High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers with Enhanced Maximum Operating Frequency

Transcription

1 High-Efficiency Harmnic-Peaking Class-EF Pwer mplifiers with Enhanced Maximum Operating Frequency Thian, M., Barakat,., & Fusc, V. (5). High-Efficiency Harmnic-Peaking Class-EF Pwer mplifiers with Enhanced Maximum Operating Frequency. IEEE Transactins n Micrwave Thery and Techniques, 6(), OI:.9/TMTT Published in: IEEE Transactins n Micrwave Thery and Techniques cument Versin: Peer reviewed versin Queen's University Belfast - Research Prtal: ink t publicatin recrd in Queen's University Belfast Research Prtal Publisher rights 5 IEEE. Persnal use f this material is permitted. Permissin frm IEEE must be btained fr all ther uses, in any current r future media, including reprinting/republishing this material fr advertising r prmtinal purpses, creating new cllective wrks, fr resale r redistributin t servers r lists, r reuse f any cpyrighted cmpnent f this wrk in ther wrks. General rights Cpyright fr the publicatins made accessible via the Queen's University Belfast Research Prtal is retained by the authr(s) and / r ther cpyright wners and it is a cnditin f accessing these publicatins that users recgnise and abide by the legal requirements assciated with these rights. Take dwn plicy The Research Prtal is Queen's institutinal repsitry that prvides access t Queen's research utput. Every effrt has been made t ensure that cntent in the Research Prtal des nt infringe any persn's rights, r applicable UK laws. If yu discver cntent in the Research Prtal that yu believe breaches cpyright r vilates any law, please cntact penaccess@qub.ac.uk. wnlad date:5. Feb. 7

2 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques High-Efficiency Harmnic-Peaking Class-EF Pwer mplifiers with Enhanced Maximum Operating Frequency Mury Thian, yman Barakat and Vincent Fusc, Fellw, IEEE bstract The recently intrduced Class-EF pwer amplifier (P) has a peak switch vltage lwer than that f Class-E P. Hwever, the value f the transistr utput capacitance at high frequencies is typically larger than the required Class-EF ptimum shunt capacitance. Cnsequently, sft-switching peratin that minimizes pwer dissipatin during OFF-t-ON transitin cannt be achieved at high frequencies. Tw new Class-EF P variants with transmissin-line lad netwrks, namely, third-harmnic-peaking (THP) and fifth-harmnicpeaking (FHP) Class-EF Ps are prpsed in this paper. These permit peratin at higher frequencies at n expense t ther P figures f merit. nalytical expressins are derived in rder t btain circuit cmpnent values which satisfy the required Class- EF impedances at fundamental frequency, all even harmnics, and the first few dd harmnics as well as simultaneusly prviding impedance matching t a 5 Ω lad. Furthermre, a nvel pen-circuit and shrted stub arrangement which has substantial practical benefits is prpsed t replace the nrmal quarter-wave line cnnected at the transistr s drain. Using GaN HEMTs, tw P prttypes were built. Measured peak drain efficiency f 9% and utput pwer f 9.5 dbm were btained at. GHz fr the THP Class-EF P. The FHP Class-EF P delivered utput pwer f 4.9 dbm with 85% drain efficiency at.5 GHz. Index Terms Class-E, Class-EF, Class-F, fifth-harmnicpeaking, GaN, HEMT, pwer amplifiers, third-harmnicpeaking, transmissin lines. substantially lwer peak switch vltage than the Class-E cunterpart but cannt facilitate sft-switching peratin since their idealized circuit tplgies d nt incrprate a shunt capacitance (C) that is cnnected in parallel with the switch. In practice, this means that the transistr utput capacitance (C OUT ) cannt be effectively absrbed. The utput capacitance f an actual transistr typically has nnlinear characteristic since it depends n instantaneus drain-surce vltage values. The analysis in [4] presented a design methdlgy fr Class-E P wherein the nnlinear utput capacitance can be adequately apprximated with an equivalent linear capacitance. (a) T I. INTROUCTION HE Class-E pwer amplifier (P) []-[5] theretically ffers % C-t-RF efficiency since its switch vltage and current wavefrms are tailred such that they d nt verlap each ther. It adpts zer vltage switching (ZVS) and zer vltage derivative switching (ZVS) cnditins s as t enable sft-switching peratin which minimizes pwer dissipatin during OFF-t-ON transitin. Hwever, the peak switch vltage f Class-E P is cnsiderably high. The Inverse Class-E P [6]-[8] and Class-F P [9]-[] ffer Manuscript received September, 4; revised Nvember, 4 and ecember 5, 4; accepted ecember, 4. This wrk was supprted by the Nrthern Ireland epartment fr Emplyment and earning (E) under Strengthening ll Island Mbile Wireless Futures prgramme and by the FP7 Marie Curie EI prgramme under RTISN prject. The authrs are with the Queen s University f Belfast, ECIT Institute, Queen s Rad, Queen s Island, Belfast, BT 9T, United Kingdm ( m.thian@qub.ac.uk). (b) Fig.. Class-EF P with lumped-element lad-netwrk: (a) Basic circuit (b) Idealized steady-state switch vltage and current wavefrms. The Class-EF P and its variants reprted in [5]-[] ffer a lw peak switch vltage f nly V C as in the Class F as well as sft-switching peratin as in the Class E, Fig.. Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

3 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques Further, since the switch vltage has maximally flat peak, Fig. (b), the Class-EF P is relatively immune t the detrimental effects that the nnlinear utput capacitance has n its perfrmance. majr challenge in Class-EF P design is that fr a given utput pwer and C supply vltage (V C ), the maximum perating frequency (f MX ) is cnstrained by the transistr utput capacitance (C OUT ), i.e., at high frequencies the value f C OUT is typically larger than the value f C, Fig. (a), that results frm the Class-EF synthesis. n external shunt inductance ( P ) can be used t tune ut the excess capacitance C X (= C OUT C) at the fundamental frequency. Hwever, the net reactance f this parallel circuit P -C X at higher harmnics (f, f, etc.) wuld be capacitive. s a cnsequence, the pen-circuit requirement at dd harmnics fr ptimum Class- EF peratin wuld be vilated. The theretical analysis in [] demnstrates that the f MX f the Class-EF P can be increased by reducing the duty rati, by switching the transistr ON fr a shrter perid. Hwever, this strategy results in lw pwer-utput capability and lw lad resistance. The fact that large devices with high-pwer-handling capability are always accmpanied with high C OUT wuld appear t render the Class-EF P tplgy unsuitable fr high pwer applicatins. In rder t address the afrementined issues, we intrduce tw new variants f the Class-EF P, namely third-harmnicpeaking (THP) and fifth-harmnic-peaking (FHP) Class-EF Ps. Synthesized in the frequency dmain, these Ps emply a simple transmissin-line lad netwrk and allw peratin at higher f MX. While the THP Class-EF P satisfies the pencircuit terminatin requirement at f alne, the FHP Class-EF P [] satisfies the requirement simultaneusly at f and 5f. On the ther hand, the requirement fr shrt-circuit terminatin at all even harmnics is satisfied thrugh deplyment f a quarter-wave (/4) line cnnected at the drain. Clsed-frm expressins are analytically derived nt nly t satisfy the Class-EF lad-impedance requirements at the fundamental frequency, all even harmnics, and the first few dd harmnics but als t simultaneusly prvide an impedance matching t 5-Ω lad thus bviating the need fr additinal utput matching circuitry. Since the pen-circuit cnditins at f and 5f are satisfied and all even harmnic cmpnents are shrted by the λ/4 line, high purity utput spectrum can be btained frm the FHP Class-EF P lad netwrk. This relaxes the design specificatins fr additinal filtering typically required at the P utput fr cmpliance with standardized ut-f-band emissin regulatins. Further, when cmpared t the Class-E F and Class E F Ps in [], the new Ps generate a less distrted utput signal. In additin, these new Ps emply nvel λ/8 pen-circuit and shrted stubs which replace the classical λ/4 transmissin line (T). This arrangement ffers better pen- and shrt-circuit terminatins and has the capability t independently cntrl pen- and shrt-circuit terminatins at the transistr s drain, which in turn imprve the P s efficiency. This paper is rganized as fllws: basic peratin f the Class-EF P with lumped-element lad netwrk alng with sme design trade-ffs awareness is briefly reviewed in Sectin II. Sectins III and IV present the theretical analysis f the THP and FHP Class-EF Ps, respectively. Circuit design examples and simulatins using ideal cmpnents are treated in Sectin V. Finally in Sectin VI, implementatin f the Ps using GaN HEMTs and measurement results are discussed. II. REVIEW OF CSS-EF POWER MPIFIER The circuit schematic fr the Class-EF P is depicted in Fig. (a). The transistr must be driven sufficiently hard such that it perates like a switch rather than a current surce. The ptimal lad impedances at fundamental frequency and higher harmnics seen by the transistr, Z OPT, are given in (). The lad netwrk will present R in series with at f, a shrt circuit at all even harmnics, and an pen circuit at all dd harmnics. Fr prescribed utput pwer (P O ), C supply vltage (V C ), and perating frequency (f ), the ptimal lad resistance R and series inductance can be calculated using ()-(). The shunt capacitance C may entirely furnish the device utput capacitance C OUT and its value is given in (4). Nte that in ()-(4) the parameter named dead time (in rad) is related t duty rati by =.5 /(). Fr example, = / rad crrespnds t =.5 meaning that the transistr will be switched ON fr a perid f 5% f the full cycle. quarter-wave line is emplyed at the drain f the transistr s as t enfrce shrt-circuit terminatin at all even harmnics. Steady-state switch vltage and current wavefrms f the Class-EF P are illustrated in Fig. (b) and the peak switch vltage is V C. By substituting C = C OUT int (4), the expressin fr f MX can be btained, (5). P MX (6a) is defined as a rati between utput pwer and the prduct f peak switch vltage and peak switch current (6b). Z OPT R R j cs at at nf, n,,, f at n f, n,,, V C () PO.5sin R () sin sin P O C cs (4) V C f MX P MX sin 4 cs C P O V OUT C cs / 4 cs / 4 sin ; / ; / () (5) (6a) Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

4 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques I R I MX I R sin where I R I C cs ; / ; / III. THIR-HRMONIC-PEKING CSS-EF P WITH ENHNCE f MX (6b) (6c) new Class-EF P circuit tplgy with transmissin-line lad netwrk is depicted in Fig.. In practice, it is impssible t realize a transmissin-line lad netwrk that culd simultaneusly satisfy Class-EF impedance requirements at the fundamental frequency as well as at all even and dd harmnics () since this wuld require an infinite number f transmissin lines. Hwever, as will be shwn shrtly, a gd apprximatin t the idealized Class-EF peratin can be achieved by satisfying the required impedances at f, all even harmnics, and nly the first few dd harmnics. Here, a third-harmnic-peaking (THP) Class-EF P is prpsed wherein the pen-circuit requirement is satisfied at f alne. The circuit is als synthesized t simultaneusly prvide direct impedance matching int a 5-Ω lad. defined as kc (k > ). sin f k MX 4 cs C P V O OUT. Basic Circuit The electrical length f the pen-circuit stub T in Fig. (a) is 9 at f and therefre it prvides a shrt-circuit terminatin t the series line T. This shrted series line behaves like an inductance ( ). This inductance must be resnated with C X in rder t prvide the required Class-EF pen circuit at f, hence (8). C tan X (8) t the fundamental frequency, the 5 Ω lad resistance (R ) is transfrmed by T and T int an admittance f /Z OPT - jω C X where Z OPT is given in (). This results in: G B G sec OPT (9) OPT B tan G tan C X tan B B tan G B tan G tan C tan (7) () where: (a) G OPT R () R B OPT () R G / R /5 () B tan / (4) By slving (8)-() simultaneusly, the values f Z (= / ), θ, and Z (= / ) can be btained. The characteristic impedance f the quarter-wave line Z must be selected sufficiently high s as t islate the supply vltage frm the RF signal. Nte that C b is a C-blcking capacitance. (b) Fig.. Third-harmnic-peaking Class-EF P with enhanced f MX emplying: (a) λ/4 line, (b) λ/8 pen and shrted stubs as well as an additinal fifthharmnic trap T (Z B, λ/). Enhanced f MX is achieved by adding extra capacitance C X t the riginal Class-EF circuit in Fig. (a) and, as a result, the device utput capacitance C OUT nw increases t C + C X. This translates int higher f MX expressed in (7) where C X is B. Mdified ad Netwrk T facilitate fr fifth-harmnic suppressin, the single pen-circuit stub (Z, ) in Fig. (a) is mdified int tw pen-circuit stubs with electrical lengths f and 8, Fig. (b). Their respective characteristic admittances and B are: tan (5) tan tan8 B. 64 where = /Z and B = /Z B. Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

5 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 4 Furthermre, nvel λ/8 pen-circuit and shrted stubs are nw used t replace the traditinal λ/4 line. The λ/8 pen stub will shrt circuit the drain f the transistr at (4m-) th harmnics whereas the λ/8 shrted stub will shrt circuit the drain f the transistr at 4m th harmnics where m =,,, etc. Tgether they will facilitate a shrt-circuit terminatin at all even harmnics. t the fundamental frequency, the λ/8 shrted stub behaves like an inductance (6) while the λ/8 pen stub behaves like a capacitance C 4 (7). This parallel C 4 circuit is designed t resnate at f (8). j jz tan 45 jz (6) 4 4 j C j tan 45 j (7) 4 C (8) 4 Substitutin f (6) and (7) int (8) results in: Z Z 4 (9) By setting Z equal t Z 4, the prpsed stub arrangement prvides an pen circuit nt nly at f but als at all dd harmnics. Fig.. Characteristics f λ/8 pen and shrted stubs vs λ/4 T. The bandwidth characteristic f the λ/8 pen-circuit and shrted stubs at f and higher harmnics is cmpared with the λ/4 T in Fig.. It can be bserved that the rejectin band ( S db) f the prpsed arrangement is twice as large as that f the λ/4 T. Fr illustratin, suppse f =.5 GHz. The new λ/8 stubs will prvide useful attenuatin db frm 4.68 GHz t 5. GHz (rejectin bandwidth = 64 MHz). t ne half these frequencies i.e., frm.4 GHz t.66 GHz (pass-band bandwidth = MHz), insertin lss is better than.7 db. Meanwhile, the traditinal λ/4 line will prvide the same level f insertin lss i.e., better than.7 db frm.8 GHz t.8 GHz (pass-band bandwidth = 64 MHz i.e., twice as large as that f the λ/8 stubs). Hwever, the rejectin levels at x these frequencies i.e., frm 4.6 GHz t 5.64 GHz are nly.875 db. Therefre it is misleading t cnclude that the pass-band bandwidth f the λ/4 line is superir. The crrect way t interpret the graph in Fig. is as fllws. The λ/4 line will prvide attenuatin db frm 4.84 GHz t 5.6 GHz (rejectin bandwidth = MHz i.e., ne half that f the λ/8 stubs) and this is translated int a passband bandwidth f 6 MHz i.e., frm.4 GHz t.58 GHz. In ther wrd, althugh the insertin lss f the λ/4 line is lw acrss.8-.8 GHz frequency range, nly a fractin f this bandwidth i.e., frm.4 GHz t.58 GHz is useful since they result in sufficient rejectin levels db. In practice, the λ/4 line in Fig. (a) cannt prvide ideal shrt-circuit terminatin i.e., Ω at even harmnics as required fr Class-EF peratin due t parasitic resistance ESR. The effect f ESR n the P efficiency becmes mre prnunced in lw-vltage high-pwer designs when the resistance that the supply vltage presents t the P (R C ) is cnsiderably small. Since the physical length f the λ/8 pen and shrted stubs in Fig. (b) is just half f that f the λ/4 line, the accmpanied ESR will be lwer and thus prvides better shrt-circuit terminatin. Mre imprtantly, the bypass capacitance C b in Fig. shuld in thery prvide a shrt circuit at the fundamental frequency as well as at all even and dd harmnics. Hwever, in practice, ne capacitr can nly be used t prvide lw impedance (typically arund Ω) at a single frequency. Fr example, in rder t prvide a shrt circuit at f and higher harmnics up t 6f, six capacitrs are needed. In cntrast, the P in Fig. (b) nly needs fur capacitrs since the shrtcircuit terminatins at the drain at f and 6f are enfrced by the λ/8 pen-circuit stub and therefre n capacitrs are required. nther practical advantage is that the λ/8 pen stub will present lwer impedance (clse t Ω) at the drain resulting in better nd and 6 th harmnics suppressin than when λ/4 T and C b are used. In additin, when implemented in IC frmat particularly at millimeter-wave frequencies, the prpsed stub arrangement ffers mre flexibility and superir perfrmance than the traditinal λ/4 line. In thery a shrted λ/4 line can prvide shrt-circuit terminatin at all even harmnics. In reality, the length f this line can be effectively tuned at just ne frequency (typically f ) s as t prvide the required lwimpedance terminatin. In the prpsed stub arrangement, the lengths f the λ/8 pen and shrted stubs can be tuned independently t prvide lw-impedance terminatin at f and 4f, respectively. IV. FIFTH-HRMONIC-PEKING CSS-EF P WITH ENHNCE f MX The circuit schematic fr the fifth-harmnic-peaking (FHP) Class-EF P is depicted in Fig. 4. Here, the Class-EF pencircuit requirement is satisfied fr the first tw dd harmnics, i.e., f and 5f rather than just f as in the THP Class-EF P. s a result it mimics idealized Class-EF peratin mre clsely than the THP Class-EF P. The FHP Class-EF P is cmprised f λ/8 pen and shrted stubs which enfrce shrtcircuit terminatins at even harmnics, C X as a means t enhance f MX, tw series transmissin lines (T, T 4 ), three pen-circuit stubs (T, T 5, T 6 ), and a shrted stub (T ). In the analysis belw, Z N, N (=/Z N ) and θ N are, respectively, the characteristic impedance, the characteristic admittance, Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

6 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 5 and the electrical length f T N. Nte that C b is a C-blcking capacitance and als has a rle in preventing the C signal frm being shrted by T. 4 j X jz tan (8) C (9) X X C tan () 4 X 4 Substitutin f () int () results in: 5tan tan () () Fig. 4. Fifth-harmnic-peaking Class-EF P with enhanced f MX emplying λ/8 pen and shrted stubs and an additinal seventh-harmnic trap T 6 Cnsider nw the fllwing: T 6 in Fig. 4 is absent, θ = 8 and θ 5 =. t 5f, the right-hand end f T will be shrted by T. Prvided θ < 8, the shrted T will act like an inductance given in (). This inductance is designed t resnate with C X at 5f s as t prvide the required Class-EF dd-harmnic pen-circuit cnditin (). 5 j5 jz tan () 5 C X () Substitutin f () int () results in: X 5 5 C tan () t f, T and T behave respectively like a capacitance C and an inductance, ()-(4). This parallel circuit is designed t resnate at f and therefre present an pen circuit, (5). s a cnsequence, T and T 4 are nw in series cnnectin. j 54 C j tan () jz tan j (4) C (5) Suppse Z = Z = Z B. Substitutin f () and (4) int (5) yields: tan54 tan (6) (7) On the ther hand, the right-hand end f T 4 will be shrted by T 5. Prvided that θ + θ 4 <, T tgether with the shrted T 4 will behave like an inductance X and this inductance is designed t resnate with C X at f, facilitating an pen circuit; see (8)-(9) with Z = Z 4 = Z. Frm (8) and (9), we btain (). With C X = C OUT - C, the characteristic admittance f T and T 4,, can be cmputed frm either () r (). t f, T T 5 tgether with C X will transfrm the lad resistance R int R + jω. This results in tw equatins ()- (4) with tw unknwn parameters B (= = ) and 5 which can be slved numerically. Nte that R and in (5)- (6) are given in ()-(). G B G sec IN OPT () OPT B tan G tan IN IN C X tan B B tan G IN IN IN B tan G tan IN IN where: G OPT tan (4) R (5) R B OPT (6) R G G (7) IN IN B IN BIN B tan8 ct (8) and G B G sec IN (9) B tan G tan tan B B tan G B tan G tan IN (4) here: tan G /5 (4) B 5 tan 5 / (4) Once 5 is btained, a simple mdificatin can be made t facilitate 7 th harmnic cmpnent suppressin by adding an pen-circuit stub T 6 ( 6,.9 ) in parallel with T 5, Fig. 4. Fr simplicity, we can assume 5_new = 6 = C and its value Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

7 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 6 can be calculated using the fllwing frmula. C 5 tan.7 (4) 5 tan tan.9 V. ESIGN N SIMUTION USING IE COMPONENTS esign examples f the THP and FHP Class-EF Ps with enhanced f MX are nw presented in rder t better understand the theretical analysis described in the previus sectins. dead time parameter = 48.5 is chsen in rder t btain P MX 5% higher than that f the Class-E as discussed in Sectin II. The results presented belw were btained frm Keysight dvanced esign Systems (S) harmnic-balance simulatins using ideal cmpnents, i.e., the transmissin lines were assumed lssless, the transistr was mdeled as a switch with mω ON resistance, MΩ OFF resistance, and instantaneus switching time, and was driven by a sine wave.. Third-harmnic-peaking Class-EF P The design bjectives are set as fllws: V C = 8 V and P O = W. The transistr which will be used in implementatin is a CGH4F GaN HEMT frm CREE with C OUT =. pf. Substituting these values int (5) results in f MX =.5 GHz, meaning that the maximum frequency at which the riginal Class-EF P in Fig. can be effectively perated is nly.5 GHz. Cnsider nw the circuit in Fig.. Given f =.5 GHz, the value f the shunt capacitance C cmputed using (4) is.6 pf. Since C OUT =. pf, the excess capacitance C X (= C OUT C) required is.4 pf, implying k = 4 i.e., f MX is increased frm.5 GHz t.5 GHz. The transmissin-line parameter values Z, θ, and Z in Fig. (a) can be btained by slving (8)-() simultaneusly. R and in () and () are cmputed using ()-(). The characteristic impedances Z and Z B in Fig. (b) can be subsequently determined using (5) and when cmpared t Z their values are higher. The value f Z must be selected as high as the practical implementatin will allw. Here it is set t 8 Ω as values higher than this may result in an impractically narrw micrstrip line. The ptimal circuit cmpnent values are summarized in Table I. The simulated lad impedances at the fundamental, secnd-, and third-harmnic frequencies, Z OPT, are pltted in Fig. 5. In accrdance with ()-(), the Class-EF mde requirements fr shrt- and pen-circuit terminatins at f and f respectively are met cncurrently, as is the ptimal impedance at f. TBE I OPTIM CIRCUIT COMPONENT VUES OF THE THIR-HRMONIC-PEKING CSS-EF P, FIG. (.5 GHz, 8 V, W) C.6 pf Z = Z 4 8 Ω C X.4 pf θ 69 Z 4 Ω θ = θ Z 9 Ω θ B 8 Z = Z B 9.8 Ω θ = θ 4 45 Fig. 5. Simulated lad impedances f the THP Class-EF P at fundamental, secnd, and third harmnic frequencies. The effect that the parameter k has n the circuit cmpnent values is studied in Fig. 6. s k increases, the values f Z and θ decrease whereas the value f Z remains relatively flat up t k = abve which it starts t descend. Intuitively, this can be explained as fllws. t f, the shrted T behaves like an inductance. This inductance must resnate with C X s as t prvide an pen circuit. s k (and accrdingly C X ) increases, the shrted T needs t prvide a smaller inductance s as t preserve the resnance at f. This is achieved thrugh reductin f Z r θ, (8). t k =, the value f θ has readily descended clse t 6 belw which tan(θ ) in (8) wuld result in negative values, thereby vilating (8). s a cnsequence, fr k >, the slpe f θ in Fig. 6 needs t settle, and in rder t cmpensate fr this, Z must be accrdingly reduced. Fig. 6. Optimal transmissin-line parameter values versus k f the THP Class- EF P. The steady-state vltage and current wavefrms f the circuits in Fig. are illustrated in Fig. 7. s can be bserved, the ZVS and ZVS cnditins are satisfied during the OFFt-ON transitin. Further, cnsistent with the thery, the maximally flat peak switch vltage (V SW ) f V C = 56 V is btained. The currents thrugh the switch and the capacitance C OUT are dented respectively as I SW and I Cut. Within the interval where V SW is kept cnstant at V C, I Cut is zer since I Cut is prprtinal t the first derivative f V SW. This distinctive feature differentiates the Class-EF P frm the Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

8 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 7 Class-E P in which I Cut has nn-zer values thrughut the OFF interval. Simulated utput pwer and C current are 9.76 dbm and 4 m leading t a drain efficiency f 99.5%. Fig. 7. Steady-state vltage and current wavefrms f the THP Class-EF P (Fig. ), fr k = 4. the fifth-harmnic level. s a result, as can be seen frm Fig. 9, the utput vltage f the P in Fig. (b) lks less distrted than that f Fig. (a). The secnd-, sixth-, and tenth-harmnic cmpnent levels f the Ps in Fig. (a) and (b) shuld theretically be identical discrepancies shwn in Fig. 8 are mainly due t numerical artifacts in S. B. Fifth-Harmnic-Peaking Class-EF P Cnsider nw the circuit in Fig. 4. The design bjectives are set as fllws: f = GHz, V C = 8 V and P O = W. The value f the shunt capacitance C cmputed using (4) is.4 pf. Since C OUT =. pf, the excess capacitance C X (= C OUT C) required is.88 pf, implying k i.e., f MX is increased frm 647 MHz t GHz. Three parameters, i.e.,, B, and C are t be determined. First, the characteristic admittance f T and T 4 i.e., is cmputed frm either () r () where the value f θ = θ 4 is given in (). By simultaneusly slving () and (4), the values f B and 5 can be btained, and subsequently the value f C is calculated using (4). The ptimal circuit cmpnent values are summarized in Table II. The simulated lad impedances at fundamental and higher harmnic frequencies (up t 5f ), Z OPT, are pltted in Fig.. In accrdance with ()-(), the Class-EF mde requirements fr shrt- and pen-circuit terminatins at even and dd harmnics respectively are satisfied, and s is the ptimal impedance at f. TBE II OPTIM CIRCUIT COMPONENT VUES OF THE FIFTH-HRMONIC-PEKING CSS-EF P, FIG. 4 ( GHz, 8 V, W) C.4 pf θ 45 C X.88 pf θ = θ 4.5 Z 8 Ω θ 8 Z = Z 4.9 Ω θ Z = Z 7.7 Ω θ 5 Z 5 = Z 6. Ω θ 6.9 Fig. 8. Simulated utput pwer spectrum f the THP Class-EF P up t f using ideal cmpnents: dtted lines fr Fig. (a) and slid lines fr Fig. (b). Fig. 9. Output vltage cmparisn: dtted lines fr Fig. (a) and slid lines fr Fig. (b). Shwn in Fig. 8 is the utput pwer spectrum f the P circuits in Figs. (a) and (b). Bth Ps are able t deliver the fundamental utput pwer level as specified earlier. T B adpted in Fig. (b) prves effective as a means t suppress Fig.. Simulated lad impedances f the FHP Class-EF P at fundamental and higher harmnic frequencies. The steady-state vltage and current wavefrms are illustrated in Fig.. Simulated utput pwer is.9 W and simulated C current is 46 m, leading t a drain efficiency Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

9 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 8 f 99.9%. The utput pwer spectrum f the P circuit in Fig. 4 is shwn in Fig. where harmnics up t the th are well suppressed. The nd, 6 th, and th harmnic cmpnents are suppressed thrugh shrt-circuit terminatin facilitated by the λ/8 pen-circuit stub. The 4 th and 8 th harmnic cmpnents are suppressed by means f shrt-circuit terminatin facilitated by the λ/8 shrted stub. The rd and 5 th harmnic cmpnents are suppressed thrugh pen-circuit terminatin facilitated by the P s lad netwrk i.e., C X, T -T 6, and λ/8 pen-circuit and shrted stubs. T 6 is respnsible fr prviding a shrt-circuit terminatin t the 7 th harmnic cmpnent. s a result, the P prduced a nearly pure sine wave at the utput (V O ), Fig.. 5 Ω series T which cnnects the input and utput prts. The characteristic impedance f the stubs is 8 Ω. The physical dimensins f the stubs are W =.46 mm and = 9.4 mm. Fr cmparisn, anther test bard cmprised f a λ/4 T (W =.46 mm and = 8.68 mm) was built, Fig. (b). The measured and simulated frequency respnses f the stubs at f =.5 GHz and higher harmnics are cmpared with the λ/4 T in Fig. (c). It can be bserved that the rejectin band ( S db) f the prpsed arrangement is as predicted i.e., twice as wide as the λ/4 T. (a) (b) (c) Fig.. Steady-state vltage and current wavefrms f the FHP Class-EF P (Fig. 4). Fig.. Simulated utput pwer spectrum f the FHP Class-EF P up t f using ideal cmpnents. VI. IMPEMENTTION N MESUREMENT In rder t validate the theretical synthesis apprach in Sectin III, we fabricated a test bard, Fig. (a). This cmprised f a λ/8 pen-circuit stub, a λ/8 shrted stub, and a Fig.. (a) Test bard f the prpsed λ/8 stubs, (b) test bard f the traditinal λ/4 T, and (c) measured and simulated frequency respnses. Fr the validatin f the THP and FHP Class-EF Ps analysis described in Sectins III and IV, tw prttypes were built. The Ps emply packaged GaN HEMTs CGH4F frm CREE with drain-surce breakdwn vltage f V and typical saturated pwer f W. The manufacturer datasheet shws that the transistr is ptentially unstable at frequencies belw.5 GHz and therefre stabilizing resistrs are needed. The Ps were realized n a.5-mm thick Rgers RO4C substrate with dielectric cnstant f.55, lss tangent f.7, and thermal cnductivity f.7 W/m/ K.. Third-Harmnic-Peaking Class-EF P The circuit cmpnent values were initially btained by cnverting the characteristic impedance (Z N ) and electrical length (θ N ) values given in Table I int the crrespnding micrstrip physical dimensins in terms f width (W N ) and length ( N ). These values were then ptimized in the simulatin in rder t give best perfrmances in terms f efficiency, utput pwer and harmnic suppressin levels. Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

10 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 9 Fig. 4. Cmplete circuit schematic f the THP Class-EF P. TBE III TRNSMISSION-INE O-NETWORK PRMETER VUES OF THE THIR-HRMONIC-PEKING CSS-EF P, FIG. (b) (.5 GHz, 8 V, W) Parameter Theretical Values (mm) Optimized Values (mm) W W W B.8.4 B W = W stable i.e., K is larger than and B is larger than, Fig. 5. The phtgraph f the P prttype with a square dimensin f 4. cm 4. cm is depicted in Fig. 6. s depicted in Fig. 7, a Keysight E857 signal generatr was used t excite the amplifier with a cntinuus-wave (CW) signal and the utput pwer was measured using Keysight N9 spectrum analyzer. Since the maximum utput pwer f the signal generatr was limited t 7 dbm, an identical replica f the amplifier was used as a driver. -db attenuatr was inserted between the P and the spectrum analyzer. Gate and drain biasing was applied using Thurlby Thandar pwer supplies ( V ). Fig. 6. The THP Class-EF P prttype. Fig. 5. Simulated stability factrs K and B befre and after adding a stabilizing parallel resistr f kω at the input. The theretical and ptimized circuit cmpnent values are presented in Table III. The cmplete circuit schematic f the THP Class-EF P which includes the input matching netwrk, biasing and stabilizing circuits is illustrated in Fig pf capacitr is used as an RF bypass capacitance as it presents lw impedance at the fundamental frequency. The input matching circuit cnsists f a.5 pf series capacitance and an pencircuit stub (T nd ). kω resistr cnnected in parallel with the.5 pf capacitance is used t make the P uncnditinal Fig. 7. Measurement setup. Fig. 8 shws measured utput pwer, gain, drain efficiency and PE versus input pwer at. GHz with V GS =.7 V and V C = 8 V. Best efficiency perfrmance Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

11 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques i.e., when drain efficiency and PE peaked at 9% and 8% respectively was achieved at utput pwer f 9.5 dbm and gain f 9. db. t this perating pint, 5 m C current was drawn frm the pwer supply. when the supply vltage V C was swept is shwn in Fig.. Results shw that drain efficiency and PE remained abve 8% and 6% respectively when V C was varied frm t V. Fig. als shws a near linear relatinship between utput vltage and V C. This feature is useful fr effective deplyment f the P in envelpe eliminatin and restratin (EER) systems r plar transmitters. By decreasing V C frm 8 t 4 V, the utput pwer was reduced by arund 6 db frm 9.5 t.4 dbm, within which range the drain efficiency remained abve 68%. Simulated utput pwer spectrum is shwn in Fig.. Fig. 8. Measured P perfrmances versus input pwer at. GHz with V C = 8 V and V GS = -.7 V. Fig.. Simulated utput pwer spectrum f the THP Class-EF P. Fig. 9. Measured P perfrmances versus frequency at V C = 8 V and V GS = -.7 V. B. Fifth-Harmnic-Peaking Class-EF P Initial circuit cmpnent values were btained by cnverting the characteristic impedance (Z N ) and electrical length (θ N ) values given in Table II int the crrespnding micrstrip physical dimensins i.e., width (W N ) and length ( N ). These values were then ptimized in the simulatin in rder t give best perfrmances in terms f efficiency, utput pwer and harmnic suppressin levels. The theretical and ptimized cmpnent values are presented in Table IV. TBE IV TRNSMISSION-INE O-NETWORK PRMETER VUES OF THE FIFTH-HRMONIC-PEKING CSS-EF P, FIG. 4 ( GHz, 8 V, W) Fig.. Measured P perfrmances versus V C at. GHz with V GS = -.7 V. The frequency behavir f the P is illustrated in Fig. 9. Within 46 MHz frequency range i.e., frm.8 t.8 GHz, the P was able t deliver 8.8±.5 dbm utput pwer with drain efficiency f at least 58%. P perfrmance at. GHz Parameter Theretical Optimized Values (mm) Values (mm) W = W = W = W W 5 = W W _shrt.67.5 _pen.67.5 The circuit schematic f the FHP Class-EF P is shwn in Fig.. The P emplys a simple -type input matching netwrk cmprised f a series capacitance.8 pf and a 6.5- mm-lng shrted stub. ue t high quality factr (Q) f the Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

12 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques Fig.. Cmplete circuit schematic f the FHP Class-EF P. Fig.. The FHP Class-EF P prttype. Fig. 5. Measured P perfrmances versus input pwer at.5 GHz with V C = V and V GS = -.8 V. Fig. 4. Measured P perfrmances versus frequency at V C = V and V GS = -.8 V. cmplex lad netwrk, the FHP Class-EF P circuit tends t be mre sensitive t instability than the THP Class-EF P. Cnsequently, a 5-Ω series resistance cnnected t the transistr s gate was required in rder t prevent scillatin, but this cmes at the expense f increased pwer lss. The prttype measures 4 cm 4 cm, Fig.. Measured P perfrmances in terms f utput pwer, gain, drain efficiency and PE at V C = V and V GS = -.8 V are pltted against frequency in Fig. 4. crss a MHz frequency range frm.4 t.7 GHz, the P delivered utput pwer >4 dbm with drain efficiency >65% and PE >6%. Pltted in Fig. 5 are the measured P perfrmances Fig. 6. Measured P perfrmances versus V C at.5 GHz. versus input pwer at.5 GHz. Peak drain efficiency f 85% and peak PE f 8% were achieved at 4.9 dbm utput pwer and. db gain. The efficiency is lwer than that f the THP Class-EF P partly due t the 5-Ω series resistr used t stabilize the P (as ppsed t the -kω parallel resistr used in the THP Class-EF P). The linear gain was abut 6 db. Fig. 6 shws the P s behavir when the supply vltage was varied. ls shwn in Fig. 6 is a near linear relatinship between utput vltage and V C. By Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

13 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques decreasing V C frm t 4 V, the utput pwer was reduced by 6.8 db frm 4.9 t 5. dbm, within which range the drain efficiency f at least 75% was achieved. Simulated utput pwer spectrum is shwn in Fig. 7. Class-EF P delivered 9.5 dbm utput pwer with 8% PE at. GHz. Measured peak PE f 8% and utput pwer f 4.9 dbm were btained at.5 GHz fr the FHP Class-EF P. Fig. 7. Simulated utput pwer spectrum f the FHP Class-EF P. (a) C. Measurement Vs. Simulatin The THP Class-EF P was designed t perate at.5 GHz. Hwever, as can be seen frm Fig. 8(a), the measured frequency shifted t a lwer frequency, arund. GHz. This disagreement is mainly due t the fact that the transistr mdel prvided by the manufacturer des nt incrprate packaged lead inductances at the gate and drain. When these inductances are included in the mdel, the simulatin agrees pretty well with the measurement result, Fig. 8(b). The same applies t the FHP Class-EF P where the design frequency is GHz and measured frequency is.5 GHz, Fig. 9. The perfrmances f the prpsed Ps when cmpared t ther published results are summarized in Table V. When cmpared with ther Ps emplying GaN HEMTs and perating at frequencies arund.5 GHz [7]-[], the THP Class-EF P exhibits the highest drain efficiency and PE at a cmparable utput pwer. The utput pwer, drain efficiency, and PE perfrmances f the.5 GHz FHP Class-EF P are superir t thse f the. GHz Ps reprted in []-[5]. (b) Fig. 8. Measured perfrmances f the THP Class-EF P cmpared with simulatin results using: (a) riginal transistr mdel and (b) mdified transistr mdel. VII. CONCUSION The analysis and design f THP and FHP Class-EF Ps including a methd t increase their maximum perating frequency has been presented. These Ps emplyed a nvel λ/8 pen-circuit and shrted stub arrangement which facilitates imprved even-harmnic suppressin and therefre yields high efficiency. Since the FHP P satisfies the Class- EF pen-circuit lad impedance requirement at nt nly f but als 5f, its C t RF efficiency is theretically higher than that f the THP P. Hwever, in practice this might nt be the case since the lad netwrk f the FHP P is mre sphisticated (thus mre lssy), and prne t instability which in turn will degrade P efficiency due t additinal lss intrduced by a stabilizing circuit. The validity f the analytical derivatin has been cnfirmed thrugh harmnic-balance simulatin and by measurement. Tw P prttypes were built using GaN HEMTs. The THP (a) Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.

14 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques (b) Fig. 9. Measured perfrmances f the FHP Class-EF P cmpared with simulatin results using: (a) riginal transistr mdel and (b) mdified transistr mdel. TBE V PERFORMNCES SUMMR N COMPRISONS WITH OTHER PS WITH OUTPUT POWER W Ref. Freq. P OUT η PE Gain V C (MHz) (dbm) (%) (%) (db) (V) [] [] [4] [5] [6] [7] [8] [9] [] [] [] [] [4] [5] THP P FHP P MOS, Gas phemt, therwise GaN HEMT REFERENCES [] S. C. Cripps, RF Pwer mplifiers fr Wireless Cmmunicatins. Nrwd, M: rtech Huse, Inc., 6. [] N. O. Skal and.. Skal, Class E new class f high-efficiency tuned single-ended switching pwer amplifiers, IEEE. J. Slid-State Circuits, vl., n., pp , Jun [] F. H. Raab, Idealized peratin f the Class E tuned pwer amplifier, IEEE Trans. Circuits Syst., vl. 4, n., pp , ec [4] M. 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Ppvic, inearity f X-band Class-F pwer amplifiers in high-efficiency transmitters, IEEE Trans. Micrwave Thery Techn., vl. 49, n. 6, pp , Jun.. [] K. W. Ecclestn, Mdified Class-F distributed amplifier, IEEE Micrw. Wireless Cmpn. ett., vl. 4, n., pp , Oct. 4. [] V. Carrubba,.. Clarke, M. kmal, J. ees, J. Benedikt, P. J. Tasker, and S. C. Cripps, On the extensin f the cntinuus Class-F mde pwer amplifier, IEEE Trans. Micrwave Thery Techn., vl. 59, n. 5, pp. 94-, May. []. Grebennikv and N. O. Skal, Switchmde RF Pwer mplifiers. New rk: Newnes, 7. [4] T. Suetsugu and M. K. Kazimierczuk, Cmparisn f Class-E amplifier with nnlinear and linear shunt capacitance, IEEE Trans. Circuits Syst. I, vl. 5, n. 8, pp , ug.. [5] S.. Kee, I. ki,. Hajimiri, and. Rutledge, The Class-E/F family f ZVS switching amplifiers, IEEE Trans. Micrwave Thery Techn., vl. 5, n. 6, pp , Jun.. [6] J. W. Phinney,. J. Perreault, and J. H. ang, Radi-frequency inverters with transmissin-line input netwrks, IEEE Trans. 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15 This is the authr's versin f an article that has been published in this jurnal. Changes were made t this versin by the publisher prir t publicatin. The final versin f recrd is available at IEEE Transactins n Micrwave Thery and Techniques 4 [] G. F. Cllins and J. Wd, Class-E pwer amplifier design at.5 GHz using a packaged transistr, IEEE Radi Wireless Symp.,, pp [] K. Chen and. Perulis,.-GHz Class-F pwer amplifier with 8% pwer-added-efficiency, IEEE Micrw. Wireless Cmpn. ett., vl., n. 8, pp , ug.. [4] J. Mn, J. ee, R. S. Pengelly, R. Baker, and B. Kim, Highly efficient saturated pwer amplifier, IEEE Micrw. Mag., vl., n., pp. 5-, Jan.. [5] P. Saad, H. M. Nemati, M. Thrsell, K. nderssn, and C. Fager, n inverse class-f GaN HEMT pwer amplifier with 78% PE at.5 GHz, Eur. Micrw. Cnf., 9, pp Mury Thian btained the B.Sc. degree frm tma Jaya Cathlic University, Jakarta, Indnesia, the M.Sc. degree frm elft University f Technlgy, elft, the Netherlands, and the Ph.. degree frm the Queen s University f Belfast, Belfast, United Kingdm, all in electrnics engineering. He was with stra Internatinal ISUZU (Jakarta, Indnesia), NXP Semicnductrs (Nijmegen, the Netherlands), the University f Birmingham (Birmingham, United Kingdm), and Infinen Technlgies (Villach, ustria) befre jining the Queen s University f Belfast (Belfast, United Kingdm) as a lecturer in. r. Thian has authred ver 4 jurnal and cnference papers and has cauthred tw bk chapters. He has been invited t chair sessins and give talks in a number f IEEE majr cnferences and wrkshps. He was a Marie Curie Fellw and the 8 finalist f the British ssciatin fr the dvancement f Science. yman Barakat (S 4) received the B.Sc. degree in electrical engineering frm in Shams University, Cair, Egypt, in 5, and the M.Sc. degree in electrical engineering frm Tampere University f Technlgy, Tampere, Finland, in. He wrked in the telecmmunicatin and electrical industry frm March 6 t July. He is currently an early stage researcher and wrking tward the Ph degree in electrical engineering at the Queen s University Belfast, Belfast, United Kingdm. His research interests include switched-mde and herty pwer amplifiers design fr multiband transmitters. Vincent Fusc (S 8-M 8-SM 96-F 4) btained his Bachelr s degree in Electrical and Electrnic Engineering (First Class Hnurs) and his Ph.. in Micrwave Electrnics frm the Queen s University f Belfast. Since 995, he has held a persnal chair in High Frequency Electrnic Engineering. His research interests include nnlinear micrwave circuit design, and active and passive antenna techniques. The main fcus fr this research is in the area f wireless cmmunicatins. t present he is technical directr f the High Frequency abratries at ECIT ( where he is als directr f the Internatinal Centre fr Research fr System n Chip and dvanced Micr-wireless Integratin (SCaM). Prf. Fusc has published numerus scientific papers in majr jurnals and in referred internatinal cnferences, and is the authr f tw text bks. He hlds several patents and has cntributed invited chapters t bks in the field f active antenna design and EM field cmputatin. He is a Fellw f the Ryal cademy f Engineering, a Fellw f the Institutin f Engineering and Technlgy (IET), a Fellw f the Institute f Electrical and Electrnic Engineers (IEEE), and f the Ryal Irish cademy. In 986, he was awarded a British Telecmmunicatins Fellwship and in 997 he was awarded the NI Engineering Federatin Trphy fr utstanding industrially relevant research. Cpyright (c) 5 IEEE. Persnal use is permitted. Fr any ther purpses, permissin must be btained frm the IEEE by ing pubs-permissins@ieee.rg.