# How to attain this transfer function?

#### lurikeen

Joined Apr 13, 2011
5
Hi, I have the following problem, for which I must find the transfer function H(s)= V2/V1:

I feel like I cannot find the transfer function (H(s) = V2/V1) without first doing a delta to wye conversion. However This gives me a circuit that looks as follows:

For which I think I just need to do H(s) = (Z2 + Z3)/(Z1 + Z3). Does this sound correct? The delta to wye conversion gives you a messy denominator on the Z1, Z2, and Z3, but it appears that they all cancel out.

Is this the correct way to complete this problem?

Thanks!

#### ErnieM

Joined Apr 24, 2011
8,007
The resistor is in parallel with the driving source V1 so it does not enter into the transfer function. Just consider the L and the C.

#### lurikeen

Joined Apr 13, 2011
5
Thanks for the reply. I see what you're saying, but I get confused because a delta to wye transformation should always leave the circuit unchanged, and thus the delta to wye version of the circuit should give the same transfer function, correct? It looks to me like it doesn't. Thoughts?

#### steveb

Joined Jul 3, 2008
2,436
Thoughts?
ErnieM is correct. As far as the voltage transfer function goes, you don't need to worry about the resistor. Any transformation you do will give you the same answer, if you do it correctly.

A transformation will include the 4 ohm resistor because the load current on the input voltage source is affected by that. Still, if you do a transformation (which is needless work in this case) and then do the voltage transfer function, you will get the same answer, which means that the resistor will cancel out somewhere in the math.

#### ErnieM

Joined Apr 24, 2011
8,007