S-Parameters LCR-LC circuit

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DeanM

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Hi all,

I was recently doing a lab experiment on s parameters. the lab described a two port network as follows. L-C-R in series followed by LC in parallel to ground. Part of the experiment was to simulate the s parameters in LTspice. Did that and it worked out fine. The next part was to verify the results by hand.

That is the bit i would like help with. I need to select a frequency and compute it by hand to find out what the output voltage at that frequency is. So i need to work out some sort of transfer function for this circuit that will allow me to put in a frequency and the lcr-LC values and get the output voltage.

Any body know what, or how i get the transfer function?
Regards,
Dean
 

If I understood well your description, you simply have a voltage divider with Z1 series and Z2 to ground.
Z1 is the series of L1, C1 and R1
Z2 is the parallel of L2 and C2
Vout = Vin*Z2/(Z1+Z2) if you are interested only to the modulus then |Vout|=|Vin|*|Z2|/|Z1+Z2|
Using the matematical model of the component in frequency:
Z1 = j*w*L1 + 1/(j*w*C1)+ R1 = (-w^2*L1*C1 + 1 +j*w*R1*C1)/(j*w*C1)
Z2 = {j*w*L2*[1/(j*w*C2)]}/{j*w*L2+[1/(j*w*C2)]} = j*w*L2/(-w^2*L2*C2+1)

w is 2*pi*f

I think now you should be ablet to find the transfer function you need.
 

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