# Analysis question

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

1. ### Veracohr Thread Starter Well-Known Member

Jan 3, 2011
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100
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-).

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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Jun 5, 2013
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Vy = Vo

Bob

3. ### Veracohr Thread Starter Well-Known Member

Jan 3, 2011
660
100
But that ignores Vin.

4. ### #12 Expert

Nov 30, 2010
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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
660
100
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.