CLASS C. James Buckwalter 1

CLASS C James Buckwalter 1

Class-C Amplifier Like class-b, I quiescent = 0 Unlike class-b, conduction angle < 180 deg Gain is low since device is turned on for only a short period Iout Imax Vmin Vmax ut match match Harmonics are shorted RL Vce Ic Vrf time Idc time James Buckwalter 2

Class-C Amplifier I quiescent = 0 I dc < I rf / p Iout Imax P out (rf) < 1/4 V rf I rf P in (dc)= V o I dc h max =p/4*(v max -V min )/(V max +V min ) Vmin Vmax ut match match Harmonics are shorted RL Vce Ic Vrf time Idc time James Buckwalter 3

Load Impedance Is A Resonant Network Short at all harmonics here Representative Z values At fo -j2w j2w 10 W match Z fo RL Z=RL at fo Z=0 at 2fo, 3fo, 4fo, At 2fo -j1w j4w 10 W fo 2fo James Buckwalter 4

Class-C Waveform Ic Idc time I ( t) = ìï í îï i PK cosq - I DC when i PK cosq > I DC 0 otherwise cosf = I DC i PK I DC is the (negative) offset i PK is the amplitude I DC = 1 F ò I ( q ) dq = 1 2p 2p 0 I DC = 1 ( p i sinf - I F PK DD ) F ò 0 ( ) i PK cosq - I DD dq I FUND = 1 p I FUND = 2 p 2p ò 0 F ò 0 ( ) I q cosqdq = 2 p ( ) I q ( i PK cos 2 q - I DC cosq )dq James Buckwalter 5 F ò 0 cosqdq I FUND = 2 æ1 p 2 i PKF+ 1 4 i ö ç PK sin2f - I DC sinf è ø I FUND = 2 p i æ 1 PK 2 F+ 1 ö ç sin2f - cosfsinf è 4 ø I FUND = i æ PK ç p F - 1 è 2 sin2f ö ø

Class-C Conduction Φ is the conduction angle during which the current conducts through the transistor. What happens for Φ of pi or 2PI? I FUND = i æ PK ç p F - 1 è 2 sin2f ö ø James Buckwalter 6

Class-C Efficiency I DC = i PK ( sinf -FcosF) p h = P RF,MAX P DC = v PK i PK 2V DD I DC = æ çf - 1 sin 2F è 2 2 sin F ( ) ö ø ( ) - Fcos( F) ( ) As conduction angle approaches 0, the efficiency approaches 100%. What is the penalty? James Buckwalter 7

Class C Waveform Analysis Calculate efficiency h = i pk æ 1 v 2 PK i PK = 1 v pk p F - 1 2 sin2f ö ç è ø V DC I DC 2 V DC i pk sinf - FcosF p æ çf - 1 è 2 sin2f ö ø sinf - FcosF f ( q 0 ) = 1 2 ( ) h = V V FUND FUND,MAX f ( q 0 ) V FUND,MAX V DC ( ) = V pk V RF,MAX f ( q 0 ) V RF,MAX V DC h = P OUT V MAX -V MIN f ( q 0 ) P OUT,MAX V MAX +V MIN lim f q 0 ( q 0) =1 lim f ( q 0 ) = p 0 q 0 p 2 4 James Buckwalter 8

Power Amplifier Comparison James Buckwalter 9

Class-C Amplifier Efficiency Class C has very good efficiency because whenever the device has current, Vds is particularly low Vds ID Vrf time Idc time James Buckwalter 10

Class-C Waveform Analysis How about the loadline resistance? Iout Imax R L = V FUND I FUND Vmin Vmaxut V FUND = V MAX -V MIN 2 æ I FUND = I S q 0-1 2 sin2q ö ç 0 è ø ( ) I MAX = I S - I O = I S 1- cosq 0 I FUND = I æ S p q - 1 0 2 sin2q ö ç 0 = I MAX è ø p R L = p V MAX -V MIN I MAX 1- cosq 0 q 0-1 2 sin2q 0 q 0-1 2 sin2q 0 1- cosq 0 RL / RL Class A 20 18 16 14 12 10 8 6 4 2 0 0 15 30 45 60 75 90 Theta (degrees) James Buckwalter 11

Gain and Conduction Angle Gain (db) Class A Class AB "ideal" Class AB "real" 6dB Class B ideal Class B real Class C "real" Pin (dbm) James Buckwalter 12

Power Amplifier Comparison Maximum voltage swing is 2V o V min Gain is 6 db lower for class-b than class-a, expect it to be even lower than class-c. Power density is the same for class A and B but lower for class C. James Buckwalter 13

Other Classes of Amplifiers PA research is focused around getting highpower power at high-efficiency. Class D Amplifiers Push-pull style amplifier Class E/F Amplifiers Switching amplifiers which can allow 100% PAE but require care with harmonics Class J Amplifier Overdriven class-a James Buckwalter 14

CLASS F James Buckwalter 15

Class F Amplifier Add harmonic tuning to Class B amplifier Nominally open circuit at odd harmonics Short circuit at even harmonics (In reality, need to optimize for given transistor) V ds begins to look like a square wave match match Harmonic tuning 3fo fo RL RL James Buckwalter 16

Class F Amplifier With added 3rd harmonic V 3fo =1/9 V fo, V fo can reach the highest value without causing clipping I quiescent = 0 I dc =I ave = I rf / p P dc = V DD I ave h = 9 8 p 4 V max -V min V max +V min Iout Imax Vds Id Iave Vmin Vmax Vrf (?) time time James Buckwalter 17 ut

Class F Strategy Adding 3rd harmonic to voltage flattens its top and bottom, so it begins to approach a square wave With 3rd harmonic added, the fundamental can be increased at fixed signal swing (before clipping) Get even better results adding 5th harmonic 1.5 1 0.5 0-0.5-1 -1.5 1.5 1 0.5 0-0.5-1 0 2 4 6 8 10 12-1.5 0 2 4 6 8 10 12 James Buckwalter 18

Fourier Series Example /2 2/p =0.63 0 -/2 Vfo / (/2) = 0.63/0.5 = 1.26: This is for perfect square wave (includes all odd harmonics) Vfo / (/2) ~ 9/8 = 1.125: This is just 3 rd harmonic time James Buckwalter 19

Class F Waveform Analysis Is there power delivered to load at 2f o? No, V 2fo =0 Is there power delivered to load at 3f o? No, I 3fo =0 Prf=1/2 Vfo Ifo= 1/4 Vfo Irf = 1/4 Irf*(Vmax-Vmin)/2 * 9/8 Pdc= Vdc Idc = Irf/p*(Vmax+Vmin)/2 Efficiency =p/4 *9/8*(Vmax-Vmin)/(Vmax+Vmin) 2 Waveforms of Transistor ltage(blue) and Current (black) Idc=Irf/p just as for Class B Ifo = Irf /2 just as for Class B Vfo= RL(fo) Ifo V, I 1.5 1 0.5 0 0 45 90 135 180 225 270 315 360 405 450 495 540 585 630 675 720 765 angle (degrees) For Class F Vmax=Vdc+8/9 Vfo Vmin=Vdc- 8/9 Vfo Vfo=(Vmax-Vmin)/2*9/8 Vmax= Vdc+Vfo Vmin=Vdc-Vfo for class B James Buckwalter 20

Class F Amplifier Implementation: Accounting for Output Capacitance m1 freq= 1.096GHz S(1,1)=0.252 / -79.574 impedance = Z0 * (0.963 - j0.509) m2 freq= 2.089GHz S(1,1)=1.000 / -179.915 impedance = Z0 * (1.514E-7 - j7.444e-4) S(1,1) m2 m1 m3 m3 freq= 2.951GHz S(1,1)=0.998 / -2.634 impedance = Z0 * (1.517 - j43.448) James Buckwalter 21 freq (100.0MHz to 10.00GHz)

Class F Amplifier Alternative Implementation Short at all harmonics here Zo=RL lo/4 match fo Z=RL at fo Z=0 at 2fo, 4fo Z=inf. at 3fo, 5fo,... RL James Buckwalter 22

Class F Example David Schmelzer and Stephen I. Long, CSICS 2006 GaN FETs at 2GHz Class F amplifier 86% PAE, 17W James Buckwalter 23

Harmonic Load Tuning X2=Im(Znet) at 2fo X3=Im(Znet) at 3fo Class F -1 Class F -1 Class F Class F Class B Znet Cds RL XL(f) James Buckwalter 24

Other Approaches for High-Efficiency Control the voltage and current waveforms to prevent conduction while the voltage Class D: Switch current and voltage Class E: ZVS and ZVS derivative switching Class F -1 James Buckwalter 25