FET transistor modeling, Large signal, model consistency, analytical method, GaN HEMT
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  medium distance fiber signal propagation after erasing/rewrit-ing is under study. 4. CONCLUSION The BER performance of a data-erasing/rewriting scheme waspresented for two different SOAs. Results for input bit-rate at40 Gb/s show the 8-mm long UL-SOA with a better perform-ance than the 2-mm long NL-SOA. The NL-SOA can still beused for AM optical signals with input ER lower than 6 dB,although with higher power penalties, and/or with lower bitrates. However, only the 8-mm long UL-SOA eraser presentsenough carrier erasing for further remodulation for downstreamsignals with high input extinction ratio and high bit rates.The main drawback is the occurrence of SPM, causing spec-tral broadening. This side effect must be controlled for high bitrates or long fiber links.  ACKNOWLEDGMENTS This work was supported in part by CNPq (2007/56024-4) andFapesp (Padtec, 2007/56024-4, and CePOF, 2005/51689-2; 2009/ 08537-8),Brazil. REFERENCES 1. L.G. Kazovsky, W. Shaw, D. Gutierrez, N. Cheng, and S. Wong,Next generation optical access networks, IEEE J Lightwave Tech-nol 25 (2007), 3428–3442.2. H. Takesue and T. Sugie, Wavelength channel data rewrite usingsaturated SOA modulator for WDM metro/access networks withcentralized light sources, IEEE J Lightwave Technol 21 (2004),2546–2556.3. S. Ho, E. Conforti, and S.M. Kang, LDOT – life-range delimitationoptical transceiver for fast routing and multicasting in wavelengthdivision multiplex (WDM) local area networks, In: Optical fiber conference OFC’94 Digest, paper WN3, 1994, pp. 171–174.4. E. Conforti, C.M. Gallep, S. Ho, A.C. Bordonalli, and S.M. Kang,Carrier reuse with gain compression and feed-forward semiconduc-tor optical amplifier, IEEE Trans Microwave Theory Technol 50(2002), 77–81.5. B. Schrenk, G. Valicourt, M. Omella, J.A. Lazaro, R. Brenot, andJ. Prat, Direct 10-Gb/s Modulation of a single-section RSOA inPONs with high optical budget, IEEE Photonics Technol Lett 22(2010), 392–394.6. N.S. Ribeiro, A.R.L. Cavalcante, C.M. Gallep, and E. Conforti, Opticalamplitude modulation extinction by a deep saturated ultra-long semi-conductor optical amplifier, Opt Express 18 (2010), 27298–27305.7. N.S. Ribeiro, A.R.L. Cavalcante, C.M. Gallep, and E. Conforti,Optical carrier sinusoidal modulation suppressed by ultra-longsemiconductor optical amplifier gain saturation, Microwave OptTechnol Lett 53 (2011), 1286–1290.8. N.S. Ribeiro, A.R.L. Cavalcante, C.M. Gallep, and E. Conforti,Data rewriting after carrier erasing by ultra-long SOA, In: Opticalfiber conference OFC 2011 Digest, paper JWA042, 2011.9. P.P. Baveja, D.N. Maywar, A.M. Kaplan, and G.P. Agrawal, Self-phase modulation in semiconductor optical amplifiers: impact of amplified spontaneous emission, IEEE J Quantum Electron 46(2010), 1396–1403.10. P. Runge, R. Elschner, C.A. Bunge, K. Petermann, M. Schlak, W.Brinker, and B. Sartorious, Operational condition for extinction ra-tio improvement in ultralong SOAs, IEEE Photonics Technol Lett21 (2009), 106–108.11. H. Takesue, N. Yoshimoto, Y. Shibata, T. Ito, Y. Tohmori, and T.Sugie, Wavelength channel data rewrite using semiconductor opti-cal saturator/modulator, IEEE J. Lightwave Technol 24 (2006),2347–2354. V C 2013 Wiley Periodicals, Inc.  ANALYTICAL METHOD FOR DERIVINGCONSISTENT LARGE–SMALL-SIGNALFIELD-EFFECT TRANSISTOR MODEL Sami Bousnina PolyGrames Research Center, Montreal, QC, Canada;Corresponding author:  Received 27 August 2012 ABSTRACT:  This article presents a detailed analytical method for deriving consistent large–small-signal field-effect transistor (FET)model. This resulted in a set of closed-form equations relating the large-signal model parameters to the small-signal model ones. An improved equivalent circuit is proposed for modeling the transistor under large-signal operation. In this circuit, RF nonlinear current sources are used to model the distributed effect of the gate–source and gate–drain junctions. The dispersion between DC and RF drain current characteristics is modeled using an improved back-gating technique. The predictive model capabilities are illustrated with measured and simulated S-parameters, output power at fundamental and harmonics frequencies of a commercial packaged GaAs FET device. The model isthen fully validated by comparing measured and simulated results of output power, efficiency, and intermodulation distortion of a class ABamplifier designed at 1.9 GHz.  V C 2013 Wiley Periodicals, Inc.Microwave Opt Technol Lett 55:1001–1008, 2013; View this articleonline at DOI 10.1002/mop.27495 Key words:  field-effect transistor; large-signal model; parameter extraction; model consistency; model validation INTRODUCTION The recent and future generations of wireless communicationsystems are planned to offer new ways to access informationand services with higher data rate and bandwidth [1]. In theinfrastructure of these systems, several crucial hardware compo-nents should be improved to meet the quality of the requestedservice. Among these components, highly linear and efficientRF power amplifiers (PAs) are considered the most challengingdesigns [2]. Indeed, the design of PAs for wireless communica-tion systems based on field-effect transistor (FET) devicesrequires an accurate large-signal model. To achieve that pur-pose, the model should account for dispersion and self-heatingeffects in addition to be able to predict intermodulation distor-tion (IMD), which is important for PAs nonlinearity analysis.Varieties of large-signal FET empirical models have beendeveloped and have demonstrated their ability to accurately predictdevice performance [3–14]. Empirical models can be of two types,the analytical and table-based one. Analytical models use equa-tions for the description of measured data. The model implementa-tion using analytical functions is fast, but it can be difficult to findfunctions that fit globally the nonlinear device model parametersover large bias ranges. The main advantages of the analytical mod-els include computational efficiency, simplicity, and ability todeliver simulation results outside the measurement range. On theother hand, table-based models use lookup tables developed fromthe measured data. In table-based models, instead of using mathe-matical expressions, multidimensional spline functions are used tofit the measured data. Therefore, they are more accurate than theanalytical models and are suitable for applications, where the func-tional forms of the model nonlinear components are unknown.The traditional large-signal modeling approach is based onderiving first the bias-dependent small-signal equivalent circuitfor intrinsic transistor, which is then used to derive the large-signal model. Both small- and large-signal models have the DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 5, May 2013  1001  same configuration of branches and terminals. In this approach,the intrinsic parameters that depend on two terminal bias vol-tages are modeled by nonlinear functions or implemented usinglookup tables. As reported in Ref. 10, this bottom-up modelingapproach introduces a problem of inconsistency such that thelinearization of the large-signal model leads to a small-signalmodel with nonconventional trans-capacitances. To solve thisinconsistency, which is essentially related to the modeling of nonlinear charges, several researchers have proposed an alterna-tive top-down approach where a modified configuration of thelarge-signal model equivalent circuit is used as a starting pointto derive the small-signal model [11–13]. In this approach, thelinearization of the defining equations of the large-signal modelunder each bias point and correlating them with the definingequations of the small-signal model is the base-line idea todetermine the nonlinear parameters of the large-signal model.At high-frequency operation, the device channel charge under the gate does not respond immediately to the stimulation signal.This requires a relaxation time to build up. This effect results inhigh-order frequencies dependency of measured parameter   Y  11  of the device. Therefore, the large and small-signal models shouldbe able to simulate this effect. Furthermore the device channeltransconductance,  G m , cannot respond instantaneously to changesin the gate voltage at high frequency. Therefore, time delay inher-ent to this process should be accounted for in the device model.In Ref. 11, the bias-dependent gate–source and gate–drain resis-tances were omitted in the model equivalent circuit. This affectsthe accuracy of the device model mainly at high-operating draincurrent/voltage where values of these resistances are non-negligi-ble. In Refs. 12 and 13, bias-dependent parameters: current time-delay  s  and gate–source and gate–drain resistances are includedonly empirically in the large-signal model.Relatively to the dispersion between DC and RF drain currentcharacteristics, previous initial research works have attempted tomodel this effect using RC circuit [8] and using back-gating tech-nique [4, 14]. In other approaches, it was modeled more accu-rately using additional drain RF current sources [7].The work presented in this article proposes an improved equiv-alent circuit of the FET large-signal model and develops a method-ology for the extraction of its parameters. The implemented large-signal model is consistent with the device small-signal model.Thereby, when it is linearized around each bias point, it reproducesthe bias-dependent small-signal parameters that were used to con-struct it. The discrepancy between DC and RF drain current char-acteristics is modeled by an improved back-gating technique wherea scaling factor of the feedback drain voltage is considered asnonlinear parameter. The developed modeling approach wasapplied to a commercial GaAs FET device with satisfactoryresults. The developed large-signal model was successfully used todesign a class AB amplifier at central frequency 1.9 GHz. 2. CORRELATION BETWEEN PARAMETERS OF THE LARGE-SIGNAL AND SMALL-SIGNAL MODELS The proposed basic equivalent circuit of the intrinsic large-sig-nal model is shown in Figure 1. It is composed of a drain non-linear current source  I  D2  and two nonlinear charge sources  Q G and  Q D . The derivatives of the charge sources model thedisplacement currents, and  I  D2  models the channel conductioncurrent. In addition, RF current sources  I  G1  and  I  D1  model thedistributed effect of the gate–source and gate–drain junctions.Detailed description of the modeling of the self-heating and DC/ RF-dispersion effects is given in Section 4.The intrinsic part of the corresponding small-signal equiva-lent circuit can be obtained by linearizing, under small-signalexcitation ( dV  g ,  dV  d ), the internal part of the large-signal model.The total gate and drain currents in the intrinsic FET equivalentcircuit shown in Figure 1 are given by:  I  GT  ¼  I  G1 ð V  g ; V  d Þþ  I  G2 ð V  g ; V  d Þ  (1)  I  G2  ¼  d dt Q G ð v g ; V  d Þ  (2)  I  DT  ¼  I  D1 ð v g ;  V  d Þþ  I  D2 ð v g2 ; V  d Þþ  I  D3 ð v g ; V  d Þ  (3) V  g2  ¼ V  g  exp ð  jw s Þ  (4)  I  D3  ¼  d dt Q D ð v g ; V  d Þ  (5)The differentials of   I  GT  and  I  DT , which are their infinitesimalchanges under small-signal excitation, are given by: dI  GT  ¼ dI  G1 ð v g ; V  d Þþ dI  G2 ð v g ; V  d Þ  (6) dI  DT  ¼ dI  D1 ð v g ; V  d Þþ dI  D2 ð v g2 ; V  d Þþ dI  D3 ð v g ; V  d Þ  (7)With dI  G1  ¼ @   I  G1 @  V  g dV  g þ @   I  G1 @  V  d dV  d  (8) dI  G2  ¼  d dt  ð dQ G Þ¼  d dt  @  Q G @  V  g dV  g þ @  Q G @  V  d dV  d   ¼  jw  @  Q G @  V  g dV  g þ @  Q G @  V  d dV  d    (9) Figure 1  Basic FET intrinsic large-signal model Figure 2  FET intrinsic small-signal model 1002  MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 5, May 2013 DOI 10.1002/mop  dI  D1  ¼ @   I  D1 @  V  g dV  g þ @   I  D1 @  V  d dV  d  (10) dI  D2  ¼  @   I  D2 @  V  g2 dV  g2 þ @   I  D2 @  V  d dV  d  (11)The differential of   V  g2  can be expressed as: dV  g2  ¼ð dV  g   jwV  g d  s Þ  exp ð  jw s Þ  (12)Assuming that | wV  g d  s    dV  g , then: dV  g2   exp ð  jw s Þ dV  g  (13)Consequently: dI  D2  ¼  @   I  D2 @  V  g2 exp ð  jw s Þ   dV  g þ  @   I  D2 @  V  d   dV  d  (14) dI  D3  ¼  d dt  ð dQ D Þ¼  d dt  @  Q D @  V  g dV  g þ @  Q D @  V  d dV  d   ¼  jw  @  Q D @  V  g dV  g þ @  Q D @  V  d dV  d    (15)Using Eqs. (6) and (7), the intrinsic  Y   parameters of the line-arized large-signal model are expressed as follows: Y  11L  ¼ @   I  G1 @  V  g þ  jw @  Q G @  V  g (16) Y  12L  ¼ @   I  G1 @  V  d þ  jw @  Q G @  V  d (17) Y  21L  ¼ @   I  D1 @  V  g þ @   I  D2 @  V  g2 exp ð  jw s Þþ  jw @  Q D @  V  g (18) Y  22L  ¼ @   I  D1 @  V  d þ @   I  D2 @  V  d þ  jw @  Q D @  V  d (19)The terms of the differentials of   I  GT  and  I  DT  can be calcu-lated through the correlation of Eqs. (16)–(19) with the definingequations of the small-signal model shown in Figure 2. The Y  -parameters of the intrinsic part of the equivalent small-signalmodel are given by the following equations: Y  11  ¼  jwC gs 1 þ  D 1 þð wC gs Þ 2  R gs 1 þ  D 1 þ  jwC gd 1 þ  D 2 þð wC gd Þ 2  R gd 1 þ  D 2 (20) Y  12  ¼  jwC gd 1 þ  D 2 ð wC gd Þ 2  R gd 1 þ  D 2 (21) Y  21  ¼ G m0  exp ð  jw s Þ  jwC gd 1 þ  D 2 ð wC gd Þ 2  R gd 1 þ  D 2 (22) Y  22  ¼  1  R ds þ  jwC ds þ  jwC gd 1 þ  D 2 þð wC gd Þ 2  R gd 1 þ  D 2 (23)  D 1  ¼ð wR gs C gs Þ 2 (24)  D 2  ¼ð wR gd C gd Þ 2 (25)The term 1/(1  þ  D i ) with  i  = 1, 2, can be expressed in a formof Taylor series: S i  ¼  11 þ  D i ¼ 1 þ X 1 n ¼ 1 ð  D i Þ n (26)The correlation between Eqs. (16)–(19) and (20)–(23) leadsto the following closed-form expressions: @   I  G1 @  V  g ¼ð wC gs Þ 2  R gs  S 1 þð wC gd Þ 2  R gd S 2  (27) @   I  G1 @  V  d ¼ð wC gd Þ 2  R gd  S 2  (28) @  Q G @  V  g ¼ C gs  S 1 þ C gd  S 2  (29) @  Q G @  V  d ¼ C gd  S 2  (30) @  Q D @  V  g ¼ C gd  S 2  (31) @  Q D @  V  d ¼ C ds þ C gd  S 2  (32) @   I  D1 @  V  d ¼ð wC gd Þ 2  R gd  S 2  (33) @   I  D1 @  V  g ¼ð wC gd Þ 2  R gd  S 2  (34) @   I  D2 @  V  g2 ¼ G m0  (35) @   I  D2 @  V  d ¼ G ds  (36) Figure 3  Complete equivalent circuit of the FET small-signal model TABLE 1 Values of Parasitic Resistances Parameter R g  ( X )  R d  ( X )  R s  ( X )Value 1 0.85 0.4 DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 5, May 2013  1003


Jul 23, 2017
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