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4.  Kenneth  K.  Clarke  and  Donald  T.  Hess,  Communication  Circuits:  Analysis and

            Design.  Reading:  Addison-Wesley,  1971.
                                                  Chapter 14

                          Mixer Circuits and Harmonic Mixers




            An  idealized mixer is a multiplier circuit that takes two signals and  literally multiplies
            the values  of each  signal  to provide an  output. In one sense,  this concept is easier
            to  understand  with  multiplication  of numbers.  For  example,  there  are  two  analog
            signals,  each  connected to an  analog-to-digital converter (ADC).  The digital outputs

            from  the two ADCs then  provide numbers from each  signal,  and  these  numbers are
            updated  over  time.  If the  outputs of the ADCs  are  fed  to  a digital  multiplier,  then
            the  output of the  digital  multiplier  will  provide  a  stream  of numbers  that are  the
            product of the  two streams  of numbers  from  the outputs of the  ADCs.  The  output
            of the digital  multiplier then  is  connected  to  a digital-to-analog  converter (DAC)  to
            provide an  analog  signal that represents the product of the two analog signals.

            But back in the days of the superheterodyne radio  in the late teens of the twentieth
            century,  multiplication,  or  an  approximation  of it,  had  to  be  done all  in  the analog
            domain.  Therefore,  vacuum  tubes  such  as  triodes  and  pentodes  were  used
            commonly  to  provide  an  analog  multiplication  effect  of two  signals  such  as  the
            radio-frequency  (RF)  signal  and  the  local  oscillator signal.  For the triode,  which  is  a
            very  linear amplification device,  a very large local  oscillator voltage was  supplied  to

            its  cathode  or  grid  to  essentially  turn  the  triode  on  and  off to  cause  a  chopping
            effect  on  the  RF  signal  such  that  the  output  signal  at  the  plate  of the  triode
            provided an  intermediate-frequency (IF) signal.
            Pentodes were handled  similarly to triodes in terms of RF  mixing, with the oscillator
            signal  and  RF  signal  combined  in  the control  grid.  The  pentode  had  a screen  grid,
            and  transconductance  depended  on  the  voltage  supplied  to  the  screen  grid.

            Usually,  the  screen  grid  was  connected  to  a direct-current  (DC)  source  to  set  a
            fixed  transconductance.  However,  some  mixer designs connected  the  RF  signal  to
            the  control  grid,  whereas  the  local  oscillator's  signal  was  connected  to  the  screen
            grid  to  modulate  the  transconductance  of  the  pentode.  The  modulated
            transconductance then provided a multiplying effect of the RF signal.

            But other analog  multiplying  methods and  circuits also were used  in the early years
            of radio.  For example, diodes could  be used  as mixers or as part of a more complex
            mixer  circuit  such  as  a  double-balanced  modulator.  And  in  particular,  in  the  late
            1920s or by  1930,  switch-mode  mixers  using  solid-state copper  oxide  diodes  were
            used  in  commutating switch-mode mixers or balanced  modulators.
            Mixers can  be viewed  in two ways:

            1. Two  (or  more)  signals  are  applied  to a nonlinear device  to generate  distortion
            and thus provide an  IF signal.
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