An Analytical Approach to the HEMT Noise Wave Model Parameter Determination

Transcription

1 SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 14, No. 1, Feruary 017, UDC: 6-1/-9: ]: DOI: 10.98/SJEE D An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton Vladca Đorđevć 1, Zlatca Marnkovć, Olvera Pronć-Rančć, Vera Markovć Abstract: Ths paper presents an analytcal approach to determnaton of the nose wave model parameters for a hgh electron-moblty transstor workng under dfferent temperature and frequency condtons. The presented approach s composed of two steps and provdes more effcent determnaton of these parameters than n the case of optmzaton procedures commonly appled for that purpose n crcut smulators. The frst step s extracton of the nose parameters of transstor ntrnsc crcut from the measured nose parameters of whole transstor usng an analytcal nose de-embeddng procedure. The second step s calculaton of the nose wave model parameters from the de-embedded ntrnsc nose parameters usng exstng formulas. The accuracy of the presented approach s valdated n a wde frequency and temperature range by comparson of the transstor nose parameters smulated for the determned nose wave model parameters wth the measured nose parameters. Keywords: Analytcal Approach, HEMT, Nose Parameters, Nose Wave Model. 1 Introducton In the last few decades, there have been a plenty of papers dealng wth the modelng of the nose parameters (Γ opt optmum source reflecton coeffcent, F mn mnmum nose fgure and R n nose resstance) n the case of mcrowave transstors [1 10]. The authors of these papers usually deal wth the transstor nose model development based on the addtonal voltage and/or current nose sources [3, 5, 6]. However, the nose wave model usng the wave representaton of nose has ganed recognton as a sutable alternatve to the most commonly used representatons of nose generated n a network [, 7 9, 11 1]. Ths s prmarly because the nose wave model has ablty to treat the network nose n terms of ncdent and reflected waves, whch further leads to the fact that the complete nose analyss can be performed usng the scatterng parameters. Ths s very mportant snce these parameters are obtaned wth a 1 Innovaton Center of Advanced Technologes, Bulevar Nkole Tesle 61, lokal 5, Nš, Serba; E-mal: vladca.djordjevc@cnt.rs Unversty of Nš, Faculty of Electronc Engneerng, Aleksandra Medvedeva 14, Nš, Serba; E-mals: zlatca.marnkovc@elfak.n.ac.rs; olvera.pronc@elfak.n.ac.rs; vera.markovc@elfak.n.ac.rs 35

2 V. Đorđevć, Z. Marnkovć, O. Pronć-Rančć, V. Markovć hgh accuracy by usng vector network analyzers, whch contrbute to the accuracy of the nose analyss [18]. Moreover, the nose wave model offers alternatve nose measurement technques [, 7, 17]. The nose wave model s characterzed by ts parameters, called the nose wave temperatures. They are usually determned from the measured transstor nose parameters usng optmzaton procedures n mcrowave crcut smulators. Nevertheless, as the nose wave temperatures are bas, temperature and frequency [14] dependent, optmzaton procedures become tmeconsumng n stuatons when repeated extractons are needed. Therefore, n such cases optmzaton procedures can be a qute nadequate extracton tool due to the need for effcent nose modelng wth acceptable extracton tme. On the other hand, the nose wave model provdes drect relatonshps between the nose wave temperatures and the nose parameters of transstor ntrnsc crcut []. Hence, t s possble to extract the nose wave temperatures analytcally avodng tme-consumng optmzaton procedures. In ths paper, the analytcal approach to determnaton of the nose wave temperatures n the case of GaAs hgh electron-moblty transstor (HEMT) s presented. The presented approach provdes extracton of the nose parameters of transstor ntrnsc crcut from the measured transstor nose parameters usng the analytcal nose de-embeddng procedure [ 5], and further calculaton of the nose wave temperatures based on the de-embedded ntrnsc nose parameters usng exstng formulas []. The paper s organzed as follows. After Introducton, a short descrpton of the nose wave model s gven n Secton. The analytcal extracton approach s presented n Secton 3. Secton 4 contans the most llustratve numercal results and the dscusson. Concludng remarks are gven n the last secton. The Nose Wave Model of Mcrowave Transstors In the case of the nose wave model, the transstor small-sgnal ntrnsc crcut, whch s a lnear nosy two-port network, can be consdered as a noseless two-port defned by transfer scatterng parameters [T] wth addtonal nose wave sources, a n and b n, referrng to the nput, Fg. 1 []. Ths representaton of nosy two-port network can be descrbed by usng the followng matrx equaton: a1 T11 T1 b an b 1 T1 T a b, (1) n where a and b, =1,, are ncdent and output waves at the -th port. 36

3 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton Fg. 1 Nosy two-port network. As already mentoned, the parameters of the nose wave model are the nose wave temperatures two real temperatures, T a and T b, and one complex correlaton temperature, T c [, 13]. They are expressed n terms of the nose parameters of transstor ntrnsc crcut, F mn,, R n, and Γ opt,, as follows []: 4R T Ta T ( F 1) Z 1 T n, 0 opt, 0 mn, 4R T 0 opt, n, 0 b 0 mn, Z 1 0 opt, T c 4R T Z 1, () T ( F 1), (3) n, 0 opt, 0 opt,, (4) where Z 0 s the normalzaton mpedance (50) and T 0 s the standard reference temperature (90K). 3 The Analytcal Approach to Determnaton of the Nose Wave Temperatures of HEMTs The analytcal approach to determnaton of the nose wave temperatures presented n ths secton s related to the equvalent crcut of HEMT n a packaged form, Fg. a [6]. It conssts of ntrnsc and extrnsc part. As the ntrnsc crcut s common to the most of mcrowave feld-effect transstor (FET) models, t s shown n Fg. b separately [6]. The extrnsc elements embedded n the crcut n Fg. a represent parastc effects and depend on the type of package. As mentoned above, the proposed analytcal procedure s composed of two steps. The frst step s extracton of the transstor ntrnsc nose parameters from the transstor measured nose parameters usng the analytcal nose deembeddng procedure [ 5]. The second step s straghtforward, and 37

4 V. Đorđevć, Z. Marnkovć, O. Pronć-Rančć, V. Markovć represents calculaton of the nose wave temperatures usng the de-embedded transstor ntrnsc nose parameters []. Both steps wll be explaned below. (a) (b) Fg. (a) Equvalent crcut of HEMT n a packaged form and de-embeddng planes, (b) Intrnsc equvalent crcut of consdered transstor. 3.1 The analytcal nose de-embeddng procedure The man purpose of the presented analytcal nose de-embeddng procedure related to Fg. a s determnaton of the transstor ntrnsc nose parameters from the transstor measured nose parameters. To acheve that, the equvalent crcut shown n Fg. a s dvded nto four planes. The nose deembeddng s done by elmnatng the nose nfluence of the extrnsc elements 38

5 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton connected n cascade, seres and parallel usng ABCD, Z and Y representatons, respectvely [ 5]. Frst, t s necessary to determne ABCD nose correlaton matrx n the plane 1, based on the transstor measured nose parameters: mn1 * n n opt CA,1=kT0 F mn1 RY n opt Rn Yopt R 39 F R Y, (5) 3 where k s Boltzmann s constant ( J/K ), Y opt s optmum source admttance assocated to Γ opt, and * ndcates complex conjugate. Then, snce transmsson lnes TL 1 and TL are connected n cascade wth the rest of the crcut, ther nose nfluence s removed by calculatng the ABCD nose correlaton matrx of crcut wthout TL 1 and TL : H 1 1 H A, TL 1 A,1 A, TL1 TL1 A, TL C ABCD C C ABCD ABCD C ABCD, (6) where ABCDTL s the ABCD matrx of transmsson lne TL 1 1, C ATL, and C 1 ATL, are the ABCD nose correlaton matrces of transmsson lnes TL 1 and TL, respectvely, ABCD ' s the ABCD matrx of crcut wthout TL 1 and TL, and superscrpt H ndcates Hermtan complex conjugate transpose. By treatng transmsson lne TL 3 as a short-crcuted lne, the Z nose correlaton matrx n the plane s calculated based on: C C C, (7) Z, Z, Z, TL3 where C Z, s the Z nose correlaton matrx correspondng to C A,, and C Z, TL s the Z nose correlaton matrx of transmsson lne TL 3 3. The Y nose correlaton matrx n the plane 3 s calculated by removng the nose nfluence of three capactors connected n parallel wth the rest of the crcut ( Cgsp, Cgdp and C dsp ): C C C, (8) Y,3 Y, Y, C where C Y, s the Y nose correlaton matrx correspondng to C Z,, and CYC, s the Y nose correlaton matrx of three capactors embedded n the crcut between the planes and 3. The nose nfluence of the last three nductors (L) and resstors (R) connected n seres wth the rest of the crcut ( L g, L d, L s, R g, R d and R s ) s removed by calculatng the Z nose correlaton matrx n the plane 4:

6 V. Đorđevć, Z. Marnkovć, O. Pronć-Rančć, V. Markovć C C C, (9) Z,4 Z,3 Z, LR where C Z,3 s the Z nose correlaton matrx correspondng to C Y,3, and C s the Z nose correlaton matrx of nductors and resstors embedded n Z, LR the crcut between the planes 3 and 4. C Ye, way: In general, the nose correlaton matrces of the seres, C Z, e, and shunt,, crcut elements, used n (7) (9) can be determned by the followng Z, e 0 C kt Re Z, (10) Ye, 0 e C kt Re Y, (11) where Z e and Y e are the Z and Y matrces of the seres and shunt elements embedded n transstor extrnsc crcut, respectvely. The ABCD nose correlaton matrces of passve elements connected n cascade wth the rest of the crcut, whch are used n (6), are derved from the nose correlaton matrces gven n (10) and (11). In the analytcal nose de-embeddng procedure, the nose correlaton matrces must be converted from Y to Z or ABCD, and vce versa. In partcular, the nose correlaton matrx conversons are based on the followng equaton: * C TC T, (1) where C and C are the nose correlaton matrces before and after converson, respectvely, and T s the transformaton matrx that depends on the parameters α and β, Table 1 []. It should be noted that the small-sgnal deembeddng procedure must precede the nose de-embeddng procedure because the extrnsc small-sgnal crcut element matrces are needed for the nose correlaton matrx conversons. Table 1 Nose correlaton matrx converson parameters. A Y Z A Y Y11 Y1 1 0 Z 1 Z11 0 Z Z Z A A 1 e Z Z Y Y A11 A 1 Y Y

7 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton Fnally, the obtaned Z nose correlaton matrx n the plane 4 should be converted to the ABCD form n order to calculate the ntrnsc nose parameters usng [ 4]: 1 Fmn, 1 (Re( CA,4 ) C 1 A,4 C 11 A,4 (Im( C A,4 )) ), (13) 1 kt0 CA,4 R 11 n,, (14) kt Y opt, 0 CA,4 C 11 A,4 (Im( C A,4 )) jim( C 1 A,4 ) 1, (15) C opt, Y Y A,411 Y Y 0 opt, 0 opt,, (16) where Y 0 s the normalzaton admttance ( Y 0 1/ Z 0 ). In addton, the overall nose de-embeddng procedure s shown n Fg Calculaton of the nose wave temperatures Ths s a relatvely smple step and represents calculaton of the nose wave temperatures based on the ntrnsc nose parameters determned n the prevous step n (13) (16). For that purpose, the nose wave model expressons gven n Secton n () (4), are used []. 4 Numercal Results and Dscusson In order to valdate the presented approach to determnaton of the nose wave temperatures, t was appled to a packaged HEMT by NEC (NE083A), workng under dfferent temperature and frequency condtons. To obtan the S and nose parameters of the consdered transstor, a measurement procedure descrbed n [6] was used. In partcular, an automated measurng system wth the ablty to measure the nose factor up to 40 GHz and software that calculates the nose parameters based on the measured data were used. The measurements were performed n the frequency range 6 18 GHz and the temperature range K, 0 K step. The measurements at dfferent temperatures were done by placng the devce test fxture n a thermo-controlled chamber. Based on the measured S parameters, the values of the transstor small-sgnal equvalent crcut elements (ECPs) were determned [6]. 41

8 V. Đorđevć, Z. Marnkovć, O. Pronć-Rančć, V. Markovć Fg. 3 The nose de-embeddng procedure flowchart. The elements to be de-embedded are reported nsde the boxes and the obtaned matrces and ther conversons are shown between the boxes. The formulaton used (ABCD, Z or Y) s reported at the rght sde of the boxes. 4

9 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton The two-step de-embeddng procedure has been mplemented wthn MATLAB [7] software envronment and used to determne the nose wave temperatures of the consdered transstor. The nose wave temperatures were determned for all sx temperatures at whch the measurements were done. For each temperature, the nose wave temperatures were calculated from 6 to 18 GHz, wth step of 0. GHz. Further, the determned nose wave temperatures were assgned to the nose wave model mplemented wthn the ADS (Advanced Desgn System) [8] crcut smulator and the nose parameters of whole transstor were smulated. After that, the smulated nose parameters were compared wth the measurements. To express the accuracy of the nose modelng usng proposed analytcal approach, average test error (ATE), worst case error (WCE) and Pearson product-moment correlaton coeffcent (r), whch are defned below, were used. ATE s defned by usng the mean value of the absolute value of the relatve error : ATE 43 1 m j m j 1, (17) where m s the number of samples of datasets contanng the parameters smulated and target (measured) values, and δ j s the relatve error of the j-th sample. Namely, δ j can be determned by the followng way: y j d j max d d j mn, (18) where y j and d j are the j-th samples of datasets contanng the parameters smulated and target values, respectvely, whle d max and d mn are the maxmum and mnmum parameters target values, respectvely. WCE s defned as: m WCE max. (19) The correlaton coeffcent r, whch s the measure of agreement between the smulated and correspondng target values, s defned as: where r m j1 y jyd j d j1 m m yj y d j d j1 j1 j, (0)

10 V. Đorđevć, Z. Marnkovć, O. Pronć-Rančć, V. Markovć 1 m yj m j 1 y, (1) 1 m d j m j 1 d. () ATE, WCE and r were calculated usng the smulated and measured nose parameters n the whole frequency and temperature range, and ther values are gven n Table. Moreover, as an llustraton, Fg. 4 presents frequency dependence of the smulated and the measured values of Fmn and R n. The results are presented n the frequency range from 6 to 18 GHz, for the temperatures from 33 to 333 K, step 0 K. In order to clearly present the results for opt and opt, ther measured and smulated values are gven as functons of temperature, Fg. 5. The results are presented n the temperature range from 33 to 333 K, for the frequences from 6 to 18 GHz, GHz step. Table Test errors for the modeled nose parameters. 333 K 313 K 93 K 73 K 53 K 33 K F mn R n Γ opt Γ opt ATE (%) WCE (%) r ATE (%) WCE (%) r ATE (%) WCE (%) r ATE (%) WCE (%) r ATE (%) WCE (%) r ATE (%) WCE (%) r

11 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton The obtaned results presented n Table and Fgs. 4 and 5 show that the smulated values of the nose parameters are very close to the measured ones n whole frequency and temperature range, whch confrms the accuracy of the proposed analytcal approach to determnaton of the nose wave temperatures. (a) (b) Fg. 4 Frequency dependence of the measured (symbols) and smulated (lnes) values of: (a) F mn and (b) R n at dfferent temperatures. 45

12 V. Đorđevć, Z. Marnkovć, O. Pronć-Rančć, V. Markovć (a) (b) Fg. 5 Temperature dependence of the measured (symbols) and smulated (lnes) values of: (a) Γ opt and (b) Γ opt at dfferent frequences. 5 Concluson Snce the nose wave temperatures are bas, temperature and frequency dependent, optmzaton procedures n mcrowave crcut smulators, usually 46

13 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton used for ther extracton, requre a lot of tme. Therefore, the analytcal procedure provdng the more effcent determnaton of the transstor nose wave temperatures s presented n ths paper. Namely, the presented analytcal approach was developed for a GaAs HEMT n a packaged form and provdes extracton of the transstor ntrnsc nose parameters from the measured transstor nose parameters, leadng to the smple determnaton of the nose wave temperatures based on the de-embedded ntrnsc nose parameters usng the exstng formulas. In order to valdate the presented analytcal approach, t was appled to a specfc GaAs HEMT devce n a packaged form. The determned nose wave temperatures were assgned to the nose wave model mplemented wthn the ADS crcut smulator and the nose parameters of whole transstor were smulated. A good agreement between the smulated and measured nose parameters proves valdty of the presented analytcal approach to determnaton of the nose wave temperatures. 6 Acknowledgment The work was supported by the TR-305 project of the Serban Mnstry of Educaton, Scence and Technologcal Development. The authors would lke to thank prof. Alna Caddem, Unversty of Messna, Italy, for provdng the measured data. 7 References [1] R.A. Pucel, H.A. Haus, H. Statz: Sgnal and Nose Propertes of Gallum Arsende Mcrowave Feld-Effect Transstors, Advances n Electroncs and Electron Physcs, Vol. 38, Dec. 1975, pp [] R.P. Meys: A Wave Approach to the Nose Propertes of Lnear Mcrowave Devces, IEEE Transactons on Mcrowave Theory and Technques, Vol. 6, No. 1, Jan. 1978, pp [3] H. Fuku: Desgn of Mcrowave GaAs MESFET's for Broad-Band Low-Nose Amplfers, IEEE Transactons on Mcrowave Theory and Technques, Vol. 7, No. 7, July 1979, pp [4] A. Cappy, A. Vanoverschelde, A. Schortgen, C. Versnaeyen, G. Salmer: Nose Modelng n Submcrometer-Gate Two-Dmensonal Electron-Gas Feld-Effect Transstors, IEEE Transactons on Electron Devces, Vol. 3, No. 1, Dec. 1985, pp [5] M.S. Gupta, O. Ptzals, S.E. Rosenbaum, P.T. Grelng: Mcrowave Nose Characterzaton of GaAs MESFET's: Evaluaton by On-Wafer Low-Frequency Output Nose Current Measurement, IEEE Transactons on Mcrowave Theory and Technques, Vol. 35, No. 1, Dec. 1987, pp [6] M.W. Pospeszalsk: Modelng of Nose Parameters of MESFET's and MODFET's and ther Frequency and Temperature Dependence, IEEE Transactons on Mcrowave Theory and Technques, Vol. 37, No. 9, Sept. 1989, pp

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15 An Analytcal Approach to the HEMT Nose Wave Model Parameter Determnaton [] H. Hllbrand, P. Russer: An Effcent Method for Computer Aded Nose Analyss of Lnear Amplfer Networks, IEEE Transactons on Crcuts and Systems, Vol. 3, No. 4, Aprl 1976, pp [3] Y.H. Wang, M.H. Cho, L.K. Wu: A Flexble Mcrowave De-Embeddng Method for On- Wafer Nose Parameter Characterzaton of MOSFETs, IEICE Transactons on Electroncs, Vol. E9-C, No. 9, Sept. 009, pp [4] G. Crup, D. Schreurs: Mcrowave De-Embeddng: From Theory to Applcatons, Academc Press, Oxford, UK, 013. [5] A. Nall, A. Raffo, G. Crup, S. D Angelo, D. Resca, F. Scappavva, G. Salvo, A. Caddem, G. Vannn: GaN HEMT Nose Model based on Electromagnetc Smulatons, IEEE Transactons on Mcrowave Theory and Technques, Vol. 63, No. 8, Aug. 015, pp [6] A. Caddem, A. D Paola, M. Sannno: Mcrowave Nose Parameters of HEMTs vs. Temperature by a Smplfed Measurement Procedure, Hgh Performance Electron Devces for Mcrowave and Optoelectronc Applcatons Workshop, Leeds, UK, 5-6 Nov. 1996, pp [7] MATLAB, The Language of Techncal Computng, MathWorks, 01. [8] Advanced Desgn System, Aglent EEsof EDA,