# Transfer Function of Parallel Resonant Band Filter-transfer function

Discussion in 'Homework Help' started by addy94, May 5, 2015.

May 5, 2015
2
0
Can anyone help me to find transfer function of this circuit. I know how to do it when there are only two loops but i do not know how to do it if there are 3 loops and how to get a Output/input equation. I will be very glad if someone help me in this.

For the circuit assume the values of V,R,L and C not given.

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2. ### MikeML AAC Fanatic!

Oct 2, 2009
5,451
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What exactly do you mean by "transfer function"?

May 5, 2015
2
0
I want an equation of Vout/Vin in terms of laplace transformation.

4. ### MrAl Distinguished Member

Jun 17, 2014
3,741
791
Hi,

You can do this several ways.

One way is to simply lump all three elements between nodes 2 and 0 into one element, then use the voltage divider technique to calculate the transfer function. Let me start you out and see how it goes.

First, all the Laplace equivalents or impedances for each element would be:
Rin => Rin
RL => RL
C => 1/(s*C) = zC
L => s*L = zL

Now combine RL, zC and zL all in parallel, call this Zo, then the transfer function is:
Vo/Vi=Zo/(Zo+Rin)

It's that simple, but a little math involved in combining the elements in parallel at first, then simplify.

Just so you have something to compare to, for your circuit we have:
Zo=(s*L*RL)/(s^2*C*L*RL+s*L+RL)

and you should be able to get this result too, then use it in the formula above to get the transfer function. Note that formula is just the voltage divider formula for two impedance elements that form a voltage divider.