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.