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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


                           Added Sine Wave Power Output
Power Added Efficiency
                           Total Additional DC Power Input


                            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

                                                load
               active device                  Rload
                          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

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

                                        Vcc


      constant current source Io

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

                     Rload                            2
                                                Vcc
0 < I <2Io                       =
             -Vcc                               Rload

                                            2
                                      Vcc
    Peak sine wave in load =
                                     2 Rload

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

                         Rload
                                                 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
                                                        Rload
 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
                            Rload   needed.
A Reminder that Active Devices are Interesting

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

                                                                             Vgs = -.2
     Ids = 200mA
                                          load line
                                                                             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
                     Rload
                                                                    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
                    Rload
                                                          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
                     Rload




 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
                     Rload




  sketch of instaneous                            Average
  device dissipation



                             textbook waveforms
Class A Waveform Analysis
                               Device Current and Voltage
         Vcc

               Big L
   Io
               Big C
        Vc     + -
                Vcc
                       Rload




   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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