We're working on filters and we got a homework assignment that's asking for the Vout at the center frequency of a parallel resonant band-stop filter. This is not something we covered in class, and although I have the book and see how they solve for it, it's an equation that's completely new to me, so I'd like to know if I'm doing it correctly.

Here's the info:
C = 330 pF
L = 10 μH
Rw = 16Ω
Rl = 330Ω
Vin = 10V

Having never done this, at first impression I would have been to find the impedance of both the cap and ind at center frequency, treat them as a parallel resistors (plus the winding resistance on the ind), then use the voltage divider equation to find the voltage across the load. As logical as this sounds to me though, it does not appear to be the answer.

The book shows the formulas:
Vout = Vin (Rl / (Rl + Zr)).
Zr = Rw (Q2 +1)

Our instructor has never went over this before, nor can I find any previous reference to what Zr is.

I've calculated the following so far:
fc = 2.77 MHz
Xl = 174Ω
Q = 10.88

So according to the example in the book, Vout @ Fc should be:

Zr = 16Ω (10.882 + 1) = 1.9KΩ
Vo = 10V (330Ω / (330Ω + 1.9KΩ)) = 1.48V

So the Vout should be 1.48V? I can follow the equations, but I don't understand what Zr is and why it's calculated as such. Could someone please explain this or point me to a website that I can read about?

Thanks!

 

What is needed is a schematic of the circuit you are proposing to use.

hgmjr

 

My apologies, I thought the name of the circuit with the values would be enough since it's just the basic kind. I found a picture of one online. Note the values in the picture are not the real values.

http://www.electronicsteacher.com/alternating-current/filters/02127.png

Vout for my problem would be the voltage across the load resistor.