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Contents
1. IntroductionIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-
2. TheoryIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-
Edge Elements
COSMOSCAVITY Modules . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
CAV3D: The Three-Dimensional Cavity Field Solver . . . . 2-2
CAVAXI: The Axisymmetric Cavity Field Solver . . . . . . . 2-3
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Conductor Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Secondary Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
The Quality Factor and RLC Equivalent Circuit Calculation 2-6
3. Description of CommandsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-
Detailed Description of Commands . . . . . . . . . . . . . . . . . . . . 3-Common Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
Material Property Commands . . . . . . . . . . . . . . . . . . . . . . 3-2
Boundary Condition Commands . . . . . . . . . . . . . . . . . . . 3-3
Integration Paths Commands . . . . . . . . . . . . . . . . . . . . . 3-1
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Analysis Options Commands . . . . . . . . . . . . . . . . . . . . . 3-12
Performing the Analysis Commands . . . . . . . . . . . . . . . 3-1
Available Results Commands . . . . . . . . . . . . . . . . . . . . . 3-1
Postprocessing Commands . . . . . . . . . . . . . . . . . . . . . . . 3-14
Graphing Results Commands . . . . . . . . . . . . . . . . . . . . . 3-15
Module-Specific Commands . . . . . . . . . . . . . . . . . . . . . . . 3-17
COSMOSCAVITY Commands . . . . . . . . . . . . . . . . . . . 3-17
4. Detailed ExampleIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-
MICAV1: A Conical Dielectric Resonator Inside
a Cylindrical Cavity (CAVAXI) . . . . . . . . . . . . . . . . . . . . . . . 4-
Creating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-
Assigning Material Properties . . . . . . . . . . . . . . . . . . . . . . . 4-8
Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-
Refining Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
Applying Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 4-15
Running Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16
Visualization of Results . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
5. Verification ProblemsIntroduction 25
MICAVV1: Multi-Mode Calculations for
Homogeneously Filled Rectangular Cavities . . . . . . . . . . . . 5-26
MICAVV2: An Inhomogeneously Filled Rectangular
Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-27
MICAVV3: A Rectangular Cavity with a Dielectric
Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2
MICAVV4: Dominant Mode Calculations for
Inhomogeneously Filled Cylindrical Cavities; a
High-Q Dielectric Resonator . . . . . . . . . . . . . . . . . . . . . . . . 5-29
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MICAVV5: Dominant Mode Calculations for
Inhomogeneously Filled Cylindrical Cavities; a
Dielectric Resonator Over a Microstrip Substrate . . . . . . . . 5-30
MICAVV6: Multi-Mode Calculations for
Inhomogeneously Filled Cylindrical Cavities . . . . . . . . . . . . 5-3
MICAVV7: Equivalent Lumped Resonant
Circuits of a Cylindrical Cavity . . . . . . . . . . . . . . . . . . . . . . 5-32
A.Material Constants . . . . . . . . . . . . . . . . . . . . . . . . . .A-1
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-
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1. Introduction
Introduction
For years the finite element method (FEM) has been the key design and simulation
tool for engineers working in a wide range of disciplines. The principle beneficiarie
of the flexibility and power of this method have traditionally been people working
on mechanical, structural, fluid, and thermal problems. Those working in the area o
high frequency electromagnetics (from radio frequencies, RF, to optics) have, on the
other hand, relied more on analytical approaches, whenever possible, on empirical
and semi-empirical models, or on simple solution techniques with limited accuracyand range of applicability. Several numerical difficulties associated with the nature
of the high frequency electromagnetic fields and their representation in a descritized
space have slowed the introduction 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 the COSMOSHFS, a High Frequency Simulation suite that contains
three basic components marked with accuracy, speed, efficiency and ease of use. The
three basic solvers are COSMOSHFS 2D, COSMOSCAVITY, and COSMOSHFS
3D as shown in Figure 1.1.
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Figure 1.1 Components of the COSMOSHFS Suite
This manual describes the COSMOSCAVITY package by presenting the theory
behind it, its implementation, some detailed step-by-step examples, and a number
of verification problems.
COSMOSCAVITYis a general frequency domain program for the analysis of
resonant structures. Its applications include the analysis and design of cavities,
dielectric resonators, frequency meters, connectors, cavity filters, and oscillators.
It solves the vector wave equation for the resonant frequency and the correspond-
ing modal field distributions. Depending on the geometry of the problem being
solved, one of two sub-modules (MICAV-3D and MICAV-AXI) will be invoked
(see Figure 1.2). MICAV-3D is a fully three-dimensional program for arbitrary-
shaped cavities. It uses an edge-based finite elements approach to represent the
electric or magnetic field in tetrahederal elements. MICAV-AXI, on the other handis a program for axially symmetric cavities. It uses a hybrid node/edge approach
to represent the electric or magnetic fields on the edges and nodes of triangular
elements. Both MICAV-3D and MICAV-AXI give spurious modes-free solutions
COSMOSCAVITIES
Axi-symmetric and Arbitrary3D Cavities and Resonant
Structures
The C OSMOSHFS System
COSMOSHFS2D
2D Guiding StructuresHigh sSpeed Digital
Interconnects
COSMOSHFS 3 D
Arbitrary 3D PassiveStructure S-parameter
Simulator
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Figure 1.2 COSMOSCAVITY Modules
COSMOSCAVITY 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 COSMOSMdocumentation. In particular, COSMOSM Users Guide and the Command
Reference manuals in addition to the on-line help in GEOSTAR are essential
complement to the this manual. The on-line help 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 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
COSMOSH FS 2D
2DHFQR
Full-wave Solut ion 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 the two
main modules ofCOSMOSCAVITY namely CAVAXI and CAV3D will be given.
Since both modules of the COSMOSCAVITY 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 or
any 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.
COSMOSCAVITY Modules
This COSMOSCAVITYpackage combines two modules
for the analysis of resonant
cavity structures as illustrated
in Figure 2.1. For arbitrary,
three-dimensional structures, the
CAV3D sub-module is used with
a fully three-dimensional mesh
of four-node/six-edge
tetrahedrons. When the cavity
has an axial symmetry,
considerable savings can be
achieved by using the CAVAXI
sub-module with only a two-dimensional mesh of hybrid node-edge triangular
elements. Both modules implement a full-wave analysis as will be illustrated
below.
CAV3D: The Three-Dimensional Cavity Field Solver
This sub-module analyzes fully three-dimensional cavities without assuming any
symmetry, hence, the structure has to be meshed in its entirety. The boundary value
problem governing these structures is also represented by a vector wave equation
and a set of boundary conditions.
Figure 2.1. A Schematic Representationof a General Resonant CavityStructure
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Upon discretization using the edge elements, we obtain a generalized eigenvalue
problem which is then solved for the eigenvalues (the resonant frequencies) and the
eigenvectors (the modal electric field distributions) for a specified number of
modes.
(2-2)
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:
(2-3)
(2-4)
The unknown
electric field is
represented by first
order tetrahedral
elements as shown in
Figure 2.2. Clearly,each tetrahedron
has six unknowns
associated with its
edges.
CAVAXI: The
Axisymmetric
Cavity Field Solver
For axisymmetric geometries, a quasi-two-dimensional analysis is performed by
considering a cross section of the cavity at any arbitrary -plane. The vector waveequation (2-2) with the boundary conditions given by equations (2-3) and (2-4) are
still valid for these geometries. However, given the symmetry of the structure, the
field is assumed to have the following -dependence:
( ) Node1
Node2
Node3 Edge2 E t2
Node4
( )
Edge1
E t1( )
Edge4
E t4
Edge
5
E
t5
(
)
Edge6
( )E t6
Edge3
( )E t3
Figure 2.2. Unknowns on a Tetrahedral Element in MICAV-3D
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(2-5)
where a cylindrical coordinate system is used.
By substituting the electric field
expression of equation (2-5) back
in the vector wave equation (2-2),
we obtain a generalized eigenvalueproblem which is then solved for
the eigenvalues (the resonant
frequencies) and the eigenvectors
(the modal electric field distribu-
tions) for a specified number of
modes. Note that m, the harmonic
number, is a parameter of the
problem that must be specified at
the time of the solution.
Since at a given constant -plane, the azimuthal direction is purely normal to thatplane, a hybrid node/edge approach is used whereby a nodal representation is used
for the azimuthal component of the field and a vector representation is used for the
transverse component as shown in Figure 2.3.
Again, each triangle has three unknowns associated with its nodes and another
three associated with its edges. Finally, note that the axis of the symmetry of the
cavity must coincide with the y-axis of the x-y coordinate system.
Boundary Conditions
In high frequency electromagnetics, there are several possible boundary conditions
COSMOSCAVITY recognizes the following:
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, COSMOSCAVITY forces
the tangential component of the electric field on those surfaces/curves to be zero.
( )( )
Node1
E
1
( )Node3E3
( )
Node2
E
2
Edge1
Et1
( )
Edge3
Et3 ( )
Edge2
Et2
Figure 2.3. Unknowns on a TriangularElement in MICAV-AXI
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Perfect magnetic conductor (pmc):
COSMOSCAVITY 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.
A special axial boundary condition for the CAVAXI sub-module is applied
internally to axisymmetric cavities and the user need not specify it explicitly. Axia
element nodes/edges should just be left as free nodes/edges or have oob-type
boundary condition.
Material Properties
COSMOSCAVITY can treat isotropic dielectric and ferrite materials with a
complex relative permittivity ( = r o, with ), a complex relativepermeability ( = 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
COSMOSCAVITY is the following:
(2-6)
where
is the angular frequency.
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 electrica
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 UserMaterial Lib) for more details).
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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 defaul
conductor properties used are those of copper. For other metals, the user shouldspecify 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 solutionsavailable through the various COSMOSCAVITY modules have been given. In
this section, we present the theoretical formulation used for the various secondary
calculations available within COSMOSCAVITY.
The Quality Factor and RLC Equivalent Circuit Calculation
In the MICAV module, the user has the option of calculating the quality factor and
of determining the RLC equivalent circuit of the resonator analyzed.
The Quality Factor
The quality factor Q of a resonator is defined as [4]:
(2-7)
where r is the angular resonant frequency and
(2-8)
However, the average power dissipated can be due to conductor loss and/or
dielectric loss; we therefore define the quality factor due to conductor loss as:
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(2-9)
where Rm is the skin-effect surface resistance and is given by:
(2-10)
where and are the conductivity and the permeability of the metal. The qualityfactor due to dielectric loss is defined as:
(2-11)
where ffi is the filling factor for the ith
dielectric region which is the ratio of theelectric energy stored in the ith region to the total electric energy stored in the
cavity. The total quality factor of the cavity is then given by:
(2-12)
Note that each mode has a different field distribution, and hence a different quality
factor.
The RLC Equivalent Circuit
The RLC equivalent circuit of a resonator is often informative, especially in giving
an idea about what minor perturbations will do to the properties of the resonator [4]
The elements R, L, and C are responsible for the power dissipated, the stored
magnetic and electric energy, respectively. Since the magnetic and electric energies
are equivalent at resonance, we can write:
(2-13)
and from the average electric energy we can compute C using the following
relationship:
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(2-14)
However, the voltage across the resonator needs to be computed first as
(2-15)
where Path follows the curve of maximum electric field. It should be clear here
that such integration path need not be a straight line and is in general formed by N
straight line segments each of which is defined by two end points. Note that the
determination of the path will depend on the particular mode being considered and
the resulting field distribution. The user may wish to make an initial examination of
the results before defining the integration path for subsequent calculations.
Once V is computed, C is obtained from equation (32). Next, L is computed using
equation (31). Finally, the equivalent resistance R, is related to the quality factor Qand the equivalent inductance L via
(2-16)
It should be clear that each mode will have a different RLC equivalent circuit and
should have an appropriate integration path to define the voltage associated with it
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 for
finite 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 ofCOSMOSCAVITY for solving high frequency electromagnetic
problems involves generating a proper finite element mesh, specifying the materia
properties, imposing the boundary conditions, and specifying the appropriate
solution parameters. All of this is done through the GEOSTAR preprocessor.
Similarly, using GEOSTAR postprocessor, the results of the various COSMOS
CAVITY modules can be viewed in graphical and text formats. The general
commands for model creation, mesh generation and postprocessing are documentedin the COSMOSM Users Guide Volume (1) and will not be described here. Only
commands that are specific to COSMOSCAVITY or that have an implementation
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 COSMOSCAVITY modules while the second describes the
module-specific commands.
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ommands
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 propertie
for HFESAP 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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ommands
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.
CBEL bel bc cond_num conductivity
permeability face_num eel increment
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ommands
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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ommands
Where:
bcurve
Beginning curve 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.
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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ommands
Where:
bsurface
Beginning surface 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.
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
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.
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
Beginning element in the pattern.
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
Ending element in the pattern.
(default is bel)
inc
Increment between elements in the pattern.
(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
Ending element in the pattern.
(default is elmax)
inc
Increment between elements in the pattern.
(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
Beginning element in the pattern.
(default is 1)
eel
Ending element in the pattern.
(default is elmax)
inc
Increment between elements in the pattern.
(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 13The 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 2DHFRQ, the command lists the
frequency points (freq), mode number (Mode), mode flag (M_Flag) and Frequency
(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 2DHFRQ and CAV3D:
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.
Note:
Refer to the COSMOSM Command Reference Manual for more help on graph-
color, line-style, symbol-type and graph-id.
Module-Specific Commands
COSMOSCAVITY Commands
HF_CAVSOLN
(Menu: ANALYSIS > HF_Emag > Cavities > HF_Cav-Soln)
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The HF_CAVSOLN command defines the solution options for the cavity simulator
Where:
model_flag
Flag to specify model type.
EQ. 0 Axisymmetric cavities.EQ. 1 3-dimensional cavities.
(default is 0)
nmodes
Number of desired modes.
(default 1)
fharmonic
First harmonic (for axisymmetric cavities).
(default 0)
lharmonic
Last harmonic (for axisymmetric cavities).
(default 0)
Example: HF_CAVSOLN, 0, 2, 1, 3
This command sets the cavity simulators solution options tosimulate an axisymmetric cavity and compute its 2 most
dominant modes for each of the harmonics: 1, 2, 3.
HF_CAVOUT
(Menu: ANALYSIS > HF_Emag > Cavities > HF_Cav-Out)
The HF_CAVOUT command sets the output options for axisymmetric and 3-D
cavity solvers.
Where:
compQ_flag
Flag for cavity quality factor computation.
EQ. 0 Quality factor is not computed.
EQ. 1 Quality factor is computed.
(default is 0)
HF_CAVSOLN model_flag nmodes fharmonic lharmonic
HF_CAVOUT compQ_flag compRLC_flag output_flag
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compRLC_flag
Flag for equivalent RLC circuit computation.
EQ. 0 Equivalent RLC circuit is not computed.
EQ. 1 Equivalent RLC circuit is computed.
(default is 0)
output_flag
Flag 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)
Notes:
1. If compQ_flag is set to 0, compRLC_flag is ignored and the RLC equivalen
circuit is not computed.
2. If compQ_flag is set to 1 and compRLC_flag is also set to 1, an integration
path must be specified for RLC computation.
Example: HF_CAVOUT, 1, 1, 1
This command sets the cavity simulators output options to computethe cavitys quality factor and its equivalent RLC circuit and to outputnodal values only of the modal electric and magnetic fields.
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4. Detailed Example
Introduction
This chapter presents step by step procedures for solving a problem with
COSMOSCAVITY.
MICAV1: A Conical Dielectric Resonator Inside
a Cylindrical Cavity (CAVAXI)
The geometry of the conical resonator,
its dielectric ring support and the metal-
lic enclosure cavity are shown in Figure
4.1. The dimensions of the problem are
h = r = 4 mm for the resonator, R = 8
mm and H = 7 mm for the cavity and,
for the ring support with square cross-
section, a = 1 mm with inner and outer
radii of 1 mm and 2 mm, respectively.
The material of the resonator is non-
magnetic and slightly lossy with r =
35.7 - j4.2x10-4 while the ring support
has a dielectric constant of 2.2.h
r
a
r
R
H
y
x
r1
2
Figure 4.1.Geometry of the ConicalResonator with a Dielectric RingSupport Inside a Metallic Cavity
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DetailedExample
To start a new problem in GEOSTAR:
1. Launch GEOSTAR. GEOSTAR starts and the Open Problem Files dialog box
opens.
2. Browse to the directory which you want to use for the new problem.
3. In the File name field, enter
micav1, for example, for the
problem name.
4. ClickOpen. GEOSTAR sets the
new problem and creates all
related database files in the
specified folder.
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 View Parameter, View. The View dialog box
opens.
4. Click OK to use the default Y-view.
The dimensions of the structure are all integer multiples of 1 mm in both x and y
directions. Therefore, defining a grid based on these values will significantlysimplify the task of model construction.
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DetailedExample
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. Enter the following values:
Origin x-Coordinate Value [0] >
(accept default)
Origin y-Coordinate Value [0] >
(accept default)
X- increment [5] > 1Z- increment [5] > 1
No of X- increments [20] > 8
No of Z- increments [20] > 7
Grid line color index [2] >
(accept default)
3. Click OK.
To re-scale the grid and fit in the display window:
1. From the Geo Panel, click the Scale Auto button .
At this stage it is a good idea to give a descriptive title of the problem we are abou
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 > Conical resonator inside a cylindrical cavity
3. Click OK.
Next, we create the seven outer curves. These curves include the cavity walls the
central axis of the cavity. Note that the axis of symmetry must coincide with the x=0
axis. The following procedure creates the necessary curves (the mouse can be used
to pick the points on the grid).
To create the seven outer curves:
1. From the Geometry menu, select Curves, Draw Polyline. The CRPCORD
dialog box opens.
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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> 1, 0, 0
X, Y, Z Coordinates of keypoint 3> 2, 0, 0
X, Y, Z Coordinates of keypoint 4> 8, 0, 0
X, Y, Z Coordinates of keypoint 5> 8, 0, 7
X, Y, Z Coordinates of keypoint 6> 0, 0, 7
X, Y, Z Coordinates of keypoint 7> 0, 0, 4
X, Y, Z Coordinates of keypoint 8> 0, 0, 0
3. Click OK.
Next, we create three additional curves which, along with curve 2, will delimit the
dielectric support rings region.
To create the curves delimiting the dielectric support rings region:
1. From the Geometry menu, select Curves, Draw Polyline. The CRPCORD
dialog box opens.2. Enter the following coordinates:
Curve [8] > (accept default)
X, Y, Z Coordinates of keypoint 1 > 2, 0, 0
X, Y, Z Coordinates of keypoint 2 > 2, 0, 1
X, Y, Z Coordinates of keypoint 3 > 1, 0, 1
X, Y, Z Coordinates of keypoint 4 > 1, 0, 0
X, Y, Z Coordinates of keypoint 5 > 1, 0, 0
3. Click OK.
Finally, we create the remaining curves to delimit the region of the cone resonator
To create the curves delimiting the region of the cone resonator:
1. From the Geometry menu, select Curves, Draw Polyline. The CRPCORD
dialog box opens.
2. Enter the following coordinates:
Curve [11] > (accept default)
X, Y, Z Coordinates of keypoint 1 > 0, 0, 0
X, Y, Z Coordinates of keypoint 2 > 1, 0, 1
X, Y, Z Coordinates of keypoint 3 > 4, 0, 4
X, Y, Z Coordinates of keypoint 4 > 0, 0, 4
X, Y, Z Coordinates of keypoint 5 > 0, 0, 4
3. Click OK. This completes the creation of all necessary 13 curves.
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DetailedExample
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 Geometry of the Model
Next, we build contours using of the curves just created.
1. From the Geometry menu, select Contours, Define. The CT dialog box opens.
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2. Enter the following options:
Contour [1] > (accept default)
Mesh flag 0 = Esize 1= Num. elems [0] > (accept default)
Average element size > 0.5
Number of reference boundary curves [1] > 3
Pick/Input Curve 1 > 1
Pick/Input Curve 2 > 10
Pick/Input Curve 3 > 11
Use selection set 0 = No 1= Yes [0] > (accept default)Redefinition Criterion 0=Prev 1=Redef 2=Max 3=Min elements [1] > (accept defaul
3. 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.
2. Enter the following options:
Contour [2] > (accept default)
Mesh flag 0 = Esize 1= Num. elems [0] > (accept default)Average element size > 0.5
Number of reference boundary curves [1] > 8
Pick/Input Curve 1 > 3
Pick/Input Curve 2 > 4
Pick/Input Curve 3 > 5
Pick/Input Curve 4 > 6
Pick/Input Curve 5 > 13
Pick/Input Curve 6 > 12
Pick/Input Curve 7 > 9
Pick/Input Curve 8 > 8
Use selection set 0 = No 1= Yes [0] > (accept default)
Redefinition Criterion 0=Prev 1=Redef 2=Max 3=Min elements [1] > (accept defaul
3. Click OK.
To define the third contour:
1. From the Geometry menu, select Contours, Define. The CT dialog box opens.
2. Enter the following options:
Contour [3] > (accept default)Mesh flag 0 = Esize 1= Num. elems [0] > (accept default)
Average element size > 0.5
Number of reference boundary curves [1] > 3
Pick/Input Curve 1 > 2
Pick/Input Curve 2 > 9
Pick/Input Curve 3 > 10
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Use selection set 0 = No 1= Yes [0] > (accept default)
Redefinition Criterion 0=Prev 1=Redef 2=Max 3=Min elements [1] > (accept defaul
3. Click OK.
To define the last fourth contour:
1. From the Geometry menu, select Contours, Define. The CT dialog box opens.
2. Enter the following options:
Contour [4] > (accept default)
Mesh flag 0 = Esize 1= Num. elems [0] > (accept default)
Average element size > 0.5
Number of reference boundary curves [1] > 4
Pick/Input Curve 1 > 11
Pick/Input Curve 2 > 12
Pick/Input Curve 3 > 13
Pick/Input Curve 4 > 7
Use selection set 0 = No 1= Yes [0] > (accept default)
Redefinition Criterion 0=Prev 1=Redef 2=Max 3=Min elements [1] > (accept defaul
3. Click OK.
With the contours complete, the next step is to generate the regions to be meshed.
To create the first region:
1. From the Geometry menu, select Regions, Define. The RG dialog box opens.
2. Enter the following options:
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.
2. Enter the following options:
Region [2] > (accept default)
Number of contours [1] > (accept default)
Pick/Input Outer Contour > 2
Underlying surface [0] > (accept default)
3. Click OK.
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To define the third region:
1. From the Geometry menu, select Regions, Define. The RG dialog box opens.
2. Enter the following options:
Region [3] > (accept default)
Number of contours [1] > (accept default)
Pick/Input Outer Contour > 3
Underlying surface [0] > (accept default)
3. Click OK.
To define the fourth region:
1. From the Geometry menu, select Regions, Define. The RG dialog box opens.
2. Enter the following options:
Region [4] > (accept default)
Number of contours [1] > (accept default)
Pick/Input Outer Contour > 4
Underlying surface [0] > (accept default)
3. Click OK.
Assigning Material Properties
We are now ready to proceed with material definition and mesh generation. Note
that regions 1 and 2 are both air and can, therefore, be meshed together under the
same material property set. We define the first material property set for air.
To define material property for air:
1. From the PropSets menu, select Material Property. The MPROP dialog box
opens.
2. Enter the following options:
Material property set [1] >
(accept default)
Material Property Name > permit_r
Property value [0] > 1.0
Material Property Name >
(to end this command)
3. Click OK.
4. Click Cancel button to end the command.
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Meshing
To mesh region 1 and 2:
1. From the Meshing menu, select Auto_Mesh, Regions. The MA_RG dialog box
opens.
2. Enter the following options:
Pick/Input Beginning Region > 1Pick/Input Ending Region > 2
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.
Next, we define the second material property set to be that of the dielectric ring
support.
To define material property for the dielectric ring support:
1. From the PropSets menu, select Material Property. The MPROP dialog box
opens.
2. Enter the following options:
Material property set [1] > 2
Material Property Name > permit_r
Property value [0] > 2.2
Material Property Name > (to end this command)
3. Click OK.
4. Click Cancel button to end the command.
To mesh the corresponding region 3:
1. From the Meshing menu, select Auto_Mesh, Regions. The MA_RG dialog box
opens.
2. Enter the following options:
Pick/Input Beginning Region > 3
Pick/Input Ending Region > 3
Increment [1] > (accept default)
Number of smoothing iterations [0] > (accept default)
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Method 0 = Sweeping 1= Hierarchical [0] > (accept default)
Element order 0=Low 1=High [0] > (accept default)
3. Click OK.
Finally, we define the third material property set to be that of the resonator using
permit_rto define the real part of the permittivity and permit_i to define the
imaginary part as follows.
To define the third material property set for the resonator:
1. From the PropSets menu, select Material Property. The MPROP dialog box
opens.
2. Enter the following options:Material property set [1] > 3
Material Property Name > permit_r
Property value [0] > 35.7
Material Property Name > permit_i
Property value [0] > 4.2e-04Material Property Name > (to end this command)
3. Click OK.
4. Click Cancel button to end this command.
To mesh the resonator region 4:
1. From the Meshing menu, select Auto_Mesh, Regions. The MA_RG dialog box
opens.
2. Enter the following options:Pick/Input Beginning Region > 4
Pick/Input Ending Region > 4
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.
This completes the initial meshing of the model which should now look as follows
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Figure 4.3 Initial Mesh of the Model
It is a good idea at this stage to turn on element colors based on material prop
erties.
To turn on element colors based on material properties:
1. From the Meshing menu, select Elements,
Activate Element Color. The ACTECLRdialog 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 based
on their material properties by repainting the screen.
Refining Mesh
So far, the initial mesh thus obtained is coarse and fairly uniform throughout the
model. However, because the dielectric resonator region has such a high permit-
tivity (i.e., the wavelength inside it is much shorter), we must refine the mesh
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inside it so as to insure that we keep a ratio of around 10 nodes per wavelength. To
do this, we must first select the elements to be refined. Because of the geometry of
the resonator, it is best to select the elements based on their reference entity. In this
case we would like to select all elements in the resonators region (region number
4).
To select the elements to be refined:
1. From the Control menu, select Select, by Reference. The SELREF dialog boxopens.
2. Enter the following options:
Selection Entity [EL] > (accept default)
Reference Entity [SF] > RG
3. Click Continue.
4. Enter the following options:
Pick/Input Beginning Region > 4Pick/Input Ending Region > 4
Increment [1] > (accept default)
Boundary element flag [0] > 1
5. Click OK
A number of elements (119) are then selected and highlighted with a different.
Note that the boundary flag should be set to 1 to avoid generating hanging nodes
Next, we proceed with refining the selected elements as follows:
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.
2. Click OK to accept all the default settings.
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Additional refinement passes on the resonator region can be carried out using the
above outlined steps. Here, we chose to refine the areas near the tips of the cone
since they can be considered as a mild singularity points. However, before each
additional refinement pass, we must make sure to unselect the elements from the
previous selection set. This can be done by re-initializing the selection set with the
command.
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.
Also, click the REPAINT button to view the new mesh. To start the second
refinement pass, we must again select which elements to refine. We will select theelements that lie within a circular region centered at the resonators top right tip.
To select the elements to be refined:
1. From the Control menu, select Select, by
Windowing. The SELWIN dialog box
opens.
2. Enter the following options:Entity Name [EL] > (accept default)
Window type 0 = Box 1 = Circle 2 = Polygon [0] > 1
Selection set number [1] > (accept default)
3. Click OK.
4. Select center point of circular window.
5. Select point on perimeter. Choose a circle centered at (4, 4) and of radius
roughly equal to 1.5.
The selected elements are once again highlighted and can now be refined.
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.
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We need to ensure smooth elements (i.e., good aspect ratios) after the refinement.
To smooth the mesh:
1. From the Meshing menu, select Elements, Smoothen Mesh. The ESMOOTH
dialog box opens.
2. Click OK to accept all the default settings.
The last refinement pass is once again accomplished by selecting the elements that
lie within a circle centered at the origin and having a radius of roughly 0.75 and
refining them.
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 select the elements to be refined:
1. From the Control menu, select Select, by
Windowing. The SELWIN dialog box
opens.
2. Enter the following options:
Entity Name [EL] > (accept default)
Window type 0 = Box 1= Circle 2= Polygon [0] > 1
Selection set number [1] > (accept default)
3. Click OK.
4. Select center point of circular window. Choose the origin.
5. Select point on perimeter. Pick a point at roughly 0.75 mm from the center.
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.
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To smooth the mesh:
1. From the Meshing menu, select Elements, Smoothen Mesh. The ESMOOTH
dialog box opens.
2. Click OK to accept all the default settings.
The resulting mesh at this stage is deemed acceptable for this problem. Before
applying the boundary conditions, we must first merge all duplicate nodes resulting
from the meshing of different regions.
To merge nodes:
1. From the Meshing menu, select Nodes, Merge.
2. Click OK to accept all default settings.
Applying Boundary Conditions
Next, we apply the boundary conditions of this problem. The only boundary
condition needed is for the conducting cavity walls which is defined as follows:
To apply the gc boundary condition to curves 1 to 5:
1. From the LoadsBC menu, select
E-Magnetic, Hi-Freq_B-C, Define
by Curves. The CBCR dialog box
opens.2. Enter the following options:
Pick/Input Beginning Curve > 1
Boundary condition type
(fc, gc, pmc, oob) [fc] > gc
3. Click Continue.
Conductor Number > 1
Conductivity value [5.8e+007] >
(accept default)
Relative permeability value [1] > (accept default)
Pick/Input Ending Curve > 5
Increment [1] > (accept default)
4. Click OK.
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The boundary condition symbols are then plotted on all edges of the elements that
fall on the above curves. The resulting final mesh with the applied boundary
conditions is shown in Figure 4.4. Note that no particular boundary condition need
be applied to the axis of the structure since the solver does take care of it internally
Figure 4.4 Final Model Mesh with Boundary Conditions
Running Analysis
We are now ready to submit the model for solution. First, we set the analysis optionto CAVAXI using the units of mm.
To set the analysis options:
1. From the Analysis menu, select Hi-Freq_EMagnetic, Analysis Option. The
A_HFRQEM dialog box opens.
2. From the Analysis Option drop-down menu,
select CAVAXI.
3. From the Units option, select mm.
4. Click OK.
Next, we set the solution options, choosing the axisymmetric model and requesting
3 modes each for harmonics 0 and 1.
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To set the solution options:
1. From the Analysis menu, select Hi-Freq_EMagnetic, Cavities, Set Option. The
HF_CAVSOLN dialog box opens.
2. Enter the following options:
Model flag 0=Axisymmetric 1=3D [0] >
(accept default)
Number of modes [1] > 3
3. Click Continue.
4. Enter the following options:
First harmonic [0] > (accept default)
Last harmonic [0] > 1
Couple to thermal analysis 0=No 1=Yes [0]
> (accept default)
5. Click Continue.
Next, we set the output options to compute the quality factor and give the nodal
fields only.
To specify the output options:
1. From the Analysis menu, select
Hi-Freq_EMagnetic, Cavities,
Output Option. The HF_CAVOUT
dialog box opens.
2. Enter the following options:
Compute quality factor 0=No 1=Yes [0] > 1
Compute RLC equivalent circuit 0=No 1=Yes [0] > (accept default)
Output option 0=None 1=Nodal 2=Elem 3=Both [0] > 1
3. Click OK.
We can now run the analysis.
To run the analysis:
1. From the Analysis menu, select Hi-Freq_EMagnetic, Run Analysis. The
analysis starts.
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Upon completion of the solution (of which a log is kept in the file micav1.zlg),
control is returned to GEOSTAR for postprocessing. As the results of the analysis
comprise both mesh-related electric and magnetic field distributions as well as
modal quantities (resonant frequency, conductor and dielectric quality factors and
in the general case, RLC equivalent circuit parameters) two types of postprocessing
analyses can be performed. First, we examine the resulting field distribution for a
given mode and of a given harmonic.
To list available results:
1. From the Results menu, select Available Results.
This gives you a list of available nodal and element results in the form of harmonic
number, mode number and mode flag. The mode flag indicates whether the
solution for that mode converged (1) or did not converge (-1). We start by
examining the fundamental mode of the structure (i.e., harmonic 0 and mode 1).
Visualization of Results
To plot the fundamental mode of the structure:
1. From the Results menu, select Plot, Electromagnetic. The ACTMAG dialog
box opens.
2. Enter the following options.
Harmonic number [1] > 0
Mode number [1] > (accept default)Entity flag 1=ND 2=EL [1] > (accept default)
Component [Ero] > Er
3. Click the Contour Plot button. The MAGPLOT dialog box opens.
4. Enter the following options:
Line Flag 0=FILL 1=LINE 2=VECT [0] > (accept default)
Beginning Element [1] > (accept default)
Ending Element [1410] > (accept default)
Increment [1] > (accept default)
5. Click OK.
Make sure the selection list is re-initialized by selecting Select, Initialize
command from the Control menu otherwise only the field at the last selected
elements will be plotted.
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You can/should turn off mesh plotting by selecting Display Option, Set
Bound Plot from the Display menu.
You can plot the points by selecting Plot, Points from the Edit menu to see the
end points of the conductors and the curves by selecting Plot, Curves from the
Edit menu to see the different curves and region boundaries.
The resulting field distribution is shown in Figure 4.5. Note that for this mode Ero
and Ez are both zero (nearly zero numerically). This can be verified by examining
the field plots for the individual field components and noting the relative
corresponding scales.
Figure 4.5 Resultant Electric Field Distribution for Harmonic 0, Mode 1
The other field distributions for other (harmonic, mode number) combinations can
be examined in a similar manner to the (0, 1) combination above. One way to decide
on which combination might be more interesting to examine is to view the modal
data results. The summary of these results can be viewed with the command:
To list the results:
1. From the Results menu, select List, HF Emag Result.
The resulting listing is as follows:
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Note from the above results the relatively low Q of harmonic 0, mode 2. A close
examination of the field distribution associated with this mode reveals the reasons
the field is concentrated mostly near the bottom tip of the cone and close to the
cavity conducting walls as shown in Figure 4.6. It is prudent to make additional
mesh refinement in the high-intensity field region to insure accurate results for this
particular mode.
Harmonic: 0 Mode: 1=======================
Resonant Frequency: 9960.8659 MHzConductor Q Factor: 51413.9778Dielectric Q Factor: 87485.3252Overall Quality Factor: 32382.9456Equivalent Resistance: Not computedEquivalent Inductance: Not computedEquivalent Capacitance: Not computed
Harmonic: 0 Mode: 2
=======================Resonant Frequency: 10895.7230 MHzConductor Q Factor: 7833.8955Dielectric Q Factor: 564302.5347Overall Quality Factor: 7726.6310Equivalent Resistance: Not computedEquivalent Inductance: Not computedEquivalent Capacitance: Not computed
Harmonic: 0 Mode: 3=======================
Resonant Frequency: 15560.5081 MHzConductor Q Factor: 63340.9538Dielectric Q Factor: 95728.6514Overall Quality Factor: 38118.8102Equivalent Resistance: Not computedEquivalent Inductance: Not computed
Equivalent Capacitance: Not computed
Harmonic: 1 Mode: 1=======================
Resonant Frequency: 11870.3619 MHzConductor Q Factor: 51554.2298Dielectric Q Factor: 91618.3162Overall Quality Factor: 32986.2501Equivalent Resistance: Not computedEquivalent Inductance: Not computedEquivalent Capacitance: Not computed
Harmonic: 1 Mode: 2=======================
Resonant Frequency: 12710.4828 MHzConductor Q Factor: 76652.5542Dielectric Q Factor: 97179.7933Overall Quality Factor: 42852.0898Equivalent Resistance: Not computedEquivalent Inductance: Not computedEquivalent Capacitance: Not computed
Harmonic: 1 Mode: 3=======================
Resonant Frequency: 15766.8231 MHzConductor Q Factor: 18839.0314Dielectric Q Factor: 210133.1835Overall Quality Factor: 17289.0219Equivalent Resistance: Not computedEquivalent Inductance: Not computedEquivalent Capacitance: Not computed
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Figure 4.6 Resultant Electric Field Distribution for Harmonic 0, Mode 2
Finally, we can use xy-plots to examine the variation of the various modal
quantities that have been computed versus harmonic number. For example, to
examine the change in resonant frequency versus harmonic number for the three
modes, we use the following command sequence:
To load the resonant frequency versus harmonic data for mode 1:
1. From the Display menu, select XY_Plots, Activate Post-Proc. The
ACTXYPOST dialog box opens.
2. Enter the following options:
Graph Number [1] > (accept default)
Mode number [1] > (accept default)
Y_Variable [RFREQ] > (accept default)
Graph Color [12] > (accept default)
Graph line style [1] > (accept default)
Graph symbol style [1] > (accept default)
Graph id [1N] > MODE_1
3. Click OK.
To load the resonant frequency versus harmonic data for mode 2:
1. From the Display menu, select XY_Plots, Activate Post-Proc. The
ACTXYPOST dialog box opens.
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2. Enter the following options:
Graph Number [1] > 2
Mode number [1] > 2
Y_Variable [RFREQ] > (accept default)
Graph Color [12] > 13
Graph line style [1] > (accept default)
Graph symbol style [1] > 2
Graph id [1N] > MODE_2
3. Click OK.
To load the resonant frequency versus harmonic data for mode 3:
1. From the Display menu, select XY_Plots, Activate Post-Proc. The
ACTXYPOST dialog box opens.
2. Enter the following options:
Graph Number [1] > 3
Mode number [1] > 3
Y_Variable [RFREQ] > (accept default)Graph Color [12] > 14
Graph line style [1] > (accept default)
Graph symbol style [1] > 3
Graph id [1N] > MODE_3
3. Click OK.
To plot the data:
1. From the Display menu, select XY_Plots, Plot Curves. The XYPLOT dialog
box opens.
2. Enter the following option:
Plot graph 1 0=No, 1=Yes [1] > (accept default)
Plot graph 2 0=No, 1=Yes [1] > (accept default)
Plot graph 3 0=No, 1=Yes [1] > (accept default)
3. Click OK.
The resulting plot is presented in Figure 4.7 showing the resonant frequencies inHz versus the harmonic number for the first three modes. Similar plots for the
different cavity Qs can be made by using the above two commands.
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Figure 4.7 Variation of the Resonant Frequency with Harmonic Numberfor the First Three Modes
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5. Verification Problems
Introduction
This chapter contains verification problems to check the accuracy of the variou
solvers. The input files for these verification problems are included in th
vprobls\hfs sub-directory in the COSMOSM installation folder. Each file may b
read to GEOSTAR through the File, Load... command. All files have the .gfm
extension
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Description:
The geometry of the problem is depicted
in Figure 5.1. The closed form solutionfor this structure can be found in [1], for
example. The particular dimensions used
in this example are: a = 0.7m, b = 0.3m,
and c = 1m. The cavity walls are assumed
to be made of copper (conductivity
= 5.8x107mhos/m, skin depth = 66.1 /f Mhz).
Results:
The first four modes for the cavity shown in Figure 5.1 with the above dimensions
and air filling are summarized in Table 5.1 and compared to the closed form
formulas [1].
References:
1. R. E. Collin, Field Theory of Guided Waves, New York: McGraw-Hill, 1960.
Table 5.1 Resonant Frequency and Quality Factor for the First Four
Modes of the Cavity Shown in Figure 5.1
MICAVV1: Multi-Mode Calculations forHomogeneously Filled Rectangular Cavities
ModeCOSMOSCAVITY Computed [1]
f(MHz) Q f(MHz)
TE101 261.27 41756 261.38
TE102 368.08 52083 368.41
TE201 452.54 53513 453.75TE103 497.38 62171 498.07
a
bc
Figure 5.1 Geometry of theHomogeneously Filled
Rectangular Cavity
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Problems
Description:
The geometry of the problem is depicted in
Figure 5.2. This structure was originallyinvestigated in [1] by both an analytical
approach and a perturbational method. The
particular case considered is for b1 = b2 = l
and the normalized resonant frequency kl =
r(l/co) is computed.
Results:
The first two dominant resonant frequenciesand the quality factors of the cavity shown
Figure 5.2 have been computed using
COSMOSCAVITY for four different materials. The results are summarized in
Table 5.2 and are compared to those obtained in [1], which were computed for the
second mode only. The metallic walls are assumed to be made of copper.
References:
1. J. Van Bladel, High-permittivity dielectrics in waveguides and resonators,IEEE Trans. on Microwave Theory and Tech., Vol. 22, pp. 32-37, Jan. 1974.
Table 5.2 Normalized Resonant Frequencies and Quality Factors for
First Two Dominant Modes of the Cavity of Figure 5.2
MICAVV2: An Inhomogeneously FilledRectangular Cavity
r ModeResults from [1] COSMOSCAVITY
Analytical Perturbation r(2fl/co) Q
2.251
2
-
2.5053
-
2.5220
2.2655
2.4995
4.770 x 104
4.348 x 104
4.01
2
-
2.5987
-
2.6048
2.3642
2.5988
2.458 x 104
2.098 x 104
9.01
2
-
2.6617
-
2.6628
2.4293
2.6641
9.132 x 103
7.569 x 103
16.01
2
-
2.6829
-
2.6833
2.4508
2.6892
4.473 x 103
3.682 x 103
a
b1c
b2 r
Figure 5.2 Geometry of the
Inhomogeneously FilledRectangular Cavity
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Description:
The geometry of the problem is depicted in
Figure 5.3. This structure was investigated in[1] by an integral equation approach as well
as measurements. The particular structure
considered is with the dielectric block
centered in the bottom plane of the
rectangular cavity and with a = 9m,
b = 4m, c = 5m, w = 4.5m, h = 2.5m and l =
2m. The first three dominant resonant modes
(resonant frequencies and quality factors for
copper walls) are computed for r = 2.05.
Results:
The resonant frequencies of the first three dominant modes and the corresponding
quality factors for cavity of Figure 5.3 have been computed using COSMOS
CAVITY. The results are summarized in Table 5.8 and are compared to those
obtained in [1] where the normalized wavenumber (koa = a/co) has been computedfor the first mode only.
References:
1. M. Albani and P. Bernardi, A numerical method based on the descretization of
Maxwells equations in integral form, IEEE Trans. on Microwave Theory and
Tech., Vol. 22, pp. 446-450, Apr. 1974.
Table 5.3 Normalized Resonant Frequencies and Quality Factors for the
First Three Dominant Modes of the Cavity of Figure 5.3
MICAVV3: A Rectangular Cavitywith a Dielectric Block
ModeResults from [1] COSMOSCAVITY
Computed Measured koa Q
1 5.55 5.22 5.459 235.5
2 - - 6.858 1126.6
3 - - 7.332 1236.0
a
b cw
h
lr
Figure 5.3 Geometry of theRectangular Cavity
with a Dielectric Block
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5erification
Problems
Description:
The geometry of the structure analyzed by COSMOSCAVITY in this example is
depicted in Figure 5.4. The dielectrics used are r1=1.031 and r2=24.6-j8.54x10-4
This high-Q dielectric resonator has been investigated by [1]. The cavity walls are
assumed to be made of copper (conductivity = 5.8x107mhos/m, skin depth = 66.1 /f MHz).
Figure 5.4 Geometry of the High-q Dielectric Resonator Investigated in [1]
Results:
References:
1. Y. Kobayashi, Y. Kabe, Y. Kogami and T. Yamagishi, Frequency and low-
temperature characteristics of high-Q dielectric resonators, 1989 IEEE MTT-S
Digest, pp. 1239-1242.
MICAVV4: Dominant Mode Calculations forInhomogeneously Filled Cylindrical Cavities;
a High-Q Dielectric Resonator
Measured [1] COSMOSCAVIYT
f
(GHz)
Q
total
f
(GHz)
Q
dielectric
Q
conductor
Q
total
8.383 19000 8.384 29712 84015 21951
z
3.37mm
5mm
5mm
8.05mm
15.61