April 2007 771527-3342/07/$25.00©2007 IEEE

Sanghoon Shin is with R.S. Microwave Inc., Butler, NJ, USA. Sridhar Kanamaluru (Sridhar.Kanamaluru@herley.com)

is with Herley Industries, Inc., Lancaster, PA, USA.

Three-dimensional (3-D) electromagnetic(EM) simulators provide simulation resultsthat are close to measurements when usedin the design of passive components such asRF filters, multiplexers, couplers, and anten-

nas. However, when the analyzed structure is complexand/or when tuning and optimization are involved, EMsimulators require more computation time than circuit-based simulators. This article investigates a techniqueutilizing the strengths of both EM- and circuit-basedsimulators (i.e., EM circuit cosimulation) to provideaccurate results with reduced computation times.

EM Circuit Cosimulation TechniqueFigure 1 shows the basic concept of the EM circuitcosimulation technique. Rather than analyzing the

entire physical structure using an EM simulator, thestructure is first separated into discrete componentsand EM analysis is performed individually. Eachcomponent’s EM analysis is carried out for a range ofdesign variables (e.g., length, width, height, cornerradius, and frequency) with fixed intervals (i.e., stepsize). The results are saved as a numerical EM model,and could be a parameterized scattering matrix[neutral model format (NMF)] [1] or a link availableon call to a circuit simulator. Interpolation of the EMresults is carried out for specific values of the vari-ables that have not been previously simulated.Ideally, most structures could be separated into astandard set of components (e.g., T-junction, bend,and step discontinuity), and the EM models are avail-able a priori.

Sanghoon Shin and Sridhar Kanamaluru

©IM

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ES

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78 April 2007

To analyze the entire structure, a circuit-based simu-lator is used. This simulator uses a combination of EM-and circuit-based models, and the optimization is car-ried out using the circuit simulator. Thus, EM analysis

for every combination of dimensions can be avoidedduring optimization, and faster simulation speed isachieved. Also, circuit-simulator-based tuning is madeavailable, and the results can be viewed in real time.

At the final design stage, the cosimulated result isvalidated with a full EM simulation of the entire struc-ture using the optimized values to confirm the cosimu-lated result. Thus, full EM simulation of the entire struc-ture is performed just for analysis and not for optimiza-tion or tuning. Using this cosimulation technique, EMsimulation type accuracy can be obtained with a circuitsimulation speed.

Various 3-D EM field solvers [finite element method(FEM), finite differencemethod (FDM), finite differ-ence time domain (FDTD),mode-matching] are com-mercially available, and eachsolver is particularly applica-ble for specific structures andapplications. Therefore, inpractice, no commercial 3-DEM simulator covers allapplications, and it is cost-prohibitive to use all EMsolvers. In this article, we usea general FEM 3-D EM solverand circuit simulator todesign a diplexer and intro-duce the EM circuit cosimula-tion approach.

Diplexer DesignTo demonstrate the EM circuit cosimulation method,H-plane waveguide diplexers, shown in Figure 2, arepresented as design examples. The design require-ments are as follows:

Center frequency: 7.5 GHz for Channel 18.15 GHz for Channel 2

Bandwidth: 500 MHz eachWaveguide: WR112

1.112 in (w) × 0.497 in (h)Passband return loss: 18 dB min

Two different diplexer configura-tions are designed: the L-shape diplexer[Figure 2(a)] and the T-shape diplexer[Figure 2(b)]. In each diplexer, twochannel filters are combined with theinput common port through a T-junc-tion. Thus, the diplexer can be dividedinto two major sections: the waveguidechannel filters and the T-junction. EachT-junction and waveguide channel fil-ter will be designed separately andcombined for circuit-simulator-based

Figure 1. EM circuit cosimulation.

Specifications

• Frequency

• Insertion Loss

• Return Loss

• Isolation

• Power Handling

• Use Circuit Models

• Call/Retrieve EM-Models

• Physical Dimension Optimization to Meet Specifications

Structure Defn.• Define Structure

• Identify Discrete Components

• Define Design Variables and Ranges

Circuit Simulator

SimilarResults

EM Simulator• Full-Wave Analysis

• Parametric Analysis

• Field Plots

• Parameterized S-Matrix or

• EM Geometry

• Physics Effects (e.g., Thermal Analysis)

EM-Based Models

Figure 3. Decomposed elements of diplexers.

1

32 Ch.1Filter

T-Junction Ch.2Filter

(a)

1 3

2

Ch.1Filter

Ch.2Filter

T-Junction

(b)

At the final design stage, the cosimulated result is validatedwith a full EM simulation of the entirestructure using the optimized valuesto confirm the cosimulated result.

Figure 2. H-plane waveguide diplexers.

Ch.2

Input

Ch.1

(a)

Ch.2

Input

Ch.1(b)

April 2007 79

optimization. Figure 3 shows each component requiredfor cosimulation [2]. In [2] and [3], thediplexer structure is analyzed using amode-matching method with a generalizedscattering matrix. A similar approach isapplied here.

T-Junction DesignThe first step in the EM circuit cosimula-tion method is the T-junction design.Figure 4 shows an H-plane T-junction witha symmetric septum. The T-junction is athree-port device, which connects the twoTE01 dominant mode waveguide channelfilters to the common input port. In thiscase, the design parameter is the length ofthe septum. By changing the length of theseptum (L) and the connecting waveguidearm length, maximum power will betransmitted to each channel filter.

To standardize the EM results for vari-ous combinations of dimensions duringlater use in the circuit simulator, the EMresults are de-embedded up to thereference planes shown in Figure 4. Thisport de-embedding also elim-inates possible higher-ordermode reflection near thejunction into the wave ports.For later circuit-simulator-based optimization, a para-metric sweep simulation isperformed by changing theseptum length from 0.15 to0.55 in using 0.1-in intervals(five steps). Then, this precal-culated parametric EMmodel is inserted into the cir-cuit schematic and optimizedto define a septum lengththat provides maximumtransmission at each chan-

nel’s frequencies into the appropriate port. The entireT-junction response is validated with the 3-D EM solverusing the calculated septum length from the circuitdomain optimizer. Figure 5 is a full wave analyzedresult using the optimized septum length from the cir-cuit simulator.

Figure 4. H-plane T-junction and waveport de-embedding:(a) 3-D view and (b) top view for T-connection.

(a)

Input(Port 1)

Ch.1(Port 2)

Ch.2(Port 3)L

Port De-embeddingReference Planes

(b)

When the analyzed structure iscomplex and/or when tuning and

optimization is involved, EMsimulators require more computation

time than circuit-based simulators.

Figure 6. Cosimulation schematic for decomposed seventh-order Chebyshev waveguidechannel filter.

1) Half Wavelength Waveguide Section from Circuit Model

2) Parameterized Full Wave EM Model for Inductive Window Coupling Generated by EM Solver

Figure 5. H-plane T junction model response of EM simulator using theoptimized septum length (L) on the circuit domain.

X1 = 7.50 GHzY1 = −3.08

X2 = 7.50 GHzY2 = −3.08

X3 = 7.50 GHzY3 = −17.99

Y1dB(S(p1,p1)) [dB]Setup1: Sweep1

Y1dB(S(p2,p1)) [dB]Setup1: Sweep1

Y1dB(S(p3,p1)) [dB]Setup1: Sweep1

TeeModel_wr112_opt0.00

−5.00

−10.00

−15.00

−20.006.50 7.00 7.50 8.00 8.50 9.00

s11,

s21

, s31

, (dB

)

Freq [GHz]

3

2

Waveguide Filter DesignThe second step in the cosimulation technique is thedesign of waveguide channel filters. A seven-section0.01-dB ripple doubly terminated Chebyshev wave-guide filter is used for demonstration. To design thewaveguide channel filter, the entire filter structurecan be decomposed into the half-wavelength res-onator section and inductive iris window couplingsection, as shown in Figure 6 [3]. For resonator sec-tions, the TE01 dominant mode rectangular wave-guide model in the circuit simulator library is used.For the inductive window coupling, a parameterizedEM model will be generated with the EM solver. Byvarying the window width from 0.15 in to 0.9 in using

TABLE 1. Initial filter design.(a) Ch1.Filter, fc1 = 7,500 MHz, BW = 500 MHz.

Resonator Cavity Inductive No. Length (in) Window (in)

1 0.8703 0.63 Ext. coupling

2 0.9895 0.3894 Int. coupling

3 1.015 0.3288 Int. coupling

4 1.018 0.3175 Int. coupling

5 1.015 0.3175 Int. coupling

6 0.9895 0.3288 Int. coupling

7 0.8703 0.3894 Int. coupling

0.63 Ext. coupling

Figure 9. Cosimulated optimization result and full EMsimulated result comparison, T-shape connection diplexer:(a) insertion loss and (b) return loss.

dB(y1)HFSS_diplexer_y

lY1

Y1 0

Ansoft CorporationXY Plot 2

diplexer_T_T_iris1_h_opti1_silver

7.00E09 7.25E09 7.50E09 7.75E09 8.00E09

Freq (Hz)8.25E09 8.50E09 8.75E09

0.00

−10.00

−20.00

Co_simulation(NMF)HFSS

−30.00S11

(dB

)

−40.00

−50.00

10.00

Ansoft CorporationXY Plot 1

diplexer_T_T_iris1_h_opti1_silver

HFSS for Ch.1

7.00E09 7.25E09 7.50E09 7.75E09 8.00E09

Freq (Hz)8.25E09 8.50E09 8.75E09

S21

and

S31

(dB

)

HFSS for Ch.2

0.00

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.00

−90.00

ldB(S31)Designer

Y1

dB(y3)HFSS_diplexer_y

Y1 0

dB(y5)HFSS_diplexer_y

Y1 X

dB(S21)Designer

Co-simulation for Ch.1 Co-simulation for Ch.2

(a)

(b)

dB(S11)NMA1

Y1 0

The circuit-based simulator uses acombination of EM- and circuit-basedmodels, and the optimization iscarried out using the circuit simulator.

(b) ch2. Filter, fc1 = 8150 MHz, BW = 500 MHz

Resonator Cavity Inductive No. Length (in) Window width (in)

1 0.772 0.55 Ext. coupling

2 0.8691 0.3258 Int. coupling

3 0.8866 0.2763 Int. coupling

4 0.8891 0.2671 Int. coupling

5 0.8866 0.2671 Int. coupling

6 0.8691 0.2763 Int. coupling

7 0.772 0.3258 Int. coupling

0.55 Ext. coupling

Figure 8. Diplexer design optimization parameters for L-shape connected channel filters.

w3

w2

w1

d1s1

s2s3

d

d1 s1 s2 s3

w1

w2

w3

h

Figure 7. Inductive window coupling and port de-embed-ding line (blue): (a) 3-D view and (b) top view.

p11

(a)

Port De-EmbeddingReference Plane

W

(b)

80 April 2007

April 2007 81

0.025-in steps with a fixed window wall thickness of0.1 in, a parameterized numerical EM model is pre-calculated for later circuit model cosimulation.Figure 7 shows the inductive window and its de-embedded reference plane [4]. Once a parameterizedinductive window model is obtained, the same EMmodel will be reused for all different sizes of induc-tive window coupling in the filter and will not berecalculated for each coupling window. Thus, this isan example where a full-wave EM solver generates acircuit model. This method is also very useful when acircuit model is not available in the library, and a cus-tom circuit model can be generated without any spe-cialized programming skills.

Table 1 shows the initial design values obtained forthe inverter-coupled Chebyshev filter using circuitmodels [5]. However, the thickness of the inductivecoupling window is not included in this initial designvalue. To find the readjusted waveguide length andopening width of the coupling window, a cosimulationoptimization is performed to get the final filter dimen-sions. Now, the filter model can be combined with aprecalculated T-junction model to design H-planediplexers.

Diplexer OptimizationTo obtain the final diplexer dimensions, both chan-nel filters are combined with an H-plane T-junctionin a circuit simulator. Figure 8 shows the design vari-ables for the L-shape diplexer. Resonator length,inductive window width, T-junction septum length,and location are optimized to match the two channelfilters to the T-junction. In this simulation, the wave-guide length from the T-junction reference plane tothe first external coupling window of the filter isoptimized. The previously stated diplexer specifica-tion is applied to the insertion and return loss at eachchannel band as optimization goals and the finaldesign parameters are optimized. To expedite theconvergence in optimization, initial diplexer dimensions

Figure 10. Cosimulated optimization result and full EM-simulated result comparison, L-shape connection diplexer:(a) insertion loss and (b) return loss.

Y1 0dB(S21)NWA1

ldB(S31)NWA1

Y1

dB(y3)diplexer_wr112_

Y1 0

dB(y5)diplexer_wr112_

Y1 X

dB(S11)NWA1

Y1 0

lY1dB(y1)diplexer_wr112_

10.00

Ansoft CorporationXY Plot 2

diplexer_h_L_junction_iris_opt

7.00E09 7.25E09 7.50E09 7.75E09 8.00E09

Freq (Hz)8.25E09 8.50E09 8.75E09

S11

(dB

)

HFSS

0.00

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.00

−90.00

(b)

Co_simulation (NMF)

10.00

Ansoft CorporationXY Plot 3

diplexer_h_L_junction_iris_opt

HFSS for Ch.1

7.00E09 7.25E09 7.50E09 7.75E09 8.00E09

Freq (Hz)8.25E09 8.50E09 8.75E09

S21

and

S31

(dB

)

HFSS for Ch.2

0.00

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.00

−90.00

Co_simulation for Ch.1 Co_simulation for Ch.2

(a)

The EM circuit cosimulation techniqueeffectively reduces the overall designtime in passive component design,while achieving accurate results.

Figure 12. Electric field plots at each channel filter, T-shape connection diplexer: (a) electric field plot at channel 1 center frequency, fc1 = 7.5 GHz, and (b) electricfield plot at channel 2 center frequency, fc2 = 8.15 GHz.

(b)

(a)

Figure 11. Electric field plots at each channel filter, T-shape connection diplexer: (a) electric field plot at channel 1 center frequency, fc1 = 7.5 GHz, and (b) electricfield plot at channel 2 center frequency, fc2 = 8.15 GHz.

(a)

(b)

82 April 2007

must be close to the final values. Otherwise, the opti-mization result will take a long time to converge or itmay not converge.

Figures 9 and 10 show final optimized cosimulationresults. A final EM simulation of the entire physicalstructure is carried out to compare and validate the cir-cuit-based results with the EM-based results.

PostprocessingAn advantage of 3-D EM simulators is the availabili-ty of field plots for the volume inside the filter struc-ture. Figures 11 and 12 show the electric field plots ateach filter’s center frequency. From the field distribu-tion, the peak electric field area inside the diplexercan be displayed, which in turn relates to the maxi-mum peak power inside the filter structure [6]. Amagnetic (H)-field plot provides the high currentareas that relate to the average power handlingcapacity.

Thermal AnalysisThe temperature of the filter plays an importantrole in its performance. The temperature of the filteris related to the ambient temperature and the tem-perature rise due to excessive power. When exces-sively high power levels are applied to the filter, orwhen the unit is exposed to high ambient tempera-tures, the filter structure is faced with structuraldeformations. As a result, the filter response isdetuned from the nominal response. Typically, thefrequency drift range is confirmed by measuringthe filter response. Temperature-compensatingmaterials or structures could be used at this stage, ifwarranted. If software that can accurately predictthe environmental effects is available, the iterative

design cycles between manufacturing and measure-ment can be reduced.

Figure 13 shows the inside temperature data atsteady state when 1 kW average power is applied tothe common input port of the diplexer at a channel 1passband edge frequency (7.72 GHz). Hot and coolspots inside the diplexer are displayed using AnsoftePhysics thermal analysis software. Due to the powerdissipation on the inside conductor surface of thewaveguide, surface temperature rises up to about 90 ◦C.Figure 14 shows the time it takes for the filter to reachthe highest temperature from 0 ◦C using transient ther-mal analysis. However, the temperature drift responseof the diplexer from the structural deformation by heatis not yet available; this function is currently underdevelopment.

ConclusionThe EM circuit cosimulation technique effectivelyreduces the overall design time in passive componentdesign, while achieving accurate results. This methodcan be extended to other passive component designs,such as comb-line filter and dielectric resonator filter,with a higher-order mode waveport calculation.

References[1] D. Crawford, “Designing high performance cavity filters,” Ansoft

2003/Global Seminars [Online]. Available: www.ansoft.com[2] Y. Rong, H.-W. Yao, K.A. Zaki, and T.G. Dolan, “Millimeter-wave

Ka-band H-plane diplexers and multiplexers,” IEEE Trans.Microwave Theory Tech., vol. 47, no. 12, pp. 2,325–2,330, Dec. 1999.

[3] H.-W. Yao, A.E. Abdelmonem, J.-F. Liang, X.-P. Liang, K.A. Zaki,and A. Martin, “Wide-band waveguide and ridge waveguide T-junctions for diplexer applications,” IEEE Trans. Microwave TheoryTech., vol. 41, no. 12, pp. 2,166–2,173, Dec. 1993.

[4] F.M. Vanin, D. Schmitt, and R. Levy, “Dimensional synthesis forwide-band waveguide filters and diplexers,” IEEE Trans.Microwave Theory Tech., vol. 52, no. 11, pp. 2,488–2,495, Nov. 2004.

[5] Ansoft Designer [Online]. Available: www.ansoft.com[6] C. Wang and K.A. Zaki, “Analysis of power handling capacity of

band pass filters,” in 2001 IEEE MTT-S Int. Microwave Symp. Dig.,May 2001, vol. 3, pp. 1,611–1,614.

An advantage of 3-D EM simulators is the availability of field plots for thevolume inside the filter structure.

Figure 13. Temperature data inside the diplexer.

Temperature [°C]

9. 5190e+0019. 3165e+0019. 1140e+0018. 9115e+0018. 7090e+0018. 5064e+0018. 3039e+0018. 1014e+0017. 8989e+0017. 6964e+0017. 4939e+0017. 2914e+0017. 0889e+0016. 8864e+0016. 6838e+0016. 4813e+0016. 2788e+001

Figure 14. Transient thermal analysis of the temperatureof the diplexer.

diplexer_wr112_full_size1

Avg

Val

(WG

) [°

C]

80.00

60.00

40.00

20.00

0.000.00 2,000.00 4,000.00 6,000.00 8,000.00

Time [s]

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