3 Linarization of Two-way Dohrty Amplifir by Using Scond and Fourth Ordr Nonlinar Signals Alksandar Atanasković and Nataša Malš-Ilić Abstract In this papr, a two-way Dohrty amplifir with th additional circuit for linarization has bn ralizd in ordr to xprimntally vrify th linarization influnc of th fundamntal signals scond harmonics and fourth-ordr nonlinar signals to th third- and fifth-ordr intrmodulation products. Th signals for linarization-scond harmonics and fourth-ordr nonlinar signals ar xtractd at th output of th paking cll, adjustd in amplitud and phas and injctd at th input of th carrir cll in Dohrty amplifir. Additionally, th linarization ffcts of thr variants of th linarization approach hav bn analyzd by Advanc Dsign Systm simulator: on that was tstd xprimntally, th cas whn th signals for linarization ar injctd only at th carrir amplifir output and whn thy ar put simultanously at th input and output of th amplifir. Indx Trms Dohrty amplifir, linarization, scond harmonics and fourth-ordr nonlinar signals, intrmodulation products. W I. INTRODUCTION ITH th advnt of spctrally fficint wirlss communication systms, linarization tchniqus for nonlinar microwav powr amplifirs hav gaind significant intrst. Dmanding rquirmnts of nw systms (CDMA000, W-CDMA, OFDMT tc.), in ordr to mt both linarity and high powr fficincy prsnt a srious task for transmittr dsignrs. Th Dohrty amplifir is capabl of achiving a high fficincy of powr amplifirs in bas station. Diffrnt linarization mthods xist with th aim to rduc nonlinar distortions whil kping powr amplifir in a nonlinar and fficint mod. Th various linarization mthods of Dohrty amplifir hav bn rportd: postdistortion-compnsation [], th fdforward linarization tchniqu [], th prdistortion linarization tchniqu [3] and combination of thos two linarization tchniqus []. Th linarization ffcts of th fundamntal signals scond harmonics (IM) and fourth-ordr nonlinar signals (IM) at frquncis that ar clos to th scond harmonics to th standard (two-way, thr-way and thr-stag) Dohrty amplifirs wr invstigatd in [5] for LDMOSFETs in carrir and paking amplifirs with th sam priphry and in [6] for priphry rlations :.5:.5. W applid th approach whr IM and IM signals ar injctd togthr with th fundamntal signals into th carrir amplifir input and put at its output [7]. In addition, thr-stag Dohrty amplifir was loadd with harmonic control circuit (HCC), which rprsnts an optimal impdanc for th scond harmonics and ithr an opn or short circuit for th third harmonics at th output of clls. Various configurations of loading wr considrd for th cas of th sam transistors in amplifying clls [], [9] and with th transistor siz ratio :.5:.5 [0]. Analysis of th linarization of Dohrty amplifirs was carrid out for sinusoidal signals and digitally modulatd signals through th simulation procss by ADS softwar. In this papr, two-way Dohrty amplifir with th additional circuit for linarization is ralizd. Th ffcts of linarization ar vrifid by masurmnts. Th linarization tchniqu applid utilizs th scond harmonics and fourth-ordr nonlinar signals at frquncis clos to th scond harmonics, which ar gnratd at th output of th paking cll. Thy ar adjustd in amplitud and phas through th linarization branch and run at th carrir amplifir input ovr frquncy diplxr. Also, th rsults of simulation that rfr to th linarization approach tstd in xprimnt, th linarization whn th signals for linarization ar ld only at th carrir amplifir output and th linarization with th signals that ar fd at th input and output of th amplifir ar givn in paralll. Th authors would lik to thank th Ministry of Education and Scinc of Rpublic Srbia for supporting th rsarch rportd in this papr within th projcts TR-305 and III006. Som rsults shown in this papr wr prsntd at 55 th ETRAN Confrnc, anja Vrućica, Jun 6-9, 0. A. Atanasković, and N. Malš-Ilić, ar with th Faculty of Elctronic Enginring, Univrsity of Niš, Alksandra Mdvdva, 000 Niš, Srbia, E-mails: [natasa.mals.ilic; alksandar.atanaskovic] @lfak.ni.ac.rs. II. THEORETICAL ANALYSIS OF LINEARIZATION TECHNIQUE APPLIED IN EXPERIMENT Thortical analysis of th proposd linarization approach is basd on th nonlinarity of th drain-sourc currnt of LDMOSFET in amplifir circuit which is xprssd by a polynomial modl [], [] undr th assumption of nglcting a mmory ffct, as rprsntd by ().
i ds K ( v, v ) 0 v gs gs ds = 0 gs 3 30 gs 0 gs 5 50 gs ( t ) + K v ( t ) + K v ( t ) + K v ( t ) + K v ( t ) + + Kvgs ( t ) vds ( t) + Kvgs ( t ) vds ( t ) + Kvgs ( t ) vds ( t ) +... () Th spctrum of a digitally modulatd fundamntal signal is givn by th xprssion: V ( jω) δ( ω ± ω0 ), whr V (jω) rprsnts a basband spctrum. Equation () conncts th nonlinarity of th drain-sourc currnt i ds, in rfrnc to th voltag v gs btwn gat and sourc, which is rprsntd by th cofficints K 0 to K 50. Highr ordr nonlinar trms K 0 and K 50 ar includd into th quation according to th analysis prformd in [] that favours th trms of output currnt as function of v gs up to th fifth-ordr. Th nonlinarity of drain-sourc currnt in trms of th voltag btwn drain and sourc, v ds, which is xprssd by th cofficints K 0 to K 03, is assumd to hav a ngligibl contribution to th intrmodulation products according to [] and [], so that thy ar omittd from th quation. Howvr, th quation ncompasss mixing trms K, K and K. Th drain-sourc currnt at IM3 and IM5 frquncis can b writtn by () and (3), whr ( ρ, ϕ, ρ and ϕ ) stand for th amplituds and phass of th IM and IM signals put at th amplifir input, whras and ϕ ρ, ϕ, ρ ar amplituds and phass of IM and IM signals that xist at th amplifir output du to both an inhrnt nonlinarity of transistor and transfrrd signals from th input. Th signal distortd by th cubic trm of th amplifir, K 30, is includd into analysis by () as th first trm. Th cubic trm is considrd as a dominant on according to [] and [] in causing IM3 products and spctral rgrowth. Th trm K 0 (scond trm) is cratd by th gat-sourc voltag of fundamntal signal and voltag of scond harmonic fd at th amplifir input. Th mixing product of th fundamntal signal and scond harmonic apparing at th amplifir output is xprssd as th third trm. Additionally, th fundamntal signal at th output of amplifir mingls with th scond harmonic injctd at th amplifir input gnrating th fourth trm. Th amplitud of output voltag at th fundamntal signal frquncy that is 0 out of phas in rfrnc to th input signal is dnotd as ρ. Th third and fourth trms can b nglctd for lowr signal powr. In cas of highr powr, thy may rduc ach othr. Th mixing trms btwn drain and gat, K and K, produc drain-sourc currnt at IM3 frquncis with th opposit phass, so that thy rduc ach othr []. 3 ( ) jϕ I ds jω IM 3 30 + 0ρ + K K ( o ) ( ) o jϕ jϕ + K ρ Kρρ () ( V ( jω) V ( jω) V ( jω) )} δ( ω ± ω0 ) According to th prvious analysis, it is possibl to rduc spctral rgrowth causd by th third-ordr distortion of fundamntal signal by choosing appropriat amplitud and phas of th scond harmonics ( ρ and ϕ ). Th first trm in (3) xprssing th drain-sourc currnt of th fifth-ordr intrmodulation products (IM5) is formd from th fundamntal signals du to an amplifir nonlinarity of th fifth-ordr, K 50. Th scond trm is th mixing product btwn th fundamntal signal at amplifir input and IM signal insrtd to its input, too. Thrfor, th original IM5 product (th first trm) can b rducd by adjusting th amplitud and phas of IM signals that ar injctd at th amplifir input. Th IM5 products ar also xprssd in trms of K 30 cofficint-th third trm in (3) mad by raction btwn two IM signals and fundamntal on at th amplifir input. Also, th fundamntal signal at th amplifir output racts with th IM signal at th amplifir input ovr K trm producing IM5 product (fourth trm). Th fifth trm is mad btwn th input fundamntal signal and IM signals at th amplifir output. All mixing trms which stand by K and K in (3) ar gnratd du to raction btwn two scond harmonics and fundamntal signal. Th signals takn in considration ar obsrvd at th input and output of th amplifir. Th K and K trms produc currnt at th frquncis of IM5 products with th opposit phass, so that thy rduc ach othr. Consquntly, thir influnc to th powr of IM3 and IM5 products can b canclld. I ds ( jω) IM 5 5 (i) ) (i) jϕ ( i j ϕ 50 0 30ρ K + K ρ + K ( o ) jϕ jϕ ρkρ + Kρ ( ) ( o ) o j ϕ j + K ρ Kρρρ ( o ) j ( ϕ ) ( ) +ϕ i j + K ρ ρ K ρρ V ( jω) V ( jω) V ( jω) V ( jω) V ( jω)} ( o ) ( ϕ +ϕ ) ϕ δ( ω ± ω0 ) As in th cas of IM3 products, third to fifth trms hav ngligibl impact for lowr powr of th fundamntal signals, whil in cas of highr powr, it can b assumd that fourth and fifth trms cancl ach othr. Howvr, for highr powr, th mixing K 30 trm (th third trm in (3)) may incras IM5 products if IM signals injctd at th amplifir input do not hav nough powr against th K 30 trm to control it. (3)
5 Fig.. Schmatic diagram of two-way Dohrty amplifir with additional circuit for linarization. III. DESIGN OF AMPLIFIER AND LINEARIZATION CIRCUITS Agilnt Advancd Dsign Systm-ADS softwar has bn usd for th dsign of convntional two-way Dohrty amplifir, which schmatic diagram is shown in Fig.. Two-way Dohrty amplifir was dsignd in standard configuration [], [], [], [5]. Th carrir and paking amplifirs hav input and output matching circuits, which transform th input impdanc of th dvic to 50Ω and th optimum load impdanc Zopt to 50Ω. In low-powr rgion, th paking amplifir should b an opn circuit and load impdanc of th carrir amplifir should b doubld to Zopt by a quartr-wav impdanc transformr with th charactristic impdanc R0=50Ω. Also, th quartr-wav transmission lin with th charactristic impdanc Rt = R 0 transforms 50Ω to 5Ω that is a load impdanc of th output combining circuit whn th paking amplifir is turnd on in highr powr rgion. Phas diffrnc of 90 is rquird at th inputs of th carrir and paking amplifir to compnsat for th sam phas diffrnc btwn thos two amplifirs causd by th quartr-wav impdanc transformr at th output. Th output impdanc of th LDMOSFET is strongly ractiv with low rsistanc so in low-powr rgion considrably powr laks from th carrir amplifir to th paking amplifir. Th output impdanc sn at th output of th paking transistor is transformd to th opn by th output matching circuit and th propr offst lin. Th carrir and paking clls wr dsignd using Frscal s MRFS LDMOSFET which non-linar MET modl is incorporatd in ADS library. Fig.. Ralizd two-way Dohrty amplifir. Fig. 3. Ralizd linarization circuit. Th transistor shows a -W pak nvlop powr. Th matching impdancs for sourc and load at GHz ar ZS=5.5+j5Ω and ZL=.5+j7.5Ω, rspctivly. Ths impdancs wr obtaind by using load-pull and sourc-pull analysis in ADS. Th matching impdancs for th scond harmonics at GHz for sourc and load ar ZS=3.-j.Ω and ZL=.5+j9.Ω, rspctivly. Ths impdancs ar takn from th authorizd Frscal catalogu.
6 Th carrir amplifir is biasd in class-a (V D =6V, V G =5.V (3.5%IDSS)), whras th paking amplifir oprats in class-c (V D =6V, V G =3.6V). In simulation of two-way Dohrty amplifir, idal lmnts from ADS library was utilizd for th linarization circuit componnts. Th linarization circuit fabricatd for th xprimnt compriss from M/A-COM PIN diod variabl attnuator MAVAT007-06T, two Mini-Circuits 0 voltag variabl phas shiftrs JSPHS-3+ to provid phas shift of 360 and Skyworks high linar W powr amplifir- SKY650. Th scond harmonics, IM, and fourth-ordr nonlinar signals at frquncis clos to th scond harmonics, IM, which ar gnratd at th output of th paking amplifir, ar xtractd through th diplxr circuit [5] that was dsignd to sparat th fundamntal signals and signals for linarization matchd to th impdanc for thir adquat powr lvl. Th linarization circuit adjusts IM and IM signals in amplitud and phas bfor thy ar insrtd at th carrir amplifir input ovr th frquncy diplxr dsignd with th indpndnt matching circuits for th fundamntal and signals for linarization. Linarization branch can vary powr of th signals for linarization from -0d to 7d in rfrnc to th gnration point at th paking amplifir output. oth, two-way Dohrty amplifir (Fig. ) and linarization circuit (Fig. 3) ar ralizd on FR substrat with.55 mm thicknss and 7.5µm mtallization layr. Th printd circuit boards for th circuits wr manufacturd on LPKF ProtoMat S00 in laboratory. output powr (dm-30dm). Ths figurs compar th linarization ffcts for thr cass of linarization dpnding on whthr th signals for linarization ar injctd at:. th amplifir input,. th amplifir output and 3. th amplifir input and output. Dnotation in th figurs is as follows: IM3- at 96MHz, IM3+ at 99MHz, IM5- at 9MHz and IM5+ at 99MHz. In th lowr powr rang (dm-dm), th prsntd rsults rlat to th cas whn th amplituds and phass of IM and IM signals ar adjustd on th optimal valus at dm output powr whr IM3 products ar supprssd for d and 7d in th first cas, 0d and d in th scond and d and d in th third cas. Th IM5 products ar mor asymmtrical bfor linarization, so that at dm IM5- product is kpt almost th sam to th lvl bfor linarization in all cass considrd, whras IM5+ is lssnd by 6d in th first and d in th third cas and dtriorats by 3d in th scond cas. In cas of highr powr (dm-30dm) th amplitud and phass of th signals for linarization wr adjustd on th optimal valus for ach singl powr lvl. As far as th whol powr rang is obsrvd th bst rduction of IM3 products was achivd by th injction of th signals for linarization at th input and output, whras th injction only at th carrir amplifir input bring slightly bttr supprssion of IM5 products. IV. SIMULATED AND MEASURED RESULTS S-paramtrs of Dohrty amplifir obtaind by ADS simulator as wll as th masurd paramtrs ar shown in Fig.. Th figur compars th charactristics achivd in th cas of th idal losslss amplifir circuit (dashd lin) and in th cas whn losss and discuntinuity ffcts of t-sctions and bandd microstrip lins ar includd into th analysis. On can notic that th amplifir oprational frquncy is shiftd from th dsign frquncy of GHz to.006ghz in th fabricatd amplifir. Fig.. S-paramtrs of two-way Dohrty amplifir. Th rsults bfor and aftr linarization for two-ton tst of two-way Dohrty amplifir at frquncis 9MHz and 990GHz ar givn in Fig. 5 for th rang of fundamntal signal a) b) Fig. 5. Simulatd intrmodulation products bfor and aftr linarization of two-way Dohrty amplifir for a powr rang: a) third-ordr; b) fifth-ordr products. Th masurd output spctra of Dohrty amplifir bfor and aftr applying th linarization for two sinusoidal signals at dm input powr at frquncis.0065ghz and
7.0075GHz ar compard in Fig. 6. Th fundamntal signal output powr is about 9.96dm bfor and 9.35dm aftr th linarization. Th third-ordr intrmodulation products at frquncis.0055mhz and.005ghz ar lowrd by linarization from -dm to -6dm and -3dm, rspctivly. Th fifth-ordr intrmodulation products ar rducd by around 6d at frquncis.005mhz and.0095ghz. Th rsults from Fig. 7 show th ffcts of two-way Dohrty amplifir linarization accomplishd for th output powr ranging from 0dm to 6dm (uppr signal powr is constraind by th laboratory quipmnt capability to th powr that is 0d blow th maximal catalogu powr lvl of th transistor applid). Ths rsults ar compard to th cas whn linarization is not carrid out. Fig. 7a) rlats to th powr rduction of IM3 at.0055ghz (IM3-) and.005ghz (IM3+), whras Fig. 7b) shows rsults connctd to th IM5 products at.005ghz (IM5-) and.0095ghz (IM5+). It is vidnt from ths figurs that th linarization with th proposd approach givs satisfactory rsults in improvmnt of IM3 products for th powr rang up to approximatly dm and bcoms asymmtrical at highr powr. Howvr, IM5 products dcras slightly at lowr powr lvls, whras thy gt wors at highr powr rang considrd, still rtaind blow th lvls of th linarizd IM3 products. According to () and (3), IM and IM signals can rduc both IM3 and IM5 products that dpnds on th rlations btwn amplituds as wll as phass of th IM and IM signals gnratd at th paking amplifir output. Howvr, whn th rquird rlations ar not fulfilld, only on kind of th intrmodulation products can b rducd sufficintly. Dohrty amplifir drain fficincy (DE) obtaind in simulation for idal circuit cas without losss, th simulatd charactristic gaind for th loss microstrip circuit with includd discontinuitis and th masurd valus ar compard in Fig.. Th good agrmnt can b obsrvd btwn th curvs rlating to th ral simulatd Dohrty amplifir and xprimntal rsults up to 3dm powr that is maximal lvl that can b rachd by th availabl laboratory quipmnt. At this powr lvl, thr is a maximal discrpancy btwn th simulatd and masurd rsult of 5%. Th maximal fficincy achivd by th ralizd circuit is 3.7%. Fig. 6. Masurd output spctra for dm input powr of fundamntal signals; bfor and aftr linarization (filld curv). a) b) Fig. 7. Masurd intrmodulation products bfor and aftr linarization of two-way Dohrty amplifir for a powr rang: a) third-ordr; b) fifth-ordr products.
Fig.. Drain fficincy of two-way Dohrty amplifir. V. CONCLUSION This papr prsnts for th first tim th xprimntal vrification of two-way Dohrty amplifir linarization by simultanous injction of th scond harmonics and fourthordr nonlinar signals at th input of carrir amplifir. Th linarization approach achivs vry good rsults in a rduction of th third-ordr intrmodulation products, vn for a widr powr rang. Whn th fifth-ordr intrmodulation products ar concrnd, th mild supprssion is obsrvd at low- powr lvls, howvr ths products dtriorat at highpowr rang. Masurmnts ar constraind by th laboratory quipmnt to th lowr powr that is 0d blow th maximal availabl powr of transistors utilizd. Additionally, th rsults of simulation obtaind by Advanc Dsign Systm program ar introducd in th papr for thr variancs of th linarization approach concrning th injction point of th signals for linarization:. input,. output, and 3. input and output of th carrir amplifir. It can b obsrvd th similar bhaviour of th dsignd and ralizd two-way Dohrty amplifir in linarization procss. W would lik to point out that th crucial mattr in th linarization approach usd for Dohrty amplifir linarization is th possibility to xploit th paking amplifir as a sourc of signals for linarization and thrfor avoid th ncssity for additional nonlinar sourcs that will incras th circuit complxity and total nrgy consumption. REFERENCES [] K. J. Chao, W. J. Kim, J. H. Kim and S. P. Staplton, Linarity optimization of a high powr Dohrty amplifir basd on post-distortion compnsation, IEEE Microwav and Wirlss Componnts Lttrs, vol.5, no., pp.7-750, 005. [] K. J. Cho, J. H. Kim and S. P. Staplton, A highly fficint Dohrty fdforward linar powr amplifir for W-CDMA bas-station applications, IEEE Trans., Microwav Thory Tch., vol. 53, no., pp.9-300, 005. [3]. Shin, J. Cha, J. Kim, Y. Y. Woo, J. Yi,. Kim, Linar powr amplifir basd on 3-way Dohrty amplifir with prdistortr, IEEE MTT-S Int. Microw. Symp. Digst, pp.07-030, 00. [] T. Ogawa, T, Iwasaki, H. Maruyama, K. Horiguchy, M. Nakayama, Y. Ikda and H. Kurbayashi, High fficincy fd-forward amplifir using RF prdistortion linarizr and th modifid Dohrty amplifir, IEEE MTT-S Int. Microw. Symp. Digst, pp.537-50, 00. [5] Alksandar Atanasković, Nataša Malš-Ilić, ratislav Milovanović, Th linarization of Dohrty amplifir, Microwav rviw, No., Vol., pp.5-3, Sptmbr 00. [6] Alksandar Atanasković, Nataša Malš-Ilić, ratislav Milovanović: Th linarization of high-fficincy thr-way Dohrty amplifir, TELFOR00, Confrnc Procdings on CD, 3.7, ograd, Srbija, 5-7. Novmbr, 00. [7] A. Atanasković, N. Malš-Ilić,. Milovanović, Th supprssion of intrmodulation products in multichannl amplifirs clos to saturation, Procdings of th WSEAS Intrnational Confrnc on Circuits, pp. 9-0, Grc, July 007. [] Nataša Malš-Ilić, Alksandar Atanasković, ratislav Milovanović: High-fficint thr-way Dohrty amplifir with improvd linarity, Rcnt Advancs in Circuits - Procdings of th 3th WSEAS Intrnational Confrnc on CIRCUITS (part of th 3th WSEAS CSCC Multiconfrnc), Rodos, Grc, July -, WSEAS Prss, pp.37-0, 009. [9] Nataša Malš-Ilić, Alksandar Atanasković, ratislav Milovanović: Harmonic-Controlld Thr-Way Dohrty Amplifir with Improvd Linarity, WSEAS Transaction on Circuits and Systms, WSEAS Prss, Vol., Issu 9, pp.769-77, Sptmbr 009, ISSN:09-73 [0] Alksandar Atanasković, Natasa Malš-Ilić, ratislav Milovanović: Harmonic controlld thr-way Dohrty amplifir with improvd fficincy and linarity, Procdings of th 9th Intrnational Confrnc on Tlcommunications in Modrn Cabl, Satllit and roadcasting Srvics - TELSIKS 009, Niš, Srbia, Octobr 7-9, Vol., pp.36-39, 009. [] MJ. P. Aikio, T. Rahkonn, Dtaild distortion analysis tchniqu basd on simulatd larg-signal voltag and currnt spctra, IEEE Trans. Microwav Thory and Tchniqus, Vol. 53, pp. 3057-3065, 005. [] A. Hiskann, J. Aikio, T. Rahkonn, A 5-th Ordr Voltrra study of a 30W LDMOS powr amplifir, Proc. IEEE Int. Symp. on Circuits and Systms (ISCAS), pp. 66-69, angkok, Thailand, 003.