PRODUCT FEATURE

The high frequency structure simulator(HFSS) is widely recognized as the toolthat brought the power of the finite ele-

ment method to three-dimensional (3-D) RFand microwave design. Finite element analysisallows complicated 3-D structures such astransitions, filters, couplers and antennas to besimulated accurately by computing the under-lying electromagnetic fields. Optimetrics™ isa powerful new capability in Ansoft HFSS thatspeeds the design process and allows users toperform parametric analysis, optimization,sensitivity analysis and other design studiesfrom an easy-to-use interface. With this newcapability, dozens of design variations can beperformed quickly and effortlessly, compo-nents can be optimized to minimize any user-defined cost function and design of experi-ments studies can be automated to derive sen-sitivities and uncertainties as a function ofmanufacturing tolerances.

Optimetrics provides integrated paramet-rics and optimization capabilities by exploitingthe macro scripting language in the simulator.An existing feature of Ansoft HFSS is its abili-ty to record macro commands whenever thesoftware is run. This capability allows any sim-ulator session to be replayed by simply rerun-ning the associated macro file. Modifying themacros modifies the operations that the HFSSperforms and allows quantities such as geome-try, materials, boundary conditions, sourcesand frequencies to be varied.

The smart parametrics and optimizationengine in Optimetrics are made possible byhaving a convenient interface to generatemacro commands. At the start of a session, the

user creates a nominal problem and definesthe independent parameters to be varied. Thedependent variables to be computed in a para-metric analysis or the cost function to be mini-mized in optimization is then defined. Thesedependent variables and cost functions can beof any quantity capable of being computed inthe simulator. Field values, S parameters, fre-quency response, eigenmode data, impedanceand antenna metrics are available at the clickof a button. The simulator performs the re-quested computations, providing the output inconvenient table format in the case of para-metric analysis or in terms of optimal designspecification in the case of optimization.

The need for the user to work with themacro commands has been largely eliminated.A user interface has been created that auto-matically and seamlessly creates HFSS macrocommands for most of the operations involvedin parametrics and optimization applications.In addition, only a single nominal project isneeded, greatly simplifying the input require-ments for the user.

PARAMETRIC STUDYA key feature of Optimetrics is its ability to

study performance characteristics with respectto changes in design. Any number of designparameters may be varied in a single nominalproject design. In general, geometric shapes,material properties, source excitations, bound-ary conditions and specified frequencies areindependent parameters; S parameters, anten-

PARAMETRICSAND OPTIMIZATIONUSING ANSOFT HFSS

ANSOFT CORP.Pittsburgh, PA

Reprinted with permission of MICROWAVE JOURNAL ® from the November 1999 issue.©1999 Horizon House Publications, Inc.

metric field solutions. Turning off thefield-saving feature saves disk space,but the parametric field solutions arenot available for later viewing. Thevalues of the dependent parametersare always retained.

Table postprocessing enables usersto plot one column against another, asshown in Figure 3. Parametric pro-jects can be viewed in the same detailas the nominal project. A macro filecreated in the nominal project togenerate plots can be run for anyparametric setup with the click of abutton. The saved plots for every rowcan be plotted together to view theeffect of changing parameter valueson the plots.

Even after the solution is complet-ed, the user may add new solutioncolumns to the table. In this case, theleft-to-right power ratio vs. offset isevaluated and plotted. Within seconds,Optimetrics creates new columns andfills them by deriving the newly re-quested data from the existing solutionsin the corresponding rows. The resultsare shown in Figure 4.

PRODUCT FEATUREna parameters, eigenmode data orother HFSS-computed quantities aredependent parameters. Users cancreate compound parameters, whichare a function of both dependent andindependent parameters. Such acompound parameter can be used forbetter visualization and understand-ing of the project or as a cost functionto be used in the optimizer. Thenumber of independent or depen-dent parameters is unlimited. All de-pendencies, such as boundary condi-tions, are restored intelligently in-cluding face picks, impedance,calibration lines, gap source lines andthe UV coordinate system of periodicboundaries. For example, if an impe-dance line has been created that isone-third wavelength from the end ofa port face, this line will always beone-third wavelength for the para-metric projects.

Consider the problem of comput-ing the power division produced by aninductive septum in a waveguide T-junction at 10 GHz, as shown in Fig-ure 1. To solve this problem as afunction of the septum offset, thenominal problem is entered andsolved. With Optimetrics, a table isset up for sweeping the offset witheach row of the table correspondingto a specific offset value. (There is nolimit on the number of rows users canenter.) Taking into account the para-meters specified for the row, solvingthe table creates an HFSS project forevery row of the table. Optimetricssupports automatic seeding for eachparametric setup. In the case whereno geometry parameter is changed,the refined nominal mesh is used asthe starting mesh for all solutions.

Dependent and compound parame-ters can be added as columns of a table.In this case, the original dependent pa-rameters of interest are the magnitudeof the scattering parameters. Upon exe-cution, the value of the dependent pa-rameter computed for this row’s solu-tion fills the far right columns as shownin Figure 2. In this case, the problemsize was 8000 unknowns and requiredthree minutes and five seconds per rowusing a 360 MHz Pentium III proces-sor. If the user is not satisfied with theaccuracy of the solution, it is possible toperform additional refinement and ob-tain a higher accuracy solution forevery row. Users can also add frequen-cy sweeps if single frequency information is insufficient.

Optimetrics offers users the choiceof either saving or deleting the para-

Fig. 1 An H-plane reactive T-junction withinductive septum. ▼

Fig. 2 Optimetrics table for organizing and simulating parameters. ▼

Fig. 3 S parameters vs. septum position for the reactive T-junction. ▼

Fig. 4 New plots of derived quantities. ▼

Consider the four-post microstripbandpass filter shown in Figure 5.This filter was designed1 in an at-tempt to meet a design goal of an 8 to9 GHz passband with less than 1 dBripple. Using traditional filter designtechniques, a filter was designed, fab-ricated, tested and published with a7.6 to 9 GHz passband and 1.5 dBripple. Using the published dimen-sions as the nominal design, this filterwas entered into Optimetrics. Theoptimization problem consists of fourparameters: the diameter of the endposts, the diameter of the centerposts, the spacing between the endand center posts, and the spacing be-tween the center posts. As shown inFigure 6, Optimetrics improved thisdesign considerably; the optimizeddesign has a passband from 8 to 9GHz with less than 0.6 dB ripple, ex-ceeding the design specifications.

CREATING A DESIGN FROM SCRATCH

In some cases, Optimetrics is ableto create an excellent design eventhough the user has little initialknowledge of a good design. This ca-pability is not foolproof; complex de-signs often have many parametersand many local minima that can con-found direct optimization. A designeris advised to perform a parametricsweep first and must use his or herjudgment to create an initial good de-sign. Nevertheless, in some simplecases, the optimizer works surprising-ly well in creating designs with mini-mal user design input.

Consider the microstrip patch an-tenna in Figure 7. The design goal forthis antenna is to produce an antennaresonant at 2 GHz and the lowest pos-sible return loss at resonance. The de-sign parameters are the length of thepatch and the feed location on the sideof the patch. The nominal patch andthe optimized patch are shown in Fig-ure 8; the corresponding return loss vs.frequency plots are shown in Figure 9.In this case it can be seen that thenominal patch is very far from an ac-ceptable design while the optimizedpatch provides good performance.

OPTIMIZATION USINGEXTERNAL OPTIMIZERS

Since Optimetrics is based on theHFSS macro scripting language, it ispossible to drive Ansoft HFSS from

PRODUCT FEATUREfield values or circuit parameters thatcan be computed in the simulator)may be used as a variable in this costfunction. Optimetrics searches thedesign space to minimize the costfunction. To accommodate maximiza-tion or compound objectives, the usermay construct partial cost functionsand/or apply appropriate weights.

To simplify cost function definitionfor standard tasks, Optimetrics pro-vides a graphical user interface that

allows the user ac-cess to commonlyused quantities(such as circuit pa-rameters) with thepush of a button. Aspecial panel for fil-ter optimization isalso provided. Theuser may choose anarbitrary number offrequency bandsand specify the re-quested filter char-acteristics. Expertusers can even cre-ate their own macro

scripts. The cost functions in themacro script may contain loops andconditional statements.

By default, optimization starts fromthe nominal settings for the design.However, if a parametric table is avail-able, Optimetrics will first scan thetable, analyze all designs that are feasi-ble and start optimization from the de-sign of least cost. Hence, the user maymanually create parameter settings forone or more candidates as the startingpoint for the optimization, or even be-gin with a parametric sweep. Beginningwith a parametric sweep is particularlyattractive when the user chooses to in-spect the response surface over a widerange of parameters and may also helpto avoid local optima.

FINE-TUNING A DESIGNTo illustrate some of the produc-

tivity gains afforded by Optimetrics,consider the problem of fine-tuningthe product design. It often happensthat a designer has the basic parame-ters for a microwave component butneeds to fine-tune these parametersto deliver a precision product. Usingcut-and-try methods, such fine-tun-ing can require weeks of prototypingand tweaking; using Optimetrics, itcan be performed overnight.

OPTIMIZATIONOptimetrics contains a powerful

internal optimization algorithm tohelp users achieve optimal designs.This optimizer employs a constrainedsuperlinearly convergent active set al-gorithm. To restrict the search regionand prevent the optimizer from cre-ating physically meaningless designs(such as overlapping geometry), Opti-metrics supports simple bounds aswell as linear constraints. The opti-mized design is guaranteed to bewithin the feasible domain.

Optimetrics also provides userswith unlimited freedom in definingcost functions for optimization. Anyalgebraic expression may be definedas the cost function and any solutionquantity (such as field strength, far-

▲ Fig. 5 A four-post microstrip filter.

▲ Fig. 6 The optimized filter’s frequency response.

Fig. 7 The modeled microstrip patch antenna. ▼

tor and driven ele-ment is denoted byS2. In order toachieve their func-tions, the reflectorshould be longerthan the driven ele-ments and the direc-tor should be short-er. (Constraints inthe optimizationwere used to en-force these condi-tions.) Two costfunctions were used:one to measure thedirectivity, the otherto measure thefront-to-back-ratio.The MatLab multi-objective goal attain-ment algorithm(fgoalattain.m) wasalso used.

The cross-sec-tional radius of theantenna elements isassumed to be0.003369λ (ln λ/2a =5). A search was per-formed to determinea combination of el-ement lengths andseparation distances

such that the directivity and front-to-back ratio are greater than 8 dB. Fig-ure 11 shows the directivity and front-to-back ratio vs. number of iterations.During the first few iterations, the op-timizer was able to achieve a front-to-back ratio greater than 8 dB, but thedirectivity was approximately 5 dB. Af-ter 34 iterations, the software found itsgoal at 8.05 and 8.46 dB. Figure 12shows the initial and optimized dimen-sions as well as how they changed vs.optimization cycle.

CONCLUSIONOptimetrics is a powerful new fea-

ture in Ansoft HFSS that providesparametric and optimization capabili-ties for 3-D RF and microwave de-sign problems. The approach used isvery general and allows any designquantity to be parameterized and op-timized. It even allows outside pro-grams such as MatLab to be used todrive the optimization. The examplesshown indicate the ease with whichparametric solutions may be set upand the power of the new optimiza-

tion capability. Significant applica-tions of Optimetrics include fine-tun-ing preliminary designs, searching thedesign space for acceptable designsand the possibility of creating excel-lent designs from scratch. All of theseapplications provide good productivi-ty improvements for designers and al-low precision designs to be createdwith minimal cost and time.

References1. MatLab Version 5.3 is a registered trade-

mark of the Mathworks Inc., Natick, MA01760, USA.

2. K.L. Wu, C. Wu and J. Litva, “Characteriz-ing Microwave Planar Circuits Using theCoupled Finite-Boundary ElementMethod,” IEEE Transactions on Mi-crowave Theory and Techniques, Vol. 40,October 1992, pp. 1963–1966.

Ansoft Corp.Pittsburgh, PA (412) 261-3200

PRODUCT FEATURE

start to finish from an outside pro-gram. This outside program may beused to adjust design parameters untilparticular postprocessing results areachieved. The outside program maybe written in C, C++, FORTRAN orany other language. Unlike the auto-mated procedures available in an in-ternal optimizer, using an outsidecomputer program for optimizationrequires a significant programming ef-fort on the part of the user. In the ex-ample described here, MatLab™ sup-plies the optimization algorithm andcontrols the input to Ansoft HFSS.

Consider the three-element Yagi-Uda antenna shown in Figure 10. Atypical Yagi-Uda antenna should havea high directivity, narrow beamwidth,low sidelobes and a high front-to-backratio. In this example, the goal was tooptimize the variables to achieve a di-rectivity and front-to-back ratio of 8dB or greater. The antenna consists ofa director, driven element and reflec-tor. The distance between the drivenelement and reflector is denoted by S1while the distance between the direc-

▲ Fig. 8 The microstrip patch antenna’s geometry.

Fig. 9 The antenna’s nominal and optimized return loss vs. frequency. ▼

▲ Fig. 10 The three-element Yagi-Udaarray antenna.

▲ Fig. 11 Directivity and front-to-backratio vs. optimization cycle.

Fig. 12 The antenna’s dimensions vs. optimization cycle. ▼