Enhancing the Accuracy of Microwave Element Models by Artificial Neural Networks

Transcription

1 RADIOENINEERIN, OL. 3, NO. 3, SEPTEMBER 4 7 Enhancng the Accuracy of Mcrowave Element Models by Artfcal Neural Networks Josef DOBEŠ, Ladslav POSPÍŠIL Dept. of Rado Electroncs, Czech Techncal Unversty, Techncká, 66 7 Praha, Czech Republc dobes@feld.cvut.cz, pospsl@jablotron.cz Abstract. In the recent PSpce programs, fve types of the aas FET model have been mplemented. However, some of them are too sophstcated and therefore very dffcult to measure and dentfy afterwards, especally the realstc model of Parker and Skellern. In the paper, smple enhancements of one of the classcal models are proposed frst. The resultng modfcaton s usable for the accurate modelng of both aas FETs and phemts. Moreover, ts updated capactance functon can serve as an accurate representaton of mcrowave varactors, whch s also mportant. The precson of the updated models can be strongly enhanced usng the artfcal neural networks. In the paper, both usng an exclusve neural network wthout an analytc model and cooperatng a correctve neural network wth the updated analytc model wll be dscussed. The accuracy of the analytc models, the models based on the exclusve neural network, and the models created as a combnaton of the updated analytc model and the correctve neural network wll be compared. Keywords aas FET, phemt, mcrowave varactor, parameters extracton, CAD, artfcal neural network.. Introducton The Sussman-Fort, Hantgan, and Huang [] model equatons can be consdered a good compromse between the complexty and accuracy they are updated from []). However, both statc and dynamc parts of the model equatons must be modfed when usng them for possble phemt or varactor modelng.e., for the elements that are often used n the mcrowave crcuts). All the model modfcatons defned below have been mplemented nto the program C.I.A. Crcut Interactve Analyzer) [6]. However, the accuracy of the updated model functons s stll of a percentage order. To be more precse, usng the artfcal neural networks s the effectve and relatve smple way because we can utlze the standard MATLAB toolbox []. There are two ways of usng the neural networks. The frst conssts n approxmatng the element by an exclusve neural network, the second combnes the analytc model wth a correctve neural network.. Improvement of the Analytc Model The dagram of the aas FET model s shown n Fg., whch s applcable for all the PSpce modelng levels [6].. Modfyng the Statc Part of the aas FET Model The fundamental voltage-controlled current source I d of the aas FET model can be defned for the forward mode d ) as T = T σ d, a) { for g T, I d = β g T ) n + λ d ) tanhα d ) otherwse, b) and by the mrrored equatons for the reverse mode d < ) T = T + σ d, a) { for g T, I d = β ) n g T λd ) tanhα d ) otherwse, b) where g = g d see the current and voltages n Fg.. The model parameters T, β, n, λ and α have already been defned n [], the parameter σ used n the boxed parts of ) and ) represents the update of the smpler classcal models. Note that the Parker-Skellern realstc model contans smlar relatons [3] as a part of complcated nternal functons a) and a) can be consdered as ther core. Although the equatons ) and ) are relatvely very smple, they contan an mprovement n comparson wth the classcal Curtce model [] n whch characterzes gate voltage nfluence on I d more precsely), and also n comparson wth the classcal Statz model [4] σ whch characterzes dran voltage nfluence on I d more precsely).

2 8 J. DOBEŠ, L. POSPÍŠIL, ENHANCIN THE ACCURACY OF MICROWAE ELEMENT MODELS BY ARTIFICIAL NEURAL NETWORKS..5 I D r D.75 C g g d Schottky junctons I d I d frequency dsperson dent) meas) D D ) ), A I I ) r S Fg. 4. Results of the phemt model dentfcaton utlzng ) and ) rms =.38 % and δ max = 8.4 %). The measured data are taken from [9]., ), ) A ) dent, C.. I A.) dent, Statz) meas) D D D I I I Fg Smplfed dagram of the aas FET model, whch ncludes the frequency dsperson. For characterzng a gate delay, a new method based on the second-order Bessel functon n frequency doman) and dfferental equaton assocated to that functon n tme doman) s suggested n [7] t uses the way proposed n [8], but wth more precse modelng the delay). ) Fg.. Fg. 3. C Comparson of the aas FET model dentfcaton utlzng ) and ) and the classcal Statz equatons [4] rms =.73 % and δ max = 8 % for the model suggested here). The measured data are taken from [5]. A B Suggested aas FET model functon for the varactor representaton. The mportance of the modfcatons a) and a) can be clearly demonstrated by the dentfcaton of the model parameters for DZ7 [5] aas FET see the results n Fg. [8]. The C.I.A. optmzaton procedure [6] has provded the values of the model parameters T =.36, β =.346 A, n =.73, λ =.8 note that the negatve value of ths parameter arses normally f σ s actvated), α =.56, σ =.4, r D =.88 Ω, and r S =.6 Ω note that the r D and r S parameters have already been estmated n [5]). To compare the achevement, the parameters of the same aas FET has also been dentfed by the classcal Statz model [4]. As shown n Fg., the model suggested here s more accurate, especally for the lesser values of the gate-source control voltage, and also for the greater values of the dran current.. Usng the Modfed Model as a phemt Representaton The modfcatons a) and a) also enable the model to be utlzed for the phemt modelng see the results n Fg. 4. The dentfcaton process has set the model parameters to T =.64, β =. A, n =.99, λ =.88, α =.6, σ =.797, r D =.3 Ω, and r S =. Ω. As seen n Fg. 4, the representaton of phemt usng ) and ) s very precse rms % only) and s slghtly more accurate than the TrQunt one n [9] see [] and [] as the exhaustve TrQunt model defntons). The model s also able to form a negatve dfferental conductance, whch s llustrated n Fg. 4. On the other hand, at very hgh frequences, the s parameter does not match the DC curves. Therefore, a correctve current source I d must be added dentfed by the s parameters measurement. Note that embeddng the frequency dsperson can also be performed n another more precse, but more complcated way, see [3].

3 RADIOENINEERIN, OL. 3, NO. 3, SEPTEMBER Modfyng the Dynamc Part of the aas FET Model In general, the aas FET gate capactance s hghly nonlnear as shown n Fg. 3. Its defnton splts nto the three parts, smlar to those n the Statz model [, 3] φ T ɛw arctan for g A, T g g A [C J ) m B + B A φ C g = π ɛw ] ɛw arctan φ T + T A φ T ɛw arctan for g > A T A g < B, π ɛw + C J ) m g for g B, φ 3) where the transtonal regon s determned emprcally [] A = T.5, B = T ) All the model parameters have been defned n [] wth the excepton of the boxed m. Ths parameter can be found among the model parameters of the recent PSpce programs only, all the classcal models always use the theoretcal value nstead of m [4, 5]..4 Usng the Modfed Model as a aractor Representaton The mcrowave varactors are hghly nonlnear wth observed dependences smlar to those n the aas FET gate capactances. Therefore, the functons n 3) can be utlzed after replacng C g and g wth the external ones,.e., wth C and. Let s emphasze that such emprcal method s often used n the aas FET modelng, especally n [3]..4. Testng the aractors of Texas Instruments Frstly, let s demonstrate ths dea by dentfyng Texas Instruments E83 gate and source [4] varactors see the results n Fg. 5 and 6. The dentfcatons confrm that the usage of 3) enables more accurate approxmaton than the 6 th order polynomal used by the authors of [4]. For the gate varactor, the optmzaton procedure has gven the values of the model parameters ɛw =.57 pf, C J =.77 pf, T =.7569, φ = 3.45!), and m =.87!). Of course, the last two parameters do not have physcal values, whch llustrates the necessty of usng the general m-power n 3). From the physcal pont of vew, the varactor s not defned for > B by the classcal juncton capactance functon however, ths formula s suffcently flexble for approxmatng t. For the source varactor, the optmzaton procedure of the C.I.A. has gven the values of the model parameters ɛw =.3587 pf, C J =.6665 pf, T =.66, φ = 3.5, and m = wth a more precse devce characterzaton let s compare the values rms and δ max., ), ) pf) dent, C.. I A.) dent, polyn) meas) C C C, ), ) pf) dent, C.. I A.) dent, polyn) meas) C C C Fg Comparson of the E83 gate varactor model dentfcaton usng 3) and the classcal polynomal functon rms = 4.5 % and δ max = 3.7 % for the model suggested here). The measured data are taken from [4], where the polynomal approxmaton a + a a) +a 3 a) 3 + +a 6 a) 6 has also been tested wth the naccurate results dashed curve) shown above n [4], the parameters a = 8, a =.54 pf, a =.3 nf, a 3 = nf 3, a 4 =.4 µf 4, a 5 =.458 µf 5, and a 6 = 3.48 µf 6 were used) Fg. 6. Comparson of the E83 source varactor model dentfcaton usng 3) and the classcal polynomal functon rms = 4 % and δ max = 6.87 % for the model suggested here). The measured data, and the polynomal approxmaton a + a a) + a 3 a) a 6 a) 6 are taken from [4] agan a = 6, a =.9 pf, a =.4783 nf, a 3 = 4.73 nf 3, a 4 =.835 µf 4, a 5 =.475 µf 5, and a 6 =.377 µf 6 were used wth the naccurate results shown by the dashed curve).

4 J. DOBEŠ, L. POSPÍŠIL, ENHANCIN THE ACCURACY OF MICROWAE ELEMENT MODELS BY ARTIFICIAL NEURAL NETWORKS dent, C.. I A.) meas) ) pf) C C, C pf) Fg. 7. Results of the ILC varactor model dentfcaton usng 3) rms = 6. % and δ max = 3.7 %). The measured data have been granted by the authors of [7]. drect MLP rms =.% measured data optmzed model Fg. 8. ) Results of the ILC varactor model dentfcaton usng the drect neural network δ max =.4 % only!)..4. Testng the aractor of Internatonal Laser Centre Secondly, the hghly nonlnear capactance model [8] of the optcal SACM APD layer structure MO457/4 [7] has been dentfed see the results n Fg. 7. The optmzaton procedure of the C.I.A. program has gven the values of the model parameters ɛw =.555 pf, C J = pf, T = , φ = 4.49, and m = Improvement of the Models Usng the Artfcal Neural Networks The root mean square devatons of the analytc models can be of the percentage order t s clearly llustrated n Sec.. To obtan lesser values, the artfcal neural networks are often used [9] for modelng the mcrowave elements. I D A) meas) dent) D D ma) I I rms =.7% = rms =.% rms =.6% rms =.6% rms =.7% Fg optmzed model measured data ) =.5 = -.5 = -. = -.5 Results of the phemt model dentfcaton usng the drect neural network MLP rms =. %). =.5/rms=.6% =-./rms=.36% =/rms=.3% =-.5/rms=.% =-.5/rms=37.4% Fg.. ) Results of the dentfcaton of dfferences between the measured data and acqured analytcal model shown n Fg. 4, whch s an outcome of the correctve neural network MLP rms = 7.56 %). A detaled descrpton of the concepton of the neural networks can be found n [9] wth the emphass to modelng the nonlnear mcrowave elements. An especal concepton of the dynamc neural networks DNN) s defned n []. A bref descrpton of the artfcal neural network concepton can also be found n []. There are two man ways for usng the artfcal neural networks. The frst conssts n utlzng an exclusve neural network,.e., wthout an analytc model, and the second uses a neural network only as a correcton tool of the dfference between the measured data and dentfed analytc model. 3. Utlzng the Drect Neural Network A neural network proposed for an approxmaton of an element wthout a cooperaton wth an analytc model can be

5 RADIOENINEERIN, OL. 3, NO. 3, SEPTEMBER 4 I D A) optmzed model measured data drect MLP = Fg.. ) = -. = -.5 = -. = -.5 Incorrect results of the aas FET model dentfcaton caused due to nsuffcent number of measured ponts. marked as drect. Frstly, the mcrowave element models dentfed n Sec. have been approxmated usng the drect neural networks to compare ther precson wth the updated analytc models. Regardng the neural networks, the standard multlayer structure [, Fg. ] has been used. The number of layers and the number of neurons n that layers have been carefully selected durng many numercal tests. The MATLAB Neural Network Toolbox [] has been used for all the numercal experments. 3.. Enhancng the Accuracy of the aractor Model The ILC varactor model has to be replaced by a neural network because the approxmaton wth the analytc functon 3) was not deal see Fg. 7 and the related values of rms and δ max. For characterzng the varactor, a smple structure MLP ncludng nput/output layers) has been used wth the results shown n Fg. 8 MLP abbrevates Mult Layer Perceptron). Emphasze that the accuracy of ths neural network s suffcent and hence there s no need to use a correctve neural network wth the analytc model 3). 3.. Enhancng the Accuracy of the phemt Model The drect neural network has also been used for approxmatng phemt see the results n Fg. 9 and Tab.. rms %) ) Analytc Neural network model Drect Correctve All Tab.. Comparson of the accuracy of the acqured analytcal model Fg. 4) wth the models created utlzng the drect Fg. 9) and correctve Fg. ) neural networks. Agan, a relatvely smple structure MLP has been chosen. As shown n Tab., the accuracy of the neural network has been approxmately ten tmes better than the updated analytcal model. 3. Utlzng the Correctve Neural Network Secondly, a neural network can be used as a correcton for the updated analytc model. In ths case, only the dfference between the measured data and prevously dentfed analytc model s approxmated usng the neural network such neural network can be marked as correctve. The accuracy of that method s expected to be greater n comparson wth the drect neural network because only a relatvely small value s approxmated see the example below. 3.. Enhancng the Accuracy of the phemt Model In Fg., the dfference between the phemt measured data and dentfed analytc model s shown and approxmated usng the correctve neural network. In ths case, a slghtly more complcated structure MLP has been chosen. The resultng accuracy of the updated analytc model wth the correctve neural network s shown n Tab.. It s clear that ths methodology gves the best precson. 3.3 Lmtatons of Usng the Neural Networks The artfcal neural networks must be used cautously. As shown n Fg., some curves do not nclude the pont [, ] therefore, ths pont must be added to the measured data before the optmzaton. Moreover, the element must be measured n a large number of ponts. Otherwse, we can obtan bzarre results as shown for the DZ7 aas FET n Fg. of course, the number of measured ponts of that aas FET s nsuffcent for the structure MLP Concluson A smple updatng of the analytc model has been verfed for the approxmaton of both aas FETs and phemts wth the precson of a percentage order. An unusual way s suggested for modelng the mcrowave varactors usng the modfed aas FET capactance model functon. Fnally, usng the drect and correctve neural networks s tested and compared from the pont of vew of accuracy. All the model parameters can be easly dentfed from measured data. Acknowledgements Ths paper has been supported by the rant of the European Commsson TARET Top Amplfer Research roups n a European Teamwork), and by the Czech Techncal Unversty Research Project MSM 34.

6 J. DOBEŠ, L. POSPÍŠIL, ENHANCIN THE ACCURACY OF MICROWAE ELEMENT MODELS BY ARTIFICIAL NEURAL NETWORKS Appendx The root mean square and maxmum devatons computed for the results n Fgs. are defned n the natural way n p = rms = δ max = max np = y dent) y dent) ) y meas) y meas) %, n p y meas) y meas) %, respectvely, where y dent) and y meas) are the dentfed and measured values, and n p s the number of all ponts. References [] SUSSMAN-FORT, S. E., HANTAN, J. C., HUAN, F. L. A SPICE model for enhancement- and depleton-mode aas FET s. IEEE Transactons on Mcrowave Theory and Technques, 986, vol. 34, no., p [] CURTICE, W. R. aas MESFET modelng and nonlnear CAD. IEEE Transactons on Mcrowave Theory and Technques, 988, vol. 36, no., p. 3. [3] PARKER, A. E., SKELLERN, D. J. A realstc large-sgnal MES- FET model for SPICE. IEEE Transactons on Mcrowave Theory and Technques, 997, vol. 45, no. 9, p [4] STATZ, H., NEWMAN, P., SMITH, I. W., PUCEL, R. A., HAUS, H. A. aas FET devce and crcut smulaton n SPICE. IEEE Transactons on Electron Devces, 987, vol. 34, no., p [5] JASTRZEBSKI, A. K. Non-lnear MESFET modelng. In Proceedngs of the 7th European Mcrowave Conference EuMC, 987, p [6] DOBEŠ, J. C.I.A. a comprehensve CAD tool for analog, RF, and mcrowave IC s. In Proceedngs of the 8th IEEE Internatonal Symposum on Hgh Performance Electron Devces for Mcrowave and Optoelectronc Applcatons EDMO, lasgow UK),, p. 7. [7] DOBEŠ, J. Expressng the MESFET and transmsson lne delays usng Bessel functon. In Proceedngs of the 6th European Conference on Crcut Theory and Desgn, Kraków Poland), 3, p [8] MADJAR, A. A fully analytcal AC large-sgnal model of the aas MESFET for nonlnear network analyss and desgn. IEEE Transactons on Mcrowave Theory and Technques, 988, vol. 36, no., p [9] CAO, J., WAN, X., LIN, F., NAKAMURA, H., SINH, R. An emprcal phemt model and ts verfcaton n PCS CDMA system. In Proceedngs of the 9th European Mcrowave Conference EuMC, Munch ermany), 999, p [] McCAMANT, A. J., McCORMACK,. D., SMITH, D. H. An mproved aas MESFET model for SPICE. IEEE Transactons on Mcrowave Theory and Technques, 99, vol. 38, no. 6, p [] SMITH, D. H. An mproved model for aas MESFETs. Techncal Report. TrQunt Semconductors Corporaton,. [] MASSOBRIO,., ANTONETTI, P. Semconductor devce modelng wth SPICE. New York: Mcraw-Hll, 993. [3] SIJERCIĆ, E., PEJCINOIĆ, B. Comparson of non-lnear MES- FET models. In Proceedngs of the 9th Internatonal Conference on Electroncs, Crcuts and Systems ICECS, Dubrovnk Croata),, p [4] CHAN, C.-R., STEER, B. R., MARTIN, S., REESE, E. Computeraded analyss of free-runnng mcrowave oscllators. IEEE Transactons on Mcrowave Theory and Technques, 99, vol. 39, no., p [5] WON, S. C. WnSPICE manual. erson.. Hong Kong: The Polytechnc Unversty, Dept. of Electronc Engneerng,. [6] PSpce A/D reference gude. erson.. San Jose: Cadence Desgn Systems, Inc., 3. [7] KLASOITÝ, M., HAŠKO, D., TOMÁŠKA, M., UHEREK, F. Characterzaton of avalanche photodode propertes n frequency doman. In Proceedngs of the 5th Scentfc Conference on Electrcal Engneerng & Informaton Technology, Bratslava Slovaka),, p [8] DOBEŠ, J. Usng modfed aas FET model functons for the accurate representaton of PHEMTs and varactors. In Proceedngs of the th IEEE Medterranean Electrotechncal Conference, Dubrovnk Croata), 4, p [9] ZHAN, Q. J., UPTA, K. C. Neural networks for RF and mcrowave desgn. Boston: Artech House,. [] XU, J., YAOUB, M. C. E., DIN, R., ZHAN, Q.-J. Neural-based dynamc modelng of nonlnear mcrowave crcuts. IEEE Transactons on Mcrowave Theory and Technques,, vol. 5, no., p [] RAIDA, Z., LUKEŠ, Z., OTEŘEL,. Modelng broadband mcrowave structures by artfcal neural networks. Radoengneerng, 4, vol. 3, no., p. 3. [] DEMUTH, H., BEALE, M. Neural network toolbox for use wth Matlab: User s gude. erson 4. Natck: The MathWorks, Inc.,. About Authors... Josef DOBEŠ receved the Ph.D. degree n mcroelectroncs at the Czech Techncal Unversty n Prague n 986. From 986 to 99, he was a researcher of the TESLA Research Insttute, where he performed analyses on algorthms for CMOS Technology Smulators. Currently, he works at the Department of Rado Electroncs of the Czech Techncal Unversty n Prague. Hs research nterests nclude the physcal modelng of rado electronc crcut elements, especally RF and mcrowave transstors and transmsson lnes, creatng or mprovng specal algorthms for the crcut analyss and optmzaton, such as tme- and frequency-doman senstvty, poles-zeros or steady-state analyses, and creatng a comprehensve CAD tool for the analyss and optmzaton of RF and mcrowave crcuts. Ladslav POSPÍŠIL was born n 97. He receved hs M.Sc. degree n electrcal engneerng from the Czech Techncal Unversty n Prague n 4. Currently he works as techncan at the Jablotron Ltd., Research and Developed Department, Secton Hgh Frequency. Hs research nterests manly consst n the actve component modelng wth the utlzaton of neural networks for mcrowave applcatons.