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Small-signal transfer function from this differential input

  1. Apr 3, 2015 #1
    1. The problem statement, all variables and given/known data
    q1.png
    2. Relevant equations

    Small Signal Equivalent Circuit, Kirchhoff Current Law, and BJT equations mentioned in the question.

    3. The attempt at a solution
    q1a_1.png
    It looks like I did something wrong. Can someone help me with fixing this?
     
  2. jcsd
  3. Apr 5, 2015 #2

    rude man

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    I would not use equivalent circuits for this. You're given all the equations you need to solve the problem without resorting to equiv. ckts.
    Hint: at some point use ex ≅ 1 + x for 0 ≤ x << 1.
    OR you can do it with just gm.
     
    Last edited: Apr 5, 2015
  4. Apr 5, 2015 #3
    I don't understand how you want to get to the answer 1/2*gm by only using gm and nothing else. And I don't see how e^0=1 would be related to this.
     
    Last edited: Apr 5, 2015
  5. Apr 5, 2015 #4

    rude man

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    I'll get you started:
    gm = dI1/d(Vb1 - Ve) = -dI2/dVe
    where Vb2 = 0 is assumed wlog ("without loss of generality"). Vb is base voltage, Ve is emitter voltage.
    That would come in handy if you choose to use I = Isexp(qVbe/kT) instead of gm directly.
    I recommend using gm directly, it's shorter.
     
    Last edited: Apr 5, 2015
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