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MICROWAVES & RF n JUNE 2000

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This article addresses a modelingapproach that uses full-wave analysistools to obtain accurate electrical dis-continuity models while operating atspeeds that are sufficient to performnumerical techniques such as opti-mization and design centering. Thearticle presents a general discussionof the steps required to realize thistype of system, and concludes with asample implementation of this sys-tem as it models a microstrip lowpassfilter circuit. The purpose of this arti-cle is to introduce this techniquewithin a commercially available

microwave computer-aided-design(CAD) package.

One impractical but obviousapproach to creating electromagnet-ic (EM)-based models (Fig. 1) is tocombine a circuit simulator with anEM simulator to automatically per-form simulations of discontinuitiesbased on the given input parameters.Unfortunately, this method is notcomputationally efficient enough tosupport tuning, optimization, or yieldanalysis of complex circuits. Despitethe practical limitations, this methoddoes have several significant advan-

Murray Shattuck Applied Wave Research, 2089Meadow Sweet Lane, Erie, CO 80516;e-mail: [email protected].

EM-Based ModelsImprove CircuitSimulators This new modeling approach uses full-wave analysis tools to obtain accurate

models and operates at high speed toperform numerical techniques.

DESIGN FEATURE

EM Discontinuities

SOPHISTICATED software programs that model the RF electricalcharacteristics of individual components and overall systems arethe cornerstone of modern high-frequency design. These programshave introduced several numerical techniques that improve design

performance and manufacturing yield, but the techniques require the pro-gram to simulate the behavior of each component thousandsif not mil-lionsof times. Modeling shortcuts have been devised to minimize simu-lation time, but they lose accuracy as frequency increases.

Input parameters

Equations derived to minimize error compared to

EM data set

Closed-form equationsS11 = W1 (er 1)1.6......

S11 S22 S120.01 0.02 0.97.... .... ........ .... ....

1. Closed-form equations are designed to minimize error when compared to EMsimulations.


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tages that drastically improve thedesign process for the user. First, theaccuracy of the model is equivalent tothe accuracy of the underlying EMsimulation engine. Second, automaticgeneration of EM structures cansave considerable time and eliminatehuman error. Lastly, the dynamicrange of the discontinuity model canbe improved to take into account awider variety of dielectric materialsand impedances than closed-formequations.

An alternative approach (Fig. 2)stems from the classical method ofmodel development. Closed-formequations from an analytically solv-able problem similar to the problemat hand are derived by mapping theinput parameters into this closed-form solution. Based on a largeamount of data, this mapping is mod-ified to minimize error between mea-surements (EM simulations in thiscase) and the output of the model.Since the end result of this method isa closed-form equation, it results in acomputationally efficient implemen-tation that is ideal for the high num-ber of evaluations required by thecircuit simulator. In theory, thismethod of model generation hasnumerous advantages and would bethe perfect solution, except for onedrawback: it is a non-systematicapproach of model development.Each model must be addressed indi-vidually, and the accuracy and quali-ty of the model strongly depends onthe developers ability to choose suit-able equations to map the inputparameters.

Yet another possibility is to storethe results of the EM simulations in afile and interpolate the results of thetable to estimate the electrical per-formance as a function of the inputparameters. This method is attrac-tive because it does not require anyprevious knowledge of the disconti-nuity or how to model it. Further,this method supports the construc-tion of a generalized program thatwould handle all types of discontinu-ities. Also, it could use a dynamicinterface to the EM simulator toallow additions to the table at anytime. However, this method has sev-eral major problems that complicateits application. The composite electri-

EM Discontinuities

DESIGN FEATURE

Input parameters

Stored EM

S11 S22 S120.01 0.02 0.97.... .... ........ .... ....

Direct

2. This diagram shows a parameterized model using direct interpolation ofstored EM simulations.

Inputparameters

Data stored

No

EM simulation

Stored data

Direct

S11 S22 S120.01 0.02 0.97

....

....

....

....

....

....

Preprocess to equivalent circuit

Post-process fromequivalent circuit

to electricalparameters

L1 C1.... ........ ....

3. This is a flow chart of the proposed EM-based discontinuity parameterizedmodel.

Radiation

Quasi-TEM mode

Surface waves

Radiation

Higher-order propagation modes

4. This diagram shows a portion of the possible propagating modes on amicrostrip line.


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cal parameters can have quicklyvarying characteristics with thepotential for step changes in parame-ters (for example S-parameter phase,or Y-parameters going to infinity).Interpolation across these types ofdiscontinuities in the data can resultin gross errors at these locations,which forces sampling of the inputparameters on a finer interval. Final-ly, the amount of computer memoryrequired to store the interpolationsamples could quickly become unre-alistic. This problem expands expo-nentially as the number and range ofthe input parameters are increased.

The approach used withinMicrowave Offices EM-based dis-continuity models is a derivative ofthe last technique, which overcomesthe disadvantages while retaining asystematic approach to the modelingprocess. In this approach (Fig. 3), theEM-simulated data are first prepro-cessed, resulting in the componentvalues of a passive equivalent circuit.After correctly determining a suit-able equivalent circuit, the resultingcomponent values are noted tobehave relatively benignly as a func-tion of the input parameters andwithout discontinuous steps in value.The interpolation is then performedon these sampled component valuesand the resulting equivalent circuit isused to evaluate the electricalparameters of the circuit.

This approach allows the data to besampled at a coarser interval, thusminimizing the number of EM simu-lations and the amount of computermemory required for a particularsimulation. In addition, this approachprovides some physical interpreta-tion of the ongoing changes as a func-tion of the input parameters, sup-porting a better grasp of theproblem. Another benefit of this typeof modeling is that it always can beconstrained so that the resulting out-put electrical parameters are repre-sentative of a causal system that con-serves energy. In the interpolation ofS-parameters, for example, it is pos-sible and highly likely that the result-ing system will create energy atsome interpolation points. This isespecially true when the modeling oflossless discontinuities as an interpo-lation error creates loss on one side

EM Discontinuities

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while creating gain on the other side.Processing the problem as an equiva-lent circuit eliminates this problem.Further, if loss is to be included in themodel, resistive terms can be addedto the model.

One must control the size of thedata base by limiting the range of theinput parameters. The allowablerange of the independent inputparameters and the sample frequen-cy determine the quantity of datawithin the filled interpolation database. In the case of the selected inter-polation model, the required sam-pling for a particular error tolerancedepends on the complexity of theinterpolation method and the localstability of the function being inter-polated. Selection of input-variableranges should be studied in the con-text of several frames of reference.First, one must look at the parameteras seen by the end user and considerwhat he or she considers to be a rea-sonable range. Secondly, one musttake a close look at the capabilities ofthe EM simulator and determineover what range reliable data can beobtained using an automated-collec-tion process. Finally, one should lookat the physical properties of the dis-continuity to determine the limits ofsingle-mode propagation.

Single-mode propagation is usuallythe limiting factor and often occurs atinput-variable values that are lowerthan the user desires. However, oncemultimode propagation is reached,the entire modeling system, as pro-posed, begins to introduce significanterrors. If one of the transmissionlines constructing the discontinuitysupports more than one propagatingmode, the circuit simulator will inac-curately predict the circuit interac-tions because it does not supportmultimode propagation within theother models. To support this sys-tem, the EM simulator would berequired to determine the general-ized scattering matrix of the disconti-nuity, separating each mode into aneffective electrical port. Further, thecircuit simulator would have to sup-port multimode excitation of all mod-els. Beyond the guided modes of aconductor, one must also investigatethe alternate modes of propagationsuch as radiation and the excitation

EM Discontinuities

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of dielectric-waveguide modes orsurface waves. Figure 4 depicts aportion of the possible propagatingmodes on a microstrip line. Depend-ing on the type of EM simulator used,excitation of these modes can resultin significant errors in the electricalparameters, thus propagating errorsinto the model. As multimode guidedpropagation is approached, the elec-trical parameters begin to behaveviolently, significantly varying fromthe desired response of the junction.All of this indicates that the upperlimit of the input variables should beset before this occurs. Although thisoften disappoints the user, imple-mentation of such a limit is in his orher best interest and will result inbetter designs.

For a particular set of discontinu-ity dimensions, excitation of theseundesired modes is typically a func-tion of frequency. Thus, choosing theupper frequency limit is in direct con-flict with selecting the ranges of thedimensional parameters. If the finitefrequency limit is set for a particularsubstrate, the conflict between fre-quency, dimensions, and the usersdesires is not resolved. Consider amicrostrip step example. If a user isworking at 70 GHz on 100 mm GaAs,the width limitation for this disconti-nuity, based on elimination of higherorder modes, may be 100 mm. How-ever, a different user working at 20GHz on the same substrate shouldnot have that same limitation.

In an attempt to resolve this prob-lem, the author takes the followingapproach, illustrated in a two- dimen-sional sense in Fig. 5. For each EMsimulation and at a particular set ofdimensions, estimates of the onset ofhigher-order modes and limitationsdue to the EM simulator areobtained. The limitation with lowestfrequency is then reduced by a cer-tain percentage to avoid problems atits onset. EM simulation then pro-ceeds to this frequency limit, and thefrequency limit is stored within theinterpolation table. Upon interpola-tion of the electrical parameters, thelowest frequency limit of all pointsused in the interpolation determinesthe upper frequency limit within thatspace. Since these limits are dynamicand require significant calculations, a

EM Discontinuities

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system of warning the user of thechanging limit is required.

A complete system of EM-baseddiscontinuities using the describedsystem has been implemented inmicrostrip. This system uses a three-dimensional (3D), planar, full-waveEM simulator incorporating thespectral-domain method of moments(MOMs). The system has also beeninterfaced to the Microwave Office2000 simulation environmentthrough the user-accessible modelinginterface. To test the models, a userwould ask, What type of differencewill these EM-based discontinuitymodels have on a real-world circuitwith multiple discontinuities? Totest this, a simple lowpass filter cir-cuit with a cutoff frequency of 5.5GHz was designed in 30-milmicrostrip with Er = 2.94. The filterdesign consists of multiple microstripdiscontinuities, including MTEEs,MSTEPs, MBENDS, and MOPENS.The circuit was modeled with theclosed-form and EM-based models.Figures 6 and 7 show a layout andphotograph of the lowpass filter.

It should be noted that this circuitwas designed to operate at frequen-cies where the closed-form modelshave degraded. Due to the fabrica-tion materials and processes avail-able, tests were conducted on 30-milsubstrates with a relative dielectricconstant of 2.94 at frequencies up to10.5 GHz. While not an extremely

high frequency, the scale of the dis-continuities tested supports multi-mode propagation at 13 GHz on thewidest lines. If one were to scalethese tests to a 10-mil substrate, testfrequencies of 31.5 GHz would berequired. Using a 100-mm substrate,test frequencies would exceed 80

GHz. The fabrication and test processes

can introduce errors that cause themeasurement to differ from the sim-ulations. These include calibrationerrors, variations in the dielectricconstant of the substrate, and dimen-sional variations in the etching pro-cess. Calibrations were made at theend of the SMA connectors on a vec-tor network analyzer (VNA), but thetransitions from coax to microstripwere not removed. Further errorsshould be expected from the effectsof inter-element coupling and radiation.

Figure 8 includes a rectangularplot of the circuit simulations and fil-ter measurements. The use of theEM-based models significantlyimproves the accuracy of the simula-tion in the passband of the filter. Infact, the discrepancies between themeasurement and the circuit simula-tion could easily be explained by theuncalibrated coax-to-microstriptransition. In the stopband, however,the measurement shows some signif-icant variations from both circuitsimulations. This is especially true

near the transmis-sion nulls that arecaused by the twoo p e n - c i r c u i t e dstubs. It is in theseregions, wherehigh currents arepresent on theshunt stubs, thatradiation and cou-

EM Discontinuities

DESIGN FEATURE

W2

Sample point

Fmax = 90 Fmax = 73

Fmax = 99 Fmax = 85

Fmax inregion 73

W1Interpolation point

5. This graphic shows a method of determining the upper frequency limitwithin an interpolation cell.

Parameter

er

H

Etch

Nominalvalue

2.94

30 mil

0

Tolerance

2 percent

61 mil

61 mil

Distribution

Uniform

Uniform

Uniform

Parameter tolerances for yield analysis

6. This is the layout of the prototype lowpass filter.


108

pling between the circuits are high-est. A full-wave EM simulation of thefilter has shown these effects, verify-ing that conclusion.

With improved confidence in thecircuit simulations using the EM-based models, one can harness theMonte Carlo analysis available with-in Microwave Office to evaluate thesensitivity of the design to fabrica-tion tolerances. Figure 8 also showsthe statistical variation in the scat-tering parameters using the EM-based models. Three input parame-ters were assigned the tolerancesshown in the table.

The variable etch refers to thefabrication process that is used topattern the conductor. The linewidths and lengths are modifiedthrough equations in the circuit sim-ulator to reflect the appropriatechanges in an over- or under-etchedcondition.

Yield analysis shows that the stop-band is not extremely sensitive tomanufacturing tolerances. There-

fore, one would expect that, evenwith the coupling and radiationeffects predicted by the full-wavesimulation, these effects are relative-ly immune to fabrication tolerance.The passband, on the other hand,experiences some dramatic changeswith the specified tolerances. Fromthis point, one could perform variousother analyses available withinMicrowave Office to improve the

design. Examples include perfor-mance optimization to improve thenominal response, or design center-ing to optimize the yield for a partic-ular set of manufacturing tolerances.It is in this regime that the EM-basedmodels show their advantage overfull-wave EM simulation, and resultin an improved design.

It has also been shown that theEM-based discontinuity models offersignificant improvements in theaccuracy of circuit simulations. Withthis new accuracy, one can haveincreased confidence in the numeri-cal optimizations and yield analysisperformed within the circuit simula-tor. The benefits of EM-based dis-continuity models within theMicrowave Office simulation envi-ronment are clear from this example.However, the EM-based discontinu-ity models will not replace the useful-ness of the EM simulator to evaluatethe effects of radiation and inter-ele-ment coupling. Ultimately, it is theintelligent application of multiple

EM Discontinuities

DESIGN FEATURE

7. This is a photograph of theprototype lowpass filter.


110

simulation methods that result in thebest-performing designs and thefastest time to market.

For further readingFang Wang, Vijaya K. Devabhaktuni, and Q.J. Zhang, A

Hierarchical Neural Network Approach To the Develop-

ment of Library of Neural Models for Microwave Design,IEEE Transactions on Microwave Theory and Techniques,Vol. 46, No. 12, December 1998, pp. 2391-2403.

P.M. Watson, K.C. Gupta, and R.I. Mahajan, Develop-ment of Knowledge Based Artificial Neural Network Mod-els for Microwave Components, IEEE Transactions onMicrowave Theory and Techniques, Vol. 46, No. 5, May1998.

John W. Bandler, Mostafa A. Ismail, Jose Ernesto Rayas-

Sanchez, Qi-Jun Zhang, Neuromodeling of Microwave Cir-cuits Exploiting Space-Mapping Technology, IEEETransactions on Microwave Theory and Techniques, Vol.47, No. 12, December 1999, pp. 2417-2427.

Norbert H.L. Koster and Rolf H. Jansen, The MicrostripStep Discontinuity: A Revised Description, IEEE Trans-actions on Microwave Theory and Techniques, Vol. MTT-34, No. 2, February 1986, pp. 213-223.

Akifumi Nakatani, Stephen A. Maas, and Jesse Castane-da, Modeling of High Frequency MMIC Passive Compo-nents, IEEE MTT-S Digest 1989, pp. 1139-1142.

Brian Easter, The Equivalent Circuit of SomeMicrostrip Discontinuities, IEEE Transactions onMicrowave Theory and Techniques, Vol. MTT-23, No. 8,August 1975, pp. 655-660.

Mohamad D. Abouzahra, On the Radiation fromMicrostrip Discontinuities, IEEE Transactions onMicrowave Theory and Techniques, Vol. MTT-29, No. 7,July 1981, pp. 666-668.

Peter Benedek and Peter Silvester, Equivalent Capaci-tances for Microstrip Gaps and Steps, IEEE Transactionson Microwave Theory and Techniques, Vol. MTT-20, No.11, November 1972, pp. 729-733.

Peter Silvester and Peter Benedek, Equivalent Capaci-tances of Microstrip Open Circuits, IEEE Transactions onMicrowave Theory and Techniques, Vol. MTT-20, No. 8,August 1972, pp. 511-516.

Peter Silvester and Peter Benedek, Microstrip Discon-tinuity Capacitances for Right-Angle Bends, T Junctions,and Crossings, IEEE Transactions on Microwave Theoryand Techniques, Vol. MTT-21, No. 5, May 1973, pp. 341-346.

Alistair F. Thomson and Anand Gopinath, Calculation ofMicrostrip Discontinuity Inductances, IEEE Transac-tions on Microwave Theory and Techniques, Vol. MTT-23,No. 8, August 1975, pp. 648-654.

M. Kirschning, R.H. Jansen, and N.H.L. Koster, Mea-surement and Computer-Aided Modeling of Microstrip Dis-continuities By An Improved Resonator Method, IEEEMTT-S International Microwave Symposium Digest, May31-June 3, 1983, pp. 495-497.

Brian C. Wadell, Transmission Line Design Handbook,Artech House, Boston, MA, 1991, pp. 289-330.

K.C. Gupta, Ramesh Garg, Inder Bahl, and PrakashBhartia, Microstrip Lines and Slotlines, Artech House,Boston, MA, 1996, pp. 179-200 and pp. 255-263.

K.C. Gupta, Ramesh Garg, and Rakesh Chadha, Comput-er-Aided Design of Microwave Circuits, Artech House,Boston, MA, 1981, pp. 189-197.

Douglas C. Montgomery, Design and Analysis of Exper-iments, John Wiley & Sons, New York, 1997.

EM Discontinuities

DESIGN FEATURE

0

3

6

9

12

15

18

21

24

27

30

S 11

dB

1 2 3 4 5 6 7 8 9 10 10.5

FrequencyGHz

0

10

20

30

40

50

60

70

80

90

100

Statistical variation S11 and S21

S 21

dB

Envelope Nominal

Envelope minimum

Mean

8. This is a rectangular plot of the circuit simulations and filter measurements.

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