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1.IntroductionIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

2. TheoryIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

Edge Elements [1] [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

COSMOSHFS 2D Analysis Modules . . . . . . . . . . . . . . . . . . 2-2

2DHFRQ: The Frequency-Dependent Field Solver . . . . . . . 2-2

XTALK: The Time-Domain Coupled Transmission

Lines Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5

2DXTALK: The Integrated FEM/Time-Domain Field

Solver/Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6

Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8

Conductor Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

Secondary Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

Impedance Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

Attenuation Constants Due to Conductor and

Dielectric Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11

3.Description of CommandsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

Detailed Description of Commands . . . . . . . . . . . . . . . . . . . . 3-1

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Common Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Material Property Commands . . . . . . . . . . . . . . . . . . . . . . 3-2

Boundary Condition Commands . . . . . . . . . . . . . . . . . . . 3-3

Integration Paths Commands . . . . . . . . . . . . . . . . . . . . . 3-11

Analysis Options Commands . . . . . . . . . . . . . . . . . . . . . 3-12

Performing the Analysis Commands . . . . . . . . . . . . . . . 3-13

Available Results Commands . . . . . . . . . . . . . . . . . . . . . 3-13

Postprocessing Commands . . . . . . . . . . . . . . . . . . . . . . . 3-14

Graphing Results Commands . . . . . . . . . . . . . . . . . . . . . 3-15

Module-Specific Commands . . . . . . . . . . . . . . . . . . . . . . . 3-18

COSMOSHFS 2D Commands . . . . . . . . . . . . . . . . . . . . 3-18

4.Detailed Description of Some ExamplesIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

HIFIS1: Coupled Microstrip Lines with Finite Conductor

Thickness (2DHFRQ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

Creating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3

Assigning Material Properties . . . . . . . . . . . . . . . . . . . . . . . 4-9

Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10

Refining Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13Applying Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 4-18

Running Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21

Visualization of Results . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22

HFIS2: Cross Talk on an Asymmetric Three-Line

Interconnection Circuit (2DXTALK) . . . . . . . . . . . . . . . . . . 4-30

Creating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

Assigning Material Properties . . . . . . . . . . . . . . . . . . . . . . 4-36

Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-37

Refining Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39

Applying Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 4-43

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HIFIS3: Cross Talk on a Four-line Interconnection

Circuit (XTALK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-56



5.Verification ProblemsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

HIFISV1: Rectangular Waveguide (WR90) . . . . . . . . . . . . . . 5-2

HIFISV2: Circular Waveguide (WC80) . . . . . . . . . . . . . . . . . 5-4

HIFISV3: Single Microstrip Line . . . . . . . . . . . . . . . . . . . . . . 5-6

HIFISV4: Coaxial Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10

HIFISV5: Coupled Microstrip Lines . . . . . . . . . . . . . . . . . . 5-14

HIFISV6: Pedestal-Supported Microstrip Line . . . . . . . . . . . 5-17

HIFISV7: Unilateral Finline . . . . . . . . . . . . . . . . . . . . . . . . . 5-20

HIFISV8: Asymmetric Coupled ThreeMicrostrip Lines . . . . 5-25

HIFISV9: Cross Talk Between Two Coupled Lines . . . . . . . 5-32

Material Constants . . . . . . . . . . . . . . . . . . . . . . . . . . .A-1

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I-1

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1. Introduction

Introduction

For many years the finite element method (FEM) has been the key design and sim-

ulation tool for engineers working in a wide range of disciplines. Due to its flexi-

bility in implementation, the finite element method has attracted so many people to

work on a wide spectrum of problems such as structural, fluid, and thermal prob-

lems. Those working in the area of high frequency electromagnetics (from radio

frequencies, RF, to optics) have, on the other hand, relied more on analytical

approaches, whenever possible, empirical and semi-empirical models, or simplesolution techniques with limited accuracy and range of applicability. Several

numerical difficulties associated with the nature of the high frequency electromag-

netic fields and their representation in a discretized space have slowed the introduc

tion of the FEM as a reliable tool in RF, microwave, millimeter-wave, and optical

designs.

Now, Integrated Microwave Technologies Inc. and Structural Research and

Analysis Corporation, bring the power of the FEM to you through their High Fre

quency Electromagnetic Simulation software (COSMOSHFS) suite with accuracy,

speed, efficiency and ease of use. The COSMOSHFS suite includes three basic

components as shown in Figure 1.1.

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Figure 1.1 Components of the COSMOSHFS Suite

This manual describes the COSMOSHFS 2D package by presenting the theory

behind it, its implementation, some detailed step-by-step examples, and a number

of verification problems.

COSMOSHFS 2D is a finite element-based package for the analysis and design

of passive mircrowave and digital circuits. COSMOSHFS 2D is an integrated

program that combines quasi-static, frequency-dependent and time domain analy-

ses. It invokes one or more sub-modules, as indicated in Figure 1.2, that provide the

user with the ability to analyze transmission-line and waveguide structures and

simulate their time domain response under specified excitation and termination

conditions. The frequency dependent module (2DHFRQ) solves the vector wave

equation using a hybrid node/edge approach to represent the electric or magnetic

fields in each element. This approach eliminates the occurrence of the nonphysical,

or spurious, modes and accurately computes both propagating and evanenscent

modes for arbitrary waveguiding structures. The time domain simulator (XTALK)

uses user-provided multi-conductor transmission line parameters with specified

excitations and terminations to solve the Tehegraphists equations and compute the

voltage response at the near and far ends of each line. Using a time domain Green's

function (time domain scattering parameters) and a convolution technique, the

cross-talk and signal distortion are calculated. The (2DXTALK) module integrates

a quasi-static field solver with the time domain simulator (XTALK). The quasi-

static solver takes a geometrical/material description of the multi-conductor trans-

mission line structure and computes, by solving Laplace's equation using a node-

based finite element approach, the per-unit length line parameters needed by

(XTALK). In addition, (2DXTALK) can generate a SPICE-Ready input file that

provides a SPICE macro model for coupled multi-conductor transmission lines.

COSMOSCAVITIES

Axi-symmetric and Arbitrary3D Cavities and Resonant

Structures

The COSMOSHFS System

COSMOSHFS2D

2D Guiding StructuresHigh sSpeed Digital

Interconnects

COSMOSHFS 3D

Arbitrary 3D PassiveStructure S-parameter

Simulator

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Figure 1.2 Analysis Modules of COSMOSHFS 2D

All COSMOSHFS 2D modules handle arbitrary conductors, dielectric and ferrite

shapes as well as dielectric and conductor losses.

This manual is intended to be used in conjunction with the standard COSMOSM

documentation. In particular, the on-line help (or the command reference manual)

is essential and should be consulted for detailed explanation of the commands

described in Chapter 3 and the ones used in the detailed examples of Chapter 4. In

addition, Chapters 2, 3 and 5 of the COSMOSM Users Guide can help you have

a more global picture of the COSMOSM system and will give you a clearer

understanding of GEOSTAR, the pre- and postprocessing interface.

2DXTALK

Quasi-static Solution ofArbitrary Ttransmission Lines

with Transient Analysis

COSMOSHFS 2D

2DHFQR

Full-wave Solution ofArbitrary 2D Guiding

Structures

XTALK

Transient Analysis ofHigh Speed Digital

Interconnects

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2. Theory

Introduction

In this chapter, a general overview of the theory and implementation of

COSMOSHFS 2D and its three analysis modules will be given. Since modules

of the COSMOSHFS 2D system rely on the use of vector basis functions,

called edge elements, to represent the electromagnetic fields in the domain of

computation, a brief discussion of these elements is first presented.

Edge Elements [1] [2]

The edge-based finite element method is based on using vector basis functions

designed specifically for the solution of vector field problems and constructed to be

divergence free. For a tetrahedral element, in 3D problems, and triangular element,

in 2D and axisymmetric problems, the vector basis function is defined as:

(2-1)

where i and j are the node numbers of the tetrahedral or triangular elements. The sare the regular node-based finite element shape functions. Clearly, the divergence

of such vector basis functions or edge element is zero. Therefore, unlike node-

based finite elements, there is no need to enforce a gauge by a penalty function or in

a least squares-sense. Since the vector field quantities are expanded in terms of

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these basis functions, they will, in turn, be divergence free leading to a complete

elimination of the vector parasites or the spurious modes. In addition, the unknown

coefficients in this approach are the tangential components of the electromagnetic

fields; hence enforcing a Dirichlet boundary condition for the electric field

formulation can be easily achieved. The edge elements also produce less populated

matrices than does the node-based approach. Such elements allow for the direct

discretization of the curl-curl form of the vector Helmholtz equation and yield a

straightforward boundary value problem that does not require any modification orany special treatment at the boundaries. In addition, as physically required, only the

tangential components of the field are forced to be continuous and the normal

components are allowed to change along material interfaces.

Elimination of spurious modes is actually due to the accurate modeling of the

null space of the curl operator by the edge elements.

COSMOSHFS 2D Analysis Modules

This COSMOSHFS 2D package combines three distinct sub-modules that

employ different formulations and solution techniques for the analysis of general

interconnects and two-dimensional guiding structures (see 5Figure 2.1). While

2DHFRQ and 2DXTALK require frequency dependent and quasi-static FEM

solutions, respectively, XTALK, on the other hand, solves the Telegraphists

equations using a time-domain Greens function approach that does not invoke any

FEM calculations. In what follows, a brief description of the theory underlying

each of these sub-modules will be given.

2DHFRQ: The Frequency-Dependent Field Solver

For a frequency-dependent analysis of general guiding structures of the type shown

in Figure 2.1.b, a full-wave solution is required. Starting with Maxwells equations

in a source-free region, and assuming a harmonic time dependence (ejt), we have

(2-2)

(2-3)

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where:

is the electric field,

is the magnetic field,

is the electric flux density,

is the magnetic flux density,

is the angular frequency and is equal to 2 f,

is the complex permittivity, and

is the complex permeability.

Combining the above equations with standard vector identities, the following

vector wave equation results:

Figure 2.1. A Generic Interconnection Circuit

(a) Gene ralconfigurationof a multi-lineinterconnectingcircuit.

(b) Cross-sectionalview of themulti-conductor

transmission line .

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(2-4)

where:

ko is the free space wavenumber and is equal to ,

r is the complex relative permittivity, and

r is the complex relative permeability.

To complete the specification of the boundary value problem to be solved, the

following boundary conditions are used (see the Boundary Conditions section

below):

(2-5)

(2-6)

Since the guide is semi-infinite, i.e., uniform along the direction of propagation

which is chosen to be the z axis, the electric field takes the form:

(2-7)

where, is the propagation constant and the .

Substituting the electric field expression

of (2-7) in the vector wave equation (2-4),

a generalized eigenvalue problem is

obtained which is then solved for theeigenvalues (the propagation constant)

and the eigenvectors (the modal electric

field) for a specified number of modes.

As mentioned earlier, the nodal approach

is known to poorly treat the spurious, or

nonphysical, modes and the edge

approach is usually preferred. However,

for semi-infinite geometries where at any

cross sectional cut the z coordinate is

purely normal to the plane of the cut, a pure edge approach may not be used. We,

instead, use a nodal representation for the z component and an edge element

representation for the transverse component as shown in Figure 2.2. Clearly, each

triangle has three unknowns associated with its nodes and another three associated

with its edges.

( )( )

Node1

E1

( )

Node3

E3

( )

Node2

E2

Edge1

Et1

( )

Edge3

Et3 ( )

Edge2

Et2

Figure 2.2. Unknowns on aTriangular Elementin COSMOSHFS 2D

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XTALK: The Time-Domain Coupled Transmission Lines Simulator

Consider the generic interconnection circuit depicted in Figure 2.1a. Signal propa-

gation along this circuit is affected by the proximity of the conductors to each other

(i.e., cross-talk), the material properties of the transmission medium (i.e., losses and

dispersion), their length (i.e., delay) and their terminating loads (i.e., distortion).

To characterize these effects, the Telegraphists equations for multi-conductor

transmission lines must be solved. These coupled equations relate the time- andposition-dependent conductor voltages [V|(z,t)] to the currents [I|(z,t)] by:

(2-8)

where:

[R] is the resistance matrix, which accounts for conductor losses,

[L] is the inductance matrix including self and mutual terms,

[G] is the conductance matrix, which accounts for dielectric losses, and

[C] is the capacitance matrix including self and mutual terms.

These line parameters are assumed to be given and must be provided by the user

before running XTALK as described in the HIFIS3 Cross Talk example in

Chapter 4.

The interconnection circuit, i.e., the multi-conductor transmission line, is a passive

network that can be easily characterized by its 2Nx2N scattering parameters matrix

([S]), where N is the number of floating conductors. These parameters are first

computed in the frequency domain from the RLCG matrices. They relate the

incident and reflected waves at a given end of a given line (a port) to those at the

rest of the ports. To incorporate the general case of non-linear terminating imped-

ances at either end of the interconnection circuit, a time domain approach is

necessary. Therefore, the frequency domain S-parameters are converted to the time

domain, via an inverse Fourier transformation, and the portal incident (ai|) and

reflected (bi |) voltage waves are written as:

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(2-9)

where * denotes a convolution operation. The time-varying, non-linear termination

impedances [Zi(t)] and any source terms [ei(t)] are accounted for through the trans-

mission [Ti] and reflection [i] coefficients according to the following equations:

(2-10)

with

(2-11)

where Zrefis the reference impedance used for S-parameter calculations. The

solution of the above equations gives the voltages at the near and far ends of the

interconnection circuit for the configuration of sources and loads chosen.

Note that in the above formulation, the frequency dependent conductor losses can

be built into the solution by specifying each element of the diagonal R matrix as a

sum of a DC term, Rdc, and a frequency dependent term, Rskffd, such that R = Rdc

+ Rskffd, with Rskdenoting the skin effect resistance, f the frequency in GHz and fd

is the frequency dependence exponent (an fd = 0.5 is usually used). The format to

input this data is shown in the HIFIS3: Cross Talk example in Chapter 4.

2DXTALK: The Integrated FEM/Time-Domain Field Solver/

Simulator

Before reading this section, please make sure you are familiar with the concepts

introduced in the previous section discussing the XTALK sub-module.

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As mentioned above, the transmission line parameters, namely the per-unit length

resistance, inductance, capacitance and conductance matrices are necessary for the

time domain solution described. In general, these quantities are both geometry and

material dependent and their accurate calculation, which is crucial to the accuracy

of time domain simulation ofXTALK, requires an electromagnetic field solution

of the corresponding problem. 2DXTALK integrates such field solver with the

time simulator XTALK in a transparent manner.

To obtain the line parameters [R], [L], [G], and [C] needed by the time domain

simulator, 2DXTALK first performs a quasi-static finite element analysis by

solving Laplaces equation in the cross-sectional domain shown in Figure 2.1.b, [3]

(2-12)

with the boundary conditions:

(2-13)

where gi is a specified voltage. The above equation is discretized using a nodal

approach and then solved for the electrostatic potential u. For N floating conductors,

N independent potential solutions are necessary to compute the NxN line parameter

matrices. 2DXTALK performs these calculations in a first stage and uses the result

ing parameters in invoking the time-domain solution, described above, in a the

second stage.

Boundary Conditions

In high frequency electromagnetics, there are several possible boundary conditions,

COSMOSHFS 2D recognizes the following:

Open outer boundary (oob):For open region problems, the unbounded domain must be truncated so that the

number of unknowns can be reduced to a reasonable size. This would require

imposing an asymptotic or an absorbing boundary condition operator on the

exterior boundary [3]. Such an operator is implemented through the oob boundary

condition for the quasi-static field solver (2DXTALK). For the other solvers, this

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boundary condition is treated as perfect electric conductor since the complexity it

adds to the problem and the added computer resources do not warrant it.

Perfect electric conductor (fc/gc):

Surfaces/curves of grounded conductors (gc) and/or floating conductors (fc) could

be assigned this type of boundary condition. As a result, COSMOSHFS 2D

forces the tangential component of the electric field on those surfaces/curves to be

zero.

Perfect magnetic conductor (pmc):

COSMOSHFS 2D forces the component of the magnetic field that is tangential

to perfect magnetic conducting surfaces/curves (usually surfaces of symmetry) to

be zero. This boundary condition could be used to terminate the mesh for open

outer boundaries.

Boundary conditions for time domain simulations:Presently, only linear resistive and capacitive terminations can be specified.

Together with excitation sources, they constitute the boundary conditions for the

time domain analysis.

Material Properties

COSMOSHFS 2D can treat isotropic dielectric and ferrite materials with a

complex relative permittivity ( = r o, with ), a complex relative

permeability ( = ro, with ), and an electrical conductivity ().In MKS units, the free space permittivity o and permeability o have the values

8.8541853x10-12 F/m and 410-7 H/m, respectively, and is in S/m. For materialshaving non-zero electrical conductivity, the complex permittivity used by

COSMOSHFS 2D is the following:

(2-15)

where

is the angular frequency.

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For each material used in the model, the user needs to specify the real and

imaginary parts of the relative permittivity and permeability as well as the electrical

conductivity. The default values are those of free space. See the on-line help for the

MPROP and USER_MAT commands (Propsets > Material Property and User

Material Lib) for more details.

Conductor Properties

In applying the boundary conditions discussed above, all conductors are treated as

perfect conductors (i.e., infinite conductivity and zero penetration depth). However,

the finite conductivity and the relative permeability of the metals are taken into

account when calculating such quantities as the attenuation constant of a

waveguide or the quality factor of a resonator due to the conductor loss. The default

conductor properties used are those of copper. For other metals, the user should

specify the values of the relative permeability and the electrical conductivity of the

metal.

Secondary Calculations

So far, only a description of the fundamental theory and the basic solutions avail-

able through the various COSMOSHFS 2D modules have been given. In thissection, we present the theoretical formulation used for the various secondary

calculations available within COSMOSHFS 2D.

Impedance Calculation

In the frequency-dependent 2DHFRQ sub-module, the user has the option to

calculate the impedance(s) of the guiding structure. Three different impedance

definitions can be used to this end: power-current (Zpi), power-voltage (Zpv) orvoltage current (Zvi). They are defined as follows:

The power (P)-current (I) impedance is defined as:

(2-16)

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where * denotes complex conjugation. The power and current are computed from:

(2-17)

(2-18)

where S is the cross-section of the guiding structure and C is a closed path ofintegration. Note that the above definition of the current is applicable only to

guiding structures that may support a TEM or quasi-TEM mode (i.e., has floating

conductors). In this case, the current calculation, which involves contour integra-

tion, is carried out through automatic choice of the integration path, C, by

2DHFRQ.

The power (P)-voltage (V) impedance is defined as:

(2-19)

where P is given by equation (17) and the voltage is computed by integrating the

electric field along a specified path, (path 1), as follows:

(2-20)

In general, the computation of the voltage is path-dependent and the user must

specify the path of integration -or the impedance line- for voltage computation.

This path should be selected along the curve of maximum electric field.

The voltage (V) current (I) impedance is defined as:

(2-21)

or equivalently Zvi = V/I. It can be computed only when floating conductors are

present and voltage integration paths are specified.

While the concept of impedance is well defined for pure TE, TM and TEM modes,

it remains approximate at best for hybrid modes. Therefore, the choice of the

definition to use is dependent on the structure to be analyzed. For TEM or quasi-

TEM supporting structures (e.g., coaxial cables, microstrip lines, striplines, etc.),

the power-current definition should be used while for waveguides with no floating

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conductors (hollow waveguides, finlines, slotlines, etc.) the power-voltage

definition is more appropriate.

Attenuation Constants Due to Conductor and Dielectric Losses

The attenuation of electromagnetic waves in a waveguide could be due to

conductor or dielectric losses. In COSMOSHFS 2D, the user has the option to

calculate these quantities. In decibels per meter (dB/m), the conductor attenuation

constant is defined as:

(2-22)

where Rm is the skin-effect surface resistance and is given by:

(2-23)

where and are the conductivity and the permeability of the metal.

The dielectric attenuation constant is defined as

(2-24)

where the loss tangent, tan, is assumed to be small enough that the perturbed fieldscan be approximated by the fields of the lossless condition.

The modal RLCG values are computed using the above quantities. These values are

then combined with the eigenvectors of the solution to obtain the generalized

matrices ZRCLG. In particular, both the characteristic impedance and the line-modal impedance matrices are computed. In case of the latter, the matrix element

Zlm corresponds to the impedance of line number l and mode number m. In

addition, the current and voltage eigenvector corresponding to the different eigen

modes are also computed and given along with the other results.

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References

[1] Daniel R. Lynch and Keith D. Paulsen, Origin of vector parasites in

numerical Maxwell solutions, IEEE Trans. Microwave Theory Tech. March

1991.

[2] A. Bossavit and I. Mayergoyz, Edge-element for scattering problems, IEEE

Trans. Magn, vol. MAG-25, pp. 2816-2821, 1989.

[3] A. Khebir, A. B. Kouki, and R. Mittra, Asymptotic boundary conditions forfinite element analysis of three-dimensional transmission line

discontinuities, IEEE Trans. Microwave Theory Tech., vol 38, pp 1427-

1432, 1990.

[4] O. P. Gandhi, Microwave Engineering and Applications, Pergamon Press,

1987.

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3. Description of Commands

Introduction

The use ofCOSMOSHFS 2D for solving high frequency electromagnetic

problems involves generating a proper finite element mesh, specifying the material

properties, imposing the boundary conditions, and specifying the appropriate

solution parameters. All of this is done through GEOSTAR, the COSMOSM pre-

and post-processor. Similarly, using GEOSTAR postprocessor, the results of the

various COSMOSHFS 2D modules can be viewed in graphical and text formats.

The general commands for model creation, mesh generation and postprocessing aredocumented in the COSMOSM User Guide Volume (1) and will not be described

here. Only commands that are specific to COSMOSHFS 2D or related to it will be

described in this chapter.

Detailed Description of Commands

This section is divided into two sub-sections. The first describes commands that are

common to all COSMOSHFS 2D modules while the second describes the

module-specific commands.

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3scription ofommands

Common Commands

These commands cover the definition of material properties, boundary conditions,

integration paths and the context-sensitive postprocessing features. They are

described in the following eight sub-sections.

Material Property Commands

You may use the library or define numerical properties directly.

USER_MAT

(Menu: PROPSET > User Material Library)

The USER_MAT command accesses COSMOSM library for electromagnetic

materials.

Where:

Material set

Material set number between 1 and 90

(default is highest set number defined + 1)

Material name

Name of the material property. Select a material from the drop-down menu.Unit-label

Units used.

MPROP

(Menu: PROPSET > Material Property)

The MPROP command is a general purpose GEOSTAR command for specifying

the material properties for different model regions. The pertinent material properties

for COSMOSHFS are given below and can be set as follows:

USER_MAT Material set Material name unit-label

MPROP set name1 value1 name2 value2 ...

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Where:

set

Material set number between 1 and 99

(default is highest set number defined + 1)

name1, name2, ...

Name of the material property.

EQ. permit_r Real part of the relative permittivity.EQ. permit_i Imaginary part of the relative permittivity.

EQ. mperm_r Real part of the relative permeability.

EQ. mperm_i Imaginary part of the relative permeability.

EQ. econ The electric conductivity.

value1, value2, ...

Corresponding real values to the material properties with defaults:

permit_r 1.0.

permit_i 0.0.mperm_r 1.0.

mperm_i 0.0.

econ 0.0.

At least one property must be defined for each material set.

Example: MPROP, 1, permit_r, 10.0, permit_i, 1.e-03

This command defines the real part of the real permittivity for

material set 1 to be 10 and imaginary part be 0.001. The remainingproperties (mperm_r, mperm_i, econ) assume their default values.

Boundary Condition Commands

The boundary condition commands are the following: CBEL, CBEDEL, CBCR,

CBCDEL, CBSF, CBSDEL, CBRG, CBRDEL, CBPLOT and CBLIST. They are

described next.

CBEL

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Define by Elements)

The CBEL command specifies a boundary condition on faces of elements in the

specified pattern.

CBE bel bc cond_num conductivity

permeability face_num eel increment

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Where:

bel

Beginning element in the pattern.

bc

Boundary condition type.

EQ. fc Floating conductor.

EQ. gc Grounded conductor.EQ. pmc Perfect magnetic conductor.

EQ. oob Open outer boundary.

(default is fc)

cond_num

Conductor number associated with the boundary condition.

conductivity

Conductivity of the conductor number cond_num.

permeability

Relative permeability of the conductor number cond_num.

face_num

Face of the elements on which the boundary condition is to be applied.

eel

Ending element in the pattern.

increment

Increment between elements in the pattern.

Example: CBEL, 4, fc, 2,,, 5 ,3, 5,,

This command defines a floating conductor number 2 on face number5 of elements 4 and 5 using the default conductivity and permeability(copper).

CBCR

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Define by curves)The CBCR command defines a boundary condition on a pattern of curves.

CBCR bcurve bc cond_num conductivity permeability ecurve increment

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Where:

bcurve

Beginning curve in the pattern.

bc





(default is fc)

cond_num


conductivity


permeability


ecurve

Ending curve in the pattern.

increment

Increment in curve numbering.

Example 1: CBCR, 2, fc, 1,,, 2,,This command defines a floating conductor on curve 2 of defaultconductivity and permeability (copper).

Example 2: CBCR, 5, gc, 1, 6.1e7,, 9, 2,

This command defines curves 5, 7 and 9 to be grounded conductorsmade of silver.

CBSF

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Define by Surfaces)

The CBSF command defines a boundary condition on a pattern of surfaces.

CBSF bsurface bc cond_num conductivity

permeability esurface increment

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Where:

bsurface

Beginning surface in the pattern.

bc





(default is fc)

cond_num


conductivity


permeability


esurface

Ending surface in the pattern.

increment

Increment in surface numbering.

Example: CBSF, 1, gc, 1,,, 6,,This command defines surfaces 1 through 6 to be grounded conductor#1 and to have the default conductivity and permeability (copper).

CBRG

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Define by Regions)

The CBRG command defines a boundary condition on a pattern of regions.

Where:

bregion

Beginning region in the pattern.

CBRG bregion bc cond_num conductivity

permeability eregion increment

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bc



EQ. gc Grounded conductor.

EQ. pmc Perfect magnetic conductor.


(default is fc)

cond_num


conductivity


permeability


eregion

Ending region in the pattern.

increment

Increment in region numbering.

Example: CBRG, 3, fc, 2,3.43e+07,, 3,,

This command defines a floating conductor (number 2) on region 3 ofconductivity 3.43e+07 mho/m and default permeability (aluminum).

CBEDEL(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Delete by Elements)

The CBEDEL command deletes previously defined High Frequency (HF) boundary

conditions for the specified face for a pattern of elements.

Where:

bel


face

Face number of the elements for which existing HF boundary condition is to be

deleted.

CBEDEL bel face eel inc

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eel


(default is bel)

inc


(default is 1)

Example: CBEDEL, 3, 2, 10, 1

This command deletes the boundary conditions on face 2 of elements3 through 10.

CBCDEL

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Delete by Curves)

The CBCDEL command deletes previously defined HF boundary conditions for

elements associated with a pattern of curves.

Where:

bcr

Beginning curve in the pattern.

ecr

Ending curve in the pattern.

(default is bcr)

inc

Increment between curves in the pattern.

(default is 1)

Example: CBCDEL, 1, 10, 1

This command deletes HF boundary conditions for elementsassociated with curves 1 through 10.

CBSDEL

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Delete by Surfaces)

The CBSDEL command deletes previously defined HF boundary conditions for

elements associated with a pattern of surfaces.

CBCDEL bcr ecr inc

CBSDEL bsf esf inc

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Where:

bsf

Beginning surface in the pattern.

esf

Ending surface in the pattern.

(default is bsf)

inc

Increment between surfaces in the pattern.

(default is 1)

Example: CBSDEL, 1, 10, 1

This command deletes HF boundary conditions for elementsassociated with surfaces 1 through 10.

CBRDEL

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Delete by Regions)

The CBRDEL command deletes previously defined HF boundary conditions for

elements associated with a pattern of regions.

Where:

brg

Beginning region in the pattern.

erg

Ending region in the pattern.

(default is brg)

inc

Increment between regions in the pattern.

(default is 1)

Example: CBRDEL, 1, 10, 1

This command deletes HF boundary conditions for elementsassociated with regions 1 through 10.

CBPLOT

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > Plot)

CBRDEL brg erg inc

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The CBPLOT command plots a predefined symbol at elements with prescribed HF

boundary condition for a pattern of elements. The symbol is shown in the STATUS2

table.

Where:

belBeginning element in the pattern.

(default is 1)

eel


(default is elmax)

inc


(default is 1)

Example CBPLOT;

The above command plots a predefined symbol at elements withprescribed HF boundary conditions.

CBLIST

(Menu: LOADS-BC > E_MAGNETIC > Hi-Freq_B-C > List)

The CBLIST command lists element HF boundary conditions for a pattern of

elements.

Where:

bel


(default is 1)

eel


(default is elmax)

inc


(default is 1)

CBPLOT bel eel inc

CBLIST bel eel inc

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Example: CBLIST, , 10, 2,

The above command lists all the specified HF boundary conditionsfor elements 1, 3, 5, 7 and 9.

For all boundary condition commands, it is recommended that the conductor

numbering for conductors (particularly for floating conductors) be sequential

starting from one.

Integration Paths Commands

HF_PATH

(Menu: ANALYSIS > Hi-Freq_Emagnetic > Integration Path> Define)

The HF_PATH command defines one or more integration paths for the 2-dimen-

sional field simulator or for cavity analysis. The integration paths are used in voltage

computation based on electric field line integrals.

Where:

PN

Path number. The maximum number of paths is 2.

Xn,Yn,Zn

X, Y, Z coordinate triplets that define the integration paths straight line

segments. The minimum number of triplets per path is 2 and the maximum is 13.The list of triplets is terminated by entering a ; or by repeating the last triplet

The path X, Y, Z triplets can be picked using the mouse on any specified

plane. For this, the grid must be turned on with the GRIDON command.

Example: HF_PATH,1,0.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,2.0;

This commands defines integration path #1 by 3 points (i.e., 2straight line segments).

HF_PATHDEL

(Menu: ANALYSIS > Hi-Freq_Emagnetic > Integration Path> Delete)

The HF_PATHDEL command deletes an integration path previously defined by the

HF_PATH command.

HF_PATH PN X1 Y1 Z1 X2Y2 Z2 X3 Y3 Z3.....

HF_PATHDEL path_number

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Where:

path_number

Path number. (1 or 2)

Example: HF_PATHDEL, 2

This commands deletes the second integration path defined.

HF_PATHLIST

(Menu: ANALYSIS > Hi-Freq_Emagnetic > Integration Path> List)

The HF_PATHLIST command lists coordinate triplets of an integration path defined

by the HF_PATH.

Where:

path_number

Path number. (1 or 2)

(default is 1)

Example: HF_PATHLIST, 1

This commands lists coordinate triplets making up the firstintegration path.

Analysis Options Commands

A_HFRQEM

(Menu: ANALYSIS > Hi-Freq_Emagnetic > Analysis Options)

The A_HFRQEM command defines the high frequency analysis to be run and sets

the distance units to be used in the analysis.

Where:

option

Analysis option.

EQ. 2dhfrq Run the 2-dimensional full-wave field solver.

HF_PATHLIST path_number

A_HFRQEM option unit

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EQ. 2dxtalk Run the 2-dimensional quasi-static field solver to compute

RLCG matrices then the time-domain cross-talk simulator

to compute cross-talk and distortion.

EQ. xtalk Run the time domain cross-talk simulator with pre-computed

RLCG matrices.

EQ. cavaxi Run the time axisymmetric cavity field solver.

EQ. cav3d Run COSMOSCAVITY (the time 3D cavity field solver).

EQ. sparam Run COSMOSHFS 3D (S-Parameter Simulator).(default is 2dhfrq)

unit

Unit for distance measurement to be used.

EQ. 0 Dimensions are in mm.

EQ. 1 Dimensions are in cm.

EQ. 2 Dimensions are in m.

EQ. 3 Dimensions are in mils.

EQ. 4 Dimensions are in inches.

EQ. 5 Dimensions are in microns.

(default is 0)

Example: A_HFRQEM, xtalk, 4

This command sets the high-frequency analysis option to run thecross-talk time domain simulator using pre-computed RLCGmatrices with lengths specified in inches.

Performing the Analysis Commands

R_HFRQEM

(Menu: ANALYSIS > Hi-Freq_Emagnetic > Run Analysis)

The R_HFRQEM command runs the electromagnetic analysis specified by the

A_HFRQEM command.

Available Results Commands

HF_RESLIST

(Menu: RESULTS > LIST > HF_RESLIST)

The HF_RESLIST command lists the results of the performed high-frequency

electromagnetic analysis based on the analysis options chosen and the solution

parameters.

R_HFRQEM

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RESULTS?

(Menu: RESULTS > Available_Results)

The RESULTS? command lists the available nodal and/or elemental results for

postprocessing from the performed analysis. For COSMOSHFS2D, the command

lists the frequency points (freq), mode number (Mode), mode flag (M_Flag) andFrequency (GHz). This listing is used to establish a correspondence between the

frequency point number and the actual simulation frequency in GHz. The mode flag

indicates whether the computed mode is propagating (M_Flag = 1) or evanescent

(M_Flag

= -1). For 2DXTALK the command lists the fundamental modes calculated.

Postprocessing Commands

MAGPLOT

(Menu: RESULTS > Plot > Electromagnetics)

The MAGPLOT command is a postprocessing command that plots the results of the

analysis.

Where:

freqn

Time step number (use RESULTS? for corresponding frequency values).

Prompted only for 2DHFRQ as frequency step number.

(default is 1)

nd/el

Flag to activate results at nodes or centers of elements.EQ. 1 Nodes.

EQ. 2 Elements.

(default is 1)

comp

Field component. Admissible components depend on the type of analysis

performed as follows:

HF_RESLIST

RESULTS?

ACTMAG freqn moden nd/el comp

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For COSMOSHFS 2D and COSMOSCAVITY:

EQ. EX Electric field intensity in the X-direction. Real.

EQ. EY Electric field intensity in the Y-direction. Real.

EQ. EZ Electric field intensity in the Z-direction. Real.

EQ. ER Resultant electric field intensity. Real.

EQ. HX Magnetic field intensity in the X-direction. Real.

EQ. HY Magnetic field intensity in the Y-direction. Real.

EQ. HZ Magnetic field intensity in the Z-direction. Real.EQ. HR Resultant magnetic field intensity. Real.

For 2DXTALK analysis:

EQ. POT Electrostatic potential. Real.

EQ. EX Electric field intensity in the X-direction. Real.

EQ. EY Electric field intensity in the Y-direction. Real.

EQ. ER Resultant electric field intensity. Real.

This command is not needed for XTALK analysis.

MAGLIST

(Menu: RESULTS > List > Electromagnetics)

The MAGLIST command is a postprocessing command that lists results of the

analysis.

MAGMAX

(Menu: RESULTS > Extremes > Electromagnetics)

The MAGMAXcommand is a postprocessing command that lists the extremes of the

results of the analysis.

Graphing Results Commands

ACTXYPOST

(Menu: DISPLAY > XY_Plots > Activate Post-proc)

The ACTXYPOST is a postprocessing command that sets the parameters to be used

for viewing X-Y type results using the XYPLOT command.

ACTXYPOST graph-num mode y-axis (line)

graph-color line-style symbol-type graph-id

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Where:

graph-num

Graph number. (1 to 6)

(default is highest defined + 1)

mode

Mode number.

(defaults is1)y-axis

For COSMOSHFS 2D:

The y-axis may be one of the components described below. The x-axis is not

prompted for and is fixed to be frequency in GHz.

ALPHA Real part of propagation constant. Non-zero for decaying

modes only.

BETA Imaginary part of propagation constant in m-1.

EPSEFF Effective dielectric constant.PHASEV Phase velocity in m/s.

ALPHAC Attenuation constant in dB/m due to conductor losses in dB/m

ALPHAD Attenuation constant in dB/m due to dielectric losses in dB/m.

(default is EPSEFF)

The following components are computed only when the number of conductors is

non-zero and are based on the power-current definitions.

ZMI Modal impedance ().LMI Modal inductance (nH/m).

CMI Modal capacitance (pF/m).

RMI Modal resistance (/m).GMI Modal conductance (S/m).

The following components are computed only when the number of integration

paths is non-zero and are based on the power-voltage definitions.

ZMV Modal impedance ().LMV Modal inductance (nH/m).

CMV Modal capacitance (pF/m).

RMI Modal resistance (/m).GMV Modal conductance (S/m).

For XTALK and 2DXTALK:

The following components are plotted versus mode number for 2DXTALK only

BETA Imaginary part of propagation constant in m-1.EPSEFF Effective dielectric constant.

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PHASEV Phase velocity in m/s.

ALPHAC Attenuation constant in dB/m due to conductor losses.

ALPHAD Attenuation constant in dB/m due to dielectric losses.

ZM Modal impedance ().LM Modal inductance (nH/m).

CM Modal capacitance (pF/m).

RM Modal resistance (/m).

GM Modal conductance (S/m).(default is EPSEFF)

The following components are plotted versus time for both XTALK and

2DXTALK.

VTLSNEAR Near end voltages (V).

VLTSFAR Far end voltages (V).

(line)

Line number (prompted only when the y-axis is VLTSNEAR or VLTSFAR in

XTALK OR 2DXTALK).

graph-color

Color to be used for plotting.

line-style

Line style to plot graph.

symbol-type

Symbol type for plotting at points on the x-y graph.

graph-id

Graph identification. Default depends on the y-axis entry.

Notes:

1. Refer to the COSMOSM Command Reference Manual for more help on

graph-color, line-style, symbol-type and graph-id.

2. The following figure illustrates the near/far end and node numbering

convention in 2DXTALK and XTALK. This convention is used in writing the

SPICE input deck from 2DXTALK.

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Figure 3.1. Naming and Numbering Convention of Multi-conductorTransmission Lines for XTALK and 2DXTALK Analyses

Module-Specific Commands

COSMOSHFS 2D Commands

HF_2DSOLN

(Menu: ANALYSIS > Hi-Frq-EMagnetic > Transmission Line > Set Options)

The HF_2DSOLN command sets the solution options for the 2-dimensional full-

wave field solver.

Where:

nmodes

Number of desired modes.

(default is 1)

freqbegin

Beginning simulation frequency (in Ghz).

(default is 1.0)

freqend

Ending simulation frequency (in Ghz).

(default is 1.0)

HF_2DSOLN nmodes freqbegin freqend dfreq

node

node

node N

node

node N+1

node N+2

node N+3

node 2N

line #1

line #2

line #3

line #N

Near End Far End

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dfreq

Frequency step (in Ghz).

(default 1.0)

Example: HF_2DSOLN, 2, 1., 10., 0.5

This command sets the 2-dimensional field solvers solution optionsto finding the first 2 modes over the frequency range starting at 1GHz

and ending at 10GHz in steps of 0.5GHz.

HF_2DOUT

(Menu: ANALYSIS > Hi-Frq-EMagnetic > Transmission Line > Output Options)

The HF_2DOUT command sets the output options for the 2-dimensional full-wave

field solver.

Where:

compute_flag

Flag to specify which quantities should be computed.

EQ. 0 Compute modal propagation constants and fields only.

EQ. 1 Compute modal propagation constants, fields, impedances and

generalized RLCG matrices.

(default is 0)

output_flagFlag to specify the type of output.

EQ. 0 No output.

EQ. 1 Output nodal values only.

EQ. 2 Output element values only.

EQ. 3 Output both nodal and element values.

(default is 0)

Example: HF_2DOUT, 0, 3

This command sets the 2-dimensional field solvers output options tocompute modal propagation constants and fields only and write outboth nodal and element values of the modal electric and magneticfields.

HF_XTKCONF

(Menu: ANALYSIS > Hi-Frq-EMagnetic > Cross Talk> Define Parameters)

HF_2DOUT compute_flag output_flag

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The HF_XTKCONF command defines the configuration parameters for the cross-

talk time domain simulator.

Where:

nlines

Number of transmission lines (maximum 10).

(default is 2)

length

Length of the transmission lines in meters.

(default is 0.1m)

duration

Duration of the time domain simulation in nano-secs.

(default is 50)

Example: HF_XTKCONF, 3, 0.0254, 50

This command configures the cross-talk simulator to run with 3 linesof length 1inch (2.54cm) and for a duration of 50 nano-seconds.

HF_XTKPULSE

(Menu: ANALYSIS > Hi-Frq-EMagnetic > Cross Talk> Define Pulse)

The HF_XTKPULSE command defines the excitation pulses on the near-end of

chosen lines. By default all lines are quite (no excitation). At least one line must have

an excitation pulse.

Where:

line_num

Number of the line for which an excitation pulse is placed at near-end.

rtime

Pulses rise time in nano-seconds.

(default is 1 ns)

width

Pulses width in nano-seconds.

(default is 12 ns)

HF_XTKCONF nlines length duration

HF_XTKPULSE line_num rtime width ftime magnitude

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ftime

Pulses fall time in nano-seconds.

(default is 1 ns)

magnitude

Pulses magnitude in volts.

(default is 5.0 V)

Example: HF_XTKPULSE, 2, 1., 12, 1., 4.0

This command defines an excitation pulse at the near end of linenumber 2 having a rise time of 1 nano-second, a duration of 12 nano-seconds, a fall time of 1 nano-second and a magnitude of 4 Volts.

HF_XTKTERM

(Menu: ANALYSIS > Hi-Frq-EMagnetic > Cross Talk> List)

The HF_XTKTERM command defines the terminations at both near- and far-ends of

each line. By default all lines are terminated by 50 resistances at the near ends anda 50 resistances at the far ends. Capacitances can be added at the far-ends usingthis command.

Where:

line_num

Number of the line for which the terminations will be altered from their defaultvalues.

rnear

Near-end resistance.

rfar

Far-end resistance.

cfar

Far-end capacitance.

Example: HF_XTKTERM, 2, 100.0, 25.0, 30

This command defines the termination for line 2 to be a 100.0 Ohmsresistance at the near-end, a 25.0 Ohms resistance at the far-end and aparallel capacitance of 30 pico-Farads at the far end.

HF_XTKTERM line_num rnear rfar cfar

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HF_XTKLIST

(Menu: ANALYSIS > Hi-Frq-EMagnetic > Cross Talk> List)

The HF_XTKLIST command lists pulse excitations and terminations for the

specified line.

Where:

line-number

Line number. (1 through 10)

(default is 1)

HF_XTKLIST line-number

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4. Detailed Description

Introduction

This chapter presents step by step procedures for solving transmission line,

waveguide, interconnect and cavity problems with COSMOSHFS. Four detailed

examples, one for each analysis option, illustrating how to set up and solve the

problems are given.

Table 4.1 List of Examples

HIFIS1: Coupled Microstrip Lines with FiniteConductor Thickness (2DHFRQ)

See page 4-2.

HIFIS2: Cross Talk on an Asymmetric Three-Line Interconnection Circuit (2DXTALK)

See page 4-30.

HIFIS3: Cross Talk on a Four-lineInterconnection Circuit (XTALK).

See page 4-56.

of Some Examples

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4Detailed

scription of

Examples

The geometry of the coupled microstrip lines is depicted in Figure 4.1. We would

like to completely characterize this structure in terms of its modal parameters and

their variation with frequency (i.e., dispersion characteristics).

Figure 4.1 Geometry of the Coupled Microstrip Lines to be Analyzed

To start a new problem in GEOSTAR:

1. Launch GEOSTAR.

GEOSTAR starts and the

Open Problem Files dialogbox opens.

2. Browse to the directory

which you want to use for

the new problem.

3. In the File name field, enter

hifis1, for example, for the

problem name.

4. ClickOpen. GEOSTAR sets the new problem and creates all related database

files in the specified folder.

HIFIS1: Coupled Microstrip Lines with Finite

Conductor Thickness (2DHFRQ)

h

Hc

wd

ws

=10.0r

h=10 milsw/h=0.7 s/h=0.4 Hc/h=10

d/h=5 =0.7 mils

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Detailedescription of

Examples

Creating the Model

To set up the proper working plane and the view:

1. From the Geometry menu, select Grid,

Plane. The Plane dialog box opens.

2. Click Ok to use the default settings.

3. From the Display menu, select ViewParameter, View. The View dialog box

opens.

4. Click OK to use the default Z-view.

From Figure 4.1, we can see that the total

width, and height of the structure are 118 and

110 mils, respectively.

To setup a drawing grid in the active plane:

1. From the Geometry menu, select

Grid, Grid On. The Grid On dialog

box opens.

2. We will use 20 increments in x- and

y-directions. Enter the following

values:

Origin x-Coordinate Value [0] > (accept default)

Origin y-Coordinate Value [0] > (accept default)

X- increment [5] > 5.9

Y- increment [5] > 5.5

No of X- increments [20] > (accept default)

No of Y- increments [20] > (accept default)

Grid Line color Index [2] > (accept default)

3. Click OK.

To best fit the grid area into the display window:

1. From the Geo Panel, click the Scale Auto button .

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At this stage, it is a good idea to give a descriptive title of the problem we are about

to solve.

To give a title to the current problem:

1. From the Control menu, select Miscellaneous, Write Title. The Title dialog box

opens.

2. Type the title in the Message field as follows:Message > Coupled microstrip lines with finite conductor thickness

3. Click OK.

Next, we will create the eight curves delimiting the dielectric substrate region. Note

that eight curves are needed to account for all the sides of the dielectric region

including separate curves for the bottom sides of the conductors. The following

procedure creates the necessary curves (the mouse can be used to pick the points on

the grid).

To create the eight curves delimiting the dielectric substrate region:

1. From the Geometry menu, select Curves, Draw Polyline. The CRPCORD

dialog box opens.

2. Enter the following coordinates:

Curve [1] > (accept default)

X, Y, Z Coordinates of keypoint 1> 0, 0, 0

X, Y, Z Coordinates of keypoint 2 > 118, 0, 0

X, Y, Z Coordinates of keypoint 3 > 118, 10, 0X, Y, Z Coordinates of keypoint 4 > 68, 10, 0






3. Click OK. Now all the curves needed

for the first region are created.

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To plot the curve labels:

1. Click the button. The Status 1

setting box opens.

2. Click the curve label checkbox as shown

in the figure.

3.Click Save.

4. Click the Repaint button to plot the

model. The model at this stage should

look as follows:

Figure 4.2 Curves Defining the Dielectric Region

Next, we create the curves delimiting the air (second) region. Since the air and

dielectric regions share the curves at the interface between them, only three new

curves must be created. These curves are created in a similar fashion to the above.

To create the curves delimiting the air (second) region:


dialog box opens.






X, Y, Z Coordinates of keypoint 4 > 0, 10, 0X, Y, Z Coordinates of keypoint 5 > 0, 10, 0

3. Click OK.

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Since the two conductors are thick, we shall create two regions for them as well but

without meshing them, i.e. they are just voids in the mesh.

To create the curves delimiting the first conductor region:


dialog box opens.




X, Y, Z Coordinates of keypoint 2 > 57, 10.7, 0




3. Click OK.

To create the curves delimiting the second conductor region:


dialog box opens.








3. Click OK.

By turning on the curves label plotting, the model at this stage should look as

follows.

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Figure 4.3 Curves Defining the Entire Model

The next step is to make contours out of the curves just created. Two contours only

need be defined: one enclosing the dielectric substrate and one enclosing the air

region. Note that the thick conductors are excluded from either contour and need

not be defined by contours or regions.

To define the first contour:

1. From the Geometry menu, select Contours, Define. The CT dialog box opens.

2. Enter the following options:

Contour [1] > (accept default)

Mesh flag 0 = Esize 1= Num. elems [0] > (accept default)

Average element size > 7

Number of reference boundary curves [1] > 8

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3. Click Continue.

Curve 1 > 1

Curve 2 > 2

Curve 3 > 3

Curve 4 > 4

Curve 5 > 5

Curve 6 > 6

Curve 7 > 7

Curve 8 > 8Use selection set 0 = No 1= Yes [0]

> (accept default)

Redefinition Criterion 0=Prev

1=Redef 2=Max 3=Min elements

[1] > (accept default)

4. Click OK. Contour 1 is now created and plotted in different color.

To define the second contour:

1. From the Geometry menu, select Contours, Define. The CT dialog box opens.


Contour [2] > (accept default)

Mesh flag 0 = Esize 1= Num. elems [0] > (accept default)

Average element size > 7

Number of reference boundary curves [1] > 12

Curve 1 > 9

Curve 2 > 10

Curve 3 > 11

Curve 4 > 7

Curve 5 > 14

Curve 6 > 13

Curve 7 > 12

Curve 8 > 5

Curve 9 > 17

Curve 10 > 16

Curve 11 > 15

Curve 12 > 3

Use selection set 0 = No 1= Yes [0] > (accept default)

Redefinition Criterion 0=Prev 1=Redef 2=Max 3=Min elements [1] > (accept default

3. Click OK. Both contours are now created.

The next step is to make regions out of the contours just created. Two regions only

need be defined: the first is the dielectric substrate and the second is the air region.

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To create the first region:

1. From the Geometry menu, select Regions, Define. The RG dialog box opens.


Region [1] > (accept default)

Number of contours [1] > (accept default)

Pick/Input Outer Contour > 1

Underlying surface [0] > (accept default)

3. Click OK.

To define the second region similarly:

1. From the Geometry menu, select Regions, Define. The RG dialog box opens.


Region [2] > (accept default)

Number of contours [1] > (accept default)

Pick/Input Outer Contour > 2

Underlying surface [0] > (accept default)

3. Click OK. Both regions are now created.

Assigning Material Properties

The next step is to define the material properties for each region before meshing.

The first material is the one filling the dielectric substrate region (Alumina, r =10.0, r = 1.0).

To define material properties:

1. From the PropSets menu,

select Material Property.The MPROP dialog box

opens.

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Material property set [1] > (accept default)

Material Property Name > permit_r

Property value [0] > 10.0

Material Property Name >

3. Click OK.

4. Click Cancel button to end the command.

Because the dielectric substrate is assumed lossless, we did not specify a val-

ue for permit_i. This way, the default value of 0 for permit_i will be used.

We did not specify r since it is equal 1.0, which is the default value. Ifr had anon-default value, it can be defined through the mperm_r (for the real part) and

mperm_i (for the imaginary part) Material Property Names.

We did not define conductivity of the material (assumed a perfect dielectric: 0

conductivity). In case of finite conductivity, the ECON (Electric conductivity)Material Property Name can be used to define it.

Meshing

To mesh region 1:

1. From the Meshing menu, select

Auto_Mesh, Regions. The

MA_RG dialog box opens.


Pick/Input Beginning Region > 1

Pick/Input Ending Region > 1

Increment [1] > (accept default)

Number of smoothing iterations [0] >

(accept default)

Method 0=Sweeping 1=Hierarchical [0] > (accept default)

Element order 0=Low 1=High [0] > (accept default)

3. Click OK. The model at this stage should look as follows.

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Figure 4.4 Initial Mesh of the Dielectric Region

The second material is the air (r = 1.0, r = 1.0).

To define the second material properties:

1. From the PropSets

menu, select MaterialProperty. The MPROP

dialog box opens.

2. Enter the following

options:Material property set [1] > 2

Material property Name > permit_r

Property value [0] > 1.0

Material property Name >

3. Click OK.

4. Click Cancel button to end this command.

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To mesh region 2 similarly:

1. From the Meshing menu, select

Auto_Mesh, Regions. The

MA_RG dialog box opens.


Pick/Input Beginning Region > 2

Pick/Input Ending Region > 2Increment [1] > (accept default)

Number of smoothing iterations [0] >

(accept default)

Method 0 = Sweeping 1= Hierarchical [0] > (accept default)

Element order 0=Low 1=High [0] > (accept default)

3. Click OK. The model at this stage should look as follows.

Figure 4.5 Initial Mesh of the Entire Model

It is a good idea at this stage to turn on ele-

ment colors based on material properties.

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To turn on element colors based on material properties:

1. From the Meshing menu, select Elements, Activate Element Color. The

ACTECLR dialog box opens.

2. From the Color Flag drop-down menu, select Yes.

3. From the Set Label option, select Material Property.

4. Click OK. You will then be able to easily distinguish the different regions basedon their material properties by repainting the plots.

Refining Mesh

So far, the mesh is coarse and uniform in the whole model which may not be

adequate for certain parts of the structure. For instance, the field varies very rapidly

around the sharp edges of the conductors and a coarse mesh may not capture such

rapid variation. Hence, a much finer mesh is usually needed around the singular

points, i.e., sharp corners and edges. In order to have a very fine mesh around thesharp edges of the conductors while keeping a smooth transition from fine to coarse

regions, the process of mesh refinement is performed in three repetitive steps. Each

refinement pass must start with the selection of the elements to be refined.

To select the elements to be refined:

1. From the Control menu, select Select, by

Windowing. The SELWIN dialog box

opens.


Entity Name [EL] > (accept default)

Window type 0=Box 1=Circle 2=Polygon [0] > (accept default)

Selection set number [1] > (accept default)

3. Click OK.

4. Select first corner point of window. Click and release the mouse button at one of

the corners of the box enclosing the area to be refined.

5. Drag the mouse towards the opposite corner of the box. You will then see theselection-area box being drawn while the following message is displayed in the

command window area:

Select second corner point of window

6. Click and release the mouse button at the second (opposite) corner of the box

enclosing the area to be refined.

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As this the first refinement pass, and to avoid having elements with poor aspect

ratio and to insure a smooth transition in element sizes and mesh density, make sure

that this first refinement box is a good distance away from the conductors. For

instance, in this case an upper left and lower right corners of approximately (25, 24,

0) and (95, 0, 0), respectively, should be appropriate. It should be understood that

the coordinates of the box corners need not be specified very precisely as long as

smooth transition of the mesh is achieved.

Once the points are entered, the selected elements are highlighted with a different

color and the number of selected elements is given. Next, we proceed to refining

the selected elements.

To refine the selected elements:

1. From the Meshing menu, select Elements, Refine Mesh. The EREFINE dialog

box opens.

2. Click OK to accept all the default settings.

We need to ensure smooth elements (i.e., good aspect ratios) after the first

refinement.

To smooth the mesh:

1. From the Meshing menu, select Elements, Smoothen Mesh. The ESMOOTH

dialog box opens.


Before the second refinement pass, make sure to unselect the elements in the first

selection set.

To initialize the selection set:

1. From the Control menu, select Select,

Initialize. The INITSEL dialog box

opens.

2. Click OK to accept all the default

settings.

To start the second refinement pass, we must again select which elements to refine

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opens.

2. Enter the following options:Entity Name [EL] > (accept default)



3. Click OK.

4. Select first corner point of window.

5. Select second corner point of window. This time, choose a rectangle closer to

the conductors (i.e., one that would be inside the rectangle of the first pass). For

example, an upper left and lower right corners of approximately (40, 14, 0) and

(80, 5, 0), respectively, should be appropriate.

Again, we refine the selected elements, smooth the mesh and re-initialize the

selection as follows.



box opens.



refinement.

To smooth the mesh:


dialog box opens.



1. From the Control menu, select Select, Initialize. The INITSEL dialog box

opens.


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The final refinement pass starts again with a selection of the elements to be refined




opens.


Entity Name [EL] > (accept default)



3. Click OK.

4. Select first corner point of window.

5. Select second corner point of window. Choose a rectangle much closer to the

conductors. For example, an upper left and lower right corners of

approximately (45, 12, 0) and (73, 8, 0), respectively, should be appropriate.

Once more, after selecting the elements, issue the following sequence of

commands:



box opens.



refinement.

To smooth the mesh:


dialog box opens.


Before the second refinement pass, make sure to unselect the elements in the first

selection set.

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1. From the Control menu, select Select, Initialize. The INITSEL dialog box

opens.


You should initialize the selection at the end of mesh refinement to ensure that

subsequent commands will not act upon the last selection set only.

The resulting mesh at this stage is deemed good but additional mesh refinement, if

desired, can be carried out in the above manner. Note that the goals of a very fine

mesh around the conductors that gradually gets coarser away from them has been

achieved as shown in the following figure:

Figure 4.6 Final Mesh of the Entire Model

The above meshing procedure usually yields duplicate nodes at the interfaces

between regions. We need to merge these nodes and renumber them sequentially:

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To merge and renumber nodes:

1. From the Meshing menu, select Nodes, Merge.

2. Click OK to accept all default settings.

3. From the Meshing menu, select Nodes, Compress.

4. Click OK to accept all default settings.

Applying Boundary Conditions

Next, the boundary conditions have to be specified. Curve 1 represents the ground

plane of the coupled lines, therefore its boundary condition code should be gc

(grounded conductor). The outer curves, namely 2, 9, 10, 11, and 8 constitute the

outer boundary of the mesh. If the coupled lines are not shielded, an open outer

boundary (oob) (or Absorbing Boundary Condition) should be applied at the outer

boundary to truncate the unbounded domain. However, for guiding structures the

field is confined to a small region around the conductors (otherwise the energy will

be leaked away resulting in high losses and the guiding structure will not then be

performing its role). It is therefore sufficient to place the outer boundary far enough

and place a gc-type boundary conditions on it. The user could as well choose oob

type of boundary condition for these outer curves, however, the COSMOSHFS

full wave solver will still treat them as gc-type of boundaries.

To apply the gc boundary condition to curves 1 and 2:

1. From the LoadsBC menu, select E-Magnetic, Hi_Freq B-C, Define by Curves.The CBCR dialog box opens.


Beginning Curve > 1

Boundary condition type

(fc, gc, pmc, oob) [fc] > gc

Conductor Number > 1

Conductivity value [5.8e+007] >

(accept default)

Relative permeability value [1] > (accept default)

Ending Curve > 2


3. Click OK.

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Note that the default metal for the conductors is copper. The user could choose

another metal by specifying its conductivity and the permeability.

To apply the gc boundary condition to curves 8-11:

1. From the LoadsBC menu, select E-Magnetic, Hi_Freq B-C, Define by Curves.

The CBCR dialog box opens.


Pick/Input Beginning Curve > 8

Boundary condition type (fc, gc, pmc, oob) [fc] > gc


Conductivity value [5.8e+007] > (accept default)


Pick/Input Ending Curve > 11


3. Click OK.

Next, the floating conductors need to be specified. The left and right conductors are

labeled 1 and 2, respectively. Note that conductor 1 is formed by curves 6, 12, 13,

and 14. Whereas conductor 2 is formed by curves 4, 15, 16, and 17. Note also that

the regions inside the conductors are not meshed because the electric field is zero

inside a conductor.

To apply the fc (conductor 1) boundary condition to curve 6:





Boundary condition type (fc, gc, pmc, oob) [fc] > (accept default)






3. Click OK.

To apply the fc (conductor 1) boundary condition to curve 12-14:



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3. Click OK.

To apply the fc (conductor 2) boundary condition to curve 4:











3. Click OK.

To apply the fc (conductor 2) boundary condition to curve 15-17:







Conductivity v

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