulation starts, an individual simulation is carried out for each element at each different frequency. The info console shows the current status of the simulation: the element, frequency, pressure, input power and the existence of Corona or not. When Corona breakdown threshold power is found with the desired precision for a certain pressure, next simulation starts.

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Understanding the results While simulation runs, it is possible to see the partial results that are being obtained in the results window.

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For each analyzed element and frequency, the Paschen curve, that is, the breakdown threshold versus pressure, is represented and its points are given in the table situated on the left side of the results window. Besides, the minimum breakdown power in whole pressure sweep is given in the table located on the top of the window. By left-clicking on a cell corresponding to a particular element and frequency, both the Paschen curve and its data table are updated to the current element-frequency pair. By left-clicking on the cell corresponding to a certain frequency, the graph shows together the Paschen curves of all the elements analyzed.

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It is also possible to compare the results obtained for the analyzed frequencies in a certain element. By left-clicking in the cell's name of an element the graph shows the Paschen curves of all the frequencies analyzed.

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With all this information, it is easy to compare the results for the selected elements and determine the critical pressure and minimum power supported by the device. In this example, the Corona analysis shows that at the center frequency of the transmission band the element with lowest Corona breakdown (critical element) is the element number 6 in the chosen range of pressures, located in the center of the circuit and that it has a Corona breakdown of 257.818 W at 12 mBars.

Running Corona video Alternatively to a corona analysis, it is possible to record a video of the electron density growing inside the 3D structure for a particular input power above the breakdown threshold. Follow the provided steps for creating your circuit and setting the simulation parameters Now, press the record video button

. The following window will appear:

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Select: 1. 2. 3. 4. 5. 6. 7. 8.

Video for element / region : Rectangular WG (W6) Number of Frames: 15 Maximum video size (MB) (0 = no limit) Accuracy: High Stop criterion: Maximum electron density aprox. (e/cm^3): 1000 Input Power (W): 255 Pressure (mBar): 12 Frequency (GHz): 9.5

The remaining parameters, such as gas and temperature, are defined in the Configuration tab. Press Ok button and choose the output file (*.v3d format). After that, the video generation will start. Note that the video is saved outside the project and will not erase previous simulation results. When the video simulation is finished, you can choose to immediately visualize it, or open it later by pressing the play video button

in the main window at any time.

The video is visualized with the 3D CAD viewer Paraview. 3D rotations, perspective customization and zoom are allowed on recorded animations. Play, pause, forward and backward buttons can be found on top.

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In the tree located on the left of the 3D CAD viewer Paraview window, there are different visualizations of the electron density evolution: Electron density: it corresponds to the electron density in the volume of the device at different video frames. Animation clip: it is a clip made on the electron density volume in order to visualize the discharge inside the device in a proper way. You can change the plane of the clip to center it in the proper place where the maximum of the discharge occurs by using the "Properties" tab or by dragging the plane on the visualization panel. ElectronDensity last frame: it corresponds to the last frame of the volume electron density. You can enable/disable each one by clicking on the eye located in their left side. The video can be exported in Paraview using File -> Save Animation... The video size, duration and format can be chosen as shown in the following pictures.

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2.3 Fest3D Manual This section describes the structure of Fest3D and documents the features of each subsystem Fest3D is composed of (Graphical User Interface, E.M. Engine, Optimizer, Convergency Study). The Fest3D manual contains the following topics: Architecture

The top-level architecture of Fest3D

Requirements

The minimum hardware and software requirements needed to run Fest3D.

Graphical User Interface (GUI)

Description of the Graphical User Interface, its features and how to use it

E.M. Engine (EMCE)

Description of the E.M. Engine, its features, and how to activate/control it from the GUI

Optimizer (OPT)

Description of the Optimizer, its features, and how to activate/control it from the GUI

Tolerance Analysis (TOL)

Description of the Tolerance Analysis, its features, and how to activate/control it from the GUI

Synthesis: The Synthesis Tools

Description of the Synthesis Tools and how to use them to create full filters with a few mouse clicks

E.M. field analysis

Description of the E.M. field computation.

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High Power

Description of the corona and multipactor threshold calculations

Engineering Tools

Small tools to perform unit conversions and simple computations

Compare Results tool

Tool for easily comparing Fest3D output results.

Convergence Study

This section explains in detail the procedure to be followed in performing convergence studies.

Architecture Fest3D is a CAD tool for linear, passive millimeter-wave and microwave components, based on cascaded discontinuities in waveguides. It allows the user to design waveguide structures, activate E.M. analysis, optimization and synthesis and perform the result visualization using an intuitive, user-friendly graphical interface. The list of elements supported by Fest3D is described in the Elements Database. At the top-level, Fest3D is composed of three subsystems: Graphical User Interface (GUI) ElectroMagnetic Computational Engine (EMCE) Optimizer (OPT) Furthermore, the publicly available Gnuplot program integrates the functionalities of the GUI by providing plotting capabilities. The GUI is a Java application. It is the part of Fest3D program in charge of interacting with the user and also executes and coordinates the other subsystems at user's demand. The EMCE implements the electromagnetic capabilities of Fest3D (except for some parts provided by the Synthesis Tools and Engineering Tools). The EMCE is designed and tuned for performance and exploits state-of-the-art techniques both in the electromagnetic and information technology research fields. The OPT provides the optimization capabilities of Fest3D. It implements a loosely coupled architecture, where the OPT is a standalone executable and exchanges data with the EMCE and reports status and progress to the GUI and thus to the user. It uses general-purpose optimization techniques, usually irrespective of the model physics, to perform variation of the parameters being optimized. Integrated with the other subsystems, the OPT aims at being an interactive and extensible optimization framework, where the user can view and interact in real-time with the optimization. Millimeter-wave and microwave circuits composed of supported elements can be analyzed, obtaining insertion and transmission losses, as well as the phase and the group delay, versus frequency. The results of the computation are displayed in graphic form and can also be printed. The multi-mode S, Z or Y matrix of such circuits can also be computed, effectively reducing a whole circuit to a single block which can be then reused as a User Defined element in a more complex circuit or system, or exported to other E.M. simulation tools. Finally, circuits can be interactively tuned by using the optimizer to reach the desired output.

2.3.1 Requirements Fest3D installation requirements are covered in the common document of the CST Studio Suite placed in: /Documentation/CST Studio Suite - Getting Started.pdf

2.3.2 Graphical User Interface (GUI)

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This section describes the architecture of Fest3D Graphical User Interface (GUI), documents its features and how to use it. The GUI section contains the following topics: The Main Window

How to use the GUI to design and edit circuits, execute the E.M. Engine (EMCE) and Optimizer (OPT).

The Elements bar

Contains all the buttons of the currently supported Fest3D Elements.

The Parameters Window

The dialog to define parameters to be used in the circuit creation, its optimization or tolerance analysis.

The General Specifications Window

The dialog to view and edit circuit specifications such as symmetries and global numeric parameters.

The Frequency Specifications Window

The dialog to view and edit frequency sweeps to be simulated and its mode (discrete or Adaptive Frequency Sampling).

The 3D Viewer Window

Draws the 3D geometry of a circuit.

The Preferences Window

The dialog to customize and configure Fest3D.

2.3.2.1 The Main Window This section describes the Fest3D Main Window and how to use it to create, edit and analyze millimeter-wave and microwave circuits. The other windows and dialogs that can be opened from the Main Window are also listed. The Main Window section contains the following topics: Menubar

The top menu bar with standard commands: Load, Save, Quit, Copy, Paste ... and also Fest3D specific commands.

Toolbar

The toolbar on the top, containing buttons for frequently used Menu commands.

Canvas

The drawing canvas, where circuit can be created and edited.

Element Properties

The dialog box to view and edit elements.

Edit Connections

The dialog box allowing to reorder the connections to an element.

S parameters

A small dialog to choose which S parameters are plotted.

The Fest3D Main Window typically looks as follows

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Menubar The menubar at the top of the Main Window gives access to all the GUI functions. The user can select any of them by using the mouse or by pressing ALT + the underlined letter of the menu item. The following figure shows the menubar as it typically appears on the screen

The menubar contains the following menus: 1. File

2. Edit

New is used to begin a new project, the old structure is discarded after a confirmation request. Open a browsing dialog box for file selection appears. By default, the user can choose among *.fest3 files. Open Examples a browsing dialog box for example file selection appears. Merge allows to load several Fest3D structures in the same canvas. Save stores the structure with the name defined before (written at the top of the window) or acts as Save As if a name was never defined. Save as stores the structure with a new name, this name becomes the new current name. A list of the last 5 opened files. Quit ends the program (closing all windows) asking the user to save modifications if not previously saved. Copy copies the selected elements and connections in the clipboard, you can Paste them later. Paste places in the editing area the elements and connections stored in the clipboard, near the original

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ones; the pasted element are automatically selected so that they can be moved. Warning: pasted elements may appear over existing ones, move them immediately to avoid errors in the analyzis stage due to non connected elements. Cut erases the selected elements and connections and stores them in the local clipboard for future Paste. Delete erases the selected elements and connections. They can be recovered only if you immediately execute an . Enable sets the selected elements to enabled status (normal). Disable sets the selected elements to disabled status. Disabled elements are ignored by the EMCE and OPT. Toggle Enable inverts the enabled/disabled status of the selected elements. 3. Execute S-Parameter Analysis starts the E.M. engine to analyze the structure. If errors are detected in the structure, a message appears and the analyzis is not performed. The resulting single-mode S parameters are stored in a file with the same name as the input file and with the extension .out. This file is saved in the same directory as the input file. The S parameters are also automatically plotted at the end of the simulation. EM Field Analysis starts the E.M. engine to compute the electromagnetic field distribution of the device under simulation. Export fields to SPARK3D allows performing an EM Field Analysis of the circuit which will be saved in a file ready to be opened with SPARK3D. High power analysis opens a window for performing Multipactor and/or Corona simulations on the circuit. Compute Generalized Z matrix starts the E.M. engine to compute multi-mode Z matrix of the structure. The result is written in a file with the same name as the input file but with .chr extension. This file is saved in the same directory as the input file. Such .chr files are suitable to be loaded by User Defined elements. Compute Generalized S matrix performs exactly the same multi-mode structure analysis as in Compute Generalized Z matrix, but produces instead multi-mode S matrix of the structure. Compute Generalized Y matrix performs exactly the same multi-mode structure analysis as in Compute Generalized Z matrix, but produces instead multi-mode Y matrix of the structure. General Specifications opens The General Specifications Window, allowing to edit the circuit specification data: frequency range and points, symmetries, global numeric parameters. Refer to EMCE code documentation for detailed description of each parameter. Frequency Specifications opens The Frequency Specifications Window, allowing to set-up the frequency sweeps that will be used in the simulation. Stop Simulation interrupts any running simulation (EMCE) or optimization (OPT). Incomplete data is lost. Compare results opens a the compare results tool for selecting and comparing different results of previously performed simulations. Show Optimizable Parameters allows to choose which parameters to optimize in each circuit element. In the Element Properties dialog, a small button will appear near the name of each optimizable parameter. Clicking on the button, it will change to indicating that the parameter will be optimized. Optimization Window opens the Optimizer (OPT) window, where the OPT can be configured, interactively executed and monitored. Tolerance Analysis Window opens the Tolerance Analysis window, where the tolerance analysis can be configured, interactively executed and monitored. 4. Export Export 3D geometry (closed ports) allows the user to create a SAT file with the geometry of the circuit built as a single metallic piece. Additionally, the existing dielectric volumes will be individually included in the SAT file as well. Export 3D geometry building blocks (closed ports) allows the user to create a SAT file with the geometry of the circuit, in which all the different Fest3D elements that have 3D volume are included as individual pieces.

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6. 7. 8.

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Export Project to CST MWS opens a wizard that allows to automatically build a CST MWS project with pre-defined settings that contains the geometry of the current Fest3D circuit, ready to be analyzed. Export Project to CST Design Studio allows to automatically build a CST Design Studio project with pre-defined settings that contains the geometry of the current Fest3D circuit as an imported block with the pins, frequencies and s-parameter task fully ready to be analyzed. Export S-parameters to Touchtone file converts the Fest3D output file to a TOUCHSTONE format. Structure Select Element allows the user to select and move elements and connections in the Canvas. Connect Element starts the connection mode. Connections between elements are established by pressing left mouse button on an element, dragging the mouse to another elements, finally releasing left mouse button. Element Properties opens the dialog box containing the selected Element Properties and allows the user to modify them. Show Icons changes the view mode from icons to numeric labels and vice versa. Add element allows selecting a new element to place in the editing area. The Elements bar can be used to perform the same operation. Synthesis allows to choose and open the Synthesis Tools dialog boxes, configure and execute them. Tools allows to choose and open the Engineering Tools dialog boxes. Options Edit Preferences opens the Preferences window, allowing to configure the cache system, and set the number of processors used. Auto-Save Options at exit if active, Fest3D options will be automatically saved at program exit (on by default). Clean Cache for current project deletes the cache files related to the open project. See Preferences to activate/deactivate the cache system. Clean Compare Folder deletes the content of the compare folder (located in the workspace folder). Change workspace configuration allows the user the change the directory used as workspace for Fest3D. Reset preferences resets the Preferences to the default installation values. Help About shows Fest3D version information. Help opens Fest3D Online Help. License diagnostics checks the license server status and writes information on the screen. This can be used in case that there is a problem with the license system.

Toolbar The toolbar is the horizontal row of buttons at the top of the window, it duplicates the most frequently used menu commands, allowing to perform the basic functions: new, open, save, print circuit, undo, copy, paste, cut, specifications, analyze, stop computation, optimization window, plot, help, 3D viewer... The following figure shows the toolbar as it typically appears on the screen

Canvas The wide area in the middle of the main window contains the block diagram representation of the current structure. Pressing the New button in the toolbar or selecting New from the File menu erases the existing structure and starts a new one. To add an element to the structure, press the left button of the mouse on an element of the Elements bar,

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move the mouse in the editing area where the element must be located, and press again the left button. To edit the properties of an element press the right button of the mouse on the element (or do it later after the structure is completed). The Element Properties dialog will appear. To connect elements, set mode to connecting by pressing the Edit Connections dialog will appear. Connections are always between a waveguide and a discontinuity. You can use the Undo, Copy, Cut, Delete and Paste functions to edit the structure. To erase a connection or delete elements press the arrow button of the elements bar, select the connection or the elements with the left button and press the scissors button (Cut) in the toolbar or select Cut or Delete from the Edit menu. To move the editing area use the scroll bars or press the middle mouse button (if available) and move it.

Element Properties To see and modify the element properties press the right button on the element in the editing area. A dialog box, allowing the user to view and edit the element properties will appear. The exact content of the dialog box depends on the element you are editing, see the Elements Database for details. The following figure shows a typical element properties dialogs as they appear on the screen.

Edit Connections The order of the connections is relevant for some elements. To modify it, the user just needs to click with the right mouse button on the connection. The Edit Connections dialog will appear, typically looking as the following figure:

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This dialogs allows the user to specify the ports of an element where each connected element should be attached. For each connected element, a row of radio-buttons is available to specify which port it should use. Attaching more than one element on the same port is not allowed.

2.3.2.2 Elements bar The elements bar gives access to all the elements supported by Fest3D, as well as to the Select and Connect menu commands. The figure on the left shows the elements bar as it typically appears on the screen. The first button (select) executes the Select command: the user can now select, move, copy, delete elements or edit properties. Use the left mouse button to select and move elements, the right one to edit properties. The middle button (if it exists) can be used to move (pan) rapidly the editing area. The second button (connect) executes Connect command, used to connect elements together. Press the left mouse button on an element, move the mouse on another element and release the left button. The order of the connections is relevant for some elements, to modify it select the arrow button and click with the left mouse button on the connection. The Edit Connections dialog will appear. Connections are always between a waveguide and a discontinuity. The other icons are used to place the corresponding elements to the Canvas.

2.3.2.3 Frequency Specifications This section explains how the user can create multiple sweeps and the types of algorithms that can be chosen to solve such sweeps. In order to configure the sweeps in a Fest3D project, click on the Frequency Specifications in the execute menu bar, or click on the Frequency Specifications ( image), will pop up:

) button in the toolbar. The frequency specifications window (see next

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Frequency Specifications window A typical window for the configuration of the frequency specifications is shown in this figure:

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In this window, different sections are highlighted: - Section 1: Selection of the type of sweep for this project. Fest3D allows selecting between frequency, theta and phi sweeps. - Section 2: Add sweep: With this button, new sweeps can be added. Fest3D allows simulating multiple sweeps. - Section 3: This is a list of all sweeps created for this project. Modification of all parameters can be done per sweep. - Section 4: This is the list of the sweeps used by the optimizer. This is a read-only list to have an easy way to see the sweeps defined in the optimizer. Optimizer sweeps can be only changed in the optimizer window.

Algorithms for sweep solution

Discrete algorithm: This is the typical sweep where all the points defined are simulated. So, for instance, if the user defines 100 frequency points, Fest3D will solve the problem in ALL 100 points. Adaptive sampling: This method is used to reduce the number of simulated points. This method is explained in detail in the section Adaptive Frequency Sampling method.

Parameters of the adaptive sampling There are two parameters to configure for the adaptive sampling: target error and the scattering parameters to be used in the error calculation (and its relative weight). In order to configure the parameters for adaptive sampling, the button "Config" must be selected, see image below:

The window that appears to configure the parameters for adaptive sampling is the following:

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These parameters are available after pushing the button "Advanced" in each adaptive sweep in the window Sweeps. In addition, each sweep is configured separately. Target error: The method stops when the current error is below this value during 3 consecutive iterations. The default value, 0.001, guarantees the convergence of the response in a wide range of circuits and cases. Parameter relevance: The internal calculations will be done only using the parameters selected by the user. In addition, in the case that two or more parameters are used, the relevance of those parameters can be selected with the "weights" column. Note 2: Regardless of what parameters are used in the internal calculations, the final response will contain all parameters of the circuit. Note 3: Internally, the weight of the selected parameters is normalized to one.

2.3.2.4 The General Specifications Window This section describes the General Specifications Window and how to use it to view and edit the circuit specification data: "symmetries" and "global numeric parameters". This window is opened from the toolbar on the top of the main window. The general specifications window section contains the following topics: Global Symmetries

The global symmetries flags supported by Fest3D.

Global Waveguide Settings

Default values for parameters common to all waveguides.

The general specifications window typically look as in the following figure:

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Global Symmetries Global symmetries and global circuit parameters can be configured from the general specifications window right tab. The following global symmetries are available, even though most elements only support a subset of them (see below): All-Inductive (H plane, constant height) The circuit has a fixed height and is invariant under vertical (Y) translations. All components must have the same height. In all discontinuities, Y offsets and Rotation must be zero. With this symmetry the Rectangular waveguides use only the TEz(m,0) modes. All-Capacitive (E plane, constant width) The circuit has a fixed width and is invariant under horizontal (X) translations. All components must have the same width. In all discontinuities, X offsets and Rotation must be zero. With this symmetry the Rectangular waveguides use only the TEz(1,n) and TMz(1,n) modes. X symmetric (symmetric under horizontal reflection) The left half and right half of the circuit are symmetric: reflecting the circuit across the plane X = 0 does not change it. In all discontinuities, X offsets and Rotation must be zero. With this symmetry the Rectangular waveguides use only the TEz(2m+1,n) and TMz(2m+1,n) modes. Y symmetric (symmetric under vertical reflection) The upper half and lower half of the circuit are symmetric: reflecting the circuit across the plane Y = 0 does not change it. In all discontinuities, Y offsets and Rotation must be zero. With this symmetry the Rectangular waveguides use only the TEz(m,2n) and TMz(m,2n) modes. All-Cylindrical (All-Centered Circular waveguides) The circuit is invariant under rotations around the Z axis. The circuit can only contain Circular waveguides and Steps. In all Steps, X and Y offsets must be zero. With this symmetry the Circular waveguides use only the TEz(1,n) and TMz(1,n) modes.

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TEM (All-Centered) The circuit is invariant under rotations around the Z axis. The circuit can only contain Circular, Circular coaxial waveguides, and Steps. In all Steps, X and Y offsets must be zero. With this symmetry the Circular waveguides use only the even TMz(0,n) modes and the Circular coaxial waveguides use the TEM and even TMz(0,n) modes. Circuits with such a symmetry should begin and finish with Circular coaxial waveguides.

Only one symmetry can be specified for a circuit, except for the following cases: All-Inductive symmetry also allows simultaneous X symmetry All-Capacitive symmetry also allows simultaneous Y symmetry X symmetry and Y symmetry be specified together if no other symmetry is active All-Cylindrical symmetry allows X and Y symmetry. Indeed, an All-Cylindrical circuit is always symmetric respect X and Y since no offsets are allowed. Then, in the GUI, when the All-Cylindrical symmetry is activated the X and Y symmetries are automatically activated as well.

Symmetries are used to discard unnecessary waveguide modes, so they allow using fewer modes which in turn results in lower computational time. If symmetries are added to a circuit, the following numeric parameters related to number of waveguide modes should be reduced accordingly. In the following section aproximate rules are explained to easily modify the numeric parameters. Number of accessible Modes, Number of MoM basis functions, Number of green function terms. If instead symmetries are removed from a circuit, the same numeric parameters should be increased accordingly. The exact amount to increase or decrease these numeric parameters depends on the circuit and there is no general formula. The following approximate rule can be used, but users are recommended to perform Convergence Study on each circuit: All-Inductive allows replacing all the number of modes with their square root All-Capacitive allows replacing all the number of modes with the double of their square root X symmetry allows dividing all the number of modes by 2 (exact rule) Y symmetry allows dividing all the number of modes by 2 (exact rule) All-Cylindrical allows replacing all the number of modes with the double of their square root TEM allows replacing all the number of modes with the half of their square root In order to specify a certain symmetry in a circuit, all elements in the circuit must allow such a symmetry. The symmetries that are allowed by each element, can be found in Allowed Symmetries section

Global Parameters Global symmetries and global circuit parameters can be configured from the general specifications window right tab. The following global parameters are available. They are used as default values for parameters common to all waveguides. Dielectric Permittivity Relative permittivty constant of the homogeneous dielectric medium that fills the waveguide (default: 1.0 i.e. vacuum). Dielectric Permeability Relative permeability constant of the homogeneous dielectric medium that fills the waveguide (default: 1.0 i.e. vacuum). Dielectric Conductivity Intrinsic conductivity of the homogeneous dielectric medium that fills the waveguide, in S/m (default: 0.0). Metal Resistivity Intrinsic resistivity of the metallic walls of the waveguide, in Ohm · m (default: 0.0).

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Number of accessible Modes Number of accessible (i.e. connecting, propagating) modes of the waveguide. Only the accessible modes of a waveguide are assumed to transmit E.M fields (and energy) across the whole waveguide length. (default: 10). Number of MoM basis functions Number of modes used in the internal MoM to calculate the discontinuities attached to the waveguide (default: 30). Number Green function terms Number of terms in the frequency-independent (static) part of the Green's function, which describes the discontinuities attached to the waveguide (default: 300). Number of Tailor expansion terms Number of terms in the Taylor expansion of the frequency-dependent (dynamic) part of the Green's function, which describes the discontinuities attached to the waveguide (default: 1). Reference port 3D Number of I/O port of the circuit used as a global reference coordinate system. See.

2.3.2.5 3D Viewer This section describes the 3D Viewer integrated with Fest3D, documents its features and how to use it.

Features The 3D Viewer window can be opened from the Fest3D GUI Main Window by clicking on the icon:

3D Viewer The 3D Viewer is a tool that allows the user to visualize a graphical 3D model of the circuit that is currently opened in the Fest3D GUI. This 3D model is created as a SAT file that contains the different elements of the circuit, classified in 3 main groups: Ports: A list of the intput/output surface ports of the circuit, sorted by ascending number. Waveguides: A list of the waveguides of the circuit with the same names that appear in the canvas, sorted by ascending number. Discontinuities: A list of the discontinuities of the circuit with the same names that appear in the canvas, sorted by ascending number. In addition, the internal details of discontinuities that belong to the coaxial library and the helical resonators groups are also shown as independent geometries. The user must also bear in mind that waveguides and discontinuities in the circuit whose geometry is not drawn as a volume (for example Step discontintuities, or waveguides with length equal to zero) will be ommited from the 3D model and therefore will not appear in the corresponding list. A typical view of the 3D model is shown in the figure below:

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Interaction with the 3D View This view shows the 3D model. Hovering with the mouse over this view will highlight elements that are currently located under the mouse. Highlighted items in the 3D view are highlighted in the navigation pane as well. The following mouse interaction is supported: Holding the left mouse button down allows changing the perspective of the view. Depending on the currently selected Mouse Mode , the view can be rotated, panned, or zoomed. Clicking the right mouse button shows a context menu, which allows invoking the actions listed in the table below. Action

Description

Hide Element

Only appears if the mouse is placed on an element of the 3D model. Allows hiding that specific element.

Mouse Mode

Sub menu to change the mouse interaction mode of the 3D view.

Mouse Mode >

Rotate the 3D view.

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Description

Rotate Mouse Mode > Rotate in Plane

Rotate the 3D view in the current view plane.

Mouse Move the 3D view. Mode > Pan Mouse Mode > Zoom

Zoom the 3D view in and out.

View Mode

Sub menu to change the perspective of the 3D view.

View Mode > Perspective

Predefined perspective view.

View Mode > Front

Rotate the model to view its front face.

View Mode > Back

Rotate the model to view its back face.

View Mode > Left

Rotate the model to view its left face.

View Mode > Right

Rotate the model to view its right face.

View Mode > Top

Rotate the model to view its top face.

View Mode > Bottom

Rotate the model to view its bottom face.

View Mode > Nearest Axis

Rotate the model to the nearest axis.

Fit View

Zoom the current view to fit the 3D model.

Resize To

Sub menu to allow resizing the 3D view. Available resolutions are: 1920x1440 , 1200x900 , 1024x768 , 800x600 , 640x480 , and 400x300 .

In addition, the following keyboard interaction is supported: Keyboard shortcuts: Space : Fits the entire 3D model into the view. 0 : Change to perspective view. 1 : Change to perspective view. 2 , 3 , 4 , 5 , 6 , 8 : Change view to Bottom , Back , Left , Front , Right , Top

Navigation & Visualizing Model Internals

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The navigation pane shows a list of available elements in the loaded model. By default, a tree view is shown. If desired, a flat list view is available as well through the context menu. When one or more elements are selected in the navigation pane, the 3D view shows all deselected elements transparently. This way the user can visualize internal details that are otherwise hidden. By default, the first input Port of the circuit will be always selected in the 3D View. In addition, it is possible to hide elements. This can be done through the context menu by choosing Hide or Hide All . The action Show All forces all elements to be visible again.

Toolbar Actions

The toolbar allows the user to quickly access the following actions: Action

Description

Navigation

Show / hide the navigation pane.

Rotate

Switch mouse interaction to rotate the 3D view.

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Description

Rotate in Plane

Switch mouse interaction to rotate the 3D view in the current view plane.

Pan

Switch mouse interaction to move the 3D view.

Zoom

Switch mouse interaction to zoom the 3D view in and out.

View Mode

Popup menu to change the perspective of the 3D view.

Fit View

Zoom the current view to fit the 3D model.

Save Picture

Save a picture of the 3D model as file.

Cutplane

If enabled, allows setting the cutplane through the 3D model along the x, y, and z axes. The position of the cutplane can be set through either the edit field, or the slider.

Help

Popup menu to access this documentation as well as the about dialog.

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2.3.2.6 The Preferences Window This section describes the Preferences Window and how to use it to customize and configure some parameters of Fest3D. The preferences window look as in the following figure:

The parameters that can be configured are: Create compare files if active, all the simulation results are saved also in the folder Compare inside the installation directory of Fest3D. This allows comparing several results of the same or different circuits. Enable cache system. This option is activated by default. When the cache system is activated, Fest3D will store, in disk , data that can be reused later on in the computations of next simulations. Fest3D automatically identifies if there were elements analysed in previous simulations that are equal to elements in the current simualtion, and loads their data from cache files avoiding to repeat certain computations. This may result on a great CPU time saving. The files containing cache data are stored in the project folder, which is located in the same folder as the input file with its same name. Thus, each Fest3D project will store and have access only to its own cache data. Since these data may consume hundreds of MB, it is recommended to delete the cache files if

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not needed(see Options->Clean Cache for current project in the Main Window menu bar), or even deactivate the cache system. Number processors used : Independently of the number of logical cores available of the processor, the user can select any number of logical cores to be used when resolving circuits. Units (mm or inches) : Selects whether to use millimeters or inches when defining the circuit parameters. Changing this will force to restart the program.

2.3.2.7 Parameters configuration This section describes how to define parameters (Par) in the Fest3D user interface. The use of parameters in a model has many advantages: It allows the user to parametrize different properties in your model that might have the same value or that might be related to other properties by means of mathematical expressions. The parameters are used to perform an optimization procedure or a tolerance analysis. The Par section contains the following topics: How to define/set parameters (parameters window)

Describes how to define parameters and set their expressions in the parameters window

Using parameters to set Model properties

Details how parameters can be used to set Model properties

How to define/set parameters (parameters window) To add a new parameter, click on Add Parameter button. An empty parameter will appear. You can easily introduce/modify the parameter: Name, the name uniquely identifies the parameter (it is case sensitive). You may give any name you want to the parameter. You only need to take into consideration that special characters are not allowed, and some key words are reserved, such as some mathematical functions or Visual Basic keywords Expression, allows setting direct values or mathematical expressions which define the parameter value or its relationship with other parameters. Expression can contain trigonometric and other functions. In particular: sin(x), the sine of x, x is in radians. cos(x), the cosine of x, x is in radians. tan(x), the tangent of x, x is in radians. sinh(x), the hyperbolic　sine of x. cosh(x), the hyperbolic　cosine of x. tanh(x), the hyperbolic tangent of x. log(x), the logarithm (base e). exp(x), the exponential value of x. sqrt(x), the square root of x. abs(x), the absolute value of x. Description, this is an optional field that may be used to make any annotation about the parameter.

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Any parameter, whose expression is a numerical value, can be selected to be used in the optimization procedure or in the tolerance analysis. The user can delete any parameter by clicking in the minus button at its right-hand side. When a parameter is deleted, it will be replaced by its value in any expression in which it was being used.

Using the parameters configuration window Once the parameters have been defined in the Parameter Window, they can be used to set any property of the Model. To do so, one can directly use them in the desired element dialog window, or even use a mathematical expression as shown in the following example:

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If the user inserts an undefined parameter to set a property, the parameter window will pop up automatically with the undefined parameter already introduced.

2.3.2.8 Compare Results tool

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The "Compare Results" Tool is used for comparing output results of Fest3D. This can be very useful if, for instance, a convergency analysis wants to be performed. By default, this tool is deactivated in Fest3D. To activate it, go to Options -> Edit Preferences -> Preferences. The following window should appear:

Activate the "Create compare files" by clicking in the corresponding box. Now, you can take a particular Fest3D input file and run it. After that, modify the file a little bit (the geometry for instance) and run again the simulation. It is important that the simulation arrives until the end of the frequency sweep. After this, please go to "Execute -> Compare Results". A window like the following one should appear:

In this case, we chose to run a file called six_pole_triple_mode_w_losess.fest3. Fest3D has saved both simulations by adding to the output file the date and time of the simulation. Now you can select both input files (for instance, keeping pressed the "control" key) and press "open". The compare window will appear:

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It is seen that both results are compared. By defult, the comparison will show the Module (in dB) of the Scattering Parameters of the all the ports of the circuit. The type of result (Phase, Group Delay, Module) and the number of scattering parameters which are compared can be modified at any moment, as in the normal results window. Please, notice that you can compare more than two results. Moreover, the Fest3D input file is also saved each time, so you can recover the input file of a particular simulation. This is very useful while performing a convergence analysis.

2.3.3 Analysis This section describes all the analysis capabilities that are present in Fest3D: EMCE

Explanation of the Electromagnetic computational engine.

Adaptive Frequency Sampling Method

Explanation of the Adaptive Frequency Sampling algorithm that allows speeding up performance in frequency sweeps.

Engineering tools

Explanation of Engineering tools, a set of tools that helps you in the creation of your project.

EM Field analysis

How to perform an EM Field analysis with Fest3D.

Convergence Study

How to perform a convergence study with Fest3D.

Parallelization

Explanation of parallelizaton of Fest3D and how to use it efficiently.

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This section describes the structure of Fest3D E.M. Engine (EMCE), documents its features and how it can be activated from the User Interface and from the command prompt. The EMCE section contains the following topics: Features

Description of EMCE features and capabilities.

Using the EMCE

How the EMCE can be activated and controlled from the User Interface or, in case you need, from the command prompt.

Features The EMCE supports passive, linear millimeter-wave and microwave devices, composed on cascaded waveguides and discontinuities. The full list of the supported elements is available in the Elements Database. Millimeter-wave and microwave circuits can be analyzed, obtaining insertion and transmission losses, as well as the insertion phase, versus frequency. The results of the computation are displayed in graphic form and can also be printed. The multi-mode S, Z or Y matrix of such circuits can also be computed, effectively reducing a whole circuit to a single block which can be then reused as a User Defined element in a more complex circuit or system, or imported from or exported to other E.M. simulation tools.

Multimode Network Representation The EMCE uses an equivalent multimode network representation, where each element is represented by a Z matrix. This way, all computations are performed in a multimode space. By combining the Z matrices of all network elements (waveguides and discontinuities), a new Z matrix representing the whole network can be created. The network structure can be excited to calculate the scattering (S) or the Z matrix. All this is done for each point of the requested frequency range. Thus, the EMCE produces as final result the scattering (S) or Z matrix at the input/output ports of the network for each frequency point.

Frequency-independent and Frequency-dependent parts Furthermore, for an efficient analysis, the computation of the Z matrix for complex structures like discontinuities, where heavy calculations take place during the simulation, is divided into two parts: the frequency-independent (static) and the frequency dependent (dynamic) parts. This is possible since the splitting is used also in the Integral Equation approach: the used integral equation is based on a kernel which has been split into these two parts. Fest3D EMCE first initialises all the network elements using the algorithms that do not depend on the frequency. This is done outside the frequency loop and the computed quantities are also stored in cache files, to allow reusing them in subsequent runs. After that, the EMCE enters the frequency loop where the frequency-dependent part is computed and combined with the frequency independent one, obtaining the Z matrix at each frequency point.

Using the EMCE The EMCE is completely integrated with the Graphical User Interface. Starting the EMCE is just a matter of clicking on the Analyze button in the Main Window, watch the progress messages, and look at the plot produced at the end of the simulation. Clicking on the Stop button in the Main Window will interrupt the simulation. Almost surely, you will want to open the General Specifications window to edit the analysis specification data: frequency range, symmetries, global numeric parameters, etc. Refer to EMCE code documentation in order to have a detailed description of each parameter. The Simulation Output window automatically opens when a simulation is running, and progress is reported in real time. If errors are detected during the simulation, a diagnostic message is produced in the Simulation Output window.

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The scattering (S) matrix is stored in a file with the same name as the input file and with .out extension. The result of Z matrix computation is written in a file with the same name as the input file but with .chr extension. Both .out and .chr files are saved in the same directory as the input file.

2.3.3.2 Adaptive Frequency Sampling Method This section explains the adaptive analysis method, how it is configured and provides key points to maximize the efficiency of the analysis. The adaptive sampling [1] is a method used to reduce the number of simulated points (reducing thus the computational time) without losing accuracy in the simulated response. The reduction is possible because the response in a broad frequency range (or angle, depending of the sweep variable) is approximated by a rational function using a reduced set of points. These points are found automatically by the method by comparing consecutive approximations. In order to perform an adaptive analysis of a sweep, the option "Adaptive" (see image) in the column Algorithm must be selected.

Note 1: The adaptive sweep only works for sweeps with more than 5 points. Example using discrete and adaptive algorithms This section shows the difference between the discrete and adaptive algorithms in terms of computational time and S parameters results. Let's consider the following band-pass filter (from the list of examples in Fest3D):

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In a particular computer, the resolution of the 100 frequency points takes (only the simulation time in the frequency loop is considered):

Discrete method: 4 seconds Adaptive sampling: 0.9 seconds

The S parameters perfectly match in both cases, as shown in the following figure, where one can verify that the results are virtually the same.

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How adaptive sampling works The steps followed by the method are: Step 1: The method starts by developing two rational approximations of each scattering parameter, one with 2 support points and one with 3 support points. The approximation with 2 support points uses the start point and the end point of the sweep. The approximation with 3 support points add a new point in the middle of the sweep to the previous ones. Step 2: An error curve between approximations is calculated using the approximations with 2 and 3 support points of each scattering parameter. Step 3: An error value is calculated from the error curve. This error term tends to cero when the difference between approximations decreases. In other words, when the approximation converges to a final response. Step 4: A new point is selected in the maximum of the error curve. By using this point and the previous points, a new approximation is done. The error curve is updated, and the new error is also determined. Step 5: The step 4 is repeated until the error value is lower than a threshold value selected by the user during three consecutive steps.

Efficiency of the adaptive sampling The error quantifies the variations between consecutive approximations and is normalized to 1, therefore the value of

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0.001 for Max error means that the final response has converged and stays stable, because the variations between the latest approximations in the whole range are less than 0.1%. The cost of the rational approximation is independent of the circuit and increases with the number of iterations. This cost depends of the number of points of the sweep (Figure 1) and the number of parameters used in the internal calculations (Figure 2). In addition, increasing the number of threads used reduces significantly the time of the rational interpolation (Figure 3). If the cost of performing each rational approximation remains negligible with respect to the cost of each electromagnetic simulation, the time saving will be related directly with the number of points which are not calculated but interpolated. If many iterations are needed to converge to the final response (for example in complex circuits as multiplexers or multiband filters), it is recommended to divide the sweep in several smaller sweeps. This can accelerate the simulation. As mentioned before, the number of S parameters which are taken to determine the error affects significantly to the time savings. In most circuits, just by enabling the parameter S11 is enough to guarantee a right convergence. This is typical in a bandpass filter (in a bandstop filter it is better choosing S21 to calculate the error). In complex circuits, it may be interesting to add to the S11 any significant S parameter in the particular range of analysis.

Figure 1: Evolution of the cost of the rational approximation with respect to the points of the sweep (1 S-parameter and 1 thread).

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Figure 2: Evolution of the cost of the rational approximation with respect to the number of scattering parameters (sweep with 500 points and 1 thread).

Figure 3: Evolution of the the cost of the rational approximation with respect to the number of threads (sweep with 500 points and 1 S-parameter).

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2.3.3.3 Engineering tools The Engineering Tools are a collection of useful tools for general Electromagnetic Design. These tools, based on analytical formulas [N. Marcuvitz, Waveguide Handbook, New York: McGraw-Hill Book Co. 1951] & [G. L. Matthaei, L. Young, and E. M.T. Jones, Microwave Filters, Impedance-Matching Networks and coupling Structures, New York: McGraw-Hill Book Co., 1964], help the user in the process of designing a passive component e.g. quality factor, constant of propagation, sorting of modes, manufacturing tolerances and so on. The Engineering Tools are activated through clicking the Tools->Engineering Tools menu on the GUI menu bar.

Fig.1. GUI menu for the Engineering Tools Next, the different Engineering Tools are described. As will be seen, they are easy to use, giving a nearly instantaneous output.

(M,N) Modes Propagation in RectWG This tool provides the propagation constant of the propagating modes and losses under cut-off for a given length in a rectangular waveguide. Fig. 2. shows its GUI, composed of the following input parameters: Width of the Rectangular Waveguide [mm] Height of the Rectangular Waveguide [mm] Length of the Rectangular Waveguide [mm] Operating Frequency [GHz] Maximum M for the (M,N) modes list Maximum N for the (M,N) modes list

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Fig. 2. GUI for the (M,N) Modes Propagation in RectWG Engineering Tool Once all the parameters are specified, the output (Fig. 3) sorts the propagating modes in the waveguide together with the propagation constant and losses in dB. Alpha is given as a negative number and Beta as positive.

Fig 3. Results given by the (3,3) Modes Propagation in RectWG Engineering Tool

Resonances in Cylindrical Resonator

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This Engineering Tool gives the resonances of a cylindrical resonator according its dimensions. The list of Input parameters are: Diameter of the cylindrical resonator [mm] Length of the cylindrical resonator [mm] Reduction factor for the unloaded Quality Factor [0-1] Maximum M for the (M,N,P) modes sorting Maximum N for the (M,N,P) modes sorting Maximum P for the (M,N,P) modes sorting Conductivity [Siemens/m]-->Introduced by the user or selected by default (Fig. 4)

Fig. 4. GUI for Resonances in Cylindrical Resonator Engineering Tool

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Its output sorts the modes in the cylindrical resonator according to its frequency, together with its unloaded and reduced / practical Quality Factor (Fig. 5).

Fig. 5. Results given by the (3,3,3) Resonances in Cylindrical Resonator Engineering Tool

Resonances in Rectangular Resonator It gives the resonances for a rectangular resonator according its dimensions. Similarly to the cylindrical resonator, here are the requested specifications: Width of the rectangular resonator [mm] Height of the rectangular resonator [mm] Length of the cylindrical resonator [mm] Resonance frequency [GHz] or length [mm] of the rectangular resonator Reduction factor for the unloaded Quality Factor [0-1] Maximum M for the (M,N,P) modes sorting Maximum N for the (M,N,P) modes sorting Maximum P for the (M,N,P) modes sorting Conductivity [Siemens/m]-->Introduced by the user or selected by default The selection between the resonance frequency or the length of the rectangular resonator is up to the user (Fig. 6). If the resonance frequency is selected, the different modes with the required length are shown (Fig. 7); on the other hand, by filling in the length of the rectangular resonator, the different modes are sorted as seen in Fig. 5.

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Fig. 6. GUI for Resonances in Rectangular Resonator Enginnering Tool

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Fig. 7. Lengths given by the (3,3,3) Resonances in Rectangular Resonator Tool (geometry fixed)

Q values at 3 dB Bandwidth in Resonators This Engineering Tool calculates the loaded, unloaded and external Quality Factor, requiring for such a calculation the following parameters (Fig. 8) : Insertion Loss [dB] Center Frequency [GHz] 3dB Bandwidth [MHz]

Fig. 8. Input Parameters for the Q values at 3dB Bandwidth in Resonators tool

Please note that, as specified in the output (Fig. 9), a symmetric coupling input-output is assumed for the calculations. The formulas to calculate all the Quality Factors are also described in order to avoid the user's confusion.

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Fig. 9. Quality Factors calculated by the Engineering Tool

Losses in CoaxWg The Input parameters are: Dielectric Permittivity Operating Frequency [GHz] Conductivity for inner conductor [Siemens/m] Conductivity for outer conductor [Siemens/m] Tan delta of permittivity * Dimensions of the outer conductor [mm] Diameter of the inner conductor [mm] It is possible to choose the outer conductor between a squared or coaxial waveguide as seen in Fig. 10. The tan of delta is used for the losses calculation.

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Fig. 10. Input parameters for the Losses in CoaxWg Tool

As seen in the output (Fig. 11), not only the losses but also the Impedance and the 1st higher order mode are calculated, all of them with their corresponding units.

Fig. 11. Output given by the Losses in CoaxWg Tool

Losses in RectWg This Engineering Tool calculates the losses in a Rectangular Waveguide. The user has to fill in the following parameters (Fig. 12) : Dielectric Permittivity Working Frequency [GHz] Width of the Rectangular Waveguide [mm] Height of the Rectangular Waveguide [mm] Length of the Rectangular Waveguide [mm] Tan delta of permittivity Conductivity [Siemens/m]-->Introduced by the user or selected by default

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In this case, the output produced gives more specific information regarding the losses in the rectangular waveguide (Fig. 13), separating the losses by conductivity and permittivity. Note that when tan delta is zero, there are no losses by permittivity. The skin depth is provided in the output as well.

Fig. 12. Losses in RectWg Engineering Tool input

Fig. 13. Losses in RectWg Engineering Tool output

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Losses in CircWg Similarly to the previous Engineering Tool, the input (Fig. 14) requested is: Dielectric Permittivity Operating Frequency [GHz] Diameter of the Circular Waveguide [mm] Length of the Circular Waveguide [mm] Tan delta of permittivity Conductivity [Siemens/m]-->Introduced by the user or selected by default

Fig. 14. Losses in CircWg Engineering Tool input

The produced output is similaro to the one for the Losses in RectWg Tool (Fig. 13).

Tolerance of Chebycheff filters This Engineering Tool gives the manufacturing tolerances for a Chebycheff band pass filter. Therefore, the input parameters are: Degree of the filter Return loss [dB] Center frequency [GHz] Bandwidth [MHz]

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Fig. 15. Tolerance of Chebycheff filters Tool

The output, given in micrometers, is depicted below in Fig. 16.

Fig. 16. Tolerance of Chebycheff filters output

Insertion Loss This Engineering Tool calculates the Insertion Loss for a band pass filter given the following specifications: Degree of the filter Return loss [dB] Center frequency [GHz] Bandwidth [MHz] Unloaded Quality Factor The GUI for the input parameters and its output are shown in Fig. 17 and 18, respectively:

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Fig. 17. Insertion Loss Tool input

Fig. 18. Insertion Loss Tool output

VSWR S11 RefCoef Ripple This Engineering Tool differs from the previous ones because instead of giving an output, it shows the relationship among the following parameters: VSWR (Voltage Standing Wave Ratio) S11 / Return loss [dB] Reflection Coefficient S21 / Ripple [dB] When the user changes one of the parameters and presses Enter, the rest of values are automatically updated according to the new specification provided. Fig. 19 shows an example, where VSWR, Reflect. Coef. and S21/Ripple have been changed automatically once the user has introduced the new value for S11/Return Loss (i.e. S11 = 30 dB).

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Fig. 19. VSWRS11RefCoefRipple Tool

dB Transformation This Engineering Tool, like the previously seen WG Dimensions Tool in the GUI of Fest3D (Fig. 1), is composed of two submenus: WdBmdBWdBc and dBNpAbs tools. WdBmdBWdBc As in the VSWRS11RefCoefRipple tool, this tool gives the relationship among the following parameters seen in Fig. 20: Watts [W] dBm dBW dBc and carrier [W]

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Fig. 20. The WdBmdBWdBc Tool In Fig. 20 the power in Watts has been changed to 40Watts, changing the rest of the parameters once Enter has been pressed. dBNpAbs This tool follows the same approach but considering the following units (Fig. 21): Decibel [dB] Neper [Np] Absolute value

Fig. 21. The dBNpAbs Engineering Tool

WG Dimensions These tool gives the waveguide dimensions for either a rectangular or circular waveguide according the established standard waveguides. As the dB transformation Tool, it is composed of two submenus depending on the type of waveguide.

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Fig. 22 GUI for the RectWG standard dimensions tool RectWG standard dimensions As seen in Fig. 22, the user selects the type of waveguide among all the list of standard waveguides. Once this action is performed, the fields corresponding to the dimensions and frequency range are updated. CircWG standard dimensions It follows the same approach seen in the last point, but in this case for a circular waveguide (Fig. 23):

Fig. 23 GUI for the CircWG standard dimensions tool

2.3.3.4 EM Field Analysis The EM field analysis section contains the following topics: Definition

What is exactly done when using this Fest3D feature.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced when computing the EM fields, and solutions or workarounds to them.

Using the EM field computation

How to use this feature in Fest3D from the User Interface or, in case you need, from the command prompt.

Visualization of EM fields How to use visualize the EM fields. Hints

Non-trivial properties of the computation of the EM field.

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Definition The EM field analysis computes the electromagnetic fields inside components. The structure is always excited with an average input power of 1 W. The fields are given in peak values.

Limitations The EM field analysis can be used in components based on rectangular, circular, coaxial, rectangular-arbitrary and circular-arbitrary waveguide elements. Most of the discontinuity elements which have 3D volume can perform EM field computations as well. If a particular circuit contains elements which are not supported, the EM fields will not be calculated on those specific elements, but only on the supported ones. In the case that the circuit contains lumped elements, the EM field can not be computed.

Errors No errors are reported for this feature.

Usage Clicking on the entry EM Field Analysis opens the following menu:

Specifications allows you to change the computational parameters that control the precision of the electromagnetic field computation. Run

starts the electromagnetic field computation.

Cancel:

Nothing will be done. However, parameters that have been changed keep their values.

Specifications

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controls the number of sampling points to represent the electromagnetic field.

Frequency

allows you to specify for which frequency the field should be computed.

Close

closes the dialog.

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Mesh size This parameter allows you to control the resolution of the electromagnetic field. Values are greater than 0. The default value is 1.

This value represents the mesh size in mm or inches used to generate a second order element mesh. Remark: Care should be taken when increasing the resolution. As a rule of thumb: doubling the resolution increases, in general, the number of sampling points in each direction by a factor of 2. For a 3D representation the number of sampling points thus increases approximately by a factor of 23=8.

Frequency

In this menu you can define for which frequency the electromagnetic field should be computed.

Output Data The calculation provides the following vectorial quantities in the complete volume of all elements: Mag(Max_E) (V/m) In time domain, the maximum value of the magnitude of the electric field in a period, which is useful for high power applications, such as corona or multipactor analysis. Mag(Max_H) (A/m) In time domain, the maximum value of the magnitude of the magnetic field in a period. Max_E (V/m) In time domain, the maximum value of electric field in a period. Max_H (A/m) In time domain, the maximum value of magnetic field in a period. S_re (W/m2) The average value of the Poynting vector.

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S_im (V*A/m2) In frequency domain, the imaginary part of (1/2)*(E x H). E_re (V/m) In frequency domain, the real part of the electric field. E_im (V/m) In frequency domain, the imaginary part of the electric field. H_re (A/m) In frequency domain, the real part of the magnetic field. H_im (A/m) In frequency domain, the imaginary part of the magnetic field.

Running EM Field Analysis from command prompt It is also possible to execute the EM Field Analysis from command prompt. The executable name is fest3d.exe on Windows platform and fest3d on Unix-like platforms, and is located in the directory where Fest3D is installed (you can view/edit the installation directory from the Preferences window). Executing the command fest3d -h (prefixed by Fest3D installation directory if necessary) will show all command-line arguments and options supported by the EMCE, including how to specify input and output files. A typical invocation of the EM Field Analysis looks as follows: --mode=emfield --chdir= --in=mycircuit.fest3 --override_frequency_mode=selected-frequency -nthreads=number-of-cores-to-use IMPORTANT NOTES It is necessary to indicate the directory where cache files are stored (by default, cache directory is located in Fest3D_WORKSPACE directory, but you can choose a different one). The option --override_frequency_mode allows choosing a frequency for EM field calculation different from the one defined in the input file. If any of the paths contain spaces, you should add double quotes. IE: --tmp="C:\path with spaces" The possibility to launch Fest3D from command line allows to use it in combination with external programs. This way, scripts to launch several executables sequentially can be generated or it can be combined with a synthesis or optmization tool.

Visualization The 3D quantities can be visualized by means of Paraview. To visualize the data, open paraview in your system and then go to "file: open data", and open the file "volume_vectorfield_FrequencyGHz_average.pvd", where "Frequency" represents the value of the frequency at which you have simulated. The structure appears in the main canvas (you can rotate it with the left mouse button). In order to visualize the fields, select the quantity you wish( Max_E, Max_H,...) in the top left side combobox. The scalar bar is activated pressing the button situated in the left side of the previous combobox. Paraview allows you to perform many operations on the data you are plotting. See the EM field tutorial for more information about visualization.

Hints Set the frequency to one single value in each simulation. Otherwise, many calculations (memory waste) are done.

2.3.3.5 Convergence Study This section explains in detail the procedure to be followed in performing convergence studies. Such a convergence study consists of several steps, which require changing all the numeric accuracy parameters involved in the Integral

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equation technique used in Fest3D, as explained below: 1. Number of accessible modes. To fix the optimum value of this parameter, we must start our study with a very reduced number of accessible modes (i.e. 5), and moderate values for the remaining parameters (i.e. 200 basis functions, 1000 Green function terms). To proceed, we must increase the number of accessible modes and see the evolution of the simulated response. If such response does not change, it means that the initial value for the number of accessible modes already provides convergent results, and then we must move to the next step, tuning the Number MoM basis functions. On the contrary, if the simulated response changes, it means the convergence has not been reached, and it will be required to increase the number of accessible modes (in steps of 5 to 10 additional accessible modes) until the response is fixed (i.e. no longer changes). 2. Number of MoM basis functions. To fix this parameter value, the user must always employ the number of accessible modes determined before, and fix the number of Green function terms to 1000. With regard to the initial number of MoM basis functions to be considered, it will be set to the previously selected number of accessible modes plus 1, with a minimum of 20. Then, we will run the software to obtain an initial response. Since the initial number of MoM basis functions is very low, this number will have to be increased (for instance in steps of 10 to 20 each time) and the new response will be computed. If no changes between both responses is observed, we can fix the number of basis functions and proceed to the next step (Number of Green function terms). If the responses are different, we must continue increasing the number of MoM basis functions until convergence is reached. It can happen that convergence is never reached even when the maximum number of basis functions allowed is used (the maximum is number of Green function terms minus one). In such a case, the number of Green function terms must be increased and the whole procedure for fixing the optimum number of MoM basis functions must be repeated. 3. Number of Green function terms (also named Number of kernel terms). The third parameter to be fixed is the number of Green function terms. To proceed, the number of accessible modes and MoM basis functions will be fixed to the optimum values already determined, and the initial value for the number of Green function terms will be the same employed in the previous step (i.e. 1000). In this case, the convergence analysis is performed in the following way: starting from the initial value for the number of Green function terms, it will be reduced (in steps of 100 to 200 terms each time) until the simulated response starts to change. The optimum value for this parameter is the previous one before the response has moved. It can happen that the response is moved with the first reduction of the number of Green function terms. In such a case, the initial number of Green function terms considered must be increased, and the convergence study must return to the step 2 (adjustment of the Number of MoM basis functions). Once these convergence studies are finished, it is recommended to compare the responses provided by Fest3D using the optimum values just determined and employing extremely high values each parameter (much higher than the optimum values found). If both results are very similar, it is guaranteed that the convergence study has provided optimum values that can be used in the next simulations of the structure under consideration.

2.3.3.6 Fest3D Parallelization Many computations in Fest3D can run in more than one processor simultaneously. In the following, it is explained how this multi-threading feature works. The parallelization section contains the following topics: Enabling multicore simulations

How to switch on the multicore mode.

How it works

Description about how Fest3D runs in parallel.

Special elements

Notes about special elements and parallelization.

Nested parallelism

Elements which can use more than one thread.

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Problems that can happen during a parallel simulation.

How it works Switching on the multicore option can be done in the combo box located at the top-right corner of the Main Window (see figure below), selecting the number of the threads wanted between one and the maximum of physical cores. By default, the number of cores for simulations will be chosen as the maximum value between one and the total number of cores detected in the machine minus one.

Nested parallelism In Fest3D, all computations are divided in a static part (frequency independent) and in a dynamic part (frequency dependent). The parallelization applies to both parts in a different way.

Static part Fest3D without parallelism computes each element separately one after another. The total time taken to finish this part is the addition of the time needed to compute each element. When more of one core is selected, each waveguide or discontinuity is assigned to a core if idle. Therefore, each thread solves the associated element it and waits for a new element to be solved. If there are no more elements, it will wait (suspended) to the frequency dependent part. There are some dependencies between elements in Fest3D. For example, a discontinuity cannot be computed until its attached waveguides are solved, or if an element is equal to another (from network), the original one has to be computed first. Time estimations here are difficult. On an hypothetical circuit in which all elements take a similar amount of time and

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the number of elements is multiple of the cores used, the computational time will be approximately the time needed in sequential mode divided by the number of threads. This is, of course, the optimum case. However, if an element is very slow compared to the rest of the elements in the circuit, the computational time shall be similar to the sequential case. Besides, some elements have nested parallelism inside them. In other words, the solution of the element (its static part) can be solved also in parallel. See the nested parallelism section for more information.

Dynamic part In this part, for each frequency, the generalized impedance (Z) matrices of each element are computed in parallel, similarly as done in the static part. But the total number of cores used for this task will not be the one specified at input. Instead, this number will be fixed to an optimum value depending on the specific circuit. However, despite this parallelization the solution of the resulting system of equations (which is built by putting together all Z matrices) is solved in sequential. In some case, it is possible that the Z matrices are solved very fast and then the multi-threading leads to a small slow down of the simulation. It is also possible that, if the circuit is too big and/or has many bifurcations, the frequency part is not significantly accelerated since the solution of the system of equations takes the longest time. Additionally, in case that a frequency sweep is solved using the Adaptive Frequency Sampling algorithm, the rational interpolation performed for the parameters not selected for optimization is also computed in parallel using all available cores.

Nested parallelism These are the elements that can use more than one thread simultaneously during their own solution.

Waveguides based on the arbitrary circular/rectangular waveguides. TE and TM modes are calculated in different cores if possible.

Constant width/height library TE and TM modes are calculated in different cores if possible.

Coaxial cavity library In the coaxial cavity library elements multicore is used to speed up the building of complex full matrices employed in the electromagnetic kernel.

EM Fields The Field analysis has an additional issue related to parallelism. The use of external tools that are not "thread-safe" forces Fest3D to run them in sequential, loosing performance. In other words, the mesh generation cannot be done in parallel. Everything else runs concurrently, just like during an S-parameter analysis.

Known limitations Computer overload It is highly recommended not to select the maximum number of cores unless the computer is going to be used mainly

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for the Fest3D simulation because it can slow down other actions to be done in the computer. Also, if you are running heavy simulations with other (or even Fest3D) software tools at the same time, the parallelism can be seriously affected and the simulation time can be even larger than with just one processor. It is recommended in such a case to reduce the number of threads to be used.

RAM use Fest3D usually requires more RAM in parallel mode than in sequential mode. The same simulation that works in sequential can fail with several cores if there is not enough memory available. As a consequence, slowdowns in the computer may occur if the circuit contains several different high memory-consuming elements such as those present in the coaxial cavity library.

2.3.4 Design This section describes the optimizer and tolerance analysis that are typically used to design circuits: Optimizer

Explanation of Fest3D optimizer and the methods available

Tolerance analysis

Explanation of the Tolerance analysis tool

2.3.4.1 Optimizer (OPT) This section describes the structure of Fest3D Optimizer (OPT), documents its features and how to configure, interactively execute and monitor it from the User Interface and from the command prompt. The OPT section contains the following topics: Features

Description of OPT features and capabilities.

Using the OPT

How to configure, interactively execute and monitor the OPT from the User Interface or, in case you need, from the command prompt.

Features The OPT is completely integrated with the GUI and allows the user to interactively access all functionalities using mouse, canvas and dialogs: Define parameters Choose which parameters to optimize Define expressions, goal functions and constraints Choose and configure the optimization algorithm Start, monitor, stop, resume the optimization algorithm Manually change the parameters and run the EMCE or OPT with the modified values. The OPT currently includes the following three algorithms: Simplex Powell Gradient

Using the OPT

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A step-by-step guide to use Fest3D OPT is also available in the Tutorial 5. Optimizer section of this manual. Performing a circuit optimization with Fest3D OPT can be divided in four steps:

1. Choose which parameters to optimize In the left side of each parameter there is a button that indicates if the parameter is selected to be optimized. Click on it to activate (green color) or deactivate (red color) its corresponding parameter. Only parameters whose expressions are a number and are used to set a model property, can be chosen to be optimized. Parameters whose expression are a mathematical expression are not eligible to optimize, for this reason the button is directly crossed out. By default, all optimizable parameters are deactivated. 2. Define expressions, goal functions and constraints Open the Optimization Window from the Execute menu or from the corresponding button ( ) in the Toolbar. Enter expressions as you need near each parameter's label. Create and enter constraints as you need in the Constraints tab. Create Goal Functions with the Add Goal Functions button, choose a goal function file (or enter a non-existing file name) and create or edit its contents with the Goal Functions Editor. Choose which circuit S parameters to compare with which goal function S parameters with the Sxy and Compare buttons. Change the Weight as you need. 3. Choose and configure the algorithm Click on the Algorithm button on the bottom to select the algorithm among the allowed ones and configure it. Currently supported algorithms are Simplex, Powell and Gradient. 4. Start, monitor, stop, resume the optimization algorithm To start the optimization click on the PLAY button ( ). The parameters values, iteration count and error function will be updated in real time. If Auto Plot in the main window Graphics menu is active, the graphic plot of the circuit analysis results will be updated in real time too. The optimization stops when the algorithm finds a (possible) minimum, or the error function reaches the target error, or the maximum number of iterations is reached. You can also stop it in any moment by clicking on the Stop button ( ). In all cases, clicking on the Apply parameter changes button, you can apply to the current circuit the values of optimization parameters obtained during the last optimization loop. At any moment that optimization is not running, you can modify the optimization parameter expressions, constraints, goal functions and algorithm. The Fest3D Optimization Window typically looks as follows

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Parameters The upper part of the window contains the parameters to optimize, which can be configured and edited in the same way as can be done in the Parameters configuration (

). Each parameter is defined by the following:

Name, the name uniquely identifying the parameter, it is case sensitive. You may give any name you want to the parameter. You only need to take into consideration that special characters are not allowed, and some key words are reserved, such as some mathematical functions or Visual Basic keywords. Expression allows setting direct values or mathematical expressions which define the parameter value or its relationship with other parameters. Expression can contain trigonometric and other functions. In particular: sin(x), the sine of x, x is in radians. cos(x), the cosine of x, x is in radians. tan(x), the tangent of x, x is in radians. sinh(x), the hyperbolic sine of x. cosh(x), the hyperbolic cosine of x. tanh(x), the hyperbolic tangent of x. log(x), the logarithm (base e). exp(x), the exponential value of x. sqrt(x), the square root of x. abs(x), the absolute value of x.

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Description, this is an optional field that may be used to make any annotation about the parameter. opt button indicates if a parameter is eligible for optimization. It allows temporarily disabling the parameter　 for the　optimizer by clicking　on the box. The color will be turned to red, indicating that the parameter will not be changed: its value will remain fixed. Clicking again re-enables the parameter and the color will turn back to green. On the other hand, in cases in which　a parameter is not defined as a numerical value, opt will be marked as crossed out, meaning that　such parameter will not be considered for direct modification by the optimizer tool　(but the parameter value may be modified indirectly in optimization steps if its expression depends on other parameters which are optimized). The current, previous, delta and initial values of the parameter. Delta value is the difference between the current and the initial value, not between the current and previous value. The current value can be directly edited by changing the expression tab, provided that optimization is not running

Goal Functions The lower part of the window contains the goal functions and constraints. The error function is computed by adding together all the contributions of the goal functions and constraints.

Each goal function is defined by the following: Circuit Sxy parameter to be tuned, taken from circuit S parameters output. The numbers x and y can range from 1 to the number of I/O ports defined in the circuit. The user can choose which part of the Sxy to consider: Module (dB), Phase (Radians) or G.D. (Group Delay). Equality or inequality that circuit Sxy parameter should satisfy with respect to goal Sxy parameters. Available settings are = (equal), = (greater or equal). = means the goal is to find a curve equal to the goal function = means the goal is to find a curve higher or equal than the goal function. Goal Sxy parameter indicates the column of the goal file to consider, and is chosen in the same way as circuit Sxy parameter. It should be chosen after selecting or creating the goal file. weight is the relative weight of this goal with respect to the other goals and constraints. It can be any number greater than zero. The contribution of each goal function to the error function is normalized (i.e. divided) by the number of points it contains, then multiplied by the weight Enable/disable flag allows to temporarily disable the goal function by clicking on the button: it will change to indicating that the goal function will be ignored by the optimizer. Clicking again re-enables the goal function. Goal file has the same format as EMCE .out S parameters files. Each goal file can contain different frequency

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sweeps (ranges). The circuit will be simulated only on the union of all used frequency sweeps. Each goal Sxy parameter will be compared to the corresponding circuit Sxy parameter only on the frequency points where they are both defined. The average of the square of the differences will be multiplied by the weight to compute the contribution of this Goal Function to the error function.

Goal Functions Editor A Goal Function can be created in two ways: 1. An existing goal file can be used. In this case use the Open button and choose the goal file you want. You can click on the Edit button to view and modify the contents of the file. Goal files have the same format as EMCE .out S parameters files. 2. A new goal file can be created. In this case, type a non-existing file name in the goal file and click on the Edit button. In both cases, clicking on the Edit button opens the following Goal Functions Editor window:

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The Goal Functions Editor window lets you view and edit the contents of a goal file as a spreadsheet table (the first column is a counter, the second is frequency): you can add or remove rows and columns and you can manually edit the values in each cell. you can remove multiple rows and columns at once by selecting them and clicking on the Remove button. if you add new rows, interpolation or extrapolation on the table values is performed automatically. modifications are saved to the goal file only when you click on the OK button. You can easily create linear progressions (or, as particular case, repetitions of a constant value) as follows: 1. type the initial value of the progression in a cell and type the final value in another cell of the same column 2. select with the mouse all the cells between the initial and final value (remember to also select the cells containing initial and final value) 3. click on the Linearize button If you select multiple column ranges, Linearize acts on them all.

Constraints The lower part of the window also contains the constraints tab, which typically looks as follows:

Each constraint is defined by the following: Weight is the relative weight of this constraint with respect to the other goals and constraints. It can be any number greater than zero. Enable/disable flag allows to temporarily disable the constraint by clicking on the button: it will change to indicating that the constraint will be ignored by the optimizer. Clicking again re-enables the constraint. Left expression can refer to all optimization parameters, even the ones whose value is defined by a expression and disabled ones. Equality or inequality that left and right expressions should satisfy. Available settings are = (equal), = (greater or equal). = means the goal is have left expression equal to right expression

Usage In order to select the specific elements of the structure to analyze, the option "Corona Analysis" of their respective dialog boxes must be marked (see for example Using the Rectangular Waveguide).The corona discharge analysis of the device under simulation is controlled through the GUI, that allows setting the input parameters.

Input tab First, the frequency of analysis must be selected in the input tab, as is shown in the following screen shot. It is possible to compute corona discharge either in a frequency sweep or in a single frequency.

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Configuration tab The configuration window permits setting the rest of the simulation parameters as is shown in the next menu:

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Minimum pressure (mBar)

Pressure at which the pressure sweep will start.

Maximum pressure (mBar)

Pressure at which the pressure sweep will finish.

Increment pressure (mBar)

Step in pressure for the pressure sweep.

Gas

Several gases can be considered in the simulation: dry air, nitrogen, helium, argon, SF6 and CO2. Data for helium, argon, SF6 and CO2 were downloaded from LXCat, which is an open-access website with databases contributed by members of scientific community. Results obtained for SF6 and CO2 should be considered as rough approximations, due to the lack of enough breakdown measurements to cross-check with our simulations and ensure their acuteness.

Temperature Ambient Temperature. The default is taken as the room temperature of 293 K. (K) Simulation type

Three different simulation types can be considered: Numerical, which corresponds to a numeric algorithm that uses an adapted FEM technique to solve the free electron density continuity equation. Analytical rule, which is detailed in high pressure analytical rule section

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Numerical & analytical, which enables both simulation types. Initial power Power from which the threshold breakdown power is looked for. It must be set for both "Numerical" (W) and "Numerical & analytical" simulation types. Its value may be set by the user or it may be taken automatically (enabling the "Automatic" check box) from the high pressure analytical approach. Precision (dB)

This parameter sets the desired precision in power level for the corona breakdown onset.

Mesh size (mm)

This parameter sets the maximum size of the elements that form the mesh used in the numerical simulation of corona analysis. Considering a small/big value of this parameter relative to the device's dimensions will produce a dense/coarse mesh.

Video Record If corona mode is selected videos can be saved by pressing the record button

and opened at any time with the

play button The record video dialog is the following

Video for element / region

Here, the region in which the video is going to be recorded is selected

Number of Frames / period

Specifies the frame rate of the recording. The higher the smoother the animation, but bigger video sizes will be generated.

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Maximum video size (MB)

If different from zero, the video will be cropped when the video file (approximately) exceeds the set size.

Accuracy

Sets the level of accuracy that will be used in the electron density computation. The higher is this level, the more accurate, time and memory consuming is the computation.

Stop criterion Sets the criterion used in the last frame of the video to stop the computation of the electron density: If "Maximum electron density approx." is selected, the maximum value of the computed electron density in the last frame of the video will be approximately the value fixed by the user. If "End time" is chosen, the electron density time evolution will be calculated till the time specified by the user. Input Power (W)

Sets the input power for this specific video recording.

Pressure (mBar)

Sets the pressure value for this specific video recording.

Frequency (GHz)

Sets the signal frequency for this specific video recording.

Other parameters are taken from current configuration, such as gas type and temperature. When the Ok button is pressed, an output file must be selected (*.v3d extension) and the simulation starts. Results from previous simulations will not be deleted. The video will be stored outside of the project and it is independent of it (can be opened from other projects, for example). Once the simulation is finished, the user can select to immediately open the video, or to open it at any time with the play video button . The videos are opened with the 3D CAD viewer software Paraview, which allows for 3D rotations, perspective customization and zoom on the saved animations. It also allows for exporting the animation to popular video formats, such as avi format for instance. See the Video Tutorial for further information.

High pressure analytical rule At high pressures, where diffusion is negligible, it is also possible to include the breakdown power threshold corresponding to a high pressure analytical rule by enabling its corresponding check-box. The obtained results are based on the well-known relation for ionization breakdown in air at sea level (W. Woo and J. DeGroot, Microwave absorption and plasma heating due to microwave breakdown in the atmosphere", IEEE Physical Fluids, vol. 27, no. 2, pp. 475487, 1984), which in the case of air corresponds to: Ebreakdown = 30.17 (pressure^2 + 2·frequency^2)^0.5 (V/cm) Similar analytical approaches are used for nitrogen, helium, argon, SF6 and CO2. These rules are conservative at all pressure ranges. At high pressures, they give an estimation for the breakdown power threshold whereas at low pressures - where diffusion losses are much more important- they only result in a very conservative breakdown onset. It is important to point out that the results are extremely dependent on the maximum value of the Electric field magnitude, Emax. This means that if this value changes, the high pressure analytical results will also change. Such a modification usually occurs in problems where the maximum electric field is concentrated on small localized regions, like in devices where metal corners are present. There are several reasons for such a variation: Change in the mesh used to compute the EM field. If the mesh is not dense enough, the maximum value found for Emax may not be the absolute maximum and small changes in the mesh may lead to different results.

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The use of non-convergent results for EM field calculation. If the EM field computation has not converged, a change in the simulation parameters may lead to different values of Emax and consequently to different results.

Running Corona Discharge Analysis from command prompt It is also possible to execute Corona Discharge Analysis from command prompt. The executable name is fest3d.exe on Windows platform and fest3d on Unix-like platforms, and is located in the directory where Fest3D is installed (you can view/edit the installation directory from the Preferences window). Executing the command fest3d -h (prefixed by Fest3D installation directory) will show all command-line arguments and options supported by the EMCE, including how to specify input and output files. A typical invocation of Corona Discharge Analysis looks as follows: --mode=corona --chdir= --ca= --tmp== --in=mycircuit.fest3 --out=mycircuit.corona --config_file=mycircuit.cin -output_path== If any of the paths contain spaces, you should add double quotes. IE: --tmp="C:\path with spaces" The full path is required since the EMCE will search for the license file in the same directory as the full path specified. It is also necessary to indicate the directory where cache and the temporary files are stored (by default, cache and temporal directories are located in Fest3D_WORKSPACE directory, but you can choose a different one). The file mycircuit.cin keeps all configuration parameters for Corona simulation and must be created before running the simulation from command prompt. Its format looks as follows: begin "corona" configuration_name gas analysis_type minimum_pressure maximum_pressure increment_pressure initial_power temperature precision simulation_type

"config1" "air" "breakdown_threshold" 6 18 3 100 293.0 0.1 "numeric"

end "corona" In the command line example given above, this file is stored in the same directory as mycircuit.fest3 file. All these parameters are described in the Usage of Corona Discharge from User Interface. The possibility to launch Fest3D from command line allows using it in combination with external programs. This way, scripts to launch several executables sequentially can be generated or it can be combined with a synthesis or optimization tool.

Output Corona module provides the threshold breakdown power of the selected elements of the structure. The simulation process can be visualized in the info window of the GUI where a sweep in input power is shown as the simulation runs, indicating how the simulator tries to approach to the corona breakdown threshold level. The results of the analysis are given both in graphic and tabular form to make their interpretation easier. There are two tables and one graph, as can be seen in the following figure:

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In the left-hand side table the threshold breakdown power for each pressure point corresponding to a certain element and signal is represented, which is selected by left-clicking on its corresponding cell in the upper table. If the high pressure analytical rule has been also selected for evaluation, the table will have three columns instead of two, where the last one corresponds to the empirical rule. The data of the left-hand side table correspond to the Paschen curve, which is represented in the graph. If the high pressure analytical rule is enabled, there will be two curves, one corresponding to the numerical analysis and the other one to the analytical rule. In the table located on the top of the results window the minimum breakdown power in the whole pressure sweep is represented for each element analyzed and for each frequency studied. Besides, through this table the user can handle the results shown both in the left-hand side table and the graph: By left-clicking on a cell corresponding to a particular region both the graph and the left-side table update their values to the current element. By left-clicking on the cell corresponding to the signal value, the whole row is selected and the graph shows together the Paschen curves of all the regions analyzed. With this information it is easy to recognize which is the most critical element for Corona discharge and the minimum breakdown power supported by the device.

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By left-clicking on the cell's name of an element, the whole column is selected and the graph shows together the Paschen curves of all the frequencies analyzed.

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the button

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or into a .csv file through

.

Hints The minimum of corona discharge breakdown occurs at pressure levels (in mBar) close to the frequency value (in GHz). It is therefore recommended to include such a value in the pressure interval to be given. It is necessary to carry out a convergence study of the threshold breakdown power as a function of the mesh used in the description of the EM fields. It is advisable to perform this previous study with a single pressure, which should be chosen close to the frequency value. Start the process with a coarse mesh. Increase progressively the number of points in the mesh to obtain denser meshes and compare the results. Once convergence is achieved, use the coarser mesh that involves convergence to analyze the entire range of pressures. It should be pointed out that for certain structures a too dense mesh, that would lead to a memory overflow, should be required in order to achieve convergent results.

LXCat references: Argon

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Dutton database, www.lxcat.net, retrieved on 09/05/2018 Jack Dutton, Survey of Electron Swarm Data, J.Phys.Chem.Ref.Data, 4, 577, 1975 Wagner, E.B., Davis, F.J., Hurst, G.S., J.Chem.Phys. 47, 3138, (1967) Kruithof A A 1940 Physica 7 519 EHTZ database, www.lxcat.net, retrieved on 09/05/2018 Haefliger P, Franck C M, 2018, Detailed precision and accuracy analysis of swarm parameters from a Pulsed Townsend experiment, Review of Scientific Instruments 89, 023114 Laplace database, www.lxcat.net, retrieved on 09/05/2018/p> Nakamura, Y., Kurachi, M., J.Phys.D: Appl.Phys. 21, 718 (1988) Kucukarpaci, H.N., Lucas, J., J.Phys.D 14, 2001 (1981); Pack, J.L., Voshall, R.E., Phelps, A.V., Kline, L.E., J.App.Phys., 71, 5363, (1992); IST - Lisbon database, www.lxcat.net, retrieved on 09/05/2018 L.L.Alves, The IST - Lisbon database on LXCat, J.Phys.Conf.Series 2014, 565, 1 Bozin J V, Jelenak Z M, Velikic Z V, Belca I D, Petrovic Z Lj and Jelenkovic B M 1996 Phys.Rev.E 53 4007 Jelenak Z M, Velikic Z B, Bozin J V, Petrovic Z Lj and Jelenkovic B M 1993 Phys.Rev.E 47 3566; Helium IST - Lisbon database, www.lxcat.net, retrieved on 29/03/2018 L.L.Alves, The IST - Lisbon database on LXCat, J.Phys.Conf.Series 2014, 565, 1 Cavalleri G 1969 Phys.Rev. 179 186; Laplace database, www.lxcat.net, retrieved on 29/03/2018 DallArmi, G., Brown, K.L., Purdie, P.H. and Fletcher, J., Aust.J.Phys., 45, 185 (1992) Pack, J.L., Voshall, R.E., Phelps, A.V., Kline, L.E., J.App.Phys., 71, 5363, (1992); Dutton database, www.lxcat.net, retrieved on 29/03/2018 Jack Dutton, “Survey of Electron Swarm Data”, J.Phys.Chem.Ref.Data, 4, 577, 1975 Stern, in Proceedings of the sixth International Conference on Ionization Phenomena in Gases(Paris, 8 - 13 July 1963) P.Hubert and E Cremieu - Alcan, eds. (Serma, Paris, 1963), Vol. 1, p. 331 Chanin, L.M.Rork, G.D., Phys.Rev. 133, A1005(1964); SF6 CHRISTOPHOROU database, www.lxcat.net, retrieved on 13/02/2018 L.G. Christophorou and J.K. Olthoff (2000) Electron Interactions With SF6. Journal of physical and chemical reference data, 29(3), p.267. UNAM database, www.lxcat.net, retrieved on 16/08/2018 L. G. Christophorou and J. K. Olthoff, Electron Interactions with SF6, Journal of Physical and Chemical Reference Data, Vol. 29, No. 3, pp.267 - 330 (2000); CO2 Dutton database, www.lxcat.net, retrieved on 05/09/2018 Wagner, E. B., Davis, F. J., Hurst, G. S., J. Chem. Phys. 47, 3138 (1967)

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Elford, M. T., Austr. J. Phys. 19, 629 (1966) Frommhold, L., Z. Physik 160, 554 (1960) Pack, J. L., Voshall, R. E., Phelps, A. V., Phys. Rev. 127, 2084 (1962) Schlumbohm, H., Z., Phys. 18 317 (1965) Schlumbohm, H., Z. Physik 184, 492 (1965) EHTZ database, www.lxcat.net, retrieved on 09/05/2018 Haefliger P, Franck C M, 2018, Detailed precision and accuracy analysis of swarm parameters from a Pulsed Townsend experiment, Review of Scientific Instruments 89, 023114 Laplace database, www.lxcat.net, retrieved on 05/09/2018 Elford, M.T., and Haddad, G. N., Aust. J. Phys. 33, 517 (1980) Roznerski W, Leja K J. Phys. D: Appl. Phys. 17, 279-285 (1984); UNAM database, www.lxcat.net, retrieved on 05/09/2018 J L Hernández-Ávila, E Basurto and J de Urquijo, Electron transport and swarm parameters in CO2 and its mixtures with SF6, Journal of Physics D, 35 2264 (2002);

2.3.6.2 Multipactor Analysis The Multipactor analysis section contains the following topics: Definition

What is exactly done when using this Fest3D feature.

Features

List of Features.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced when performing the Multipactor analysis, and solutions or workarounds to them.

Using the Multipactor module

How to use this feature in Fest3D.

Output of a Multipactor simulation

Description of the output of a multipactor simulation.

Hints

Non-trivial properties of the use of the Multipactor module.

Definition The Multipactor analysis computes the multipactor breakdown power threshold of one or more particular elements of the structure. It supports single and multi-carrier operation. The breakdown power for each carrier is calculated at input port 1. For a more detailed information about multipactor theory and results see: C. Vicente, M. Mattes, D. Wolk, H. L. Hartnagel, J. R. Mosig, and D. Raboso, "Fest3D: A simulation tool for multipactor prediction," in Workshop on Multipactor, RF and DC Corona and Passive Intermodulation in Space RF Hard- ware, pp. 11–17, ESTEC, Noordwijk, The Netherlands, Sept. 12-14 2005.

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S. Anza, C. Vicente, B. Gimeno, V. E. Boria, and J. Armendariz, "Long-term multipactor discharge in multicarrier systems," Physics of Plasmas, vol. 14, pp. 082112–082112–8, Aug. 2007. S. Anza, C. Vicente, D. Raboso, J. Gil, B. Gimeno, V. E. Boria, “Enhanced Prediction of Multipaction Breakdown in Passive Waveguide Components including Space Charge Effects", in IEEE 2008 International Microwave Symposium , June 2008, Atlanta (Georgia), USA. E. Sorolla, S. Anza, B. Gimeno, A.M. Perez, C. Vicente, J. Gil, F.J. Perez-Soler, F.D. Quesada, A. Alvarez, V. Boria, "An analytical model to evaluate the radiated power spectrum of a multipactor discharge in a parallel- plate region", IEEE Transactions on Electron Device Letters , vol.55 no. 8, pp. 2252-2258 Aug. 2008. S. Anza, C. Vicente, J. Gil, B. Gimeno, V. E. Boria, and D. Raboso, "Non-stationary Statistical Theory for Multipactor," Physics of Plasmas, vol. 17, June 2010.

Features Single-carrier and multi-carrier simulations with arbitrary number of carriers and phase schemes. Custom SEY curves. Possibility of using Predefined SEY materials (according to ECSS standards), user defined parameters or import from text file. Computation of electron evolution for each applied input power. Automatic multipactor threshold determination. Advanced 3D output statistics with average impact energy, average SEY, and emitted electron density for the different surfaces in the structure. Possibility to add external uniform DC magnetic field. Electron path algorithm with adaptive refinement which allows for faster and more accurate simulations. The electron trajectories are now computed with a certain error introduced by the user. Different multipactor criteria. The multipactor criteria allows for automatically stop the simulation and decide whether there is multipactor discharge or not. The election of one or another have implications on the accuracy and speed of the simulation. This is of special importance in multi-carrier simulations. The user can easily change the criteria from the configuration window. The available criteria are: charge (automatic), charge (fixed factor) and charge trend. Impact angle dependence for SEY curves imported from text files. Multipactor video recording feature. The user can export videos of electrons moving in a 3D structure and open them at any time. 3D rotations, perspective customization and zoom are allowed on recorded animations. Final export to popular video formats (such as .avi) can also be done. Automatic power loop, in which input power levels are automatically computed to find the multipactor threshold, and Custom power loop, in which the user can specify as many arbitrary input power levels as desired Multipactor analysis can be carried out in elements in which the EM field can be computed. In addition to the magnetic case, homogeneous electric DC field can be added to the simulation. List of SEY properties for ECSS standard materials and Aerospace Corporation aluminium (TOR-2014).

Limitations Due to numerical limitations on the electron path integration, in rare cases and for very high fields, false singlesurface discharges may occur at very low multipactor orders (below 0.05). These are easily identified and must not be taken as real discharges. If this occurs, please contact technical support for possible solutions to this issue.

Errors Due to the nature of the phenomenon, the results can slightly differ from simulation to simulation. This deviation can be considered an intrinsic error caused by the phenomenon itself. However, this error is normally so small that it is not relevant for practical applications.

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A step-by-step guide on how to use the multipactor analysis module is also available in Tutorial 7.Multipactor Analysis. In order to select the specific elements of the structure to analyze, the option "Multipactor Analysis" of their respective dialog boxes must be marked (see for example Using the Rectangular Waveguide). The multipactor analysis of the device under simulation is controlled with the Execute -> High power analysis menu. First, the frequency of analysis must be selected in the input tab, as is shown in the following screenshot:

Input tab In the input tab of the multipactor analysis, the properties of the input signal are configured such as simulation mode (single or multi-carrier) and frequency of operation. Single carrier

If single carrier mode is selected, the simulation will be done with only one carrier at the specified frequency

Multicarrier In this mode, an arbitrary number of carriers are combined at the input port. The frequency, power mode and relative phase of each one can be configured independently.

Single carrier mode This section configures the input signal when single carrier mode has been selected.

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Single Specify a single frequency point for the simulation. frequency (GHz) Frequency Specify a frequency sweep (start, end and number of points) for the simulation. loop Automatic If selected, the multipactor module will search automatically for the multipactor threshold, starting power from the initial power and stopping when the desired precision is reached. Bisection method is loop employed, and the multipactor criterion (to determine whether there has been a discharge or not) is set by the Multipactor criterion in the Configuration tab below. The parameters are: Precision (dB): This parameter sets the precision in power level desired for the multipactor breakdown onset. The default is 0.1 dB. Initial power (W): This will be the initial input power used to search the multipactor breakdown onset. This can be changed to an input power level close to the final breakdown onset if some information is known a priori. Maximum power (W): Sets the maximum allowed power for multipactor breakdown search. The default is 100 kW. Custom power loop

If selected, the input power steps are selected by the user by pressing the edit button, see the figure below. A multipactor simulation will be done for each step. The criterion for stopping the simulation can be chosen from: Stop based on multipactor criterion: The simulation will stop if a discharge (or not discharge)

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is detected, using the selected criterion in the Configuration tab below. Stop on fixed time: The simulation time is fixed, no matter whether there is a discharge or not, unless the number of electrons decreases to 0, or reaches the maximum allowed number of electrons (1e15 for numerical stability reasons).

If Custom power loop is selected, the user can choose the input power steps by pressing the edit button. The following window appears,

where arbitrary number of power steps with arbitrary power value can be defined.

Multicarrier mode This section configures the input signal when multicarrier mode has been selected. In this mode an arbitrary number of carriers is combined at the input port of the device. The frequency, initial power and relative phase of each carrier can be individually configured. The output of the simulation is the breakdown power per carrier for the selected element. Notice that the power ratio of each carrier is fixed by the initial power per carrier set in the simulation parameters (for example if the initial power of the first carrier is twice the others, all the tested powers per carrier in the simulation will keep this ratio).

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Specify the number of rows in the carrier definition table. When apply button is pressed, the table changes its dimension to the specified value.

Import Imports a carrier table from a file in ECSS Multipactor Tool format. from Multipactor Tool Carrier table

It specifies the configuration of each carrier, including frequency, initial power and relative phase. The "ON" check in the right side allows for switching on and off each carrier individually. Notice that the power ratio for all carriers during the simulation is constant and fixed by the initial power per carrier set in this table.

Apply same When apply button is pressed, the value in this field is applied to all carriers. power to all (W) Maximum power per carrier (W)

Sets the maximum allowed power per carrier for multipactor breakdown search.

Precision (dB)

This parameter sets the precision in power level desired for the multipactor breakdown onset. The default is 0.1 dB.

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Configuration tab The configuration window permits setting the rest of the simulation parameters as is shown in the next menu:

Material Allows you to choose metals with well studied Secondary Electron Yield (SEY) properties. It also allows you to create new materials and save them for future simulations.

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Material name

Six materials are included with their SEY properties. User defined materials can be saved and loaded.

Maximum secondary emission coefficient

Maximum SEY of the material. Typical values are between 1.5 and 3.

Secondary emission coefficient below lower crossover

SEY of elastically reflected electrons at low impact energies.

Lower crossover electron energy (eV)

The lowest electron impact energy at which the SEY crosses the value of 1. This is a typical value between 20 and 45 eV for the materials for space applications.

Electron energy at maximum SEY (eV)

The electron impact energy at which the SEY is maximum. Typical values are between 150 and 300 eV.

It is also possible to use a custom SEY by importing it from an input file. The file must be in CSV (comma-separatedvalue) format, which is text file with .csv extension that consists on tabulated data. The SEY file should have 2 columns: the first one contains the electron impact energy in eV and the second one corresponds to the SEY of the material at normal incidence. FEST3D will automatically add the angle dependence for each electron impact. For energies outside the range defined in the input file, the SEY will be set to 0. Press the button with the icon curve.

close to a SEY definition to open a new window with a plot of the selected SEY

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The selection and definition of the SEY curve has an important effect on the multipactor simulation. See some practical considerations when selecting the material properties.

DC fields By selecting the B fields or the E fields check boxes, uniform external DC fields are added to the simulation. The uniform B and E DC fields are given in Tesla and V/m respectively.

Simulation preferences

Initial number of electrons

This defines the initial number of electrons launched in a particular component element. This number can vary in order to obtain reliable results. The default value of 100 electrons should be quite accurate in single-carrier mode and in waveguide elements where the parallel plate approximation holds. However, if the length of the waveguide element is of the order of its height more electrons could be necessary. For a complete simulation, the best idea is to start with a low number of electrons in order to get a fast idea of the approximated breakdown power level. After that, more electrons can be launched using an input power level close to the one obtained in the simulation with few electrons. In general, multi-carrier simulations need a higher number of initial electrons to reach convergence. In this case, an initial number of electrons of 500 is a good starting point.

Mesh Size (mm)

This parameter sets the density of the 3D mesh of the element under study. The mesh size sets the maximum length of the edges of the tetrahedra in the mesh. The smaller the value the denser the mesh, the higher the precision but the longer the simulation. A good starting point is to set this value to one tenth of the largest dimension.

Multipactor Multipactor criterion is the mechanism that automatically decides whether there is a discharge or not criterion at a certain input power and stops the simulation. Then, next power is simulated until the precision is

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reached. There are three different criteria, all of them based on the electron population: Single-carrier operation Charge (automatic), only for single-carrier: This is the default mode. At each RF half-cycle, the ratio between the current number of electrons and the initial ones is checked. This criterion establishes a factor depending on the current number of simulated half-cycles. If the number of electrons is above such a factor, multipactor is detected. Basically, it sets higher factors for lower number of half-cycles (beginning of the simulation) and more relaxed ones for larger number of half-cycles (longer simulations). This is done in order to avoid false detection during the initial stages of the simulation. Additionally, if after a certain number of cycles, the ratio is below a certain number, the simulation is stopped and no multipactor is detected. This is done in order to avoid excessively large simulations in which there is not a clear electron growth. Charge (fixed factor): It is equivalent to the automatic one, where the factor is not automatic but set by the user. Gives more control on the simulation but needs of more trim and knowledge from the user side. It does not have any check for low number of electrons. Only populations decreasing to zero are considered no discharges. Therefore there is a risk of long simulations. Charge trend: It fits the electron evolution to a exponential curve and checks whether there is positive or negative growth. It detects both discharges and no discharges. In general, this method detects multipactor much faster than the others. However, it may suffer from higher variability between consecutive simulations. In such cases, it is advisable to use a high number of initial electrons.

Multi-carrier operation Charge (fixed factor): It is equivalent to the single-carrier one. Charge trend: This method, takes the advantage of the multi-carrier envelope periodicity. First, it checks the electron ratio. If it is higher than 1e7, multipactor is detected. In addition, it checks inter-period accumulation. This is, it stores the maximum population at each period of the envelope and compares it with the initial one. If noticeable growth is detected, then there is a multipactor discharge.

Other simulation options Write 3D stats

It writes advanced statistics in paraview mesh format that can be visualized from the results tab (see output section): Average SEY: It shows the average SEY of the impacting electrons in each surface of the mesh. Average Impact Energy: It shows the average impact energy of the impacting electrons in each surface of the mesh. Impact Density: It shows the electron impact density (impacts/m2) for each surface of the mesh. Emission Density: It shows the electron emission density (emitted electrons/m2)for each surface of the mesh. It can be positive (more electrons were emitted than absorbed) or negative (more electrons were absorbed than emitted).

Restore Gives back to the configuration parameters used in the last simulation. values

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Advanced Dialog The Advance Dialog allows for setting extra simulation parameters which are not usually needed for typical simulations but that provides extra control for advanced users.

The Advance Dialog allows for setting the following parameters: Relative error for adaptive electron path integration: This parameter specifies the maximum error in the electron path integration. The FEST3D electron tracker incorporates an automatic step refinement for each electron at each time step. This implies that the integration step for electrons in high field regions will be smaller than for those in low field regions, ensuring a maximum error for all of them. This process is iterative. Large values imply less accurate simulations but less adaptive iterations and thus faster simulations. Small values imply more accurate but slower simulations. The default value (1%) is normally a good trade-off for most cases. Homogeneous initial electron distribution: Normally, initial electrons are located on high electric field locations on metallic surfaces. If this option is checked, initial electrons will distribute uniformly on all surfaces. This can be useful in situations where high electrical field is present in reduced areas (metal edges) and multipactor is known to occur in other places.

Video Record If multipactor mode is selected videos can be saved by pressing the record button the play button The record video dialog is the following

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Here, the region in which the video is going to be recorded is selected

Number of Frames / Specifies the frame rate of the recording. The higher the smoother the animation, but bigger period video sizes will be generated. Maximum video size (MB)

If different from zero, the video will be cropped when the video file (approximately) exceeds the set size.

Start time (ns)

Sets the initial time for video recording.

End time (ns)

Sets the maximum time for video recording.

Input Power (W)

Sets the input power for this specific video recording.

Frequency (GHz)

Sets the signal frequency for this specific video recording.

Other parameters are taken from current configuration, such as SEY definition, number of electrons, multipactor criterion, single or multi-carrier simulation, etc . Autofill button completes the fields based in the last simulation (using results such as breakdown power, multipactor order, etc. When the Ok button is pressed, an output file must be selected (*.v3d extension) and the simulation starts. Results from previous simulations will not be deleted. The video will be stored outside of the project and it is independent of it (can be opened from other projects, for example). Once the simulation is finished, the user can select to immediately open the video, or to open it at any time with the play video button . The videos are opened with the 3D CAD viewer software Paraview, which allows for 3D rotations, perspective customization and zoom on the saved animations. It also allows for exporting the animation to popular video formats, such as avi format for instance. See the Video Tutorial for further information.

Running Multipactor Analysis from command prompt It is also possible to execute Multipactor Analysis from command prompt. The executable name is fest3d.exe on Windows platform and fest3d on Unix-like platforms, and is located in the directory where Fest3D is installed (you can view/edit the installation directory from the Preferences window). Executing the command fest3d -h (prefixed by

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Fest3D installation directory) will show all command-line arguments and options supported by the EMCE, including how to specify input and output files. A typical invocation of Multipactor Analysis looks as follows: --mode=multipactor --chdir= --ca= --tmp== --in=mycircuit.fest3 --out=mycircuit.multipactor -config_file=mycircuit.min --output_path== If any of the paths contain spaces, you should add double quotes. IE: --tmp="C:\path with spaces" The full path is required since the EMCE will search for the license file in the same directory as the full path specified. It is also necessary to indicate the directory where cache and the temporary files are stored (by default, cache and temporal directories are located in Fest3D_WORKSPACE directory, but you can choose a different one). The file mycircuit.min keeps all configuration parameters for Multipactor simulation and must be created before running the simulation from command prompt. Its format looks as follows: begin "multipactor" begin "power_steps" num_steps 1 100.0 end "power_steps" multipactor_criterion_sc "charge_automatic" criterion_fixedfactor_sc 100.0 multipactor_criterion_mc "charge_fixed_factor" criterion_fixedfactor_mc 100.0 material_name "silver" ext_DC_BField 0 B_DC_x 0.0 B_DC_y 0.0 B_DC_z 0.0 ext_DC_EField 0 E_DC_x 0.0 E_DC_y 0.0 E_DC_z 0.0 write_3D_stats 0 m_pdf_report 0 maximum_secondary_emission_coefficient 2.3 secondary_emission_coefficient_below_lower_crossover lower_crossover_electron_energy 35.0 electron_energy_at_maximum_SEY 165.0 initial_number_of_electrons 500 sc_precision 0.1 sc_initial_power 500.0 sc_max_power 1000000.0 iteration_type "bisection" custom_fixed_time 1 custom_max_time 1.0E-8 mc_precision 0.1 mc_initial_power 0.0 mc_max_power 1000000.0 SEE_statistics "maxwellian_velocity" path_rel_precision 1.0 homogeneous_emission 0 metallic_contours 0 analysis_type "breakdown"

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sey_type "vaughan" end "multipactor" In the command line example given above, this file is stored in the same directory as mycircuit.fest3 file. All these parameters are described in the Usage of Multipactor Discharge from User Interface. The possibility to launch Fest3D from command line allows using it in combination with external programs. This way, scripts to launch several executables sequentially can be generated.

Output The multipactor module provides the input power breakdown threshold per carrier of the selected elements of the structure. The simulation process can be visualized in the info window of the main FEST3D canvas, where a sweep in input power is shown as the simulation runs, showing how the simulator tries to approach the breakdown threshold. Multipactor results are given both in tabular and graphic form. They can be seen in run-time through the results window, which looks as follows:

There are two tables and one graph: 1. The left-hand side table shows for each analyzed power whether there has been breakdown or not. When breakdown occurs for a certain input power, the multipactor order is given in the second column of the table whereas when there is no breakdown the message "No break" appears. 2. In the graph it is represented the electron evolution with time for each power analyzed. This way it is easy to follow the increase/decrease of the electron population as the simulation runs. When left-clicking on the cell corresponding to a certain power of the left-side table, its corresponding curve is highlighted on the graph for a better recognition. 3. The upper table contains the threshold breakdown power for each element under study. Through this table the user can handle the results shown both in the left-side table and the graph: By left-clicking on a cell corresponding to a particular element both the graph and the left-side table

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update their values to the current element. By right-clicking on a cell corresponding to a particular element an option "Show 3D Stats" appears. This option launches a paraview window and shows the position of the electrons in the structure, and the 3D stats, if enabled in the configuration tab (see 3D statistics section). By left-clicking on the cell corresponding to the signal value, the whole row is selected and a bar diagram appears in the graph comparing the threshold breakdown power for all elements. With this information it is easy to recognize which is the most critical element for Multipactor and the minimum breakdown power supported by the device.

The data represented in the graph can be saved into a .png file through the button

the button

or into a .csv file through

.

3D statistics As explained in Output section above, when a cell of the general results table (upper table) is right-clicked, a context menu indicating "Show 3d Stats" appears.

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If clicked, a Paraview window opens with the 3D statistics of the multipactor simulation associated to the region and the signal of the cell. Different datasets are present: Init_Elec_Positions.vtu: Initial electron positions at time t=0. Final_Elec_Positions_X_W.vtu: Electron positions at the moment of the discharge for input power X W. This dataset is only present if a multipactor was detected at this power during the simulation. Mesh3DFields_X_GHz.vtu: Electromagnetic fields for the region at the input frequency X GHz Surface3D_stats_X_W.vtu: Collection of 3D surface statistics for the region at the specific input power of X W. These datasets are only present if the option "3D statistics" is enabled in the configuration tab. Different statistics can be visualized for this dataset: Avg_Impact_energy: For each of the surfaces (triangles) in the region, this represents the average impact energy of all impacting electrons. Avg_SEY: For each of the surfaces (triangles) in the region, this represents the average SEY value of all impacting electrons. Emission_Density: For each of the surfaces (triangles) in the region, this represents the total number of emitted electrons minus the total number of absorbed electrons, divided by the area of the surface. The units are electrons / m2. Therefore, a positive number indicates that surface contributed positively for the discharge (source) and a negative number indicates that it contributed negatively to the discharge (sink). Impact_Density: For each of the surfaces (triangles) in the region, this represents the total number of impacting electrons divided by the area of the surface. The units are impacts / m2.

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Hints To speed up the simulation use the multipactor module with the minimum accuracy possible to have a rough idea about the breakdown level. However, the EM fields do normally need more modes for convergence, so it is recommended to increase the number of accessible modes in the element where multipactor is going to be computed. Set the multipactor criterion to charge-trend. This will speed up the simulations significantly. This is of special importance in multi-carrier simulations. Only if high variability is found between simulations change back to charge (automatic), or charge (fixed factor) criteria. Set the frequency to one single value in each simulation. Otherwise, many calculations are done.

2.3.6.2.1 Multipactor Practical Considerations Secondary Emission Yield (SEY) The multipactor discharge is a complex physical phenomenon which is strongly related to many factors. Concretely, the most important one is the Secondary Emission Yield (SEY) of the surfaces of the device. The correct modeling of the SEY properties of the surface is crucial for having reliable simulations. FEST3D multipactor module, allows for using custom SEY parameters or even import ASCII SEY definition files (see material definition). Unfortunately, in the real world, there is a high uncertainty with the real values of the SEY: First of all, the SEY of a certain surface depends not only on the material itself but on the microscopic roughness, impurities, cleanness, and oxidization processes. This means that there are no "universal" SEY curves for the different materials. For example the SEY of the silver coating of a company may differ from the SEY of the silver coating of another company. In addition, there are more caveats. The SEY properties of a material may change with time in which is known as Ageing process. That means that a certain sample may present important deviations of the SEY

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measured at a particular time, and the SEY measured some time later. In [1] it has been reported the variations of the SEY during 6 and 18 months of many types of coatings coming from different companies. As a result, it has been observed that the Ageing can cause an important variation in the multipactor breakdown (2dB-7dB). See below an example in Table 1, where the measured SEY properties of silver coatings coming from different companies are compared (extracted from [3], company names are confidential). A big difference can be observed. Values measured at different moments are also presented, showing a noticeable variation. Table 1: Comparison of Silver SEY for different companies and variation with time (Ageing). Initial

After 6 months

After 18 months

E1

SEYmax

Emax

E1

SEYmax

Emax

E1

SEYmax

Emax

Company1

20

2.8

380

20

3.1

298

20

3.1

268

Company2a

40

1,9

410

29

2,1

322

24

2,6

288

Company2b

44

2,0

484

39

2,3

376

39

2,2

376

Company3

43

1,7

210

34

2,1

366

34

2,1

385

With all this in mind, the engineer must interpret the breakdown discharges given by the software with caution, expecting some margin in experimental measurements. Our recommendation is to do a SEY sensitivity analysis, simulating the same structure with different SEY curves, to see the impact on the breakdown power, since this impact will strongly depend on the particular component under analysis.

Standard SEY materials FEST3D includes typical SEY parameters for most relevant materials, extracted from European ECSS standard [2] and American Aerospace Corp. standard [3]. Both standards give worst-case multipactor breakdown charts which may be useful to easily estimate the breakdown levels for the parallel-plate case. For real structures, numerical simulation with FEST3D provides more accurate results. The ECSS standard figures correspond to different materials and come from the fitting of the multipactor breakdown results to a particular test campaign done in [4]. For that reason, numerical simulations with FEST3D (with simple structures, close to parallel-plate geometry) and ECSS SEY parameters, provide results similar to those of the ECSS standard. In turn, the SEY parameters provided by the Aerospace standard do not correspond to real measurements, but correspond rather to a single material which represents theoretically the worst-case (lowest breakdown levels). On the other hand, the Aerospace Corp. standard is based on the classical multipactor theory for parallel plates without experimental data fitting. As a result, numerical simulations with FEST3D (with simple structures, close to parallel-plate geometry) and the Aerospace Corp. SEY, provide more realistic (higher) breakdown levels. Fig. below shows the difference (around 3 dB).

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References [1] ESA-ESTEC TRP AO/1-4978/05/NL/GLC "SEY Database", Final Report, December 2011. [2] "Space Engineering: Multipacting Design and Test", volume ECSS-20-01A, edited by ESA-ESTEC. ESA Publication Division, The Netherlands, May 2003. [3] AEROSPACE REPORT NO. TOR-2014-02198, "Standard/Handbook for Radio Frequency (RF) Breakdown Prevention in Spacecraft Components" [4] A. Woode and J.Petit. "Diagnostic investigations into the multipactor effect, susceptibility zone measurements and parameters affecting a discharge". Technical report, ESTEC working paper No. 1556, Noordwijk, Nov. 1989.

2.3.7 Export tools This section describes the export tools present in Fest3D. There exist 5 different exportations:

Export 3D geometry (closed ports): This option allows exporting the complete device as a single block to a Standard ACIS Text (SAT) file. Additionally, the existing dielectric volumes will be individually included in the SAT file as well. The geometry generated by Fest3D considers that all input/output ports are closed, as mere walls of the whole circuit.　

Export 3D geometry building blocks (closed ports): This option allows exporting the device to a Standard ACIS Text (SAT) file. By using this option, the different elements used to build the device in the Fest3D

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schematics will be embedded in the SAT file as different ACIS bodies. The geometry generated by Fest3D considers that all input/output ports are closed, as mere walls of the whole circuit. No information about dielectric objects is given in this option.　Thus, if the user intends to simulate the exported geometry with another CAD tool, the dielectric parts must be specified manually inside the new software, as well as the possibility of using them as input/output ports, before performing any analysis.

Export S-Parameters to Touchstone file: Converts the Fest3D output file to TOUCHSTONE format. The generated file has the same name as the original .fest3 file, but with snp extension. Export Project to CST MWS®: One may generate a CST Microwave Studio® project from a Fest3D project. For this purpose, one may: Open in Fest3D the. fest3 file that you want to export. Go to Export-> Export Project to CST MWS®. The following window will pop up.

You may choose the exportation units to be used in CST MWS®.

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Export Project to CST Desing Studio®: One may generate a CST Design Studio® project from a Fest3D project. Selecting this way of export, a CST Studio project will be created with a single block component. Also pins will be created too. For this purpose, one may: Open in Fest3D the. fest3 file that you want to export. Go to Export-> Export Project to CST Design Studio®. A window requesting the location of the exported project in ".cst" format.

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2.3.8 CLI The executable file to launch Fest3D in command-line mode can be found in the installation directory of Fest3D. The file is different depending on the platform where it is being used: fest3d.exe for Windows platforms fest3d for Linux platforms. The executable can be invoked with different combinations of options. Options can be: optional (enclosed with square brackets "[ ]" ), required (shown between parens "( )" ) or mutually exclusive (separated by pipes " | "). All options are required by default, if not included in brackets "[ ]". However, sometimes options are marked explicitly as required with parens "( )". For example, when they belong to a group of mutually-exclusive or mutually-dependent options. Together, these elements form valid usage patterns, each starting with Fest3D executable.

Usage patterns Fest3D has two patterns for different usages in command-line mode: fest3d.exe --help

To show the usage and all comand-line options

fest3d.exe

To launch Fest3D in different modes

[ (-Z | -S | -Y) ] [--mode= (sparameter | emfield | visualization)] --chdir=

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--in= --out= [--licenseServer=] [--nthreads=n] [other options depending on mode]

Options The table below collects Fest3D command-line options in both long and short forms together with their description. Options with arguments are followed by "arg" in the table. Option

Usage and meaning

--help [-h]

prints help usage.

--licenseServer =

ANALYSIS OR EXPORT --mode=

define type of analysis. can be: sparameter (default) emfield multipactor corona visualization exportfile exportfileblocks export_emfield exportcst exportResults2DES *1 IF --MODE IS NOT WRITTEN, IT WILL BE ASSUMED "--mode=sparameter"

CHARACTERIZATION -Z

calculate multi-mode impedance matrix Z

-S

calculate multi-mode scatter matrix S

-Y

calculate multi-mode admittance matrix Y

MANDATORY PARAMETERS FOR ANY TYPE OF LAUNCH --chdir=

set working directory

--in=

set .fest3 input file

--out=

set output file

[--nthreads=]

set number of threads used in the calculation. Although it is optional, it is heavily recommended to use it. Default value is 1

EXTRA ARGUMENTS DEPENDING ON SIMULATION MODE EMFIELDS parameters

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Specifies the frequency point in which the electromagnetic fields will be calculated. The value is in GHz and must be a non-negative

MULTIPACTOR AND CORONA SIMULATIONS --chdirHP=

set working directory for HP simulation (relative to chdir)

--output_path=

path relative to chdir where High Power simulation stores output data

--config_file=

path and file name (relative to chdir) where High Power (Corona/Multipactor) input parameters are defined

EXPORTATION --efile=

path and name of the file where the export will be created

--eunits=

set the type of units to which export the circuit. Types can be meters, mm (default), inches

--esatversion=

indicates the version of ACIS in which the exported SAT file will be written

EXTRA MODIFIERS CACHE MODIFIERS --disable_init_lastsimpr

disable use/creation of cache files

OTHER MODIFIERS -verbose=

set mildest severity that is reported (default: info)

Launching mode examples S-PARAMETER LAUNCH FORMAL LAUNCH

--chdir="" --in=.fest3 --licenseServer=27000@localhost --out=.out --nthreads=

EXAMPLE

"C:\Program Files (x86)\Fest3D-2019\fest3d.exe" --chdir="D:\workspace\Examples\Analysis\Rectangular\Bandpass\Bandpass" -in=bandpass.fest3 --licenseServer=27000@localhost --out=bandpass.out --nthreads=4

EM-FIELDS LAUNCH FORMAL LAUNCH

--chdir="" --in=.fest3 --licenseServer=27000@localhost --nthreads=

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--mode=emfield --override_frequency_mode="" EXAMPLE "C:\Program Files (x86)\Fest3D-2019\fest3d.exe" --chdir="D:\workspace\Examples\Analysis\Rectangular\Bandpass\Bandpass" -in=bandpass.fest3 --licenseServer=27000@localhost --nthreads=4 --mode=emfield --override_frequency_mode=13.0

EXPORTATION LAUNCH FORMAL LAUNCH

--chdir="" --in=.fest3 --licenseServer=27000@localhost --out= --mode=exportfile --esatversion= --efile=.sat --eunits=

EXAMPLE "C:\Program Files (x86)\Fest3D-2019\fest3d.exe" --chdir="D:\workspace\Examples\Analysis\Rectangular\Bandpass\Bandpass" -in=bandpass.fest3 --out=bandpass.messages --licenseServer=27000@localhost --mode=exportfile --esatversion=27.0 -efile="D:\workspace\tmp2019\3dview.sat" --eunits=mm

MULTIPACTOR LAUNCH FORMAL LAUNCH

--chdir="" --chdirHP= --in=.fest3 --licenseServer=27000@localhost --nthreads= --config_file= --output_path= --mode=multipactor

EXAMPLE "C:\Program Files (x86)\Fest3D-2019\fest3d.exe" --chdir="D:\workspace\examples\HP\Multipactor\single_carrier\lowpass -chdirHP=multipactor_lowpass --licenseServer=27000@localhost --in=multipactor_lowpass.fest3 --nthreads=4 -config_file=sims/m_confs/conf1/conf1.min --output_path=sims/m_confs/conf1/out --mode=multipactor

CORONA LAUNCH FORMAL LAUNCH

--chdir="" --chdirHP= --in=.fest3 --licenseServer=27000@localhost --nthreads= --config_file= --output_path= --mode=corona

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EXAMPLE "C:\Program Files (x86)\CST Studio \FEST3D\fest3d.exe" --chdir="D:\workspace\examples\HP\Corona\lowpass_air" -chdirHP=corona_lowpass --in=corona_lowpass.fest3 --nthreads=4 --config_file=sims/c_confs/conf1/conf1.cin -output_path=sims/c_confs/conf1/out --mode=corona --licenseServer=27000@localhost

OPTIMIZER LAUNCH FORMAL LAUNCH

--chdir="" --in=.fest3 --out-curr= --out-prev= --engine= ---licenseServer=27000@localhost --nthreads=

EXAMPLE "C:\Program Files (x86)\CST Studio \FEST3D\OPT3D_CLI_launcher.bat" -chdir="D:\workspace\Examples\Analysis\Circular\Page_URSI_2001\Page_URSI_2001_to_optimize" -in=Page_URSI_2001_to_optimize.fest3 --outcurr="D:\workspace\Examples\Analysis\Circular\Page_URSI_2001\Page_URSI_2001_to_optimize\Page_URSI_2001_to_optimize.out" -outprev="D:\workspace\Examples\Analysis\Circular\Page_URSI_2001\Page_URSI_2001_to_optimize\Page_URSI_2001_to_optimize.out.prev" --engine=C:\Program Files (x86)\Fest3D-2019\bin\64\fest3d -- --licenseServer=27000@localhost --nthreads=4

2.4 Elements Database This section describes the components supported by Fest3D, as well as the dialog boxes used to view and edit them. In Fest3D, the term "element" and its synonim "component" indicates each elementary building block of a circuit. The elements supported by Fest3D are divided in two classes: waveguides and discontinuities. Waveguides can only be connected to discontinuities, and vice-versa. Each element has its own reference system, whose position and orientation depend, firstly, on the type of component and, ultimately, on the element's location inside the current circuit. On the one hand, discontinuities set the reference system of each one of their ports. On the other hand, taking into account that the reference systems of the components connected to each other must match, waveguides' reference system is settled by its counterpart located in the discontinuities connected to them. However, there is an ambiguity in the determination of elements' coordinate systems, in general, which is solved by setting the global property reference port 3D. Once we select an I/O port number for this global property, a reference system is anchored to this I/O waveguide port and the ambiguity of the whole circuit is solved through the ports' matching between waveguides and discontinuities. The Elements Database section contains the following topics: Waveguides

Definition of waveguide, and the list of waveguides supported by Fest3D.

Discontinuities

Definition of discontinuity, and the list of discontinuities supported by Fest3D.

Symmetries

Description of the symmetries, and the list of the available ones for each element.

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2.4.1 Waveguides This section describes all the waveguides supported by Fest3D, and how they can be used as building blocks to compose circuits. The waveguides section contains the following topics: Definition

What is exactly a Fest3D waveguide, and how it can be used in a circuit.

Waveguides List

All waveguides supported by Fest3D.

Common Properties

The common properties to all waveguides, their meaning and the dialog box to view/edit them.

Definition In Fest3D, a waveguide is an element with uniform cross-section (with a single exception). Waveguides can be either normal transmission lines, open-ended (I/O port) or closed on a load. Waveguides can only be connected to one or two discontinuities.

Coordinate System The coordinate system in a waveguide port is imposed by the one corresponding to the discontinuity port connected to it. The coordinate system in the other waveguide port will be parallel to the previous one. The next figure shows this behavior with a rectangular arbitrary waveguide.

Waveguides List Fest3D supports a large number of different waveguides. In the following, all these waveguides are described and grouped by their type:

Basic Waveguides Rectangular

The classic, uniform waveguide with rectangular cross section.

Circular

The classic, uniform waveguide with circular cross section.

Coaxial

The classic, uniform waveguide with an external and an internal circular contours.

Rectangular-Contour Based Waveguides Here is the list of all waveguides based on an Arbitrary Waveguide with Rectangular-Contour (ARW): Arbitrary A uniform waveguide with arbitrary (i.e. defined by the user) cross-section. Supports inner Rectangular conductors (and thus TEM modes), strip lines and fin lines. The cross-section contour can be

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composed by straight segments, arcs and elliptic arcs. It uses BI-RME method on a Rectangular reference section. Coaxial

A uniform waveguide with a circular inner conductor and with an external conductor either rectangular or circular. Always has a single TEM mode.

Square coaxial

A uniform waveguide with both rectangular inner and external conductors.

Cross

A uniform waveguide with two arms of a given width. The extremes of the arms can be rounded.

Draft

A uniform rectangular waveguide in which the lateral walls have a triangular shape due to manufacturing processes.

Elliptic

A uniform waveguide with elliptic cross-section (can be rotated).

Ridge

A uniform waveguide with ridged cross-section.

Slot

A uniform rectangular waveguide with rounded corners.

Truncated

A uniform circular waveguide which has been truncated by horizontal and/or vertical rectangular segments.

Waffle

A uniform rectangular waveguide with rectangular metallic insertions in the top and/or the bottom walls. Also called a multi-ridge waveguide.

Ridge-gap

A uniform rectangular waveguide with rectangular metallic insertions symmetrically placed with respect to the central axis in the top and/or the bottom walls.

Lateral coupling circular waveguide

The lateral coupling circular waveguide is a dumbbell-shaped element which allows a lateral rectangular coupling between two circular cavities.

Circular-Contour Based Waveguides Here is the list of all waveguides based on an Arbitrary Waveguide with a Circular Contour (ACW): Arbitrary A uniform waveguide with arbitrary (i.e. defined by the user) cross-section. Implemented as a Circular Circular waveguide with perturbations. Supports fin lines, but not strip lines or inner conductors (and thus no TEM modes). The cross-section contour can be composed by straight segments and by arcs belonging to the unperturbed Circular waveguide. Uses BI-RME method on a Circular reference section. Arbitrary A uniform waveguide with a elliptic section (axes can have any rotation). Circular with an Ellipse Arbitrary A uniform waveguide with a cross-shaped section. Circular with a Cross Arbitrary A uniform waveguide with a "circular with screws" section. Circular with Screws

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Other Waveguides Here is the list of all waveguides that do not fit in the previous groups: Radiating A mathematical representation of an infinite, periodic array of rectangular or circular I/O ports opened Array in the free space. Can only be used as I/O Port. It is currently the only Fest3D component with antenna-like characteristics. Curved

A waveguide with rectangular cross-section, constant curvature radius and curved either left or right. There are also techniques to obtain waveguides curved up or down.

CircularElliptic iris

An optimized elliptical iris that can be connected only to two circular waveguides.

Common Properties Each waveguide can be used in one of the following three modes (SubType): Transmission Line. It is the normal type. It has two connections (ports), one at each side, attached to two discontinuities. Input/Output port. The waveguide terminates one of its sides with an input/output port. The user has to define the Port Number, consequently identifying the input/output port, and the order number of the Excited mode, in the range [1, Number of accessible Modes]. It is also possible to use different order numbers for the Input mode and Output mode, which must be in the same range. Termination. The waveguide terminates with an adapted load or short circuit on one of its sides. The user has to define the reflection coefficient within the range [-1,1]. The waveguide has only one connection, attached to a discontinuity. The waveguides have the following common modal parameters which set the accuracy of the computation: Number of accessible Modes Number of accessible (i.e. connecting, propagating) modes of the waveguide. Only the accessible modes of a waveguide are assumed to transmit E.M fields (and energy) across the whole waveguide length. (default: 10) Number of MoM basis functions Number of modes used in the internal MoM to calculate the discontinuities attached to the waveguide (default: 30) Number of Green function terms Number of terms in the frequency-independent (static) part of the Green's function, which describes the discontinuities attached to the waveguide (default: 300) By clicking on the Use General Specifications button, each waveguide can be configured to use either the default values for these properties (stored in the General Specifications window) or the values specified by the user in each waveguide. The dialog box of all waveguides contains a Specific tab, where the SubType and some related parameters can be edited:

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Fest3D waveguides have three common sets of properties: Ports, that shows which discontinuities are attached to the current waveguide, Material, which contains a basic set of physical material properties, and EM Field, which involves the resolution of the electromagnetic field calculated for the current waveguide. They typically look as follows:

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The Ports cannot be edited. To change the connections among elements, see the Elements Bar paragraph in the Main Window section. By clicking on the Use General Specifications button in the Material or in the EM Field tab, each waveguide can be configured to either use the default values for these properties (stored in the General Specifications window) or to per-waveguide user-specified values. The material parameters are the following (they are also described in the General Specifications window): Dielectric Permittivity Relative dielectric constant of the dielectric homogeneously filling the waveguide (default: 1.0 i.e. vacuum) Dielectric Permeability Relative dielectric constant of the dielectric homogeneously filling the waveguide (default: 1.0 i.e vacuum) Dielectric Conductivity Intrinsic conductivity of the dielectric homogeneously filling the waveguide, in S/m (default: 0.0) Metal Resistivity Intrinsic resistivity of the metallic walls of the waveguide, in Ohm · m (default: 0.0)

2.4.1.1 Basic Waveguides 2.4.1.1.1 Rectangular Waveguide This section describes the Rectangular waveguide and how to use it, as well as its features and limitations. The Rectangular waveguide section contains the following topics:

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Definition

What is exactly a Rectangular waveguide.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Rectangular

How to create, edit and use this element from Fest3D.

Hints

Non-trivial properties of this element.

Definition The Rectangular waveguide is a uniform waveguide with rectangular cross section, as shown in the following figure:

Limitations The Rectangular waveguide has no limitations.

Errors The Rectangular waveguide should never produce errors.

Using the Rectangular The dialog box of the Rectangular waveguide is quite minimal, yet it is the standard base for the dialog boxes of all other Waveguides.

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The Enabled/Disabled button allows enabling and disabling this element, as described in the Main Window Edit menu. The SubType option allows defining the waveguide subtype and related parameters, as described in the Waveguides Common Properties section. By clicking on the Use General Specifications button, each waveguide can be configured to use either the default values for the modal parameters (stored in the General Specifications window) or the values specified by the user in each waveguide. The following parameters can be edited: A (mm) the waveguide width B (mm) the waveguide height L (mm) the waveguide length Additionally, in order to fill the A and B parameters, one can choose between a set of standard rectangular waveguives by clicking in the box of Use Standard Waveguide. In order to perform either Multipactor Analysis or Corona Analysis in such a waveguide just click in the corresponding box. Material and EM Field tabs allow customizing, respectively, the physical material properties and the electromagnetic resolution for the current waveguide, as described in the Waveguides Common Properties section. Ports tab shows the discontinuities connected to this waveguide, as described in the Waveguides Common Properties section.

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Hints The length of this waveguide can be zero.

2.4.1.1.2 Circular Waveguide This section describes the Circular waveguide and how to use it, as well as its features and limitations. The Circular waveguide section contains the following topics: Definition

What is exactly a Circular waveguide.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Circular

How to create, edit and use this element from Fest3D.

Hints

Non-trivial properties of this element.

Definition The Circular waveguide is a uniform waveguide with circular cross section, as shown in the following figure:

Limitations The modes of the Circular waveguides are pre-computed. The maximum number of supported modes is approximately 160000. In case that "all-cylindrical" symmetry is used, this basically means that NO more than 795 terms of the green function can be used. However, this number should be more than enough to reach convergence and it is not a real limitation. In case that TEM symmetry is used, this basically means that NO more than 200 terms of the green function can be used. However, this number should be more than enough to reach convergence and it is not a real limitation.

Errors If the user specifies more than approximately 160000 modes (the maximum supported), an error is produced and the simulation stops. The Circular waveguide produces no other errors.

Using the Circular The dialog box of the Circular waveguide is the following:

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The Enabled/Disabled button allows enabling and disabling this element, as described in the Main Window Edit menu. The SubType option allows defining the waveguide subtype and related parameters, as described in the Waveguides Common Properties section. By clicking on the Use General Specifications button, each waveguide can be configured to use either the default values for the modal parameters (stored in the General Specifications window) or the values specified by the user in each waveguide. The following parameters can be edited: R (mm) the waveguide radius L (mm) the waveguide length The user can choose standard circular waveguides by clicking the corresponding box and selecting one of the waveguide numbers. In order to perform either Multipactor Analysis or Corona Analysis in such a waveguide just click in the corresponding box. The first mode of the circular waveguide is chosen as the one with vertical polarization. Material and EM Field tabs allow customizing, respectively, the physical material properties and the electromagnetic resolution for the current waveguide, as described in the Waveguides Common Properties section. Ports tab shows the discontinuities connected to this waveguide, as described in the Waveguides Common Properties section.

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Hints The length of this waveguide can be zero. This is sometimes useful if the direct coupling between two waveguides is not available in Fest3D.

2.4.1.1.3 Coaxial waveguide This section describes the circular coaxial waveguide and how to use it, as well as its features and limitations. The coaxial waveguide section contains the following topics: Definition

What is exactly an circular coaxial waveguide.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the circular coaxial waveguide

How to create, edit and use this element from Fest3D.

Hints

Non-trivial properties of this element.

Definition The coaxial waveguide is a uniform waveguide with circular cross section, as shown in the following figure:

Limitations The direct coupling of this element to the circular waveguide can be done only in the case that the circuit has TEM symmetry. Circuits with such a symmetry should begin and finish with coaxial waveguides, no offsets should be present and the circuit can be only composed by coaxial and circular elements.

Errors In the case of coaxial-circular connections, only the discontinuities showed in the following picture can be directly computed with a step.

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Other cases should be tackled by using an intermediate zero length circular waveguide of the same radius than the outer bigger radius of the attached waveguides. The coaxial waveguide produces no other errors.

Using the coaxial The coaxial waveguide is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes. The following picture shows a typical Element Properties dialog box for the coaxial waveguide.

The Enabled/Disabled button allows enabling and disabling this element, as described in the Main Window Edit menu. The SubType option allows defining the waveguide subtype and related parameters, as described in the Waveguides

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Common Properties section. By clicking on the Use General Specifications button, each waveguide can be configured to use either the default values for the modal parameters (stored in the General Specifications window) or the values specified by the user in each waveguide. The number of basis functions for the coaxial waveguide is automatically given as a function of the number of terms of Green's function terms: TEM symmetry: the number of basis functions is two times Number of Green's function terms. The maximum number is set to 150 since this provides around 45000 modes. Without symmetry: the number of basis functions is three times the square root of the Number of Green's function terms. IMPORTANT: If a large amount of accessible modes is desired, and the number of Green's funcions is not high enough, a warning message will appear inidicating the recommended number of Green's functions for computing the high modes with a certain accuracy. If this requirement is not fulfilled, numerical instabilities may occur in the simulation. The following parameters can be edited: L (mm): waveguide length. Outer Radius (mm): radius of the outer circular. Inner Radius (mm): radius of the inner circular. Ports tab shows the discontinuities connected to this waveguide, as described in the Waveguides Common Properties section. Material tab allows customizing the physical material properties for the current waveguide, as described in the Waveguides Common Properties section.

Hints When the symmetry TEM is active, it is recommended to reduce a lot the number of Green's function terms. Values around 20 or even below of this number could already provide convergent results.

2.4.1.2 Arbitrary Rectangular Waveguides 2.4.1.2.1 Arbitrary Rectangular (ARW) This section describes the Arbitrary Rectangular waveguide and how to use it, as well as its features and limitations. The Arbitrary Rectangular waveguide section contains the following topics: Definition

What is exactly an Arbitrary Rectangular waveguide.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Arbitrary Rectangular

How to create, edit and use this element from Fest3D.

Hints

Non-trivial properties of this element.

Definition

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The Arbitrary Rectangular waveguide computes the modal chart of any waveguide with an arbitrary cross section defined by a combination of linear, circular and elliptical arcs, which must be included in a fictitious, bigger rectangular waveguide (reference box). The reference box is a fictitious rectangular waveguide that surrounds the contour of the Arbitrary Rectangular waveguide and is needed by the mathematical theory used by this element (BI-RME Method). The cross-section of this element can be composed by one or more contours, which define its geometry. Each contour can be defined by means of straight, circular and elliptical arcs, as well as of any possible combination between these three kinds of segments. The user must define only the portions of the arbitrary contour that not coincide with the surrounding rectangular box. In the following picture the contour of the arbitrary waveguide divides the reference box into an internal area S and a complementary area.

The cross-section to be analyzed can have multiple inner contours, such as the ones shown in the following picture, which defines the internal areas S,S1,S2,S3. In this case the user must be careful, since there are four regions (or areas) that the program can use to perform the analysis. Only one region of interest (S1, S2, S3 or S) must be indicated for modal analysis purposes.

The Arbitrary Rectangular waveguide supports TEM modes when the arbitrary contour has inner conductor(s). The number of TEM modes present in an Arbitrary Rectangular waveguide is equal to the number of inner conductors. Important: The hollow section of the arbitrary waveguide is defined by the "X" point present in the mesh editor/file.

Limitations The Arbitrary Rectangular waveguide has some limitations and caveats you should be aware of. 3D Visualization

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This element can be only visualized in 3D by making use of the 3D Viewer which is accessible from the main Window top menu bar. Connections to other elements The Arbitrary Rectangular waveguide can only be connected to Step or N-Step. It is possible to connect the remaining ports of those Steps and N-Steps to Rectangular, Circular, Arbitrary Rectangular, (or derived, as Coaxial and Elliptic) waveguides. If the connected waveguides have the same reference box as this element and their X,Y offsets and rotation are zero, a specialized routine is used to compute the coupling integral, which is faster and more accurate than the general case. Invalid contours A contour cannot exceed the rectangular surrounding box. Contours cannot touch or intersect one another but can touch the external reference box. Contours cannot contain invalid parameters: the radius of a circular portion must be grater than zero the minor semi-axis of an elliptical portion must be lesser than the major semi-axis and greater than zero only one region of interest of the cross-section can be specified (this is handled automatically by Fest3D) If a contour defined by the user is invalid, the program generates a fatal error and stops the simulation. Tangent contours Each contour can take any shape, and it can be therefore also tangent or incident to the external box as in the pictures below. Some precautions should be taken in this case. If a circular or elliptical arc is tangent to the external rectangular box in points different to the starting and ending points of the arc, this will not be detected by the program. For this reason, the user must split or rearrange the arcs so that only the starting and/or ending points of the arc are tangent to the rectangular box. Furthermore, in this case some errors may happen. Such errors must be adequately treated as discussed in convergence failed paragraph below. Very big or very small cross-section areas (>95% or 2): as a circular box where the ports are located around it at equidistant distance. The size of the box depends on the number of ports of the network. no EM field can be computed on this element use of the number of accessible modes Although the Touchstone discontinuity allows connections with waveguides with any number of accessible modes, the characteristic impedances of the ports connected to the element only take into account the first accessible mode to calculate the frequency response (Please, note that the number of the accessible modes of each waveguide connected to the Touchstone element must be the same). simulation frequency range The simulation frequency range of the whole circuit must be contained within the frequency range specified in the Touchstone element. Noise parameters are not allowed The noise data of linear active devices will be omitted if they exist in the Touchstone® file.

Errors The Touchstone discontinuity can produce the following errors under certain circumstances related to the loading of the Touchstone® file:

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Error loading the option line in touchstone file. The allowed values for the frequency units are: GHz, MHz, KHz and Hz. Error loading the option line in touchstone file. Only Scattering parameters (S) are allowed. Error loading the option line in touchstone file. The allowed values for the format data are: RI for realimaginary, MA for magnitude-angle and DB for dB-angle (dB=20*log10|magnitude|). Error loading the option line in touchstone file. The reference resistance to which the parameters are normalized must be a positive number in Ohms. Zero value will consider the parameters as not renormalized. Error loading the option line in touchstone file. The option line must be formatted as follows: # R . Error loading the option line in touchstone file. Option parameters not found in touchstone file.

Using the Touchstone The Touchstone discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes, as the one shown below: The following figure shows a typical Element Properties dialog box for the Touchstone discontinuity:

The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The name and path of the file can be either entered directly (hit the Enter key when done) or chosen with the help of an Open File dialog.

2.4.2.1.8 Rounded corner iris 3D This section describes the Rounded corner iris 3D discontinuity and how to use it, as well as its features and limitations. The Rounded corner iris 3D discontinuity section contains the following topics: Definition

What exactly is a Rounded corner iris 3D discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Rounded corner iris 3D

How to create, edit and use this element from Fest3D.

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Definition The Rounded corner iris discontinuity represents an iris with rounded corners which are built in the H- or E-plane. Top and side views for both planes are sketched in the figures below.

Basic geometrical scheme of side view for E-plane

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Basic geometrical scheme of side view for H-plane

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Basic geometrical scheme of top view for H-plane

Basic geometrical scheme of top view for E-plane

The Rounded corner iris 3D discontinuity is an extension of the rounded corner iris (2D), which allows geometries not purely inductive or capacitive.

Limitations This element has some limitations and caveats you should be aware of: High memory consumption using parallelization in circuits with many irises If small values of mesh sizes are specified (for high accuracy or convergence tests), then very large meshes and dense matrices are required in the simulation, consuming an important amount of RAM. Once the meshing of the element is performed, the information window will show an estimation of the maximum total memory that will be used during calculations. Besides, the software will automatically detect if the memory requirements are greater than the RAM memory available in the system, and will stop the simulation if necessary. If there are several different irises in the circuit, and multicore simulation is desired, it is important to take into account that these RAM requirements are increased, and a slowdown in the computer performance might be encountered. For those cases, it is recommended to employ a lower number of processors, which may allow successfully completing a simulation that cannot be performed using more cores due to memory limitation problems. If reducing the number of processors the memory problems still persist, it is advisable to increase the mesh size values (reduce precision) of the posts or rounded corners in the cavity (explained in the specifications section below) for performing the simulation.

Errors The Rounded corner iris 3D discontinuity can produce the following errors under certain circumstances. For each error,

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the possible solutions or workarounds are explained. FATAL ERROR. Not even a single resonant mode can be obtained for this cavity. Please change the cavity dimensions or increase the Maximum Frequency of the Solver BI-RME 3D RWG The maximum frequency introduced is under the cut-off frequency of the cavity that contains the 3D iris, used by the Solver BI-RME 3D RWG. Provided that the dimensions of the iris and the ports are correct, the solution is to increase the value of this maximum frequency. It is recommended to set it to a value two or three times the maximum frequency of the desired analysis band.

FATAL ERROR. No 3D mesh detected. Please re-check the geometry, or try to reduce the mesh size If this error appears, it means that the meshing algorithm was able to create a 2D mesh, but not a 3D. This 3D mesh is necessary to compute data employed for the EM fields calculations. For this reason, the simulation is forbidden if the 3D mesh is not available. This situation may happen if a wrong geometry has been specified. Error building mesh file This error occurs when there is some problem building the mesh. This can occur if there are failures while generating the geometry. It is advisable to check if the geometry can be visualized with the 3D viewer. If this is the case, then the problem is related to the meshing algorithms, due to the same reasons explained for the previous error related to failure of the 3D mesh. FATAL ERROR, mesh file not found This message will appear if the meshing needed by the internal routines is not found. This error is usually related to the building mesh error explained before, and should not appear in the case of a correct mesh generation. LAPACK error: some error message The admittance matrix is not invertible at the simulated frequency point. This can only happen during the frequency loop. This error is very unusual and it can be produced if a simulated frequency point is too close to a pole. In this case the problem can be solved by slightly changing the frequency points.

cmalloc() failed: Out of memory!: This happens when too much memory is required to solve the system. It is recommended, in this case, to reduce the Maximum Frequency value, and/or increase the mesh size values. Simulation error (no further explanation): This error is also related with memory limitations, and may occur if too much precision is demanded. Besides, this problem can appear when performing simulations with several cores, due to the higher memory requirements of this feature. Reducing the number of processors is necessary to successfully perform the simulation.

Using the Rounded corner iris discontinuity The Rounded corner iris discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes and can view it in the 3D viewer. Connections to other elements This element must be connected to two Rectangular waveguides (one for each port). The following picture shows a typical Element Properties dialog box for the Rounded corner iris discontinuity.

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Specific properties of the Rounded corner iris 3D

The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following parameters can be edited: R (mm/inches): Radius of the external corners. Ai (mm/inches): Width dimension of the iris (X axis). Bi (mm/inches): Height dimension of the iris (Y axis). Li (mm/inches): The length of the iris (Z axis). Iris offset X (mm/inches): The offset of the iris in the x-axis direction, relative to the reference box center. Iris offset Y (mm/inches): The offset of the iris in the y-axis direction, relative to the reference box center. Mesh size (mm/inches): This value specifies the size of the triangles which are used for meshing the geometry of this element (iris walls and rounded corners) during the simulation. The user should change this mesh size for each particular case, taking into account the maximum and minimum dimensions employed. The smaller the mesh size, the finest the internal meshing, which will lead to more accurate results, but it will also slow

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down the simulation time. Also, very small values may produce memory allocation problems, due to large size of matrices involved with the meshing. Dielectric permittivity (relative) : Relative permittivity of the medium inside the cavity (air by default). Dielectric permeability (relative) : Relative permeability of the medium inside the cavity (air by default). Select type of geometry (E-plane or H-plane): To select whether the round corners of the iris are build in the E or the H plane (see the possibilities depicted in legend figures above) . Maximum Frequency (GHz): This parameter is required for the BI-RME 3D Solver, and specifies the maximum value of the frequencies of the resonant modes of the cavity to be computed during the analysis.

The particular geometry of this element is analyzed using the electromagnetic Solver BI-RME 3D RWG. This Solver considers Rao-Wilton-Glisson (RWG) basis functions for modelling the surface currents of the posts. This Solver requires that the geometry is meshed with triangular patches onto which the RWG basis functions are defined. Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figures below. This discontinuity always considers two ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element. For the case of the second port tab, X and Y offsets can be set. These offsets are defined with respect to the port 1 as depicted in the legend figures (parameters p2_off_x and p2_off_y).

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Port 1 properties of the Rounded corner iris 3D

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Port 2 properties of the Rounded corner iris 3D

Important considerations about the ports If two rectangular waveguides of the same section are used, the internal solver performs an analytical treatment to the ports. In other cases, if one of the port sections is bigger than the other, an internal mesh of the smaller port section is required by the BI-RME 3D RWG electromagnetic Solver. For this case, the optional parameter Mesh size port must be set , which specifies the size of the triangles that are used for the port meshing. It is important to remark that the correct choice of this parameter is critical for the accuracy of the electromagnetic

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analysis. The mesh density employed for the port must be increased for large numbers of accessible modes of the rectangular waveguide, in order to maintain the accuracy of the method. As a consequence, a large number of accessible modes in the waveguide port will require a higher computational cost. In order to help the user to take into account these considerations, it is recommended to set this value to zero, allowing this way Fest3D to automatically choose an adequate value as a default. The automatic criterion employed obeys the following rules: If 30 or less accessible modes are employed in the rectangular waveguide, the triangle size is chosen as 1/5 of the minimum dimension (a,b) of the waveguide. If the number of coaxial modes is between 30 and 45, the triangle size is chosen as 0.2 times the cut-off wavelength associated to the largest mode number desired in the rectangular waveguide. If 45 or more modes are employed for the coaxial, the triangle size is chosen as 0.1 times the cut-off wavelength associated to the largest mode number desired in the rectangular waveguide. If a large amount of accessible modes is desired for the smaller waveguide port, it is necessary to take into account that very fine meshes will be created using the automatic criterion, slowing down the simulation time and increasing the memory consumption. Thus, it is not recommended to employ a high number of accessible modes unless it is mandatory. If this is the case, one way to deal with the mentioned drawback is to set manually the mesh size value for those cases, using the value that is shown in the element information as a reference. Tests with larger values can be performed in order to find a tradeoff between convergence, accuracy and computational cost. Finally, it is important to remind again that the Mesh size port value is only necessary for the cases of different port sections connected to this element, and only applies to the smaller port section. Values set to the larger port or to any of the ports if both sections are equal, will not take any effect during simulation.

The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended to manually set a tradeoff value taking into account the dimensions of the cavity under consideration.

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Specific properties of the Rounded corner iris 3D EM Field

2.4.2.2 Junctions library The Junctions library contains the following discontinuities:

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Cubic Junction T-Junction Y-Junction (60 deg) Y-Junction general with N screws 2D OMT 2D Compensated Tee

2.4.2.2.1 Cubic Junction This section describes the C-Junction discontinuity and how to use it, as well as its features and limitations. The C-Junction discontinuity section contains the following topics: Definition

What is exactly a C-Junction discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the C-Junction

How to create, edit and use this element from Fest3D.

Definition The C-Junction discontinuity is a cubic or parellelepiped cavity. Each surface of the cavity can be connected to zero or one rectangular waveguide. The dimensions of the C-Junction are taken from the adjacent waveguides. As a maximum, the total number of waveguides connected to the C-Junction is six. This type of discontinuity enforces a fixed position of the coordinate system in each port. The next figure shows this distribution.

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Limitations The C-Junction can be connected only to rectangular waveguides. Two rectangular connected waveguides with common sides must have the same dimensions on that sides. The dimensions a, b and c of the C-Junction can not be left undefined so at least two rectangular waveguides have to be connect to the discontinuity. The waveguides located in opposite C-junction faces must have the same number of accessible modes. EM Fields can not be computed on this element

Errors The C-Junction discontinuity can produce the following errors under certain circumstances. For each error, the possible solutions or workarounds are explained. error: unsupported coupling integral You connected a non-Rectangular waveguide to the C-Junction. The only solution is to change the circuit and include a zero-length rectangular waveguide between the C-junction and the connected waveguide. error: inconsistent geometry You did not connected enough rectangular waveguide to the C-Junction in order to be able to extract the a, b and c dimensions. Or you connected rectangular waveguides whose dimensions can not match in a C-Junction. The first problem can be solved connecting 2 or more waveguides (depending on the position in the CJunction). The solution of the second problem is to change the circuit and include a zero-length rectangular waveguide between the C-junction and the connected waveguide.

Using the C-Junction The C-Junction discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes. The following figures show a typical Element Properties dialog box for the C-Junction discontinuity:

The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following C-Junction parameters can be edited:

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Modes Front-Back: number of modes used for Front-Back coupling. Modes Left-Right: number of modes used for Left-Right coupling. Modes Top-Bottom: number of modes used for Top-Bottom coupling. These number of modes must be higher than the corresponding number of accessible modes of the adjacent waveguides. Setting this value to 0 the number of modes taken will be equal to the corresponding number of accessible modes. In the lower part of the window, the number of ports are defined and the situation of each port in the C-junction is given: front, back, right, left, top and bottom.

2.4.2.2.2 T-Junction This section describes the T-Junction discontinuity and how to use it, as well as its features and limitations. The T-Junction discontinuity section contains the following topics: Definition

What is exactly a T-Junction discontinuity.

Limitations

What are the limitations you should be aware of.

Using the T-Junction

How to create, edit and use this element from Fest3D.

Definition The T-Junction discontinuity is a parallelepiped cavity connected to three Rectangular waveguides, forming a T-like shape. It is a special case of the more general element C-Junction. The dimensions of the parallelepiped cavity are determined as the intersection of the connected Rectangular waveguides. Please refer to the C-Junction element for further details and examples, remembering that a T-Junction is a special case of it.

Limitations The T-Junction discontinuity has the same limitations and caveats as the C-Junction.

Using the T-Junction The T-Junction discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes. The following figures show a typical Element Properties dialog box for the T-Junction discontinuity:

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The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. In the lower part of the window, the number of ports are defined and the situation of each port in the C-junction is given: front, back, right, left, top and bottom.

2.4.2.2.3 Y-junction General with N screws This section describes the General Y-junction with N screws discontinuity and how to use it, as well as its features and limitations. The General Y-junction with N screws discontinuity section contains the following topics: Definition

What is exactly a General Y-junction with N screws discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Y-junction

How to create, edit and use this element from Fest3D.

Hints

Non-trivial features of the Y-junction.

Definition The General Y-junction with N screws discontinuity, based on the Arbitrary shape , represents a generalized Y-junction among three Rectangular waveguides. Additional posts (rectangular metal insertions and screws) can be considered inside the Y-junction as well. This element is a template that lets you to specify the geometry of the circuit defining a reduced number of parameters, without using the Arbitrary Shape Editor. For these reasons many of the limitations and remarks of the Arbitrary shape element apply to this element as well. The only difference comes from the definition of the coordinate system on each of the three ports. The user can specify the geometry as shown in the following figure:

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The user must specify the lengths L12, L13, L2 and L3, and the angles 2 and 3 (in degrees). All lengths and widths must be positive. Angles can be positive, negative or zero. Examples: A symmetric (120°) Y-junction requires α2 = α3 = 60° A T-junction with port 1 and port 2 on the same waveguide requires α2 = 0°, α3 = 90° A T-junction with port 2 and port 3 on the same waveguide requires α2 = α3 = 90°

Limitations This element has the same limitations and caveats as the Arbitrary shape it is derived from. In addition to this, the user should be aware that only some of the most common errors (negative lengths or port widths) are detected and suitable error messages are issued. In general, it is up to the user to ensure that the geometry is valid.

Errors The Y-junction discontinuity can produce the same errors as the Arbitrary shape it is derived from.

Using the Y-junction (general) with N screws The Y-junction discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes. The following picture shows a typical Element Properties dialog box for the Rounded corner iris discontinuity.

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The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following parameters can be edited: L12: Distance from port 1 to the point where port 2 branch starts. L13: Distance from port 1 to the point where port 3 branch starts. L2: Length of port 2 branch. L3: Length of port 3 branch. Angle 2: Angle between port 2 and port 1. Angle 3: Angle between port 3 and port 1. Dielectric Permittivity: the relative dielectric permittivity of the homogeneous medium filling this element (1.0

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is vacuum). Dielectric Permeability: the relative dielectric permeability of the homogeneous medium filling this element (1.0 is vacuum). Select type of geometry: Here the geometry can be specified to be Constant width or Constant height. Maximum frequency (GHz): the highest frequency for the analysis of the component. By default, it is set to 0.0, which means that this value is taken automatically as the double of the maximum frequency analyzed in the circuit. A modification of the maximum simulated frequency can result in a change of the S parameters. It could also slow down the simulation unnecessarily.

To conclude with the specific properties tab, two checkboxes allow the user to perform Multipactor and Corona analysis of this discontinuity. Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figure below. This discontinuity always considers three ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element.

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Another part of the specifications of this element is the General posts tab, as shown in the figure below. Here, additional posts (full constant width/height) can be inserted in the geometry if desired, by pressing the Add button. Two post shapes can be selected: Rectangular metal insertions. The parameters of these insertions are the same as the ones defined in the Waveguide step with N metal inserts discontinuities. Screws. The parameters of these insertions are the same as the ones described in the Waveguide step with N

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screws discontinuities.

The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the

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calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended to manually set a tradeoff value taking into account the dimensions of the cavity under consideration.

Hints If the two angles of the arms are set to 90 degrees, a T junction is created. The electromagnetic Solver will perform more efficient analysis for small values of lengths of the different branches. Larger ports can be easily considered by increasing the length of the respective waveguides attached to this element.

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2.4.2.2.4 Y-Junction (60 deg) Definition The Y-junction (60 degrees) discontinuity is based on the General Y-junction with N screws discontinuity, and has the same characteristics and limitations. The only considerations to be taken is that the angles of the arms are fixed to 60 degrees and that no screws can be positioned inside of the Y-junction.

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2.4.2.2.5 2D OMT This section describes the 2D OMT discontinuity and how to use it, as well as its features and limitations. The 2D OMT section contains the following topics:

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Definition

What is exactly a 2D OMT.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the 2D OMT

How to create, edit and use this element from Fest3D.

Hints

Non-trivial features of the 2D OMT.

Definition The 2D OMT, based on the Arbitrary shape, represents an OMT among three Rectangular waveguides. Additional posts (rectangular metal insertions and screws) can be considered inside the OMT as well. This element is a template that lets you to specify the geometry of the circuit defining a reduced number of parameters, without using the Arbitrary Shape Editor. For these reasons many of the limitations and remarks of the Arbitrary shape element apply to this element as well. The only difference comes from the definition of the coordinate system on each of the three ports. The user can specify the geometry as shown in the following figure:

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The user must specify the lengths dn and ln for every step. Additionally port lengths lp1, lp2 and lp3 can be set. A radius for every edge of steps can be set. Lp1, Lp2 and Lp3 and radius can be zero. Offset can be positive, negative or zero. Rest of dimensions must be positive.

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This element has the same limitations and caveats as the Arbitrary shape it is derived from. In addition to this, the user should be aware that only some of the most common errors (negative lengths or port widths) are detected and suitable error messages are issued. In general, it is up to the user to ensure that the geometry is valid.

Errors The 2D OMT discontinuity can produce the same errors as the Arbitrary shape it is derived from.

Using the 2D OMT The 2D OMT discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes. The following picture shows a typical Element Properties dialog box for the 2D OMT.

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The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following parameters can be edited: Number of steps: (1 by default). For each step, a specific tab will appear, in which two parameters are set: li (mm/inches): Distance l of each step (shown in the legend). di (mm/inches): Distance d of each step (shown in the legend). Lp1 (mm/inches): Distance from port 1 to the point where port 2 branch starts. It can be zero. Lp2 (mm/inches): Distance from port 2 to the point where port 1 branch starts. It can be zero. Lp3 (mm/inches): Distance from port 3 to the point where port 1 branch starts. It can be zero. P3 Offset (mm/inches): Offset of the port 3 respect to the center of that wall. R: Optional rounding radius used in the external corners (shown in the legend). Dielectric Permittivity: the relative dielectric permittivity of the homogeneous medium filling this element (1.0 is vacuum). Dielectric Permeability: the relative dielectric permeability of the homogeneous medium filling this element (1.0 is vacuum). Select type of geometry: Here the geometry can be specified to be Constant width or Constant height. Maximum frequency (GHz): the highest frequency for the analysis of the component. By default, it is set to 0.0, which means that this value is taken automatically as the double of the maximum frequency analyzed in the circuit. A modification of the maximum simulated frequency can result in a change of the S parameters. It could also slow down the simulation unnecessarily.

To conclude with the specific properties tab, two checkboxes allow the user to perform Multipactor and Corona analysis of this discontinuity. Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figure below. This discontinuity always considers three ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element.

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Another part of the specifications of this element is the General posts tab, as shown in the figure below. Here, additional posts (full constant width/height) can be inserted in the geometry if desired, by pressing the Add button. Two post shapes can be selected: Rectangular metal insertions. The parameters of these insertions are the same as the ones defined in the Waveguide step with N metal inserts discontinuities. Screws. The parameters of these insertions are the same as the ones described in the Waveguide step with N screws discontinuities.

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The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab

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allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended to manually set a tradeoff value taking into account the dimensions of the cavity under consideration.

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The electromagnetic Solver will perform more efficient analysis for small values of lengths of the different branches. Larger ports can be easily considered by increasing the length of the respective waveguides attached to this element.

2.4.2.2.6 2D Compensated Tee This section describes the 2D Compensated Tee discontinuity and how to use it, as well as its features and limitations. The 2D compensated Tee section contains the following topics: Definition

What is exactly a 2D Compensated Tee.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the 2D Compensated tee

How to create, edit and use this element from Fest3D.

Hints

Non-trivial features of the 2D Compensated Tee.

Definition The 2D Compensated Tee, based on the Arbitrary shape, represents a T-junction among three Rectangular waveguides. Additional posts (rectangular metal insertions and screws) can be considered inside the T-junction as well. This element is a template that lets you to specify the geometry of the circuit defining a reduced number of parameters, without using the Arbitrary Shape Editor. For these reasons many of the limitations and remarks of the Arbitrary shapeelement apply to this element as well. The only difference comes from the definition of the coordinate system on each of the three ports. The user can specify the geometry as shown in the following figure:

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The user must specify the lengths Lp1, Lp2, Lp3 and the dimensions of the insertion Wi, Li, Ri, Re, Rp and its offset. Lp1, Lp2 and Lp3 and radius can be zero. Offset can be positive, negative or zero. Rest of dimensions must be positive.

Limitations This element has the same limitations and caveats as the Arbitrary shapeit is derived from. In addition to this, the user should be aware that only some of the most common errors (negative lengths or port widths) are detected and suitable error messages are issued. In general, it is up to the user to ensure that the geometry is valid.

Errors The 2D Compensated Tee discontinuity can produce the same errors as the Arbitrary shapeit is derived from.

Using the 2D compensated Tee The 2D Compensated Tee discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes. The following picture shows a typical Element Properties dialog box for the 2D Compensated Tee discontinuity.

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The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following parameters can be edited: Lp1: Distance from port 1 to the point where port 2 branch starts. It can be zero. Lp2: Distance from port 2 to the point where port 1 branch starts. It can be zero. Lp3: Distance from port 3 to the point where port 1 branch starts. It can be zero. Offset: Offset of the insert from the mid point of port 1. Wi: Width of metal insert.

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Li: Length of metal insert. Re: Base radius of the insert. It can be 0. Ri: Top radius of the insert. It can be 0. Rp: Radius of the port1. It can be 0. Dielectric Permittivity: the relative dielectric permittivity of the homogeneous medium filling this element (1.0 is vacuum). Dielectric Permeability: the relative dielectric permeability of the homogeneous medium filling this element (1.0 is vacuum). Select type of geometry: Here the geometry can be specified to be Constant width or Constant height. Maximum frequency (GHz): the highest frequency for the analysis of the component. By default, it is set to 0.0, which means that this value is taken automatically as the double of the maximum frequency analyzed in the circuit. A modification of the maximum simulated frequency can result in a change of the S parameters. It could also slow down the simulation unnecessarily.

To conclude with the specific properties tab, two checkboxes allow the user to perform Multipactor and Corona analysis of this discontinuity. Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figure below. This discontinuity always considers three ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element.

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Another part of the specifications of this element is the General posts tab, as shown in the figure below. Here, additional posts (full constant width/height) can be inserted in the geometry if desired, by pressing the Add button. Two post shapes can be selected: Rectangular metal insertions. The parameters of these insertions are the same as the ones defined in the Waveguide step with N metal inserts discontinuities. Screws. The parameters of these insertions are the same as the ones described in the Waveguide step with N screws discontinuities.

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The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended to manually set a tradeoff value taking into account the dimensions of the cavity under consideration.

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Hints The electromagnetic Solver will perform more efficient analysis for small values of lengths of the different branches. Larger ports can be easily considered by increasing the length of the respective waveguides attached to this element.

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2.4.2.3.1 Stepped Bend This section describes the Stepped Bend discontinuity and how to use it, as well as its features and limitations. The Stepped Bend discontinuity section contains the following topics: Definition

What exactly is a Stepped Bend discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Stepped Bend

How to create, edit and use this element from Fest3D.

Definition The Stepped Bend discontinuity based on the Arbitrary shape (constant width/height) , represents a special bend shape between two rectangular waveguides (ports 1 and 2), in which the non-shared corner of the bend is made out of steps. An optional rounding radius can be considered for defining the stepped geometry, as shown in the figure below.

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Using the Stepped Bend discontinuity The Stepped Bend discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes and can view it in the 3D viewer. The following picture shows a typical Element Properties dialog box for the Stepped Bend discontinuity.

The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu.

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The following parameters can be edited: R (mm/inches): Optional rounding radius used in the external corners (shown in the legend). Length port 1 (mm/inches): Piece of length of the port 1 (shown in the legend). Length port 2 (mm/inches): Piece of length of the port 2 (shown in the legend). Number of steps (1 by default). For each step, a specific tab will appear, in which two parameters are set: li (mm/inches): Distance l of each step (shown in the legend). di (mm/inches): Distance d of each step (shown in the legend). Dielectric Permittivity: the relative dielectric permittivity of the homogeneous medium filling this element (1.0 is vacuum). Dielectric Permeability: the relative dielectric permeability of the homogeneous medium filling this element (1.0 is vacuum). Bend direction: This direction of the turn of the bend from port 1. It can be set as "Right", "Left", ""Up" or "Down". Depending on this parameter, the geometry will be automatically set as Constant width or Constant height. Max Frequency (0 = auto) (GHz): the highest frequency for the analysis of the component. In most cases it can be set to “auto”, which means that this value is taken automatically as the double of the maximum frequency analyzed in the circuit. A modification of the maximum simulated frequency can result in a change of the S parameters. It could also slow down the simulation unnecessarily. To conclude with the specific properties tab, two checkboxes allow the user to perform Multipactor and Corona analysis of this discontinuity.

Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figure below. This discontinuity always considers two ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element.

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The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the

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calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended to manually set a tradeoff value taking into account the dimensions of the cavity under consideration.

Limitations This element has the same limitations and caveats as the Arbitrary shape discontinuity.

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Errors This element can produce the same errors as the Arbitrary shape.

Hints Better convergence is achieved if non-zero values of Length of port 1 and 2 are used (typically 1/10 of the size of each respective port).

2.4.2.3.2 Mitered Bend This section describes the Mitered Bend discontinuity and how to use it, as well as its features and limitations. The Mitered Bend discontinuity section contains the following topics: Definition

What exactly is a Mitered Bend discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Mitered Bend

How to create, edit and use this element from Fest3D.

Definition The Mitered Bend discontinuity based on the Arbitrary shape (constant width/height) , represents a special bend shape between two rectangular waveguides (ports 1 and 2), in which the non-shared corner of the bend is a mitered corner, which may have an additional intermediate point(depending on the parameters' values L1' and L2' given by the user). An additional rounding radius can be also considered. Geometry examples are shown in the figure below.

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Using the Mitered Bend discontinuity The Mitered Bend discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes and can view it in the 3D viewer. The following picture shows a typical Element Properties dialog box for the Mitered Bend discontinuity.

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The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following parameters can be edited: L1 (mm/inches): Distance defined from port 2 to the mitered corner (shown in the legend). L2 (mm/inches): Distance defined from port 1 to the mittered corner (shown in the legend). L1' (mm/inches): Distance defined from L1 to the position of an optional intermediate point in the mitered corner (shown in the legend). L2 '(mm/inches): Distance defined from L2 to the position of an optional intermediate point in the mitered corner (shown in the legend). Length port 1 (mm/inches): Piece of length of the port 1 (shown in the legend). Length port 2 (mm/inches): Piece of length of the port 21 (shown in the legend). R (mm/inches): Optional rounding radius used in the external corners (shown in the legend). Dielectric Permittivity: the relative dielectric permittivity of the homogeneous medium filling this element (1.0 is vacuum). Dielectric Permeability: the relative dielectric permeability of the homogeneous medium filling this element (1.0 is vacuum). Bend direction: This direction of the turn of the bend from port 1. It can be set as "Right", "Left", ""Up" or "Down". Depending on this parameter, the geometry will be automatically set as Constant width or Constant height. Max Frequency (0 = auto) (GHz): the highest frequency for the analysis of the component. In most cases it can be set to “auto”, which means that this value is taken automatically as the double of the maximum frequency analyzed in the circuit. A modification of the maximum simulated frequency can result in a change of the S parameters. It could also slow down the simulation unnecessarily. To conclude with the specific properties tab, two checkboxes allow the user to perform Multipactor and Corona analysis of this discontinuity.

Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figure below. This discontinuity always considers two ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element.

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The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended

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Limitations This element has the same limitations and caveats as the Arbitrary shape discontinuity.

Errors

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This element can produce the same errors as the Arbitrary shape.

Hints Better convergence is achieved if non-zero values of Length of port 1 and 2 are used (typically 1/10 of the size of each respective port).

2.4.2.3.3 2D Curved This section describes the 2D Curved discontinuity and how to use it, as well as its features and limitations. The 2D Curved discontinuity section contains the following topics: Definition

What exactly is a 2D Curved discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the 2D Curved

How to create, edit and use this element from Fest3D.

Definition The 2D Curved discontinuity based on the Arbitrary shape (constant width/height) , represents a curved bend shape between two rectangular waveguides (ports 1 and 2). The user can specify the geometry as shown in the following figure:

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Limitations This element has the same limitations and caveats as the Arbitrary shape it is derived from. In addition to this, the user should be aware that only some of the most common errors (negative angle or different port sizes) are detected and suitable error messages are issued. In general, it is up to the user to ensure that the geometry is valid.

Errors The 2D Curved discontinuity can produce the same errors as the Arbitrary shape it is derived from.

Using the 2D Curved discontinuity The 2D Curved discontinuity is completely integrated into Fest3D. The user can create, view and edit this element properties using dialog boxes and can view it in the 3D viewer. The following picture shows a typical Element Properties dialog box for the 2D Curved discontinuity.

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The Enable/Disable button allows enabling and disabling this element, as described in the Main Window Edit menu. The following parameters can be edited:

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Angle (degrees): Curvature angle (range: 0 < angle< 360) Mean radius (mm/inches): Mean radius of the curve Curvature direction: This direction of the turn of the bend from port 1. It can be set as "Right", "Left", ""Up" or "Down". Depending on this parameter, the geometry will be automatically set as Constant width or Constant height. Dielectric Permittivity: the relative dielectric permittivity of the homogeneous medium filling this element (1.0 is vacuum). Dielectric Permeability: the relative dielectric permeability of the homogeneous medium filling this element (1.0 is vacuum). Select type of geometry: Here the geometry can be specified to be Constant width or Constant height. Maximum frequency (GHz): the highest frequency for the analysis of the component. By default, it is set to 0.0, which means that this value is taken automatically as the double of the maximum frequency analyzed in the circuit. A modification of the maximum simulated frequency can result in a change of the S parameters. It could also slow down the simulation unnecessarily.

To conclude with the specific properties tab, two checkboxes allow the user to perform Multipactor and Corona analysis of this discontinuity. Continuing with the description of the Element Properties, the different excitation ports of the discontinuity are configured in the Ports tab, as shown in the figure below. This discontinuity always considers two ports. For each port, a specification tab is shown. A waveguide must be selected from the Attached waveguide list, which will be filled with the connections already associated to this element. Please note that input and output waveguides must have same dimensions when being connected through this element.

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The electromagnetic fields of this discontinuity can be computed and visualized. For this purpose, The EM Field tab allows one to specify a mesh size value associated to the maximum size of the tetrahedra employed in the meshing of the air volume region inside the cavity. An explanation figure of the parameter is also shown in the tab. This value can be chosen as the same as specified in the general properties of the field computation, or can be specified for the particular element. A small value will give a more detailed resolution of the fields, but will require a longer time for the calculations. On the other hand, very large values will lead to a poor resolution in the visualization. It is recommended to manually set a tradeoff value taking into account the dimensions of the cavity under consideration.

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Hints For Curvature Angle > 90 degrees, it is recommended to split the bend into multiple sub-bends (connected by zero-length waveguides) to improve performance For Mean Radius > A, it is recommended to split the bend into multiple sub-bends (connected by zero-length waveguides) to improve performance.

2.4.2.4 Const width/height discontinuities 2.4.2.4.1 Arbitrary shape This section describes the Arbitrary shape (constant width/height) discontinuity and how to use it, as well as its features and limitations. The Const width/height arbitrary shape discontinuity section contains the following topics:

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Definition

What is exactly a Arbitrary shape (constant width/height) discontinuity.

Limitations

What are the limitations you should be aware of.

Errors

The possible errors produced by this element, and solutions or workarounds to them.

Using the Arbitrary shape (constant width/height)

How to create, edit and use this element from Fest3D.

Definition The Arbitrary shape (constant width/height) discontinuity represents a microwave circuit that is constant along a certain direction, but is otherwise arbitrary in the normal plane. It is employed to model rectangular waveguide junctions where all the waveguides have the same width (parameter 'A') or height (parameter 'B'). In addition, the centre of these waveguides must be contained in the same plane (perpendicular to the constant direction) as shown in the following figures.

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In order to geometrically define a Arbitrary shape (constant width/height) discontinuity, one must describe the arbitrary 2D contour of the component and the position of the ports. Additionally, the user must define whether the 2D contour is extruded in the direction of the width (A) or height (B) of the connected waveguides by choosing the appropriate "Constant height" or "Constant width" radio button. The contour of the Arbitrary shape (constant width/height) discontinuity is described in a .mesh file that can be generated and modified using the Arbitrary Shape Editor integrated in Fest3D. It contains a collection of straight segments, circular and/or elliptical arcs that define a closed path (open contours are not supported). Multiple contours are allowed, representing elements that are multiply-connected (ie. having one or more "holes"). However, this contours cannot intersect or be mutually tangent. Furthermore, an internal contour cannot be placed within another internal contour (see figures).

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The ports of the structure can be defined as the interfaces between the discontinuity and each of the connected Rectangular waveguides. There is no limit in the number of ports that an Arbitrary shape (constant width/height) discontinuity can support. To define their position, the segments that define the intersection between the plane containing the arbitrary section and the transversal plane of each connected waveguide must be marked as ports in the Arbitrary Shape Editor. Each port has its own fixed coordinate system, and the waveguide that is connected to such port adopts the same coordinate system. In the previous figures, the two examples of the constant-height and constant-width components included each port coordinate system as a reference. For other structures, the procedure to determine unambiguously the orientation of the coordinate system for each port can be described as follows: Starting from the 2D arbitrary contour, define the vectors tangent to the contour at the ports (t) in a counter-clockwise sense and the normal vectors (n) pointing inwards. From t and n, vector u can be found as u = t X n The constant dimension of the ports will be aligned with u , meaning that for constant-height discontinuities u = y and for constant-width discontinuities u = x. Knowing one of the waveguide transversal components u, the other that remains unknown v (ie. v = x for constant-height discontinuities and v = y for constant-width components), can be found following this rule: For port #1: v = t which implies that the waveguide direction points inwards (ie. from the waveguide towards the discontinuity). Otherwise, v = -t which implies that the waveguide direction points outwards (ie. from the discontinuity towards the waveguide). Regarding the parameters of the electromagnetic Solver based in the BI-RME 2D method that analyzes this component, the user must fix a maximum frequency value as well. The maximum frequency value is related to the higher resonant mode considered within the discontinuity when all the ports are short-circuited. A material different from vacuum can be chosen to fill the discontinuity. In such a case, the dielectric properties (relative dielectric permittivity and permeability) of this material must be specified. Although this element typically represents an E-plane or H-plane component, the discontinuity accepts any rectangular waveguide mode as excitation. Consequently, it can be regarded as a full-wave element. However, if this element is indeed used within an E-plane or H-plane circuit, it is advised to select the general "All-capacitive" or "All-

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inductive" symmetry option in the specifications of the circuit. The use of the appropriate symmetry will speed up considerably the analysis of the discontinuity since less modes are computed.

Limitations The Const width/height discontinuity has some limitations and caveats you should be aware of. Connections to other elements This element can only be connected to Rectangular waveguides (one for each port). The width and height of the ports of this element must be equal to the dimensions of the Rectangular waveguides attached to the component. No full check for valid geometry The code performs only a limited (incomplete) geometry validation. It is the user's responsibility to ensure the specified geometry is valid. Invalid geometries Examples of invalid contours are: open contours intersecting or tangent contours contours internal to other internal contours cross-section profile with