3-d em simulations for passive devices

Digital Object Identifier 10.1109/MMM.2008.929696

50 December 20081527-3342/08/$25.00©2008 IEEE

©DIGITAL STOCK

Ming Yu, Antonio Panariello, Mostafa Ismail, and Jingliang Zheng

Microwave/RF passive devices aremission-critical components for avariety of electronics systems.Using three-dimensional (3-D)electromagnetic (EM) field simu-

lators to design such devices is considered a must formost microwave/RF engineers today. Since today’spersonal computer outperforms many super com-puters from ten years ago, commercial EM simula-tors are widely available and can solve many practi-cal problems on a low-cost desktop system. At thesame time, many companies continue to spend sig-nificant effort on their in-house EM software tools totackle very specific problems for best efficiency. Inmany cases, virtual prototyping can take place insideEM simulators rather than in a real lab bench. Asmicrowave industries continue to invest heavily inEM simulators, it is very important to understandtheir capabilities in order to use them effectively. Inthis article, resonators, filters, ortho-mode transduc-ers (OMTs), and switches are selected as examples ofpassive components to be solved and designed in a

Ming Yu ([email protected]), Antonio Panariello, Mostafa Ismail, and Jingliang Zheng are with COM DEV,

Cambridge, Ontario, Canada.

Authorized licensed use limited to: University of Waterloo. Downloaded on November 25, 2008 at 20:50 from IEEE Xplore. Restrictions apply.

story-telling fashion using EM simulators and state-of-the-art CAD techniques. These components typicallyhave a very high number of design parameters andcomplex geometry. They are commonly used andconsidered as essential components of satellite-basedcommunication systems.

The state of the art of EM analysis of complex passivestructures has experienced tremendous progress in the

last two decades. The fundamental EM code is often con-sidered mature and well established. EM simulators canbe divided into two main types: modal-analysis-basedand element mesh-cell-based. The word cell is used as ageneral term for elements, which can also take on differ-ent names in different software. For example, cell isequivalent to “tetrahedron” in an Ansoft HFSS simula-tor. Table 1 gives a short summary of EM simulator types

and their applications. Interested readers are recom-mended to check a recent book [1] for more details. Themarket offers quite a variety of 3-D EM simulators, mak-ing it very difficult for microwave engineers to choosethe most suitable one for a given problem. It is theauthors’ opinion that there is no bad software, only badsoftware usage. It is important for the user to understandthe weaknesses and strengths of different tools and act

accordingly. The other tricky part istranslating the EM model into actualdimensions considering tolerancesand manufacturing processes, but thisis beyond the scope of this article.Since any commercial software willtypically give the correct answer ifproperly used, the focus of this articleis on selecting the best tools for agiven problem. Popular CAD tech-niques that work nicely with thosesimulators will also be discussed.

Simulators considered in this arti-cle are those available to the authorsor their colleagues. A complete list isgiven in Table 2, which by no meansrepresents any endorsement by theauthors. Readers are encouraged tovisit the listed Web sites for moreinformation. Typical parametersneeded in designing passive devicesare: resonant frequencies, quality fac-tor (Q), scattering matrix, electro-magnetic fields, and voltages.

Resonant Frequencies of One or Two Resonators—Eigen Mode SolversAlthough a single resonator withoutany external coupling does not existin practice, it is the starting point ofcoupled resonator filter design. Adesigner often uses an eigen modesolver to model a completelyenclosed resonator to obtain resonantfrequencies and quality factors. Ithelps to select basic filter technology

such as coaxial combline, waveguide, or dielectric anddetermine the spurious mode locations. A coupled res-onator eigen mode solution is also desired in order todesign coupling mechanisms such as irises and probes.

Interestingly enough, most modal-analysis-basedsimulators do not provide eigen mode analysissince they can only deal with canonical structuressuch as standard waveguide sections. Often analytical

December 2008 51


52 December 2008

solutions (close form) exist forthose types of resonators any-way using hand calculations or,more conveniently, Excel for-mulae. 3-D EM eigen modesolvers are the most commontools for filter designers todaybecause the problem is relative-ly small and it is perceived thatlittle effort is needed.

A combline resonator thatwas studied extensively in litera-

ture [2] is used as an example to illustrate the softwarecapabilities for eigen mode simulation. As shown inFigure 1(a), it consists of two simple conductive cylindri-cal objects of φ1.5 × 1.26 in and φ0.42 × 1.12 in. As thisproblem can also be solved by modal-analysis-based sim-ulators such as mode-matching codes and two-dimen-sional (2-D) finite element model (FEM) code FlexPDE, itis an ideal candidate to compare with cell-based EM sim-ulators such as Ansoft HFSS and CST microwave studio(MWS). Table 3 summarizes the results with comparableaccuracy from different simulators.

This problem is easily solved by both HFSS version 11and MWS 2008 SP2, which produce similar answers. Itis noticed that MWS converges smoothly with anincrease in the number of cells. For HFSS, it is oftenmore efficient to use polygons to represent the cylindri-cal objects, which leads to fewer cells used than forMWS, which actually prefers perfect cylindrical-shapedobjects. The tested version of MWS 2008 allows import-ing of HFSS version 11 files directly, which makes thecomparison of many examples in this article much eas-ier. At this time HFSS cannot import MWS files, butother common CAD formats like SAT/STEP can beused for data exchange. The virtual object shown inFigure 1(b), an artificial object added into the model, isused per HFSS recommendation. In this case, it is acylinder that is slightly bigger than the φ0.42 × 1.12in resonator. It forces the HFSS mesh engine to allocatemore mesh cells near the resonator and leads to betteraccuracy or faster convergence with a lower number oftotal mesh cells. This technique relies on the user’s EMfield knowledge for a given structure. It is also worth-while to point out that simply increasing the number of

Figure 2. A more realistic resonator design. (a) HFSSmodel. (b) MWS mesh view.

(b)(a)z

Figure 1. A combline resonator. (a) Single-resonatormodel. (b) Virtual object and its mesh.

(b)(a)

TABLE 1. Types of EM simulators.

Simulator Type Application Structure Parameter

Modal Analysis

Mode Matching Very general, can be applied Canonical Structure Resonant Frequency Scattering Integral Equation to any filter type Matrix, Electromagnetic Fields

Cell Based

Frequency Domain FEM Narrow-band Structure Canonical and Arbitrary Shape Eigen Value, Q, Resonant Time Domain FIT/FD-TD Wide-band Structure with Frequency, Scattering Matrix,

low stored energy Electromagnetic Fields

TABLE 2. Simulators considered in this article.

Simulator Type Method Web Link

Ansoft HFSS Frequency Domain FEM www.Ansoft.com

CST MWS Time Domain FEM/FIT www.Cst.de

In House Code Frequency Domain Mode Matching www.Comdev.ca

FEST 3D Frequency Domain Integral Equation www.Aurorasat.es

MICIAN Frequency Domain Mode Matching www.Mician.com

FLEX PDE Frequency Domain FEM 2-D www.Pedsolutions.com


December 2008 53

mesh cells in bothsimulators will leadto similar results inthis simple case.

The next exam-ple evolves fromFigure 1(a) into amore realistic res-onator design asshown in Figure2(a). Cylindricalholes of φ0.15 inand bottom radiusof 0.2 in wereadded to the res-onator. It is interest-ing that these littlefeatures make theconvergence much harder. The difference between theresonant frequencies by HFSS and MWS is more than15 MHz. The MWS mesh shown in Figure 2(b) seems tofavor this structure more than HFSS as it gives betterresults. In this case, increasing the number of cells inHFSS to over 100,000 did not help much and the PCused ran out of memory.

The remedy for better convergence and accuracy is toutilize the geometrical symmetry to add two magneticwall boundary conditions after cutting away three-fourths of the object as shown in Figure 3. By combiningthe symmetry and virtual mesh (HFSS only), a satisfacto-ry comparison of resonant frequencies can be establishedfor both simulators (HFSS: 1.932 MHz, MWS: 1.928MHz). Up to this stage the process is valid even if the cav-ity has square cross sections. For cylindrical cavities,using one-eighth of the object can further improve con-vergences (HFSS: 1.932 MHz). This process can be repeat-ed until an infinitely thin slice of the object is left. A 2-DFEM solver like FlexPDE is enough to solve it (note that itcannot handle cavities with square cross sections).

Electrical field strength is another parameter ofinterest as it is used for power breakdown analysis [3].The electrical field values in HFSS are normalized to1 V/m, while in MWS, field values are calculated basedon 1J stored energy. In order to compare the results, themaximum electric field Emax is normalized to thesquare root of stored energy. Table 4 shows very goodagreement under the condition that enough mesh cellsare used. Figure 4 shows the electrical field distributionnear the high field region by both simulators.

All those results are obtained because the mesh cellscan be increased by a factor of four using symmetry.The example reveals that, when more details are addedto the model, especially with large aspect ratios goodconvergence is much more difficult to achieve withoutproper care for the number of mesh cells.

As demonstrated through multiple examples, bothHFSS and MWS provide adequate results for most

practical applications.From the authors’ expe-rience, the eigen modesolver from MWS pro-vides more stable resultswhen using a smallernumber of mesh cells.Even if the number ofmesh cells is not enough,the resonant frequenciesare only off by a smallamount, but with veryclose estimated Q factors,

Figure 3. A quarter-cutresonator model.

Figure 4. Electrical field displays from HFSS and MWS.(a) HFSS. (b) MWS.

(b)(a)x

z

y

TABLE 3. Results from different simulators with the same accuracy.

Frequency (GHz) Q Number of Cells Comments

In-House Codes 1.87 5592 Mode Matching Technique

FlexPDE 1.877 5608 2-D FEM

HFSS 1.8875 – 22345 Using a cylinder

1.8812 – 14304 Using a polygon

1.8805 – 9442 Using a polygon plus virtual object

1.8739 5391 10437 Using a cylinder plus virtual object

CST MWS 1.851 5353 7488

1.865 5379 48120

1.869 5394 15600

1.870 5387 363968

TABLE 4. Electrical field calculation.

Simulator HFSS CST MWS

Max E Field (V/m) 1 1.97e9

Stored Energy (J) 2.52e-19 1

Normalized Emax 1.99e9 1.97e9


54 December 2008

say 5%. As Q is calculated using a perturbationmethod, the solver runs very fast under lossless con-ditions. That allows designers to quickly cyclethrough many design options without worrying aboutconvergence too much in the early stages. As it will beshown later, when the gap between the resonator andcavity top wall (lid) is very small, HFSS will providebetter results. Modal-analysis-based methods or 2-DFEM solvers such as FlexPDE are definitely multiplemagnitudes faster, but they can only handle a smalleramount of canonical structure types.

Wide-Band DevicesWhen the proportional bandwidth of a device is morethan 10%, it is often considered a wide-band design(>5% in some cases is also treated as wide band). Thisclass of devices is most suitable for all EM simulatorsto produce tuneless designs. Modal-analysis-basedtechniques such as mode-matching or integral equa-tion techniques are often the most effective choice ifthe filters can be constructed using the existing mod-ules in the simulator. Three simulators of this kind arelisted in Table 2.

As an example, an OMT is shown in Figure 5(a). Itsvertical polarization mode works in two bands while itshorizontal polarization mode works only in the lowband. All dimensions of the OMT are given in Table 5.Figure 5(b) and (c) shows the return loss of two modessimulated by two different full-wave analysis tools:HFSS and in-house code based on the mode-matchingtechnique. The simulation results from both tools arevery close. On a Quad-core 2.66-GHz PC with 16 GB ofRAM, the HFSS simulation takes about 48 minutes(partial band only). The in-house mode matching codeon a dual core 3.4-GHz PC with 2 GB of RAM takesonly about seven seconds for one single-frequencypoint and about ten minutes for the full-frequencyband. It is worthwhile pointing out that the first PCshould be multiple times faster than the second (for thesame problem).

In modal-analysis-based methods (such as modematching), the whole structure needs to be divided intoregions, which are either uniform or canonical. Forregions with different shapes, the mode groups for rep-resenting the EM fields are different. For different inter-faces between two or more regions, the integral equa-tions derived from boundary conditions are different.This means that there are many different procedures forsolving problems in different structures. Which proce-dure is suitable for a given problem depends not onlyon the shapes of two or more neighbored regions in thatproblem but also on the shape of the interface betweenthe regions. In order to solve more types of problems,all EM simulators based on modal analysis techniqueshave their own module library with dozens (or evenhundreds) of modules, which can be used to build mostpractical waveguide structure problems. However, itcannot be used to solve all 3-D EM problems with anarbitrary shape or overly complicated structure. Forsuch problems, mesh-cell-based methods such as HFSSor MWS are more powerful alternatives.

Figure 6 shows a ridged waveguide lowpass filter.The filter body has a small waveguide with a few ridgedwaveguide sections and a transformer at each of its twoports. Again, the filter is simulated by MWS and HFSSusing a moderate number of mesh cells. Reasonableagreement was achieved as shown in Figure 6(c) and(d). The structure was originally designed using in-house software (modal analysis) and agreed nicely with

Figure 5. An ortho-mode transducer modeled by HFSSand in-house mode matching code. (a) An ortho-modetransducer. (b) Horizontal polarization. (c) Vertical polar-ization.

(a)

Ret

urn

Loss

of V

ertic

al M

ode

(dB

)

0

−5−15−20−25−30−35−40−45

−10

16 18 20 22 24 26 28 30Frequency (GHz)

(c)

0

−5

−10

−15

−20

−25

−30

−35

−40

Ret

urn

Loss

of H

oriz

onta

l Mod

e (d

B)

16 17 18 19 20 21Frequency (GHz)

(b)

In-House Code

HFSS

In-House Code

HFSS

Port 1 A B C D E

JH

Port 2

Port 3

K

I

LF

G


December 2008 55

measured data as shown in Figure 6(e). It is interestingto point out in this case that both HFSS and MWS resultsare actually lower in frequency compared with mea-sured data, because not enough mesh cells are used. Thelessons learned from this example are that even if closeresults from two simulators are obtained; they may stillnot be valid.

Let’s consider another high-low impedance low-pass filter at the S-band. The filter provides rejectionmainly in the X-band and it is implemented usingcoaxial technology as shown in Figure 7(a) and (b). Thefilter’s complicated geometry and dielectric loadingmakes it difficult to solve using modal-analysis-basedsimulators. On the other hand, it is ideal for simula-tions by MWS and HFSS. The results are in agreementand show very similar return loss, and rejection roll-off

at 3.66 GHz (simulation times of 5 min, 38 s and 5 min,28 s, respectively) as shown in Figure 7(c) and (d). Inthis case, the number of mesh cells was increased sig-nificantly where there is strong variation of field com-ponents. Once mesh convergences were achieved, bothfrequency-domain and time-domain solvers take asimilar amount of time. The result was also later con-firmed by actual measurements.

The next example is a waffle iron filter shown inFigure 8, which provides good selectivity for up to fourtimes the center frequency. This device has a very widestop band range given the ability to reject TEM0, but therejection level of each mode is different. Moreover,modes with a horizontal component of the electric fieldcan excite slot modes, which can propagate through thestructure. For these reasons a waffle iron filter is

Figure 6. A ridged waveguide lowpass filter. (a) 3-D view from HFSS. (b) Cross section view. (c) MWS. (d) HFSS. (e)Simulated (in-house code) and measurements.

(a) (b)x

0

−10

0.00

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.00

−20

−30

−40

−50

−60

−706 6.5 7 7.2

S1,1S2,1

6.00 6.20 6.40 6.60 6.80 7.00

0

−10

−20

−30

−40

|S| (

dB)

−50

−60

−70

−80

S11(In-House Code)

S21(In-House Code)

S11(Measure)

S21(Measure)

Frequency (GHz)

(e)

6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2

Frequency (GHz)

(c)

Frequency (GHz)

(d)

Curve InfodB (S (Wave Port 1, Wave Port 1))Setup 1: Sweep 1

dB (S (Wave Port 1, Wave Port 2))Setup 1: Sweep 1

7.20


56 December 2008

considered a challenging structure to analyze. The EManalysis is more complicated due to the involvement ofhigher-order modes, as well as the large frequencyrange of interest. The best analysis tool for this structureis the modal analysis technique, which is well known in

literature. Getting accurate results with HFSS and MWSsolvers is more difficult but is still possible with rea-sonable computational effort.

The frequency response to the TE10 mode usingMWS and HFSS (interpolating sweep) are shown inFigure 8(c) and (d). In the passband, both simulatorsgive excellent results that are confirmed by measureddata (not shown). In theory, the out-of-band charac-teristics for the TE10 mode excitation should be veryclean (without any spikes) because the model is sym-metrical. It appears that MWS met the challenge andcan provide faster and more accurate results (exceptsome minor glitches/ripples). The HFSS response hasmultiple “glitches” due to its different meshing mech-anism. It also implies that mode conversion is actual-ly happening. With a further increase in the numberof mesh cells, the HFSS response can be improved atthe expense of simulation time. For this example,MWS has an easier time dealing with this very com-plicated problem.

To perform complete analysis of the structure, it isimportant to characterize the response for higher-ordermodes as shown in Figure 8(e) using MWS. For the pur-pose of this article only TE01 (blue), TE20 (green), andTE30 (red) are considered. When asymmetric disconti-nuities exist in the feeding network, the energy of theTE10 can couple into TE20, and so on. It is obvious thatFigure 8(e) reveals that actual rejection will be much

Figure 7. A high-low impedance lowpass filter. (a) MWS model of a lowpass filter. (b) Cross-section view. (c) Simulatedresponse by MWS. (d) Simulated response by HFSS.

(a) (b)

0

−10

−20

−30

−40

−50

−60

−70

−801 2 3 4 5 6 7 8

Frequency (GHz)

S-Parameter Magnitude (dB)

(c)

−10.00

0.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.001.00 2.00 3.00 4.00 5.00 6.00 7.00

Frequency (GHz)

(d)

Ansoft Corporation XY Plot 1 HFSS Design 1Curve Info



8.00

TABLE 5. Dimensions of designed OMT (unit: inch).

Waveguide Section Width Height Length

Port 1 0.368 0.184 0.200

Port 2 0.510 0.255 0.200

Port 3 0.368 0.368 0.200

A 0.368 0.209 0.170

B 0.368 0.222 0.183

C 0.368 0.278 0.192

D 0.368 0.288 0.172

E 0.368 0.368 0.054

F 0.368 0.169 0.300

G 0.368 0.169 0.300

H 0.368 0.368 0.030

I 0.368 0.368 0.347

J 0.501 0.135 0.045

K 0.532 0.282 0.074

L 0.347 0.050 0.030


December 2008 57

less when considering excitation of those higher-ordermodes. For example, Figure 8(e) predicts the rejection at16 GHz will be around 30 dB, while Figure 8(d) givesabout 80 dB.

Narrow-Band DevicesNarrow-band devices such as filters with a band-width less than 5% are very sensitive to manufactur-ing tolerances and the use of tuning elements isrequired in order to achieve the desired perfor-mance. For this reason the designer needs to under-stand the required accuracy of the EM analysis,which is also linked to the tunability of the device.This consideration will establish a good compromisebetween accuracy and computational effort. In many

cases, complete EM simulation of the device may beunnecessary as bench tuning on the actual hardwarecould make up the differences. When using this phi-losophy, only one- and two-resonator eigen modeanalysis is sufficient to design a complete narrow-band filter.

Because of wide availability of EM simulators, a newtrend for many microwave designers is to model thecomplete device in a 3-D EM solver. This approach willprovide complete information on the device, such asresponse shape distortion due to frequency variation ofcoupling elements, unwanted coupling effect, spuriousresponse of high order mode, and field values forpower handling analysis. Armed with this information,a designer can now finish the design in one iteration.

Figure 8. A waffle iron lowpass filter. (a) Waffle iron filter model. (b) Cross section of waffle sections. (c) MWS simulation.(d) HFSS simulation. (e) TE01 (blue), TE20 (green), and TE30 (red) modes.

(a) (b)

2

0

−50

−100

−150

−200

S1,1S2,1


Frequency (GHz)10 15 20 25 30 35 40

(c)

Ansoft Corporation

Frequency [GHz]

(d)

0.00

−50.00

−100.00

−150.00

−200.00

HFSS Design1XY Plot 1

10.00 15.00 20.00 25.00 30.00 35.00 40.00

Curve InfodB (S(Wave Port 1, Wave Port 1))

Setup 1: Sweep 1dB (S(Wave Port 1, Wave Port 2))

Setup 1: Sweep 1

0

−50

−100

−150

−20016 20 30 40 45

S2(2),1(2)S2(3),1(3)S2(8),1(8)


Frequency (GHz)

(e)


58 December 2008

Finally, the true first-pass success is achieved; i.e.,design, build, tune, and success the first time.

For a narrow-band filter, time-domain techniquesrequire long simulation times due to the slow energydecay and hence are not suitable for this application.MWS will be less effective unless using the newlyintroduced modal order reduction (MOR) solver. In thenext example, a combline four-pole Chebyshev filterwas studied with HFSS and the MWS (MOR) solver.Figure 9(a) illustrates the filter model. It is well knownthat this type of filter has very good tunability. If thecenter frequency deviation is less than half of the filterbandwidth, the results are often considered adequate

for most practical applications. But when power han-dling and temperature compensation also come intopicture, it will become more important to achievehigher accuracy.

Figure 9(b) shows the results of the MWS (MOR)simulation using two different meshes. When mesh sizegoes from a few hundred mesh cells to a couple ofmillion, the change on frequency alignment is less than5 MHz. Similar results are achieved with HFSS asshown in Figure 9(c), where the mesh sizes are 18,000(red) and 62,000 (blue). The run time for both HFSS andMWS is very similar. The MWS result is slightly lowerin frequency, which may imply not enough mesh. It isbelieved that HFSS’s result is closer to reality.

Figure 10(a) shows a variation of combline filterheavily loaded by a capacitive “mushroom head.” Thegap between the resonator and cavity wall is extremelysmall compared with the resonator length. The use ofhexahedral mesh in MWS is not suitable for this appli-cation. In this case, even driving up the mesh size toover one million, MWS still gives inaccurate results. Onthe other hand, HFSS had a much easier time in dealingwith this structure and achieved good simulationaccuracy as shown in Figure 10(c). Simulation time was49 min, 20 s with a mesh size of 147,017 tetrahedrons.Since MWS also provides tetrahedral meshes, the simu-lation was rerun in the frequency domain. It turned outthat MWS also converged and produced the correctanswer as shown in Figure 10(d). In this case, HFSS isquite a bit faster.

From all the cases presented, it is clear that it is pos-sible to achieve good results independent of the simu-lator used. The key is that the user should understandthe limitations of the software and should have a goodunderstanding of the behavior of the structure underanalysis in order to recognize simulation error and actaccordingly.

CAD Techniques for EM SimulatorsAs demonstrated in the previous sections, state-of-the-art EM simulators can accurately model most passivedevices with good accuracy, however, they are still verycomputation intensive, which makes them impracticalto use in direct optimization for most practical applica-tions. Special CAD techniques such as neural-network[6] and space-mapping optimization have proven to bevery efficient for the modeling and design ofmicrowave circuits. Space mapping uses a fast coarse(circuit) model for optimization while the fine model(full-wave simulation) is used only for verification orcalibration of the coarse model. For example, a space-mapping-based algorithm for filter design has beendeveloped in [3] and successfully applied to design ten-channel dielectric resonator (DR) output multiplexerswith more than 100 design parameters. In this section,we consider the application of space-mapping opti-mization to high-order DR filters and T-switches.

Figure 9. (a) A combline four-pole Chebyshev filter. (b)MWS MOR analysis. (c) Filter response versus HFSSmesh size.

(b)Frequency (GHz)

0

−10

−20

−30

−40

−504.00 4.05 4.10 4.15 4.20

S1,1S1,1_4S1,2S1,2_4

S_Parameter Magnitude (dB)

(c)Frequency [GHz]

−50.00

−40.00

−30.00

−20.00

−10.00

0.00

Y1

4.00 4.05 4.10 4.15 4.20

(a)

uWV


December 2008 59

High-Order DR Filter DesignHigh-order DR-loaded cavity filters are used in theinput multiplexer of a satellite system because of theirhigh quality factor and excellent in-band performance.Direct EM-based optimization of such filters is formida-ble because of the large number of design parametersand the complexity of the filters. A variation of the filterdesign algorithm in [3] has been applied to design theten-pole DR-loaded cavity filter shown in Figure 11.This filter is typically used in theinput multiplexer stage of a satel-lite communication system. Thefilter works in the Ku-band with acenter frequency of 10.7 GHz and abandwidth of 41 MHz (0.38%). Thefilter has two pairs of transmissionzeros to ensure both near pass-band and out-of-band rejectionsare met. It also has four complextransmission zeros to equalize in-band group delay.

The filter has 25 design para-meters. The input/output cou-plings are realized by couplingprobes. Sequential and positivecross couplings are realized byirises while negative cross cou-plings are realized by couplingprobes (see Figure 11). HFSS isused for fine-model EM simula-tion. The ideal filter response andthe EM simulation at the initialdesign parameters are shown inFigure 12(a). The algorithm termi-nated at the sixth iteration. Theideal filter response and the EMsimulation response at the optimalspace mapping iteration areshown in Figure 12(b). An EMsimulation of this filter takes 2.5hours on a 3.6-GHz CPU and 3.5-GB RAM machine.

T-Switch DesignThe T-switch [4] is a four-portelectromechanical RF switch that iscommonly used for redundancy inspacecraft telecommunicationspayloads. The T-switch presentsdesign challenges because theswitch topology necessitates thatalternate paths have some ele-ments in common (near port inter-faces) and other elements that areexclusive and different. The designof any path is therefore constrainedby the design of alternate paths. A

typical coaxial T-switch is shown in Figure 13. Theswitch consists of six paths. From symmetry, the wholeswitch can be designed by considering only two paths asshown in Figure 13. Each of the two paths works on a dif-ferent state than the other (that is, when one path is “on”the other path is “off”). The two paths share some com-mon parameters. In [4] a multiple space-mapping algo-rithm has been developed for T-switch design. The algo-rithm iteratively enhances the coarse model of each path

Figure 10. A heavily loaded combline filter. (a) MWS model. (b) Cross section view.(c) HFSS simulation. (d) MWS frequency domain solver with tetrahedrons mesh type.

Curve InfodB (S (Wave Port 1,Wave Port 1))Setup 1: Sweep 1dB (S (Wave Port 1,Wave Port 2))Setup 1: Sweep 1

0.00

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

Y1

Ansoft Corporation HFSS Design1XY Plot 1

145.00 150.00 155.00 160.00 165.00 170.00 175.00

(c)Frequency [MHz]

(a) (b)

(d)

−0

−10

−20

−30

−40

−50

−60

−70145 150 155 160 165 170 175

S1,1S2,1S1,2S2,2

Frequency (MHz)



60 December 2008

by establishing a mapping between the coarse and finemodel parameters. The two coarse models of the switchpaths proceeded by the mapping (enhanced coarse mod-

els) are then optimized to meet the required specifica-tions. In this optimization, the common parameters inthe two paths are restricted to the same value. The algo-rithm stops if the solution is acceptable.

The design specifications of the T-switch are that the returnloss of both paths is less than 25 dB in the C- and Ku-bands:

• |S11| < −25 dB• 3 GHz < freq < 5 GHz• 10 GHz < freq < 13 GHz.

The coarse models are simulated in MicrowaveOffice [5] and the HFSS solver is used to simulate finemodels. Figure 14 shows the coarse (circuit) models ofthe first and second switch path, respectively. Thecoarse model of each path is composed of coaxial andstrip transmission lines, as well as shunt capacitors. Theshunt capacitors are extracted beforehand and keptfixed during the design process. The first path is sym-metrical and has no distinct parameters. The commonparameters are the coaxial transmission line lengths L1,L2, L3, and L4. The distinct parameters of the secondpath are L5, L6, L7, and L8 as shown in Figure 14(b).

The algorithm in [4] has been applied to the twoswitch paths. It reached a very good solution in only fouriterations. Fine model simulations of the two paths takeabout two hours on a 2.8-GHz Intel CPU computer.Figure 15 shows the fine model responses at the initialand optimal iteration as well as the enhanced coarsemodel response at the optimal iteration for the two paths.

Conclusions3-D EM simulators are made much easier to use and arewidely available from multiple commercial vendors.Many people consider the fundamental numerical algo-rithms for solving Maxwell’s equation to be well estab-lished. Using commercial and/or proprietary simula-tors, many practitioners including the authors haveachieved accurate results in designing complicatedpassive devices. It is very important to point out that itis still quite an involved process and in-depth under-standing of electromagnetics is still required to achievethose results. The process must be coupled with a goodknowledge of the meshing and numerical algorithm fora simulator of interest. This knowledge is the key toreduce problem size, achieve good numerical

Figure 13. Coaxial T-switch.

Path 1

Path 2

Figure 11. Ten-pole DR cavity-loaded filter.

DR

1

10 9 8 7 6

2 3 4 5

InputProbe

OutputProbe

Coupling Probe

IrisDR Support

Figure 12. Ideal (solid line) versus (a) initial EM response(dashed line) of the filter in Figure 11 and (b) EM response(dashed line) at the optimal space-mapping iteration.

0.0

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.00

IL a

nd

RL

(d

B)

10

.64

0

10

.65

3

10

.66

7

10

.68

0

10

.69

3

10

.70

7

10

.72

0

10

.73

3

10

.74

7

10

.76

0

Frequency (GHz)(b)

0.0

−10.00

−20.00

−30.00

−40.00

−50.00

−60.00

−70.00

−80.00

IL a

nd R

L (d

B)

10

.64

0

10

.65

3

10

.66

7

10

.68

0

10

.69

3

10

.70

7

10

.72

0

10

.73

3

10

.74

7

10

.76

0

Frequency (GHz)(a)

The state of the art of EM analysis ofcomplex passive structures hasexperienced tremendous progress inthe last two decades.


December 2008 61

convergence, and enable true virtual prototyping withfirst-pass success. It is the authors’ opinion that there isno bad software, only bad software usage. It is impor-tant for the users to understand the weaknesses andstrengths of different tools and act accordingly.

The EM simulators must be combined with otherCAD tools in order to solve practical and complicateddesign problems for passive devices when efficiency is adriving factor. Typical CAD tools include nodal analysissoftware, space mapping, and neuronetwork models.

Before the birth of EM simulators, microwave engi-neering was often considered a “black magic art,”because it involved a lot of trial and error. To some extent,the powerful modern PC and EM software has made itmuch easier, but using EM tools to solve complicateddesign problems for passive devices is still an art today.

References[1] D.G. Swanson and W. Hoefer, Microwave Circuit Modeling Using

Electromagnetic Field Simulation. Norwood, MA: Artech House, 2003.

[2] M. Yu, “Power handling capabilities for RF filters,” IEEE MicrowaveMag., vol. 8, no. 5, pp. 88–97, Oct. 2007.

[3] M.A. Ismail, D. Smith, A. Panariello, Y. Wang, and M. Yu, “EM-based design of large-scale dielectric resonator multiplexers byspace mapping,” IEEE Trans. Microwave Theory Tech., vol. 52, pp.386–392, Jan. 2004.

[4] M.A. Ismail, K. Engel, and M. Yu, “Multiple space mapping for RFT-switch design,” in IEEE MTT-S Int. Microwave Symp. Digest, FortWorth, Texas, 2004, pp. 1569–1572.

[5] Microwave Office, 2002, Ver. 5.5, Applied Wave Research, Inc.,1960 E. Grand Avenue, Suite 430 El, Segundo, CA 90245.

[6] H. Kabir, Y. Wang, M. Yu, and Q.J. Zhang, “Efficient neural networkmodeling techniques for applications in microwave filter design,” IEEETrans. Microwave Theory Tech., vol. 56, pp. 867–879, Apr. 2008.

Figure 14. The coarse model of the T-switch (a) first and (b) second path.

(a)

Z0=50 Ω

TL1, L1

TL2, L2

TL3, L3

TL4, L4

InpOut

Strip Line,z0=50 Ω

C1 C2 C1

(b)

InpOut

Strip Line,z0=50 Ω

C2C3 C1

TL4, L3

TL3, L3

TL2, L2

TL1, L1

TLinp,Z0=50 Ω

TL6, L6

TL5, L5

TL7, L7

TL8, L8

Figure 15. Responses of the (a) first and (b) second path: initial fine model (dash-dot line).

(a)

1 3 5 7 10 13 15

Frequency (GHz)

−50

−40

−30

−20

−10

0

−60

RL

(dB

)

(b)

1 3 5 7 10 13 15Frequency (GHz)

−50

−40

−30

−20

−10

0

−60

RL

(dB

)


3-d em simulations for passive devices

Documents

d em simulators

em simulators canbe

em model

fundamental em code

commercial em simulators

inem simulators

commercial software

different software