MICROWAVE COMPONENT ANALYSIS USING A NUMERICAL ELECTROMAGNETIC FIELD SOLVER

Transcription

1 LLN R. JLON, CRIG R. MOORE, and JOHN E. PENN MICROWVE COMPONENT NLYSIS USING NUMERICL ELECTROMGNETIC FIELD SOLVER With the ret developmt of numerial eletromagneti field solvers, mirowave gineers an aurately predit the performane of arbitrarily shaped eletromagneti strutures. This artile desribes the use of a numerial eletromagneti field solver in the analysis of speifi mirowave omponts inluding transitions, waveguide strutures, monolithi mirowave integrated iruits, and mirostrip antnas. Multipator breakdown analysis is also disussed. INTRODUCTION urate modeling and analysis of mirowave iruit omponts are esstial for the effiit, ost -effetive design of mirowave systems. In the past, modeling of mirowave omponts onsisted of empirial, stati, and quasi-stati models, many of whih laked suffiit auray. Many waveguide omponts and transitions were too omplex to model, and only ostly ut-and-try tehniques ould be used in their design. With the advt of numerial eletromagneti field solvers, three-dimsional mirowave strutures an be aurately modeled. Numerial eletromagneti field solvers ave time and money beause of fewer design iteration. Mirowave omponts that are now aurately modeled inlude monolithi mirowave integrated iruit (MMIC) omponts, waveguide omponts, transitions betwe transmission media, and ertain antna problems. Sine numerial eletromagneti field solvers gerate eletri field data, system problems, suh as multipator breakdown analyses, an also be solved. Mirowave gineers in the PL Spae Departmt have used a numerial eletromagneti field solver to analyze mirowave omponts and problems. This artile disusses some of the analyses and problem solutions. THE HIGH-FREQUENCY STRUCTURE SIMULTOR We used the Hewlett-Pakard high-frequy struture simulator (HFSS) 1 as the primary numerial eletro mag - neti field olver. The HFSS is a finite-elemt-based software pakage that solves Maxwell's equations in mirowave strutures. The region inside an arbitrarily shaped struture, suh a a waveguide-to-oaxial transition, is brok into a mesh oftetrahedra (Fig. 1). The eletri and magneti fields inside eah tetrahedron are approximated with a polynomial funtion ontaining unknown amplitudinal oeffiits. The solution is obtained by omputing these oeffiits. The mesh is refined iteratively until the errors are redued to an aeptable level, produing a onverged solution. Sine the solution proess gerates large matries of eletromagneti field data and is memory- and proessor-intsive, a very fast omputer with a large hard disk and with a large random aess memory (RM) is needed to solve problems. typial onfiguration inludes a 57-million-instrutions-per-seond (MIPS) proessor with 64 Mbytes of RM and a 75-Mbyte hard disk. The primary output of the HFSS analysis is the sattering (S) parameters for the ompont under analysis. S-parameters desribe the relationship betwe the input, output, and refleted signals of a ompont or iruit (Fig. 2). In addition to the S-parameter output, the HFSS an display graphial represtations of eletri and magneti fields. These fields an also be viewed moving Figure 1. To solve Maxwell's equations in a mirowave struture, the region inside the struture, suh as this waveguide-to-oaxial transition, is brok into a mesh of tetrahedra. The eletri and magneti fields inside eah tetrahedron are th approximated with a polynomial funtion ontaining unknown amplitude oeffiits. The solution is obtained by omputing these oeffiits. 38 Johns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994)

2 S11 Two-port network S21 '" Mirostrip trae S12 S22 Mirostrip board S1 1 = Input return loss S12 = Reverse gain (or insertion loss) S21 = Forward gain (or insertion loss) S22 = Output return loss a 1 = Port 1 input signal b 1 = Port 1 output signal b 2 = Port 2 output signal a 2 = Port 2 input signal Coaxial setion Figure 2. Sattering parameters are voltage ratios betwe the signals tering a iruit and the signals exiting the iruit. The nomlature Snm signifies the ratio of a signal exiting port n (i.e., onnetion point) to an input signal applied at port m. For example, an amplifier with port 1 as its input and port 2 as its output is desribed by its forward gain as S21 ' its reverse gain as 8 12, and its input and output return losses as 8 11 and 8 22, respetively. symmetri, lossless, two-port passive struture, unlike an amplifier, passes signals equally in both diretions (8 21 = 8 12 ), and the input and output impedanes (or return losses) are equal (8 11 = 8 22 ), For passive strutures, 8 21 and 8 12 are also known as "i nsertion losses." through the struture as a funtion of time. This apability gives the mirowave gineer valuable insight into the operation of mirowave strutures. MICROW VE TRNSITION NLYSIS Numerial eletromagneti field solvers are partiularly useful for the analysis of mixed media strutures suh as waveguide-to-mirostrip transitions. Several transitions betwe mirowave transmission media have be analyzed, inluding several waveguide-to-mirostrip transitions and a stripline-to-oaxial transition. Waveguide Waveguide-to-Mirostrip Transitions Mirowave gineers at PL developed a waveguideto-mirostrip transition (Fig. 3) for an array of MMIC transmit-reeive modules. The measured and HFSS alulated return losses are shown in Figure 3C. The HFSS alulated data are in lose agreemt with the measured data, onfmning the auray of the analytial tool. The waveguide-to-mirostrip transition was designed using ut-and-try tehniques; many iterations were needed to produe the final design, and the proess was timeonsuming and ostly. The use of a numerial eletromagneti field solver would have eliminated the need for the physial design iterations, and the transition ould have be built only one, after the design and analysis were omplete. The analysis took advantage of the symmetry of the transition (Fig. 3) to redue omputation time and disk usage. If an objet has geometri symmetry, the HFSS field solution an be obtained by solving for the fields in only half the struture. Sine the solution matrix is redued, the use of symmetry saves proessor time, RM, and disk storage spae. Figure 3 shows an eletri field plot gerated by the HFSS. Numerial eletromagneti field solvers are partiularly useful for analysis of mixed media strutures suh as a 3-GHz stepped fin waveguide-to-mirostrip transition (Fig. 4). The stepped fin struture serves to ontrate ' -1 iii' :s -15 (f) (f).q -2 :: :; HFSS alulated Measured -35 LL Frequy (GHz) Figure 3. Waveguide-to-mirostrip transition analysis.. Highfrequy struture simulator (HFSS) model.. Eletri field plot gerated by HFSS (: magnitude of eletri field [volts/ meter]). C. Measured and alulated return losses. Johns Hopkins PL Tehnial Digest, Volume 15, Number J (1994) 39

3 . R. lablon, C. R. Moore, and 1. E. Pn z xy Waveguide Mirostrip 1.51e+4 finned waveguide. The HFSS was also used to determine the depth of the final fin for optimum oupling into the 25-mil-thik alumina mirostrip. Figures 4 to 4D show the eletri field distribution in the vertial tral plane as the exiting field is varied in 6 inremts. This phase variation has the effet of dupliating the animation available on the workstation sre that shows the ergy moving down the waveguide and into the mirostrip. The seque shows that ergy attempts to radiate into the transverse eletri retangular waveguide (TE\O) mode off the bak of the final fin. Therefore, it is important to house the mirostrip in a waveguide beyond utoff to prevt ergy loss to this unwanted mode. Some work on the dimsions of the step preeding the final fin ould improve the refletion oeffiit. Stripline-to-Coaxial Transition Engineers at PL designed a stripline-to-oaxial transition (Fig. 5) for a mirostrip antna array. The transition inludes a guard trae, or mode suppressor, to prevt a parallel-plate waveguide mode from propagating beyond the d of the stripline trae. The guard trae is onneted to the top and bottom stripline ground planes using via holes. The top dieletri layer of the stripline is shown in Figure 5 using its tetrahedra mesh. The bottom stripline dieletri layer and the oaxial setion are drawn as solids. One again, the symmetry of the struture was used to redue omputation time. Figure 5 is a field plot showing the eletri field rossing the transition; the figure shows the utility of the HFSS in simulating onnetions betwe layers in multilayer mirowave boards. Multilayer boards will beome inreasingly ommon in the future for phased-array antna feed networks. o Field peak e+4 Figure 4. Stepped fin waveguide-to-mirostrip transition:. Highfrequy struture simulator (HFSS) model.. through D. Seque of field plots shows a wave propagating through the transition in phase steps of 6 (: magnitude of eletri field [volts/meter]). the eletri field into a ross setion with dimsions omparable to the mirostrip struture. The fins were designed using quarter-wavelgth transformer theory, whih gives ratios of the impedanes at eah step. The HFSS was used to quikly develop a urve of impedane and wavelgth ver us single fin depth in WR28 (26.5 to 4 GHz) waveguide. This analysis was performed beause the literature deals only with dual (symmetri) WVEGUIDE COMPONENT NLYSIS Mirowave gineers at PL designed a five-port, radial-avity, E-plane, retangular waveguide juntion at 32 GHz aording to a retly published theory.2 Engineers analyzed the design (Fig. 6) at several frequies aross the waveguide band. The sattering parameters produed by swept frequy analysis (Fig. 6C) indiated that the equal amplitude power split ours at 35 GHz instead of the 32-GHz design frequy. Figure 6 shows the HFSS simulation at 35 GHz, where equalamplitude inidt signals of appropriate phase delay on four ports are summed ohertly at the fifth port. nine-way power splitter in WR62 (12 to 18 GHz) waveguide is shown in Figure 7 ; the eletri field distribution at 15 GHz in the tral plane and at eah port is shown in Figure 7. Nine-way power splitter waveguide problems are analyzed fairly quikly sine the aspet ratio betwe the smallest and largest feature is usually only about 1. Strutures that ombine waveguide and mirostrip oft have aspet ratios exeeding several hundred and take hours to solve. MMIC COMPONENT NLYSIS Design gineers an use numerial eletromagneti field solvers to aid in the design of MMIC'S. Determining parasitis and oupling betwe losely spaed ompo- 4 Johns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994)

4 Mirowave Compont nalysis Using a Field Solver 8 Stripline top ground plane ] (J) } Top dieletri layer : } ottom dieletri layer Stripline bottom (f) ground plane E r--- Coaxial setion.v.;...-:----- Stripline trae 2.92e+4 (.LJ...:t--?-'''' Guard pin (attahed to guard trae)..j)piii Guard trae O.OOe+OO Figure 5. Stripline-to-oaxial transition for a mirostrip antna array.. High-frequy struture simulator (HFSS) model.. Eletri field plot (: magnitude of eletri field [volts/meter]). nts in a MMIC layout is one area where field solvers suh as the HFSS are invaluable. field solver is also invaluable in aurately analyzing transitional strutures suh as a launh from a oplanar eletromagneti field into a mirostrip on the MMIC. Linear simulators are normally used to analyze mirowave iruits and MMIC'S; but linear simulators, whih use empirial and theoretial mathematial models to analyze the iruits, are not apable of determining eletromagneti field effets suh as parasitis and oupling betwe iruit omponts. Refere 3 ompares linear simulator models, measuremts, and HFSS simulations done at PL for some MMIC apaitors, indutors, and a few mirostrip strutures; Refere 3 also reports the lose agreemt betwe HFSS simulations and measuremts for various MMIC elemts. Three examples OfMMIC strutures that require a field solver are oplanarto-mirostrip launhes, MMIC 5- alibration standards, and ganged transistor feed for a power amplifier. Coplanar-to-Mirostrip Launh Numerial eletromagneti field solvers an be invaluable in the analysis of physial or eletrial transitions used in ompont pakaging or in hanges in propagation modes. Wafer probe stations employed for MMIC testing use oplanar launhes. MMIC design typially uses a mirostrip for interonnetion. MMIC oplanarto-mirostrip launh (Fig. 8) provides a low-loss, wellmathed transition betwe the probe station and the MMIC under test. Linear simulation of this launh is not suffiitly aurate wh the launh is part of an onwafer alibration standard. more aurate determination of the oplanar launh harateristis has be made by numerially extrating the S-parameters for a single launh from a measuremt of two launhes bak-tobak (i.e., there is no method for measuring a single launh). The numerial extration method for deriving S-parameters for two sequtial or ganged launhes is a good approximation, but it does not have a unique solution for the S II and S22 of the launh. eause of the symmetry of the two bak-to-bak launhes, only two unique measuremts are obtained for the ganged launh Johns Hopkins PL Tehnial Digest, Volume 15, Number I (1994 ) (i.e., SII * = S22*; S12* = S21* [*S-parameters of two bakto-bak launhes]). However, the single launh is not symmetrial and thus has three unknowns (S II, S22' and S12 = S21), whih are solved by assuming that the input and output impedanes are equal (Sll = S22)' (Sll-input return loss; SITreverse gain; S21-forward gain; S2TOUtpUt return loss). The launh has be simulated using the HFSS and has be ompared with the numerially extrated S-parameters. Figure 8 shows the launh tered into the HFSS with the launh struture formed by a 1-j-tm-thik gallium arside substrate and the metal ondutor. Figure 8C shows the eletri field lines at the oplanar side of the launh, and Figure 8D shows the eletri field lines on the mirostrip side. Visualizing the field lines with HFSS gives insight into some of the problems of transitioning propagation modes; visualizing the field lines also shows that the design is operating in the modes desired and that no unantiipated extraneous propagation modes dominate its operation. In the HFSS simulation, S II and S22 are nearly equal in magnitude but not in phase. Sine physial differes betwe the two ds of the launh exist, the results orrespond to intuitive expetations. Simulations of loss in the launh are not predited as well with HFSS as with the numerial extration. Figure 9 shows the simulation results. hybrid S-parameter desription of the launh using HFSS'S predited input and output impedanes and the numerially extrated insertion loss would seem to be a reasonable desription of the launh harateristis. Giv the auray of the measuremts, this hybrid launh desription ould not be proved to be better than the numerially extrated S-parameters. esides the measuremt limitations, another limit was that the HFSS analysis of the launh struture required onsiderable omputing resoures. mahine with 57 MIPS, 192 Mbytes of RM, and over 1 Gbyte of disk spae was required to ahieve reasonable onverge. Ev with the additional solve iterations allowed by a mahine with this power, it was still diffiult to determine wh the HFSS solution was suffiitly onverged. 41

5 . R. Jablon, C. R. Moore, and J. E. Pn Port 3 Port 2 MMIC 5- Calibration Standard Several ret PL MMIC designs inluded on-wafer alibration standards, whih provided very good measuremt agreemt with several differt alibration tehniques up to about 26 GHz. Wh attempts were made to measure up to 5 GHz, the measuremt auraies and the limited ability to measure the oplanar-tomiros trip launhes did not yield the lose agreemt observed up to 26 GHz. The HFSS provided insight into why one of the alibration standards ould not be aurately used. Two 1- resistors onneted in parallel aross the oplanar-tomirostrip launh (Fig. lo) provided a 5- resistane to ground as a measuremt standard. n attempt was made to de-embed the launh struture from the resistor measuremt using the numerially extrated S-parameters for the launh. y analyzing the eletromagneti Port e e Q +=' CD E d(s21) Port 2 -- d(s31) Port 3 d(s41) Port 4 -- d(ss1) Port 5 4.e+3-1L- -L -L Frequy (GHz) Figure6. Five-port, radial-avity, E-plane, retangularwaveguide juntion analysis.. High-frequy struture simulator (HFSS) model.. Eletri field plot (: magnitude of eletri field [volts/meter]). C. Sattering parameters. O.OOe+OO Figure 7. Nine-way power splitter in WR62 waveguide.. Highfrequy struture simulator (HFSS) model.. Eletri field distribution (: magnitude of eletri field [volts/meter]). 42 f ohns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994)

6 Mirowave Compont nalysis Using a Field Solver COPlana V<J txj ground = (...= 22 E (1j.. Key COPla trae COPlana ground =J ir Mirostrip trae ; V<J Simulations of both types of 5- terminations are shown in Figure 1C. The HFSS simulation of the launh onneted to two 1- resistors in parallel as a oplanar 5- termination agrees reasonably well with the measured data. In Figure 1C, R WR5 is the measuremt of a launh plus the oplanar termination. The HFSS simu- m.q -.25 o ID - HF88 simulation 8 21 =J Gallium arside substrate =J Metal ondutor -Via hole C - Numerial extration '-----'---'------'----'---'---'-- '-----'- --'------' 25 5 o Frequy (GHz) HF88 simulation 8 21 (End view) -5 - Numerial extration 8 21 D Gallium arside substrate I Metal ondutor o 25 Frequy (GHz) Indutive region Capaitive region 5 Input and output mathes 8 11 and 8 22 (End view) Figure 8. Monolithi mirowave integrated iruit (MMIC) oplanar-to-mirostrip launh analysis.. Two bak-to-bak oplanarto-mirostrip launhes (short through).. High-frequy struture simulator (HFSS) model. C. Coplanar mode eletri field (d view). D. Mirostrip mode eletri field (d view). propagation modes, the flaw in the de-embedding tehnique was realized. Two bak-to-bak launhes were measured where the oplanar mode from the probe station hanged to a mirostrip mode in the substrate and th bak into the oplanar mode. In the alibration standard used, the oplanar mode launhed from the probe head never hanged to a mirostrip mode beause the two resistors formed a oplanar termination. The alibration standard must terminate in a 5- impedane that fores the eletri field into the mirostrip mode (Fig. lo) ) HF88-8 simulation 22-8 =8 } Numerial approximation.75 Normalized resistane (ohms) Figure 9. S-parameter plots for oplanar-to-mirostrip launh:. Magnitude plot of high-frequy struture simulator (HFSS) simulation versus numerial extration for Phase plot of HFSS simulation versus numerial extration for S21. C. Smith hart plot of HFSS simulation versus numerial extration for S11 and S22 Johns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994) 43

7 . R. Jablon, C. R. Moore, and J. E. Pn lation COPMCR5 of the oplanar 5- termination mathes fairly well. If the resistor terminates in a "mirostrip mode," th the results with the launh are dramatially differt from the launh with resistors in a oplanar. Coplanar ground Coplanar (\j trae a. u Coplanar ground -- =J Indutive region RWR5 Measured launh and 5- oplanar termination COPMCR5 HF88 simulation launh and 5- oplanar termination COPMR52 HF88 simulation launh and 5- mirostrip mode EGVR5 Launh plus HF88 simulation of 5- resistor =J Capaitive region Normalized resistane (ohms) Figure 1. Monolithi mirowave integrated iruit 5- alibration standard analysis.. Coplanar-to-mirostrip launh with oplanar termination.. Coplanar-to-mirostrip launh with series termination. C. Differes in oplanar launh with 5- oplanar termination versus 5- mirostrip mode termination (HFSS = highfrequy struture simulator). 44 onfiguration. In Figure 1C, COPMR52 is the HFSS simulation of a resistor terminated after the mirostrip mode is launhed. Ganged Transistor Feed for a Power mplifier Wh designing a power amplifier, several field-effet transistors (FET) are typially ombined in the final amplifier stage to inrease the power output. For a ret MMIC power amplifier designed at PL, gineers used a simple feed struture to ombine four FET'S in the final stage of the amplifier. alaning the eletrial lgths of the input and output feeds to the four FET'S is ritial so that the output power will ombine in phase. ny phase imbalane tds to derease the output power. Figure II is a shemati and layout of the linear simulation of the feed struture used in one of the amplifier designs. The feed is nearly symmetrial, but the feeds to the two middle FET'S may parasitially ouple bak to the main feed. The HFSS was used to simulate this struture and ompare the phases. s expeted, a relatively small phase imbalane ourred for this design (Figs. li and lic). 6 phase imbalane at 13.6 GHz is negligible, but at a higher frequy this feed design would ause a pronouned loss of power. MICROSTRIP NTENN NLYSIS The Laboratory has used a numerial eletromagneti field solver to aid in the design of mirostrip antnas. lthough antna analysis is omputationally intsive beause of the requiremt for a boundary approximating free spae, analysis using HFSS provides valuable insight into the operation of the mirostrip antna. ny struture analyzed by the HFSS must be ompletely surrounded by boundaries perfetly ondutive by default; these boundaries an also be redefined as ports, perfet magneti boundaries, imperfetly onduting boundaries, or as resistive surfae boundaries. The simulation of free spae is required for aurate antna simulation. For the mirostrip antna, free spae is simulated by reating a hemispherially shaped air dieletri spae above the antna and by defining the boundary betwe the hemisphere and the bakground as a 377--per-square resistive surfae. Figure 12 shows the HFSS struture for a oaxial-probe-fed mirostrip antna. The analyzed struture has be ut in half to take advantage of symmetry. Mirowave gineers at PL have suessfully modeled two differt mirostrip antnas and determined their return losses. Modeling an be used to help determine the optimum loation for the feed probe, the bandwidth, and the effets of differt substrate thiknesses and dieletri onstants. Using the HFSS graphial field output option, a propagating wave an be se (Fig. 12) traveling from the mirostrip path edges to the 377- resistive boundary for a 1-GHz mirostrip antna. Figure 12 learly illustrates the radiation of the fields from the mirostrip antna edges. The field di play gives the design gineer valuable insight into the operation of the antna. Engineers onduted an HFSS simulation for a mirostrip path radiator at 31.5 GHz. The swept-frequy Johns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994)

8 FET 1 (Port 2) Mirowave Compont nalysis Using a Field Solver ir FET 2 (Port 3) Input (Port 1) FET 3 (Port 4) -6. FET 4 (Port 5) Mirostrip path antna o HF CIl CIl.Q :;:; Q; CIl E HF Linear simulator 8 21 and 8 31 Coaxial setion C Frequy (GHz) -15 Propagating wave OJ -3 CIl o. - - HF HF Frequy (GHz) Figure 11. Power amplifier feed for four parallel field-effet transistors (FETS).. Layout and 8 31 amplitude omparison betwe high-frequy struture simulator (HFSS) results and linear simulator results. C and 8 31 phase omparison betwe HFSS results and linear simulator results. C 5 4 a: 3 (f) > sattering parameters derived from the HFSS analysis with three and six iterations are ompared with the theoretial preditions in Figure 12C. The use of a resistive boundary makes the mirostrip antna problem omputationally intsive. In addition, strutures having high-quality fator resonanes, suh as mirostrip antnas, are partiularly troublesome for this type of simulator. It takes a number of onverges over a range of frequies to "home in" on the resonane. The six -iteration solution for the 31.5-GHz antna analysis was done on a 75-MIP mahine with 128 Mbyte of RM Frequy (GHz) Figure 12. Coaxial-probe-fed mirostrip antna analysis:. High-frequy struture simulator (HFSS) model.. Eletri field plot (: magnitude of eletri field [volts/meter]). C. Visual standing wave ratio (VSWR) for a three- and six-iteration solution versus lassial theory. Johns Hopkins PL Tehnial Digest, Volume 15, Number J (1 994) 45

9 . R. JabLon, C. R. Moore, and J. E. Pn running for several days. This problem represts the urrt limit of omplexity that the software an handle on the most powerful workstations available in It is antiipated that the HFSS will be used in the future to determine the input return loss for other antnas suh as waveguide horns. MUL TIP CTOR REKDOWN NLYSIS Componts in high-power mirowave systems operating in a spae vironmt may be subjet to multipator breakdown, whih is an eletron resonane disharge phomon that ours only in a vauum. 4 Multipator breakdown an adversely affet the performane of omponts by ausing exessive noise, resonant avity detuning, erosion of ompont surfaes, and failure. In the past, approximate analytial tehniques were used to predit the possibility of multipator breakdown in omponts having simple geometries; for omponts having more ompliated geometries, expsive and oft unreliable testing was required. Past analytial tehniques and tests an now be replaed by a numerial eletromagneti field solver that an provide an exat analysis of the eletri fields inside the omponts. One the magnitude of the fields is known, the pottial for multipator breakdown an be determined by omparing the field strgth data with a plot of the multipator existe region of the ompont. Mirowave design gineers at PL have performed a multipator breakdown analysis of the Midourse Spae Experimt X-band antna feed (Fig. 13) using the HFSS.5 The HFSS model (Fig. 14) showing the portion of the feed relevant to the analysis onsists of an input oaxial setion followed by a half-wave oax to two-wire (unequal diameters) balun. Figure 14 shows an eletri field plot for this struture. The alulated voltages at z xj.. y 2: OJ (5 > (1j a u= 18 ev k = 1.89 o alun o alun-oax interfae Figure 13. Midourse Spae Experimt X-band antna. 46 o Transformer edge Frequy x spaing (MHz m) Figure 14. Multipator breakdown analysis for the Midourse Spae Experimt X-band antna feed.. High-frequy struture simulator (HFSS) model.. Eletri field plot (: magnitude of eletri field [volts/meter]). C. Calulated voltages and multipator breakdown existe region. Voltages falling above the mode velope indiate possible multipator breakdown problems. Voltages falling below the mode velope indiate that no multipator breakdown an our. The voltages alulated for three setions in the antna feed indiate that no multipator breakdown an our in the feed. U = eletron kineti ergy. k = onstant (determined by minimum kineti ergy required for seondary eletron emission). Johns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994)

10 Mirowave Compont nalysis Using a Field Solver various points on the feed are plotted with the multipator breakdown existe region plot in Figure 14C. Sine the voltages in the feed fall below the multipator breakdown existe region, multipator breakdown annot our in this feed struture. This analysis eliminated the need for expsive vironmtal testing. CONCLUSION Mirowave gineers at PL have suessfully used a numerial eletromagneti field solver (the Hewlett Pakard HFSS) to aurately model mirowave omponts suh as transitions, waveguide omponts, MMIC omponts, and antnas. The field solver is a new modeling tool that will ontribute signifiantly to the effiit, ost-effetive design of prest and future mirowave systems. REFERENCES I nger,., "Software Computes Maxwell' s Equations," Mirowave J. 33(2), (2 Feb 199). 2ialkowski, M. E., "nalysis of an N-Port Consisting of a Radial Cavity and E-Plane Coupled Retangular Waveguide," IEEE Trans. Mirowave Theory Teh. 4(a), (Sep 1992). 3pn, J. E., and Moore, C. R., "Model Verifiation of Passive MMIC Strutures Through Measuremt and 3D Finite Elemt Simulation," in Pro. 3rd nnual Johns Hopkins Univ. Mirowave Symp., altimore, Md., pp. I1-Il3 (1992). 4Clany, P. F. "Multipator Control in Mirowave Spae Systems," Mirowave J. 3, (Mar 1978). SJablon,. R., "Spaeraft ntna Multipator nalysis Using a umerial Eletromagneti Simulator," in Pro. 3rd nnual Johns Hopkins Univ. Mirowave Symp., altimore, Md., pp. IXl-IXI2 (1992). THE UTHORS LLN R. JLON is a member of the PL Sior Staff and is an gineer in the Mirowave and RF Systems Group in the Spae Departmt. He reeived an M.S. in eletrial gineering from The Johns Hopkins University G.W.e. Whiting Shool of Engineering in 199 and a.s.e.e. from Virginia Polytehni Institute and State University in Sine joining PL in 1986, he has worked in antna de ign, developmt, and testing as well as in RF systems, and mirowave iruit design. He has designed and developed antnas for the TOPEX, SLT, and MSX spaeraft programs. CRIG R. MOORE is a member of PL's Prinipal Staff. He reeived.e.e. and M.S. degrees from Cornell University in 1962 and 1964, respetively. He previously served as assoiate division head at the National Radio stronomy Observatory, prinipal researh assoiate for the ustralian governmt, and group manager at dix Field Engineering Corporation, before joining PL in His work at the Laboratory has involved improvemts to the hydrog maser, work on ultra-high Q ryogi mirowave resonators, and MMIC design and testing. He is urrtly projet manager for an ultra-small satellite terminal design effort. Mr. Moore is a sior member of the IEEE and has authored more than twty papers. He teahes MMIC design at The Johns Hopkins University G.W.e. Whiting Shool of Engineering. JOHN E. PENN is a member of PL'S Sior Staff. He reeived a.e.e. from The Georgia Institute of Tehnology in 198, and M.S. degrees in eletrial gineering and omputer sie from The Johns Hopkins University in 1982 and 1988, respetively. Mr. Pn joined PL in 198, where his work has involved ustom integrated iruit design, semi-ustom design, silion ompiler design, digital design, programming, and, more retly, mirowave design. He left the Laboratory in 199 to work as an appliations gineer for Silion Compiler Systems, whih beame part of Mtor Graphis. In 1992, he rejoined the Laboratory in the S2R Group where he has be designing MMIC'S. Mr. Pn o-teahes a MMIC design ourse with Craig Moore at The Johns Hopkins University G.W.e. Whiting Shool of Engineering. Johns Hopkins PL Tehnial Digest, Volume 15, Number 1 (1994) 47