Transistor Characterization and Modeling and the Use of Embedding Device Models for the Design of Microwave Power Amplifiers

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1 Transstor Characterzaton and Modelng and the Use of Embeddng Dece Models for the Desgn of Mcrowae Power Amplfers Patrck Robln, Francsco J. Martnez-Rodrguez,, Hsu Chen Chang, Chenggang Xe and Jose I. Martnez-opez Electrcal and Computer Engneerng, The Oho State Unersty, Columbus, OH 40, USA Facultad de Ingenera, Unersdad Naconal Autonoma de Mexco, Mexco Cty 0450, Mexco Rockwell Collns, Cedar Rapds, IA 5498, USA Abstract Crcut-based large-sgnal dece models reman extensely used to desgn ntegrated and hybrd mcrowae crcuts. It has been recently demonstrated that dece models can also be proftably appled under the form of a nonlnear embeddng dece model to help wth the synthess of mult-transstor power amplfers (PA) such as Doherty PAs. In ths paper we shall dscuss ths new desgn process from dece modelng to PA desgn. Frst an example of an Artfcal Neural Network (ANN) SOS-MOSFET model drectly extracted from large-sgnal measurements wll be reewed and ts companon ANN nonlnear embeddng dece model presented. Nonlnear embeddng dece models can be mplemented for other models such as the Angelo model to desgn PAs. A general methodology for desgnng twotransstor Doherty or Chrex PAs usng an embeddng dece model wll be presented and prelmnary smulaton results on the desgn of a GaN Chrex amplfer usng an Angelo nonlnear embeddng dece model wll be reported. Index Terms Dece modelng, embeddng dece model, Chrex power amplfers. I. INTRODUCTION Crcut-based large-sgnal dece models reman the tool of choce to desgn ntegrated and hybrd mcrowae crcuts usng crcut smulaton. It has recently been demonstrated that dece models can also be proftably used under the form of a nonlnear embeddng dece model to help wth the synthess of mult-transstor power amplfers (PA) [-]. In ths paper we shall dscuss the assocated desgn process startng from the dece modelng to the PA desgn process. Frst an example of an artfcal neural networks (ANN) SOS-MOSFET model drectly extracted from large-sgnal measurements wll be reewed and ts companon ANN nonlnear embeddng dece model presented. Nonlnear embeddng dece models can be mplemented for other models such as the Angelo model to desgn PAs []. A general methodology for desgnng twotransstor PAs such as Doherty or Chrex PAs usng an embeddng dece model wll be presented. Fnally, prelmnary smulaton results on ts applcaton to the desgn of a GaN Chrex amplfer usng an Angelo nonlnear embeddng dece wll be reported. II. DEVICE MODEING The deelopment of a crcut-based mcrowae dece model s usually an ntense process. Howeer wth the adent of NVNAs, crcut-based nonlnear mcrowae models can nowadays be extracted for a targeted range of operaton from a few large-sgnal measurements [-7]. An example of SOS-MOSFET model wth memory effects extracted from a sngle 0 ms real-tme acte load pull (RTAP) was recently reported [8]. The effcent phase sweepng of the RTAP drastcally reduces the number of large-sgnal measurements needed for the model deelopment and erfcaton whle mantanng the same ntrnsc oltage coerage as n conentonal passe or acte load pull systems. The bas dependence of the charges and the current-oltage (IV) characterstcs are smultaneously extracted from these measurements usng ANNs. Memory effects assocated wth the parastc bpolar effect was also extracted that way for mproed modelng accuracy. Smlarly other memory effects (self-heatng, trappng) can be mplemented n ANN models for GaN deces [5]. III. EMBEDDING DEVICE MODE A general topology for an FET wthout memory effect for smplcty s shown n Fg.. A nonlnear transfer network lke the one shown n Fg. can be deeloped to moe the oltages and the currents from the IV currentsource reference plane (red) to b) the ntrnsc (green), c) the extrnsc (can), d) the package (blue) and e) the testbed (black) reference planes dependng on the needs or applcaton targeted /5/$ IEEE

2 Fg. : Dece model ncludng the (a) the current source (red), (b) the ntrnsc (green), (c) the extrnsc (can), (d) the package (blue) and (e) the tesbed (black) reference planes. The embeddng transfer network n Fg. has the same functon as ABCD parameters for lnear crcuts n the frequency doman but apples nstead to nonlnear crcuts operatng n the tme-doman. Combnng the transfer network wth the IV characterstcs lke s shown n Fg. yelds the embeddng dece model. Note that self-heatng or trappng models can be ncluded as part of the currentoltage plane crcut f the dece s affected by lowfrequency memory effects. practcal crcut mplementaton for the Angelo embeddng dece model. Fg. : Conceptual realzaton of an embeddng dece model from a) the ntrnsc current-oltage (IV) reference planes (nternal and external red boxes) to the b) extrnsc reference planes (blue box). Fg. : The embeddng dece model realzed by combnng the Embeddng Transfer Network and the IV characterstcs of the FET. Self-heatng s also ncluded as part of the IV. Conceptually an embeddng dece model can be realzed by usng negate resstances, capactances, nductance and charges to negate and eentually de-embed the dece back to ts IV characterstcs. Ths ant-crcut mplementaton s not, howeer, usually possble n commercal harmonc balance smulators due to stablty ssues. The reader s referred to [] for an example of a An embeddng dece model for the ANN dece model mentoned n Secton II and reported n [8], can be smlarly mplemented by replacng the nonlnear analytc IV and charge expressons of the Angelo model by neural networks used to represent them. To test the functonalty of ths ANN embeddng dece model t s suffcent to dre the ANN dece model by the ANN embeddng dece model as shown n Fg. 4. The mutual consstency between these two types of ANN model s demonstrated n Fg. 5 for the targeted ntrnsc load lnes (a) and projected extrnsc load lnes (b) of an SOS-MOSFET.

3 dece model (ncludng low-frequency memory effects f needed) has already been deeloped usng for example the model topologes dscussed n Secton II. Fg. 4: Embeddng dece model (left) connected to the dece model (rght) to test ther consstency. DS (t) (A) DS (t) (A) DS (t) (V) (a) (b) FET model embeddng dece FET model embeddng dece DS (t) (V) Fg. 5. Targeted ntrnsc load lnes (a) and extrnsc load lnes (b) as predcted by the ANN embeddng dece model (blue lne) and erfed usng the ANN dece model (red thck dashed-lne).. Model-Based Embeddng PA Desgn The desgn of sngle transstor PAs usng nonlnear embeddng has been extensely nestgated [9-0] and multple PA desgns were successfully demonstrated [- ]. These orgnal embeddng PA desgn approaches reled on combnng measured low-frequency loadlnes and the charge models separately extracted so as to account for memory effects. In ths paper we are focusng nstead on the model-based embeddng PA desgn whch uses an embeddng dece model [] and assumes that a relable Our focus n ths work s on the desgn of two-transstor Doherty and Chrex PAs. An account for the Doherty PA has been already reported [] but a new and general treatment for the redesgn of the Doherty or Chrex combner after nonlnear embeddng s gen here. The strategy s as follow. In the conentonal textbook case, the two transstors are replaced by ther IV characterstcs as shown n Fg. 6 (a). The two transstor outputs are then combned together usng a -port loss-less recprocal network and delered to the load R as shown n Fg. 6 (a) for the textbook case. Typcally these crcuts nole an nerter (Doherty) or offset lnes (Chrex, Doherty) and some transformers to realze the optmal mpedance targeted at the fundamental frequency. The harmonc termnaton s assumed to be accounted wth a separate network (not shown) before the combner. Class F operaton s selected for the Chrex PA example. The ntrnsc reflecton coeffcents for the Chrex amplfer are shown n Fg. 7 (black and purple crcles) under Chrex load modulaton. The detals of the deal Chrex combner used wll be reported elsewhere. The extrnsc load mpedances at the fundamental requred at the package planes for the upper and lower transstors as predcted by the embeddng dece model from the desred ntrnsc loads are shown usng blue and green crcles. The queston arses now on how to deelop the combner to mantan the desred ntrnsc Chrex load pull acton. Care must be taken to achee both the correct large-sgnal mpedance and sgnal njecton snce the two FET deces are nteractng. j parameters can be defned for ths two-port network (red box) at the peak and backoff ponts. It can be erfed (see Appendx) that a recprocal lossless -port can be extracted only f the - portj parameters are recprocal = and the followng loss constrant holds: Re { } e{ } { } Re Ths holds een f a complex load Z s used nstead of a real load R. Some small departures from these condtons are usually obsered due to the nonlnear nature of the embeddng process. For the -port j parameter extracton, focus s placed on the large-sgnal FET operaton at the peak and back-off ponts. Nonetheless the recprocty and

4 constrant lead to an oer-determned system of equatons. An analytc least square extracton or a geometrcal aerage can then be used to obtan j parameters erfyng exactly these constrants. Once j parameters erfyng these constrants are obtaned, the resultng -port loss-less recprocal crcut can then be syntheszed exactly from them by usng, for example, three dfferent -port crcuts as shown n Fg. 6 (c). Analytc expressons are also dered for ths process. enforce the requred recprocty and loss constrants. Howeer, note that the paths of the outphasng Chrex PA no longer exhbt exactly the same reflecton coeffcents at the peak (θ=0) and backoff (θ max ) outphasng angles. Dece Model Fg. 6: (a) Combner used for the textbook FET IV and (b) new - port combner wth the full FET model. The crcut n (c) shows a realzaton of the -port combner usng three -port crcuts. et us consder a 6 db backoff Chrex PA operatng n class F and based on the FET IV characterstcs. The trajectores under Chrex load modulaton of the nternal G and external (projected) Gp reflecton coeffcents are shown n Fg. 7 at the fundamental ω and harmoncs frequences. Both of the paths of ths Chrex PA are seen to exhbt the same reflecton coeffcents G(ω) and Gp(ω) at the peak (θ=0) and backoff (θ max ) outphasng angles. Fg. 8 Resultng extrnsc Gp(ω) (blue and green crcles) and ntrnsc G(ω) (black and purple crcles) load reflecton coeffcents obtaned wth the dece model when usng the Chrex combner analytcally extracted from the embeddng data obtaned n Fg. 7. Embeddng Dece Model Fg. 7 Requred extrnsc load reflecton coeffcents Gp(ω) (blue and green crcles) at the fundamental for the upper and lower transstors predcted by the embeddng dece model from the ntrnsc load reflecton coeffcents G(ω) (black and purple crcles) under Chrex load modulaton wth the FET IV. Applyng the extracted -port loss-less combner crcut to the Chrex PA usng the full FET model, the nternal and external Chrex load modulaton shown n Fg. 8 can stll be obsered despte the approxmate soluton obtaned to Fg. 9 Smulated effcency obtaned for a 6 db Class F Chrex PA usng: ) the IV characterstc only (top blue lne) and ) the full FET models wth the syntheszed -port network (center red lne). The deal Chrex effcency wth Class B operaton s also shown for reference (bottom black lne). The effcency (mddle red lne) obtaned wth the full FET model whle usng the syntheszed loss-less recprocal network s shown n Fg. 9 to hae degraded by 6% compared to the effcency obtaned usng the FET IV. The deal Chrex PA wth Class B operaton s also shown for reference (bottom black lne). IV. CONCUSION In ths paper we hae reewed the desgn of multtransstor PA usng an embeddng dece model. The

5 applcaton of ths method to the desgn of a two-path Doherty or Chrex amplfer was then dscussed. For the the Doherty or Chrex combner crcut to be mplemented at the fundamental frequency usng a loss-less crcut, the equalent two-port network extracted at the peak and backoff ponts must satsfes both a recprocty constrant and a loss constrant. Some small departures from these condtons are usually obsered due to the nonlnear nature of the embeddng process. An approxmate desgn enforcng these constrants can then be deeloped for the Doherty or Chrex combner so that the transstors operate close to the targeted nternal mode of operaton at the peak and backoff ponts. ACKNOWEDGEMENT Ths work was supported by the Natonal Scence Foundaton (NSF) Collaborate under Grant ECS- 90 and by Rockwell Collns under a project grant. REFERENCES [] Haedong Jang, Patrck Robln, and Zhjan Xe, Model-based nonlnear embeddng for power amplfers desgn, IEEE Trans. Mcrowae Theory and Technques, Vol 6, No. 9, pp , Sept. 04. [] Haedong Jang, Patrck Robln, Chrstophe Qundrot, qoa n and Robert Pond, Asymmetrc Doherty Power Amplfers Desgned Usng Model-Based Nonlnear Embeddng, IEEE Trans. Mcrowae Theory and Technques, Vol. 6, pp , No., Dec. 04. [] M. C. Curras-Francos, Table-based nonlnear HEMT model extracted from tme-doman large-sgnal measurements, IEEE Trans. Mcrowae Theory and Technques, ol. 5, no. 5, pp , 005. [4] J. Xu, D. Gunyan, M. Iwamoto, A. Cognata, and D. Root, Measurement-based non-quas-statc large-sgnal FET model usng artfcal neural networks, n Mcrowae Symposum Dgest, 006. IEEE MTT-S Internatonal, pp , 006. [5] J. Xu, J. Horn, M. Iwamoto, and D. E. Root, arge-sgnal FET model wth multple tme scale dynamcs from nonlnear ector network analyzer data, n Mcrowae Symposum Dgest (MTT), 00 IEEE MTT-S Internatonal, pp , 00. [6] D.-P. Schreurs, J. Verspecht, S. Vandenberghe, and E. Vandamme, Straghtforward and accurate nonlnear dece model parameterestmaton method based on ectoral largesgnal measurements, IEEE Trans. Mcrowae Theory and Technques, ol. 50, no. 0, pp. 5 9, 00. [7] M. Curras-Francos, P. Tasker, M. Fernandez-Barcela,. Campos-Roca, and E. Sanchez, Drect extracton of nonlnear FET QV functons from tme doman large sgnal measurements, IEEE Mcrowae and Guded Wae etters, ol. 0, no., pp. 5 5, 000. [8] oungseo Ko, P. Robln, A. Zarate-de anda, Apolnar Reynoso-Hernandez, D. Nobbe, C. Olson, F.J. Martnez, Artfcal Neural Network Model of SOS-MOSFETs Based on Dynamc arge-sgnal Measurements, IEEE Trans. Mcrowae Theory and Technques, ol. 6, no., pp , 04. [9] A. Raffo, F. Scappaa, and G. Vannn, A new approach to mcrowae power amplfer desgn based on the expermental characterzaton of the ntrnsc electron-dece load lne, IEEE Trans. Mcrowae Theory and Technques, ol. 57, no. 7, July 009. [0] A. Raffo, V. Vadal`a, S. D Falco, F. Scappaa, and G. Vannn, Hybrd approach to mcrowae power amplfer desgn, Workshop on Integrated Nonlnear Mcrowae and Mllmeter-Wae Crcuts (IN-MMIC), pp.-6, 00. [] A. Muso, V. Vadal`a, F. Scappaa, A. Raffo, S. D Falco, and G. Vannn, A new approach to class-e power amplfer desgn, Workshop on Integrated Nonlnear Mcrowae and Mllmeter-Wae Crcuts (INMMIC), pp.-4, 0. [] S. u, and D. M. M.-P. Schreurs, Intrnsc class-f RF GaN power amplfer wth commercal transstor based on a modfed Hybrd approach, Workshop on Integrated Nonlnear Mcrowae and Mllmeter-Wae Crcuts (IN- MMIC), pp.-, 0. [] V. Vadal`a, A. Raffo, S. D Falco, G. Bos, A. Nall, and G. Vannn, A loadpull characterzaton technque accountng for harmonc tunng, IEEE Trans. Mcrowae Theory and Technques, Vol. 6, No. 7, pp , Jul. 0. APPENDIX The -port combner used by the -path Doherty or Chrex PAs s a recprocal loss-less dece whch admts the followng -parameter representaton: + y + y + y + y where the -port -parameters y j are pure magnary. The -port network defned n Fg. 6 (a) admts thus the followng -parameters: = + = + where the loaded -port and -port -parameters are related by the smple relatonshp: The -port network s lossy and thus the -port - parameters feature a non-zero R real part: wth R + j I e + y + y yr + R y yr + R y { } and I = Im{ }. yyr + R y. () () ()

6 Now snce the terms R, y, y and yy are real, and the y pure magnary, we hae the followng denttes: Equatng (4) and (5) we obtan the fnal dentty: R = RR or equalently: e { } { } Re{ }. Re The same constrant s also requred f a complex load Z s used nstead of the real load R. y y y. From (), () and () we hae the followng ratos: y y R = = y y R y y R = =. y y R (4) (5)

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