# Finding the transfer function for a parallel resonant circuit

## Homework Statement

Hello, so I'm trying to solve the transfer function for a parallel RLC filter that goes like

-------Resistor -------------------
|XXXXXXXXXXXXXXXXX|XXXX|
|XXXXXXXXXXXXXXXXX|XXXX|
VinXXXXXXXXXXXXXXXXCXXXXL
|XXXXXXXXXXXXXXXXX|XXXX|
|XXXXXXXXXXXXXXXXX|XXXX|
|---------------------------------
the Xs are just empty space, multiple space bars wouldn't show up correctly
so I'm given the equation for the transfer function which is
I just realized that the problem actually had 2 parts.
First, the equation to use to solve transfer function is:

H(w) = ZLC / Ztot
I found ZLC to be [(+jwL)(-j/wC)] / (jwL) + (-j/wC)
and Z total to be {[(+jwL)(-j/wC)] / (jwL) + (-j/wC)} + R
I'm having trouble getting rid of the js in the equation and solving it.
I keep trying to do basic math operations and js just keep stacking up like j^2 and j^3.. I'm pretty sure they're not even supposed to be treated as normal variables.

Also, the second part which may be a little easier is to take the above equation and rearranging it and prove that the above equation is equal to the equation below. I'm stuck on this one as well since I haven't solved the first part.

H(f) = 1/ (1 + j*Qp* (f/f0 - f0/f))

So this is a bandpass filter, and the bandwidth is 20000 Hz, and resonant frequency is 980000 Hz and I've found the quality factor to be 49 by taking Qp = f0 / B

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