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I have an equation that was derived from a schematic in order to find the transfer function of a filter (electrical engineering) but my algebra is not agreeing with the actual result.

The transfer function is defined as: $\frac{V_o}{V_i} = H(\omega)$

The current equation I have:

$\frac{(Vi(\frac {R}{(R+R)}) - V_i)}{R} +\frac{(Vi(\frac {R}{(R+R)}) - V_0) }{ Z_f} = 0 $

where $Z_f$ is equal too: $Z_f = \frac {RZ_c}{(R+Z_c)} $ and $Z_c = \frac {1}{(j\omega c)}$

My result was $\frac {V_o}{V_i} =\frac {(1/2 j \omega RC)}{(j \omega Rc +1)}$

Which I don't believe is right. Can someone please help me find the correct transfer function.

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    I'm very sorry; I'd m$a$de a mistake. Your result is actually correct; I've added an answer with a derivation.2012-10-12

1 Answers 1

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Your result is correct.

We can simplify the equation by cancelling the $R$s and dividing through by $V_i$, which yields

$ \frac{\frac12-1}R+\frac{\frac12-V_0/V_i}{Z_f}=0 $

with solution

$ V_0/V_i=\frac12\left(1-\frac{Z_f}R\right)=\frac12\left(1-\frac{Z_c}{R+Z_c}\right)=\frac12\frac R{R+Z_c}\;, $

which coincides with your result if we substitute $Z_c$ and multiply through by $\mathrm j\omega C$.