Analysis question

Discussion in 'General Electronics Chat' started by Veracohr, Sep 18, 2013.

  1. Veracohr

    Thread Starter Well-Known Member

    Jan 3, 2011
    551
    76
    I'm trying to derive a transfer function I found in a paper and I'm having trouble with part of it.

    The following is part of an OTA-based high-pass filter from the paper. Vx is an intermediate voltage, and the transfer function of the OTA is Iout = gm(V+ - V-).

    [​IMG]


    My question is: how do you figure out what voltage point Vy is? I feel like my circuit analysis skills should be enough, but the more I think about it the more I go in circles.
     
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  2. BobTPH

    Active Member

    Jun 5, 2013
    782
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    Vy = Vo

    Bob
     
  3. Veracohr

    Thread Starter Well-Known Member

    Jan 3, 2011
    551
    76
    But that ignores Vin.
     
  4. #12

    Expert

    Nov 30, 2010
    16,284
    6,797
    What is the transfer function for a DC input through a resistor? (I forgot)
    Vo = -gm dv Rl/Rin?

    You need an Rl. As long as Rl is infinity, Vo will be Vx.
     
  5. Veracohr

    Thread Starter Well-Known Member

    Jan 3, 2011
    551
    76
    Never mind, I was thinking about it the wrong way.

    For the (partial) circuit above, the better way to think about it is:

    I_{out} = \frac{V_o-V_{in}}{(1/sC)}
    Also,
    I_{out} = gm(V_x-V_o)

    so

    gm(Vx-Vo) = (V_o - V_{in})sC

    Which works out to:

    V_o = \frac{sCV_{in} + gmV_x}{sC + gm}

    Going by that method, I correctly got to the transfer function displayed.

    Unfortunately, the circuit it describes didn't actually work in practice, which is why I wanted to verify the TF in the first place.
     
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