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Designing High Performance
Cavity Filters
Authored by:
Devin CrawfordAnsoft Corporation
Ansoft 2003 / Global Seminars: Delivering Performance
Presentation #7
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Link the Power of Circuit andFinite Element Analysis
w Many problems can be broken down intoconstituent parts:w Waveguide and Cavity Filters
w Large Circuits: package board - component
w Any components connected by transmisison lines orwaveguides!
w The divide and conquer strategy leadsto very efficient and accurate solutions.
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Strategy for combining full-wavethree-dimensional solutions
w Determine how best to subdivide largeproblems.
w
Solve the constituent problemsparametrically.
w Construct models from constituent parts.The existence of parametric 3-D models
enables fast design and optimization ofvery large structures!
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What is the Transfinite ElementMethod?
w The Finite Element method is used to solve Maxwellsequations in the volume of arbitrary three-dimensionalstructures.
z
nnn j +=
and characteristic impedance (specifiesa relationship between E and H)
n
n
propagation constant
attenuation
A single port solution (mode) yields a
propagation constant
w The transfinite element methodis used to determine thetwo-dimensional field solution at the port.
z
n eyxEy= ),(E
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Transfinite Element Method in aNutshell
w Generalized s-parameters fully characterize theblack-box behavior of a three-dimensionalstructure.
w Structures that have identical port solutions, butdifferent internal geometries may often beanalyzed separately and joined at the ports.
w The use of generalized s-parameters that weredetermined using the transfinite element
method insures that the fields are matched atthe port boundary.
Lets look at some examples
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The basic approach
1. Select the building blocks (parametric models) for thedesired structure.
2. Verify the technique on a simple, easily verifiablemodel.
3. Define the parameter space: what range of valuesshould the parameters cover?
4. Synthesize and optimize the desired three-dimensionalstructure using parametric models generated fromHFSS.
5. Verify the design using the full-wave solution of theentire structure.
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Example 1: Waveguide Filter
w The waveguide filter is comprised of e-plane irises thathave been characterized parametrically in HFSS.
1
2
3
4
5 Parametric model
based on full-wave
analysis.
),(),(),(),(
2221
1211
dSdSdSdS
S-parameters depend on
frequency and aperture width.
d
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Realization of a Waveguide Filter
1. Define parameterized model by generating a grid of coarsely spacedsolutions in the parameter space.
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Realization of a Waveguide Filter
2. Create the entire filter from individual components.
The model is fully parameterized!
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Parameterized Port Impedance
w An important aspect of the circuit model is the frequencydependent port impedance:
if(k>kc10,z10,0)
Z10 is the frequency dependent characteristic impedance.
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Realization of a waveguide filter
3. Optimize the filter response byinterpolating existing solutions.
Theaccuracyo
fthefull-wave
analysisisaccessible
byinterpolating
existingsoluti
ons!
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Realization of a Waveguide Filter
3. Optimization continued: thegoal response for theoptimization can begenerated using the filtersynthesis tool.
Optimized response using interpolation of
coarsely spaced HFSS solutions
Optimizationg
oal
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Realization of a Waveguide Filter
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-40
-30
-20
-10
0
9.5 9.7 9.9 10.1 10.3 10.5
Frequency (GHz)
d
B
After optimization using interpolated HFSS solutions, accuracy can
be improved by Simulating missing solutions
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Comparison between HFSSand Ansoft Designer
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-50
-40
-30
-20
-10
0
9.6 9.8 10 10.2 10.4
Frequency (GHz)
-40
-35
-30
-25
-20
-15
-10
-5
0
9.5 9.7 9.9 10.1 10.3 10.5
Frequency (GHz)
HFSS
Designer|S21|
|S11|
4. Improve the solution accuracyby generating exact full-wavesolutions for the optimizedparameter values.
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Example 2: dielectric/coaxialresonator cavity filter
w Waveguide components are generally simplebecause the behavior is accurately described bysingle mode interaction between components.
w How do we approach structures that are not easilydescribed by single mode behavior?
w Use the example of a mixed resonator filter toinvestigate the approach.
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Single Dielectric Resonator
w As usual, take advantage ofthe symmetry when possiblefor full-wave analysis.
E-field
H-field
Perfect E-
symmetry plane
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Analysis of a Single DielectricResonator
w A single resonator cavity is perfect for investigating theproposed approach because solutions can be obtained very fast,and various methods can be used to obtain the sameinformation.
1.Resonant frequency and Q determinedfrom the Eigenmode solver in HFSS.
2.Solve the driven problem with portexcitations (also gives resonant
frequency and Q)
3. Create a parametric model in HFSS andanalyze this model by matching portmodes in Ansoft Designer (the transfiniteelement method).
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Subdivision of DielectricResonators
w Eigenmode solver, driven solution, and transfinite elementanalysis were used to verify the equivalence of the threeanalysis methods.
+=
3-dimensional
Eigenmode solution
Port solution
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Defining Parameter Space
w The equivalent circuit can be equated to physical dimensions byequating resonant frequencies of the two simulations.
Open circuit = perfect magnetic conductor
Short circuit = perfect electric conductor
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Design and Analysis of a 5pole filter
w 3 parametric models are required to createthis filter.
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5 Pole Cavity Filter
w Only 3 Modes are needed to represent the TE01Dielectric resonator mode.
1 2
3
4
1
2
3
4
5
6
7
1
2
3
4
5
6
7
12
3
4
1
2
3
4
5
6
1
2
3
4
5
6
U4Ideal5pole1
Goal Response
5 Pole Filter
Generated in HFSS
Optimization goal is inserted in
the same schematic as the HFSS
subcircuits
Each connection represents
a mode (port solution)
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5 Pole Filter
w Filter synthesis is carried out in Designer, usingparameterized models that were generated in HFSS.
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-2
-1
0
1.92 1.94 1.96 1.98 2.00
Freq (GHz)
S21
(dB)
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-40
-20
0
1.85 1.90 1.95 2.00 2.05 2.10
Freq (GHz)
Simulate missing solutions
Solution in Designer
when HFSS models
are interpolated
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Optimized 5-pole filter in HFSS and Designer
|H|
Field magnitude
from HFSS at
1.96 GHz
|S21|dB
|S11|dB
Response in HFSS after optimizationin Designer
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Conclusion
w A new approach to filter design and synthesis hasbeen demonstrated.
w The speed of circuit analysis along with theaccuracy and flexibility of the finite elementmethod will bring filter design and synthesis to thenext level.