CHAPTER 5 BROADBAND CLASS-E AMPLIFIER

CHAPTER 5 BROADBAND CLASS-E AMPLIFIER 5.0 Introduction Cla-E amplifier wa firt preented by Sokal in 1975. The application of cla- E amplifier were limited to the VHF band. At thi range of frequency, cla-e amplifier ha hown to exhibit efficiencie a high a 96% [Sokal, 1975]. A few year a go, it wa hown that Cla E amplifier can be ued at higher frequencie [T. Sowlati, et al, 994]. Several paper have reported cla-e amplifier operating at a frequency above the VHF band [T. Mader and Z. Popovic, 1995; F. Javier, et al, 1998; V. Gudimtla and A. Kain, 1999]. A tated earlier, a cla-e i nonlinear amplifier, in the ene that variation in input ignal amplitude will not reproduced at the output in any acceptable form. Moreover, cla-e configuration prove to have higher efficiency with impler circuit than conventional reduced conduction angle clae. New lumped-element and tranmiion-line baed circuit are preented in thi chapter. Thee circuit how good performance over a wide bandwidth of frequency. 54

55 5.1 Cla E Operation and Analyi Figure.5.1 how an ideal cla-e amplifier [R. Zulinky and J. Steadman, 1987]. It conit of a witch S, a bia choke L b, a capacitance C, a tuned circuit L-C, and a load R L. The tranitor witch S i ON in half of the period, and OFF in the other half. When S i ON, the voltage acro S i zero, and when it i off, the current through S i zero. The capacitance C include the paraitic capacitance acro the tranitor. The L-C circuit reonate at the fundamental frequency of the input ignal and only pae a inuoidal current to the load R L. Figure.5.2 how ideal cla E voltage and current waveform. The analyi of the cla-e amplifier ha been reported in everal paper [Sokal, 1975; M. Kazimierczuk, 1983; F. Raab, 1978]. The analyi i reproduced here. When the witch S i off, the voltage V, a hown in Fig.5.2, i given by olving the equation dv C = I ( 1 ain( ω t + φ)) (5.1) d dt Where, ω i the ignal frequency, I d i the dc portion of the drain current, and contant a and φ are yet to be calculated. V can be repreented a I d v ( t) = ( ω t + a(co( ω t + φ) coφ)) (5.2) ω C

56 Optimum operation of a cla-e amplifier require two condtion [F. Raab, 1989] dv T ( ) = 0 dt 2 (5.3) T v ( ) = 0 (5.4) 2 Thee conditon avoid power diipation due to either horting the capacitor C while V ha value or nonzero witching time at tranition. Uing thee condition, contant a and φ were calculated: a 1.86 φ -32.5 o. The voltage V and the capacitor current i are known in the whole range: I d v ( t) = (( ω t) + a(co(( ω t) + φ) coφ)) 0 ω t π (5.5) ω C v ( t) = 0 π ω t 2π i ( t) = 0 ω t π 0 i ( t) = I (1 a in( ω t + φ)) π ω t 2π d (5.6) (5.7) (5.8)

57 From equation (5.5) and (5.8), the load Z L at the fundamental frequency i: Z net1 v = i 1 net1 0.28 Ο j49 = ω C e (5.9) Figure 5.1. Ideal cla-e amplifier

58 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 1 0.8 0.6 0.4 0.2 0-0.2 0 2 4 6 8 10 12-0.4-0.6-0.8-1 Figure 5.2. Ideal cla-e voltage and current waveform. Many network configuration can atify equation (5.9). To implify the analyi, the imple load network hown in Fig.5.3 will be ued here. The input impedance of the load network i given by Z 1 = jω L + R 1 (5.10) jω C net +

59 The load component value are obtained by equating the real and imaginary part of equation (5.9) and (5.10) [T. Mader, 1995]: C = 1 2 π π 2π f R ( + 1)( ) 4 2 (5.11) C C 5.447 1.153 ( )(1 + ) Q Q 1.153 L L (5.12) where, Q L Q L ω L = (5.13) R

60 Figure 5.3. Simple RLC load network 5.2 Non-Ideality of Cla-E Amplifier In the ideal ituation, the efficiency of a cla-e amplifier i 100%. However, in practice, the witch ha a finite on-reitance, and the tranition time from the off-tate to the on-tate and vice-vera are not negligible. Both of thee factor reult in power diipation in the witch and reduce the efficiency. Figure.5.4 (a) and (b) how the tranitor output admittance veru frequency in the ON and OFF tate, repectively.

61 (a) (b) Figure 5.4. Tranitor ATF-46100 output impedance: a) ON tate b) OFF tate

62 The tranitor can be modeled a a reitor in parallel with a capacitor, a hown in Fig.5.5. During the ON tate, the effect of the reitor i the dominant while during the OFF tate the capacitor i the dominant one. For the ATF-46100, the ON reitor i around 7 and the OFF capacitor i around 0.9pF. Figure 5.5. Tranitor output impedance model A a reult of the witch non-ideality, the analytical equation decribed by different author and reproduced earlier cannot be eaily ued for the ucceful optimization of the cla-e amplifier. The recent improvement in the modeling of active device and imulation tool have made it poible to ue computer imulation to deign uch amplifier with ufficient accuracy. The commercial oftware ued in thi work i the ADS (Advanced Deign Sytem) by Hewlett Packard.

63 5.3 L-band Cla E Amplifier A hown in equation (5.9), a tranitor require a pecific load to operate in the cla-e mode. At the fundamental frequency, the magnitude of the load i frequency dependent and the phae of the load i contant. Alo, the load preented at the output terminal of the tranitor need to be high inductive at the harmonic of the input ignal. Thee condition make the deign of a broadband cla-e amplifier difficult tak. 5.3.1 Lumped Element Cla E Circuit A cla-e amplifier with a 30% bandwidth wa propoed in [V. Gudimtla and A. Kain, 1999]. The center frequency wa 1GHz and the output power wa 23 db. The deign procedure for a cla-e amplifier with a 50% bandwidth are preented in thi ection. The HP ATF46100 MESFET i ued in thi deign. V GS and V DS are choen to be 5V and 5.3V, repectively. The optimum load at many frequency point in the band of interet (1.70-2.7 GHZ) i obtained uing the load-pull technique. Another variable that need to be tuned to obtain better performance in term of the efficiency and output power i the input power. Having the optimum load, the next tep i to ue the E-Syn oftware to realize the load network. The E-Syn oftware i a network ynthei program capable of providing a catalog of poible network with the deired pecification for lumped and ditributed component [HP Advance Deign Sytem Manual]. A lumped, Butterworth, band-pa repone with a paband of 1.7 to 2.7 GHz wa elected to realize the load network uing the E-Syn. The load network obtained i hown in Fig.5.6.

64 Figure 5.6. Lumped, Butterworth load network Deigning the input-matching network require knowing the input impedance Z in with the load network connected. Figure.5.7 how the input impedance veru the frequency. Over the deired band of frequency, Z in can be approximated by a reitor (1.5Ω) in erie with a capacitor (1.3 pf) a hown in Fig.5.8 (a). The Chebychef bandpa filter i deigned uing the E-Syn to realize the input-matching network, a hown in Fig.5.8 (b).

Figure 5.7. The input impedance of the tranitor ATF-46100 65

66 (a) (b) Figure 5.8: (a) Input impedance model of ATF-46100 (b) Input-matching network A a reult of the ytematic approach to the deign of the amplifier and ue of the network ynthei, no further optimization of the complete amplifier (Fig.5.9) wa required to give a atifactory performance. A indicated in Fig.5.10, over mot of the range 1.7 to 2.7 GHz, the gain i greater than 16 db and the output power i almot flat 23 db. The power added efficiency i greater than 61% over mot of the deired band of frequency.

67 Figure.5.11 how the output voltage and the drain voltage and current waveform of the cla-e amplifier at 2.2GHz. A reult of the non-ideality of the tranitor witch, an overlap occur between the drain voltage and current. Thi overlap caue a power diipation that degrade the efficiency.

68

Figure 5.10. Gain (db), Pout (dbm), and PAD veru Frequency 69

70 (a) (b) (c) Figure 5.11. Cla-E waveform: a) Drain voltage Vdt (V) b) Drain current (A) c) Output voltage Vdt (V)

71 5.3.2 Tranmiion Line Cla-E Circuit In the previou ection, a broadband cla-e amplifier baed on lumped-element ha been deigned. The lumped-element deign generally work well at low frequencie, but two problem arie at microwave and millimeter-wave frequencie. Firt, lumped element uch a inductor and capacitor are generally available only for a limited range of value and are difficult to fabricate at the microwave and millimeter frequencie. In addition, at the microwave and upper frequencie the ditance between a circuit component are not negligible. For thee reaon, tranmiion line are often preferred over lumped element at the microwave and upper frequencie. Baed on Richard tranformation, a hunt inductor can be replaced with a hortcircuited tub, while a hunt capacitor can be replaced with an open-circuited tub. Moreover, a erie element (inductor or capacitor) can be tranformed to a hunt one uing a tranmiion line. Figure.5.12 how a tranmiion-line broadband cla-e amplifier. Thi amplifier i deigned baed on the amplifier hown in Fig.5.9. The lumped element are replaced with tub and tranmiion line uing Richard tranformation method. The length and width of the tub and tranmiion line are adjuted to give better performance. Figure.5.13 how the performance (the added efficiency and the output power) of the tranmiion-line broadband cla-e amplifier, which i cloe to the reult hown in Fig.5.10.

72

73 Figure 5.13. Tranmiion-line broadband cla-e amplifier power added efficiency and output power.

74 5.4 X-band Cla-E Amplifier Few cla-e circuit have been developed at the X-band frequency (8-12GHz). Shijie [L. Shijie, 1998] preented two X-band cla-e high efficiency amplifier. The firt one ue the Fujitu FHX35X HEMT tranitor and achieve an output power of 30 mw, and drain efficiency of 80% and PAE (power-added efficiency) of 64% at 11.2 GHz. The econd one ue the Fujitu FLR056XV MESFET tranitor and deliver an output power of 186 mw, drain efficiency of 72% and PAE of 56% at 9GHz. 5.4.1 Lumped and Ditributed Element Cla-E Circuit In thi ection, two X band cla-e amplifier are preented. Both circuit ue the Fujitu FHX35X HEMT tranitor [Fujitu Data Book, 1993]. In contrat to the cla-e circuit hown in Fig.5.9 and 5.12, there i no need for the external hunt capacitance C S. The hunt capacitance C S conit olely of the output capacitance of the tranitor. A hown in Fig.5.14, the firt one i baed on lumped element. It achieve drain efficiency above 72%, PAE above 60%, and flat output power 18dBm over wide bandwidth (8.5-13.3 GHz), Fig.5.15. The lumped element cla-e amplifier hown in Fig.5.14 i tranformed to tranmiion-line cla-e amplifier hown in Fig.5.16. The tranformation proce i explained in the previou ection. Figure.5.17 how the tranmiion-line cla E drain efficiency, PAE, and the output power veru the frequency. Both circuit have a imilar performance, which prove the ucce of the tranformation.

75

76 Figure 5.15. The X-band-lumped element cla-e drain efficiency, PAE, and the output power

77

78 Figure 5.17. The X-band-Tranmiion-line cla-e drain efficiency, PAE, and the output power

79 5.5 Technique to Improve Cla-E Amplifier Efficiency A dicued in ection 5.2, the non-ideality of the tranitor limit the efficiency of the cla-e amplifier. In thi ection, a new technique that improve the amplifier efficiency i preented. Two paive network are added to the cla-e circuit. A hown in Fig.5.18, the Z S network i connected in erie with the hunt capacitance and the Z X network i connected to the tranitor ource terminal. To achieve the optimum performance, the characteritic impedance of the paive network at the harmonic frequencie i obtained uing the load-pull technique. Figure.5.19 how the drain voltage and current waveform. The drain efficiency how an improvement. The drain efficiency i 82 % in contrat to 63% without the Z S and Z X network. The paive network help in reducing the power diipation at the output terminal of the tranitor by minimizing the overlap of the drain voltage and current waveform. PAE did not how improvement. The increae in the input power prevent the improvement of PAE.

80

81 Fig.5.19: Cla-E voltage and current waveform.

82 5.6 Cla-E veru Cla-F amplifier Thi ection provide a comparion between the performance of cla-e and F amplifier. A explained in ection 2.2.4, the cla-f amplifier derive it improved efficiency from the ue of reonator to control the harmonic content of the drain (collector) voltage and current. Variou type of tranitor (Si bipolar, Si MOSFET, GaA MESFET, and HEMT) have been ued to tudy the performance of cla-e and F amplifier. Figure.5.20 how the configuration ued to tet the performance of cla-e and F amplifier. A indicated in Table 5.1, the two clae have a imilar performance (output power, and efficiency). The drain (collector) peak voltage for cla-e and F amplifier are cloe to 3V d and 2V d, repectively. The breakdown voltage of the tranitor put a limitation on the drain (collector) peak voltage and in equence put limitation on the maximum output power. Cae 3 in Table 5.1 i an example of the peak voltage limitation, where the maximum bia voltage for cla-e and F are 18V and 22V, repectively.

83

84 Table 5.1. Summary of reult for cla-e and F uing variou tranitor. Tranitor Freq (Ghz) Amplifier Cla Pout (mw) PAD % Si bipolar NEC24600 Si MOSFET MRF136 GaA MESFET ATF4600 HEMT FHX35X 0.5 0.1 1.75 11 E 258 76 F 446 72 E 9171 85.5 F 14060 87.8 E 300 60- F 365 62.7 E 79.6 65.9 F 75 69 Alo, the performance of cla-e and F amplifier have been compared at low voltage deign. At low voltage deign, the cla-e amplifier ha a better performance than the cla-f amplifier, Table 5.2.

85 Table 5.2. Summary of reult for low voltage cla-e and F. Tranitor Freq (Ghz) Amplifier Cla Pout (mw) PAD % GaA MESFET ATF4600 Si bipolar NEC24600 1.75 0.5 E 80 60.7 F 86 53 E 85 61 F 73 59 Another advantage of the cla-e amplifier over the cla-f amplifier i it imple configuration. A explained earlier, the cla-e amplifier require high load impedance at the harmonic while the cla-f amplifier require high impedance at odd harmonic and low at even harmonic. Thee requirement make deigning a wide-band cla-e amplifier much eaier than a wide-band cla-f amplifier. The intermodulation tet i one of the important tet ued to meaure the nonlinear behavior of the analog circuit. Commonly the intermodulation tet ue a twotone ignal. When the two-tone are applied to a nonlinear ytem, the output ignal exhibit ome component that are not the harmonic of the input frequencie. Thee frequencie are generated from the mixing of the input frequencie and are called intermodulation (IM). Of particular interet are the third-order IM product (2f 1 -f 2, and 2f 2 -f 1 ). The importance of thee product arie from the mall frequency ditance between them and the deired ignal, which make filtering off the third-order IM a difficult tak. The IM tet etup i imilar to the one hown in Fig.5.20 with the two-tone input ignal applied. Table 5.3 how comparion between cla-a, E, and F interim of the output power, PAD, gain, intermodulation. The intermodulation i expreed in dbc

86 (the difference in db between the IM power and the fundamental frequency power). Cla-A how better output power, gain, and linearity than the other clae. A explained earlier, the output voltage waveform of the ideal cla-e and F are half ine and quare waveform, repectively and their Fourier repreentation are given a: V cla E ( t) = A + B in ω + C in( 2ω) + D in(4ω) +... E E E E (5.14) V cla F ( t) = A + B in ω + C in(3ω ) + D in(5ω ) +... F F F F (5.15) A indicated in equation (5.15), the output voltage of the ideal cla-f amplifier doe not contain the econd harmonic of the input ignal (2ω). The abence of the econd harmonic eliminate the third IM (2f 1 -f 2, and 2f 2 -f 1 ) at the output. In reality, due to the non-linear behavior of the tranitor there will be third IM at the output. Thi give cla-f the advantage over cla-e of having lower third IM. Table 5.3. Summary of reult for cla-a, E and F amplifier linearity. Amplifier Cla Pout (mw) PAD % Gain (db) 3 rd IM dbc 5 th IM dbc 7 th IM dbc A 265 20 22-51 -55-60 E 195 52 16-16.5-34.5-50 F 220 56 15.5-26 -34-51

87 In general, cla-e and F amplifier how a imilar performance. However, in ome application one of them how a better performance than the other. For example, the cla-f amplifier ha a better performance in the high-output power amplifier application and cla-e amplifier ha better performance in wide-band and low voltage application.