# PAefficiency1

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```					Power Amplifier Efficiency
2 day Master Class

Rick Campbell PhD
Portland State University
References and Acknowledgements
textbook:
Steve C. Cripps, RF Power Amplifiers for Wireless
Communications, 2nd edition, Artech House 2006

useful references
Wes Hayward, Rick Campbell, and Bob Larkin,
Experimental Methods in RF Design, ARRL 2003

Herbert Krauss, Charles Bostian, and Frederick Raab,
Solid State Radio Engineering, Wiley 2000

acknowledgement
Many ongoing conversations with Frederick Raab, Steve
Cripps, and Wes Hayward since 1996
Class Outline:

Morning Day 1
Definitions and Fundamentals: Class A, B, C, D

Afternoon Day 1
Switches and Waveforms: Class E and Class F

Morning Day 2
New Developments: Class J, interstage design, drive

Afternoon Day 2
Detailed Study of Current Design Examples
Definitions and Fundamentals

Total RF Power Output
Efficiency
Total DC Power Input

Communications Effectiveness
Efficiency
Handset Battery Life

Useful Information Transfer
Efficiency
Impact on Planet Earth
Common Definitions

Sine Wave Power Output
Efficiency
DC Input to PA Collector

Watts
Power Utilization Factor
dollar
Amplifier Classes A, B, C, D, E, F, ....J

Classic Amplifier Classes A, B, C

Old Terminology that has evolved and muddied

Efficiency numbers are for active device dissipation

Theoretical efficiency may not be a useful concept

For example, rigorously applying PA efficiency concepts to my
laptop reveals that it dissipates no energy...but the language and
descriptive math models are still useful.
A Little Symbolic Math

Io Vcc = P DC          Power Supply DC

2
Vp                     Sine wave RF power in
= P RF            Resistive load RL
2R L

= P Device

Instaneous device dissipation in ideal class A
amplifier with maximum pure sine wave output
Class A Amplifier

Vcc

constant current source Io

0 < I <2Io
-Vcc
A Little Textbook Math

= P Device
Vcc
using:       = Io   R L = Rload line
RL
2
Vcc                                              = P Device
RL

Vcc 2                                        2
= P Device
RL
using:
cos a cos b = 1 cos (a + b) + 1 cos (a - b)
2               2
End of Math
Vcc 2                                2
= P Device
RL

=   1 cos 0 + 1
2         2

Vcc 2 1
= P Device
RL 2

Vcc 2 1
dt =      P Device
RL 2

1 Vcc 2                average device
= P Device     dissipation = half
2 RL
of supply power
Class A Amplifier

Vcc

constant current source Io

0 < I <2Io
-Vcc
no signal DC device dissipation = Vcc x Io
Class A Amplifier

Vcc

constant current source Io

0 < I <2Io
-Vcc
no signal DC device dissipation = Vcc x Io
2
Vcc
Peak sine wave in load =
Vcc
no signal DC device dissipation = Vcc x Io
Io
Vcc
=    Vcc x

Vcc
0 < I <2Io                       =

2
Vcc
Peak sine wave in load =

since DC power supply can’t tell the difference between peak
output and no output, at peak output, half of DC power is
converted to sine wave in load and half dissipated in device
From Model to Real Amplifier
model is only useful if it helps us understand and improve
real amplifiers

12 v 50 mA                 250 mW output at 12.0 volts
375 mW output at 15.0 volts
100n       L1
L2         1nF       L3            L4    50 MHz
Vcc

Io
1nF
22           56         120              56

L1 6t FT37-43    L2 10t T37-6     L3, L4 5t T25-6
0 < I <2Io                  150
-Vcc                           All Transistors MPN5179           Rick Campbell
23 December 2008

Class A model                 Designed, Built, and Measured Amplifier

...more parts, but real parts

...class A model is too simple, but still useful
From Model to Real Amplifier
Vcc                         Vcc

Io                              Big L               Vc = Vcc - L di
Big C                  dt
Vc
Rload                               With fast transistor and appropriate
0 < I <2Io                                                     choice of Rload, Vc can be any-
-Vcc                                              thing. Same circuit for PA, switch-
ing power supply, ignition system,
Class A model                                                  transistor killer...

Vcc

Big L
Inductor stores power supply energy and can supply
Io
Big C           extra voltage when needed. Capacitor stores power
Vc      + -                supply energy and can supply extra current when
Vcc
A Reminder that Active Devices are Interesting

1 watt ZorchFET
Vgs = +.2
Ids = 300mA
Vgs = 0
Idss

Vgs = -.2
Ids = 200mA
Vgs = -.3
Ids = 100mA
Vgs = -.4
Vgs = -.5
Ids = 0                                                             Vgs = Vp

Vds = 0   Vds = 2        Vds = 4   Vds = 6   Vds = 8
Vdd

...and resistive loads are laboratory devices

Next: Waveform Analysis
Introduction to PA Waveform Analysis

Vcc                         2Vcc
Vc
Big L
Io
Big C                  Vcc

Vc     + -
Vcc                    0
Vo

-Vcc

2Io   2Vcc

Device Current          Io   Vcc
and Voltage

0    0

device dissipation is product of I and V
Class A Waveform Analysis

Vcc
2Io   2Vcc                    2Vcc x 0       0
Big L
3      1
Io
Vcc x Io     0.75
Big C
2      2
Vc     + -
Vcc
Io   Vcc                     Io x Vcc       1
3     1
Io x Vcc 0.75
2     2
0    0                      0 x 2Io        0
Device Current   Device Power
and Voltage
Class A Waveform Analysis

Vcc                            Device Current
Big L                    and Voltage
Io
Big C
Vc     + -
Vcc

sketch of instaneous
device dissipation

note slightly real waveforms
Class A Waveform Analysis

Device Current
Vcc
and Voltage
Big L
Io
Big C
Vc     + -
Vcc

sketch of instaneous                            Average
device dissipation

textbook waveforms
Class A Waveform Analysis
Device Current and Voltage
Vcc

Big L
Io
Big C
Vc     + -
Vcc

sketch of instaneous
device dissipation

Note: this might still be a perfectly linear class A amplifier--the output signal is a
perfect replica of the input signal.
Class A Efficiency Review:
“The efficiency of a Class A amplifier” is not a number at the
end of several pages of arcane math in a textbook

slight deviation from textbook waveform has big impact on
device dissipation

textbook waveforms only appear in textbooks

waveform engineering is our primary tool to reduce device
dissipation--even at frequencies where we can’t observe
waveforms

Next: an alphabetical listing of amplifier classes

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