Transfer Function

ozerozdal

1. The problem statement, all variables and given/known data
Find the transfer function Vout(s)/Vi(s) of the circuit


2. Relevant equations
Zr = R; Zl=Ls; Zc=1/Cs; KVL; KCL


3. The attempt at a solution
I have to find the transfer function of the complete circuit I send.For this, I divided the all circuit into small pieces.I tried to write the function for the smallest one,and then I realized that all circuit is not a series circuit.By the way, Vac source our input, and output is in front the R2.For this reason,I didnt add R2 into transfer function ? Am I right or should I add it ? Also how can I find the transfer function for the second and the complete circuit ? Can you give me an idea ?

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berkeman

Welcome to the PF.

Yikes, that last circuit is involved!

For the first circuit, yes you need to include R2 in the calculation, since it loads the rest of the circuit. Are you told to assume the coupling coefficient of the transformers is 1?

ozerozdal

Thanks for your reply.Yes I assume the coupling coefficient of the transformers 1:1Actually I am confused for the grounds.How can I think them ?

rude man

Get simulation software like SPICE - quick!

ozerozdal

Is there a software which gives us the transfer function of the systems directly? Also,will it be too hard to calculate by hand ?

rude man

SPICE does not generate transfer functions. It allows time response to various input functions, and frequency domain information (Bode plots).

You can input transfer functions but you don't get transfer functions generated from circuits input'ed into the software.

i know of no software that does that, but it's conceptually feasible so maybe there is some out there.

Doing a circuit like your #3, or even #2, by hand is next to impossible. Only possibility I see is application of two-terminal network theory (ABCD parameters etc.) but even there the mutual inductances seem to complicate the situation. Also, who knows, maybe constant-k or m-derived theory - I'm not conversant with those.

berkeman

But you can plot Vo/Vi with SPICE, at least I can with MicroCAP...

rude man

Of couse, but the OP was asked to find the transfer function, which I understood to be in closed form, e.g. Laplace. But maybe Bode plots is what the question had in mind after all.

ozerozdal

Yeah I can plot signal-frequency, phase-frequency with LT Spice but to compare it,I wanna draw the same graphs with MATLAB using transfer function of the circuit.Actually this is my some kind of homework.