OVERDRIVEN AMPLIFIERS. James Buckwalter 1

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1 OVERDRIVEN AMPLIFIERS James Buckwalter 1

2 Overdriven Amplifiers For very large input signals, the output waveform is driven into the "saturation" region (bipolar) or "linear" region (FET) - and becomes limited by the on-resistance of the device. Waveform behavior is determined by harmonic terminations. Theory is not simple. The amplifier goes into compression (gain drops but not precipitously) and can still get good efficiency. James Buckwalter 2

3 Classical Device Model Underlying assumption: simple model of transistor Transistor acts like current source, with Iout a linear replica of vin, except for limitations of cutoff when vin<vth => For sinewave input, output current is a sinewave, possibly with clipping vin iout Iout Imax Vout James Buckwalter 3

4 Overdriven Device Model Transistor acts like current source, with Iout a linear replica of vin, except for limitations of cutoff when vin<vth When Vout gets low enough, transistor acts like voltage source Iout Imax vin vout Vout James Buckwalter 4

5 Iout Imax Overdriven Class B Amplifier Vo Harmonics are shorted match Vmin Vo Vmax Vout match RL Vds Must be sinusoidal Vo Vdc fixed Id time Vds(t) is fixed!! Iave Irf time Ids(t) must change

6 Overdriven Class B amplifiers can have strange waveforms

7 Overdriven Class F amplifiers can have strange waveforms If output voltage tries to go below zero the voltage waveform becomes progressively more like a square wave The current is mostly zero when the voltage is nonzero. The load line is traversed only during transitions Overdriven Class F amplifiers approach switching mode operation Vce Vo Iout Imax Vmin Vo Vmax Vout Vrf time James Buckwalter 7

8 Comparison of Overdriven Classes James Buckwalter 8

9 Waveform Engineering

10 Waveform Engineering Spreadsheet Model transistor as current source with constant gm, together with saturation Input is a sinewave of voltage with specified bias point Class A, Class AB, etc) (can set Specify output voltage in terms of fundamental and harmonics of voltage Spreadsheet calculates actual current, taking into account saturation: Iout= Ioutnom / (1+exp(Vth-Vin/Vsat)) this provides smooth clipping Spreadsheet computes what impedances Z1, Z2, Z3 would have to be to create the voltage waveform assumed For this to be a valid amplifier, you should 1) Check that the impedances have positive real part. 2) Check that the voltage waveform is positive only (otherwise adjust voltage dc bias)

11 Vsin Waveform Specification Iout Vt1 Vt2 Vin Irf Vsin is centered around zero You specify Vt to control conduction angle

12 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 1.02 V Vth -1 V Vfund 1 0 V Vin 1 V V2nd 0 0 V Vknee 0 V V3rd 0 0 V Vsat V Summary of Calculated Results Pdc 1.02 W Pout W Vdc 1.02 V Pdiss W Efficiency % Idc 1 A Inefficiency Zfund Re 1 ohm Z2nd Re ohm Z3rd Re ohm Zfund Im E-06 ohm Z2nd Im ohm Z3rd Im ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees) Fundamental Voltage (blue) & Current 2nd Harmonic Voltage (blue) &

13 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 1.02 V Vth 0 V Vfund 1 0 V Vin 1 V V2nd 0 0 V Vknee 0 V V3rd 0 0 V Vsat V Summary of Calculated Results Pdc W Pout W Vdc 1.02 V Pdiss W Efficiency % Idc A Inefficiency Zfund Re 2 ohm Z2nd Re E-05 ohm Z3rd Re ohm Zfund Im E-05 ohm Z2nd Im E-07 ohm Z3rd Im ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees)

14 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 0.99 V Vth 0 V Vfund 1 0 V Vin 1 V V2nd 0 0 V Vknee 0 V V3rd 0 0 V Vsat V Summary of Calculated Results Pdc #NUM! W Pout #NUM! W Vdc 0.99 V Pdiss #NUM! W Efficiency #NUM! % Idc #NUM! A Inefficiency #NUM! Zfund Re #NUM! ohm Z2nd Re #NUM! ohm Z3rd Re #NUM! ohm Zfund Im #NUM! ohm Z2nd Im #NUM! ohm Z3rd Im #NUM! ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees)

15 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 1.2 V Vth 0 V Vfund 1 0 V Vin 1 V V2nd 0 0 V Vknee 0 V V3rd V Vsat V Summary of Calculated Results Pdc W Pout W Vdc 1.2 V Pdiss W Efficiency % Idc A Inefficiency Zfund Re ohm Z2nd Re E-05 ohm Z3rd Re ohm Zfund Im E-05 ohm Z2nd Im E-07 ohm Z3rd Im ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees)

16 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 0.9 V Vth 0 V Vfund 1 0 V Vin 1 V V2nd 0 0 V Vknee 0 V V3rd V Vsat V Summary of Calculated Results Pdc W Pout W Vdc 0.9 V Pdiss W Efficiency % Idc A Inefficiency Zfund Re ohm Z2nd Re E-05 ohm Z3rd Re ohm Zfund Im E-06 ohm Z2nd Im E-07 ohm Z3rd Im ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees)

17 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 0.78 V Vth 0 V Vfund 1 0 V Vin 1 V V2nd V Vknee 0 V V3rd 0 0 V Vsat V Summary of Calculated Results Pdc W Pout W Vdc V Pdiss W Efficiency % Idc A Inefficiency Zfund Re 2 ohm Z2nd Re ohm Z3rd Re ohm Zfund Im E-06 ohm Z2nd Im E-06 ohm Z3rd Im ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees)

18 V, I Power Amplifier Waveforms Inspired by Steve Cripps Rev 1: Still being checked out, user beware!!! Input Parameters Magnitude Angle Imax 1 A Vdc 0.75 V Vth 0 V Vfund 1 42 V Vin 1 V V2nd V Vknee 0 V V3rd 0 0 V Vsat V Summary of Calculated Results Pdc W Pout W Vdc V Pdiss W Efficiency % Idc A Inefficiency Zfund Re ohm Z2nd Re E-06 ohm Z3rd Re ohm Zfund Im ohm Z2nd Im ohm Z3rd Im ohm Waveforms of Transistor Voltage(blue) and Current (black) angle (degrees)

19 Class J Amplifier New designation introduced by Steve Cripps V DD Amplifier design is very straightforward corresponds to what many designers do without knowing it! Class L - Lazy man's amplifier? Input matching network C ds L s R L The harmonic matching is provided by the device output capacitance only => external matching is only done for the fundamental For many traditional transistors, Cds provides a short to all harmonics => class AB, B, etc. For some modern transistors, Cds is low (good!). Then should change the fundamental match to optimize efficiency!

20 Class J Amplifier If Cds is not very large, 2 nd harmonic is not shorted. V DD Use 2 nd harmonic to achieve voltage waveform with flat bottom Higher efficiency Input matching network C ds L s R L Best efficiency but requires Z2f with negative real part!!

21 Class J Amplifier If Cds is not very large, 2 nd harmonic is not shorted. V DD Use 2 nd harmonic to achieve voltage waveform with flat bottom Higher efficiency Input matching network C ds L s R L Best efficiency but requires Z2f with negative real part!! Good efficiency and realizable. Use Zf inductive.

22 Class J Amplifier Characteristics Fundamental impedance: RL + j X1, with X1~RL 2 nd Harmonic impedance: j X2, with X2~ RL 3 rd Harmonic impedance: j X3 ~ 2/3 RL Ideal Efficiency ~ similar to Class B peaks at ~ %

23 Formal Class J Characteristics For I(q) = cos q (-p/2<q<p/2, 0 otherwise) V(dc) = 1 Vfund (q) ~ cos(q-p/4) ~ cosq cosp/4 + sinq sin p/4 ~ cos q + sin q V2fo(q) ~ sin 2q ~ cos q sin q Vtotal (q) = 1 - cos q - sin q + cos q sin q Vtotal (q) = (1-cos q)*(1-sin q) Note that <Vtotal(q) > =1 (just like for Class B) ½*Re {fundamental[vtotal] * fundamental[i]} = ¼ (just like for Class B) Ideal Efficiency ~ similar to Class B peaks at ~ %

Continuous Classes Mathematical formulations are emerging which show the characteristics of some of the high efficiency regions These are leading to new insights for broadband

24 Continuous Classes Mathematical formulations are emerging which show the characteristics of some of the high efficiency regions These are leading to new insights for broadband design For I= cos q (-p/2<q<p/2, 0 otherwise) V= 1- cos q for class B V= (1-cos q)*(1-sin q) for Class J V= (1-cos q)*(1- a sin q) for more general class with same efficiency Steve Cripps

25 Continuous Class F For I= cos q (-p/2<q<p/2, 0 otherwise)

26 Broadband Continuous Class F PA Design

27 Are There Other Matching Configurations That Yield High Efficiency??? YES!!

28 Output Waveforms to Optimize Efficiency (1) Vce Vo IC Iave IC Iave Vce Vo time time time time V(t) is square wave has fundamental + odd harmonics I(t) is rectified sine wave has fundamental + even harmonics Power is only at fundamental! V is minimum when I>0, h is max Dual solution Power only at fundamental V is minimum when I>0

29 Output Waveforms to Optimize Efficiency (2) Class E There are plenty of other waveforms that can achieve efficiency = 100% Don t need square wave for V(t) or I(t). Need to satisfy V=Z*I, where Z has non-negative real part at all harmonics in order to be realizable.

30 Harmonic Load Tuning Simulated Efficiency vs Harmonic Load Reactance 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) X1=0

31 Harmonic Load Tuning Simulated Efficiency vs Harmonic Load Reactance Class E X1=RL*0.7

32 Basic Power Amplifier Design Process 1) Decide on Vdd, and identify power transistor with sufficient power handling capability and breakdown voltage 2) Using dc characteristics, decide on resistive load line. Verify that sufficient Pout can be obtained 3) Determine input impedance and match transistor input - using bias condition of "average dc current corresponding to average output power" 4) Determine load susceptance and match output to obtain RL and BL 5) Provide output match at harmonic frequencies 6) Set up bias network 7) Optimize using simulator Steps 2, 3, 4, 5, and 7 can be carried out experimentally with load pull system

Class E Amplifier. V=0 dv/dt=0. Clever resonant load is constructed so that V(t)=0 when the switch closes!! This avoids 1/2CV 2 f loss.

Class E Amplifier. V=0 dv/dt=0. Clever resonant load is constructed so that V(t)=0 when the switch closes!! This avoids 1/2CV 2 f loss. Class E Amplifier Clever resonant load is constructed so that V(t)=0 when the switch closes!! This avoids 1/2CV 2 f loss. V=0 dv/dt=0 Vo driver Cp Voltage across switch is brought to zero when switch closes