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Common base amplifier current gain

  1. Jun 26, 2009 #1
    Hi folks - I'm trying to follow along in a textbook the derivation of the common-base current gain equation, and I'm having a bit of trouble. The common base current gain is supposed to be approximately [tex]\alpha[/tex], where [tex]\alpha = \frac{\beta}{\beta+1}[/tex]. Doing a nodal analysis with the signal applied to the emitter through the intrinsic emitter resistance, the base grounded, and the collector current equal to [tex]I_c = \frac{\beta}{\beta+1}I_e[/tex] (Ie is the emitter current) I have:

    [tex]\frac{I_i}{I_o} = \frac{\frac{V_in}{r_e}} {\frac{\beta}{\beta+1}{\frac{V_in}{r_e}}}} = \frac{\beta+1}{\beta}[/tex]. Unfortunately the correct answer is obviously [tex]\alpha = \frac{\beta}{\beta+1}[/tex], which the equation I have doesn't evaluate to. Can anyone see where I went wrong?
     
  2. jcsd
  3. Jun 26, 2009 #2
    Nevermind, I see it now that I typed it up! It should of course be [tex]\frac{I_o}{I_i}[/tex], not the other way around. :biggrin:
     
  4. Jun 26, 2009 #3
    The real advantage in common base bipolar transistor RF amplifiers is the high voltage gain from a low impedance source.
     
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