T he high frequency structure simulator (HFSS) is widely recognized as the tool
that brought the power of the finite ele-ment method to three-dimensional (3-D) RF and microwave design. Finite element analysis allows complicated 3-D structures such as transitions, filters, couplers and antennas to be simulated accurately by computing the under-lying electromagnetic fields. Optimetrics™ is a powerful new capability in Ansoft HFSS that speeds the design process and allows users to perform parametric analysis, optimization, sensitivity analysis and other design studies from an easy-to-use interface. With this new capability, dozens of design variations can be performed 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 of manufacturing tolerances.
Optimetrics provides integrated paramet-rics and optimization capabilities by exploiting the macro scripting language in the simulator. An existing feature of Ansoft HFSS is its abili-ty to record macro commands whenever the software is run. This capability allows any sim-ulator session to be replayed by simply rerun-ning the associated macro file. Modifying the macros modifies the operations that the HFSS performs and allows quantities such as geome-try, materials, boundary conditions, sources and frequencies to be varied.
The smart parametrics and optimization engine in Optimetrics are made possible by having a convenient interface to generate macro commands. At the start of a session, the user creates a nominal problem and defines the independent parameters to be varied. The dependent variables to be computed in a para-metric analysis or the cost function to be mini-mized in optimization is then defined. These dependent variables and cost functions can be of any quantity capable of being computed in the simulator. Field values, S parameters, fre-quency response, eigenmode data, impedance and antenna metrics are available at the click of a button. The simulator performs the re-quested computations, providing the output in convenient table format in the case of para-metric analysis or in terms of optimal design specification in the case of optimization.
The need for the user to work with the macro commands has been largely eliminated.
A user interface has been created that auto-matically and seamlessly creates HFSS macro commands for most of the operations involved in parametrics and optimization applications. In addition, only a single nominal project is needed, greatly simplifying the input require-ments for the user.
PARAMETRIC STUDY
A key feature of Optimetrics is its ability to study performance characteristics with respect to changes i
n design. Any number of design parameters may be varied in a single nominal project design. In general, geometric shapes, material properties, source excitations, bound-ary conditions and specified frequencies are independent parameters; S parameters, anten-
P ARAMETRICS
AND O PTIMIZATION
U SING A NSOFT HFSS
A NSOFT C ORP.
Pittsburgh, PA
Reprinted with permission of MICROWAVE JOURNAL®from the November 1999 issue.
reactive materials studies©1999 Horizon House Publications, Inc.
metric field solutions. Turning off the field-saving feature saves disk space,but the parametric field solutions are not available for later viewing. The values of the dependent parameters are always retain
ed.Table postprocessing enables users to plot one column against another, as shown in Figure 3. Parametric pro-jects can be viewed in the same detail as the nominal project. A macro file created in the nominal project to generate plots can be run for any parametric setup with the click of a button. The saved plots for every row can be plotted together to view the effect of changing parameter values on the plots.Even after the solution is complet-ed, the user may add new solution columns to the table. In this case, the left-to-right power ratio vs. offset is evaluated and plotted. Within seconds,Optimetrics creates new columns and fills them by deriving the newly re-quested data from the existing solutions in the corresponding rows. The results are shown in Figure 4.na parameters, eigenmode data or other HFSS-computed quantities are dependent parameters. Users can create compound parameters, which are a function of both dependent and independent parameters. Such a compound parameter can be used for better visualization and understand-ing of the project or as a cost function to be used in the optimizer. The number 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 and the UV coordinate system of periodic boundaries. For example, if an impe-dance line has been created that is one-third wavelength from the end of a port face, this line will always be one-third wavelength for the para-metric projects.
Consider the problem of comput-ing the power division produced by an inductive septum in a waveguide T-junction at 10 GHz, as shown in Fig-ure 1. To solve this problem as a function of the sept
um offset, the nominal problem is entered and solved. With Optimetrics, a table is set up for sweeping the offset with each row of the table corresponding to a specific offset value. (There is no limit on the number of rows users can enter.) Taking into account the para-meters specified for the row, solving the table creates an HFSS project for every row of the table. Optimetrics supports automatic seeding for each parametric setup. In the case where no geometry parameter is changed,the refined nominal mesh is used as the 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 magnitude of 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 shown in Figure 2. In this case, the problem size was 8000 unknowns and required three minutes and five seconds per row using a 360 MHz Pentium III proces-sor. If the user is not satisfied with the accuracy of the solution, it is possible to perform additional refinement and ob-tain a higher accuracy solution for every row. Users can also add frequen-cy sweeps if single frequency information is insufficient.Optimetrics offers users the choice
of either saving or deleting the para-Fig. 1  An H-plane reactive T-junction with inductive septum.
w Fig. 2  Optimetrics table for organizing and simulating parameters.
w Fig. 3  S parameters vs. septum position for the reactive T-junction.
w Fig. 4  New plots of derived quantities. w
Consider the four-post microstrip bandpass filter shown in Figure 5.This filter was designed 1 in an at-tempt to meet a design goal of an 8 to 9 GHz passband with less than 1 dB ripple. Using traditional filter design techniques, a filter was designed, fab-ricated, tested and published with a 7.6 to 9 GHz passband and 1.5 dB ripple. Using the published dimen-sions as the nominal design, this filter was entered into Optimetrics. The optimization problem consists of four parameters: the diameter of the end posts, the diameter of the center posts, the spacing between the end and center posts, and the spacing be-tween the center posts. As shown in Figure 6, Optimetrics improved this design considerably; the optimized design 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 able to create an excellent design even though the user has little initial knowledge of a good design. This ca-pability is not foolproof; complex de-signs often have many parameters and many local minima that can con-found direct optimization. A designer is advised to perform a parametric sweep first and must use his or her judgment to create an initial good de-sign. Nevertheless, in some simple cases, 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 for this antenna is to produce an antenna resonant at 2 GHz and the lowest pos-sible return loss at resonance. The de-sign parameters are the length of the patch and the feed location on the side of the
patch. The nominal patch and the 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 the nominal patch is very far from an ac-ceptable design while the optimized patch provides good performance.OPTIMIZATION USING EXTERNAL OPTIMIZERS Since Optimetrics is based on the
HFSS macro scripting language, it is possible to drive Ansoft HFSS from field values or circuit parameters that can be computed in the simulator)may be used as a variable in this cost function. Optimetrics searches the design space to minimize the cost function. To accommodate maximiza-tion or compound objectives, the user may construct partial cost functions and/or apply appropriate weights.To simplify cost function definition
for standard tasks, Optimetrics pro-
allows the user ac-cess to commonly used quantities (such as circuit pa-
rameters) with the push of a button. A special panel for fil-ter optimization is also provided. The user m
ay choose an arbitrary number of frequency bands and specify the re-quested filter char-acteristics. Expert users can even cre-ate their own macro scripts. The cost functions in the macro script may contain loops and conditional statements.
By default, optimization starts from the nominal settings for the design.However, if a parametric table is avail-able, Optimetrics will first scan the table, analyze all designs that are feasi-ble and start optimization from the de-sign of least cost. Hence, the user may manually create parameter settings for one or more candidates as the starting
point for the optimization, or even be-gin with a parametric sweep. Beginning with a parametric sweep is particularly attractive when the user chooses to in-spect the response surface over a wide range of parameters and may also help to avoid local optima.FINE-TUNING A DESIGN To illustrate some of the produc-tivity gains afforded by Optimetrics,consider the problem of fine-tuning the product design. It often happens that a designer has the basic parame-ters for a microwave component but needs to fine-tune these parameters to deliver a precision product. Using cut-and-try methods, such fine-tun-ing can require weeks of prototyping and tweaking; using Optimetrics, it can be performed overnight.OPTIMIZATION Optimetrics contains a powerful internal optimization algorithm to help users achieve optimal designs.This optimizer employs a constrained superlinearly convergent active set al-g
orithm. To restrict the search region and prevent the optimizer from cre-ating physically meaningless designs (such as overlapping geometry), Opti-metrics supports simple bounds as well as linear constraints. The opti-mized design is guaranteed to be within the feasible domain.Optimetrics also provides users with unlimited freedom in defining cost functions for optimization. Any algebraic expression may be defined as the cost function and any solution quantity (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. w
tor and driven ele-ment is denoted by S2. In order to achieve their func-tions, the reflector should be longer than the driven ele-ments and the direc-tor should be short-er. (Constraints in the optimization were used to en-force these condi-tions.) Two cost functions were used:
one to measure the directivity, the other to measure the front-to-back-ratio.The MatLab multi-objective goal attain-ment algorithm (fgoalattain.m) was also used.
The cross-sec-
tional radius of the antenna elements is assumed to be 0.003369λ(ln λ/2a =
5). A search was per-formed to determine a combination of el-ement lengths and
separation distances such that the directivity and front-to-back ratio are greater than 8 dB. Fig-ure 11shows 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 the directivity was approximately 5 dB. Af-ter 34 iterations, the software found its goal at 8.05 and 8.46 dB. Figure 12sho
ws the initial and optimized dimen-sions as well as how they changed vs.optimization cycle.CONCLUSION Optimetrics is a powerful new fea-ture in Ansoft HFSS that provides parametric and optimization capabili-ties for 3-D RF and microwave de-sign problems. The approach used is very general and allows any design quantity to be parameterized and op-timized. It even allows outside pro-grams such as MatLab to be used to drive the optimization. The examples shown indicate the ease with which parametric solutions may be set up and the power of the new optimiza-
tion capability. Significant applica-tions of Optimetrics include fine-tun-ing preliminary designs, searching the
design space for acceptable designs and the possibility of creating excel-lent designs from scratch. All of these applications provide good productivi-ty improvements for designers and al-low precision designs to be created with minimal cost and time.References 1.MatLab Version 5.3 is a registered trade-mark of the Mathworks Inc., Natick, MA 01760, USA.2.K.L. Wu, C. Wu and J. Litva, “Characteriz-ing Microwave Planar Circuits Using the Coupled Finite-Boundary Element Method,” IEEE Transactions on Mi-crowave Theory and Techniques , Vol. 40,October 1992, pp. 1963–1966.Ansoft Corp.Pittsburgh, PA (412) 261-3200start to finish from an outside pro-gram. This outside program may be used to adjust design parameters until particular postprocessing results are achieved. The outside
program may be written in C, C ++, FORTRAN or any other language. Unlike the auto-mated procedures available in an in-ternal optimizer, using an outside computer program for optimization requires a significant programming ef-fort on the part of the user. In the ex-ample described here, MatLab™ sup-plies the optimization algorithm and controls the input to Ansoft HFSS.Consider the three-element Yagi-
Uda antenna shown in Figure 10. A typical Yagi-Uda antenna should have a high directivity, narrow beamwidth,low sidelobes and a high front-to-back ratio. In this example, the goal was to optimize the variables to achieve a di-rectivity and front-to-back ratio of 8dB or greater. The antenna consists of a director, driven element and reflec-tor. The distance between the driven element and reflector is denoted by S1while the distance between the direc-v Fig. 8  The microstrip patch antenna’s geometry.Fig. 9  The antenna’s nominal and optimized return loss v Fig. 10  The three-element Yagi-Uda array antenna.

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