# Transfer function of an RLC circuit

I'm trying to simulate an RLC circuit using transfer function. Circuit is there: http://i.stack.imgur.com/MC8ME.png (I'm a new user therefore I cannot post images)

But I can, L.Motl...

Main current (I) is the output and V is the input. So far, I'm stuck at this:

TF = (Q1(s) + Q2(s)) / ((30 + s)(Q1(s) + Q2(s)) + 20 * Q1(s))

I need to get rid of Q1 and Q2, but I cannot find a way.

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Best to ask your teacher next week. – Johannes Jan 22 '11 at 17:29
This looks very like a homework problem, so I doubt you will find anyone to give you the answer here. For this reason I have also voted to close the question. However, I will point you in the right direction: What you are looking for is Kirchoff's laws (en.wikipedia.org/wiki/Kirchoff%27s_circuit_laws). – Joe Fitzsimons Jan 22 '11 at 18:02
Homework problems should be tagged as such (which I did) and only be answered with hints - besides that they are perfectly valid questions for this site. – Sklivvz Jan 22 '11 at 20:37
@Sklivvz is right. There is no reason to close this question, as long as it is tagged as homework. – Noldorin Jan 22 '11 at 21:37

This circuit contains only passive components, and, by inspection, can be decomposed into series and parallel combinations. You can solve it simply by writing down the complex impedance (as a function of frequency) for each of the components, and then combining those expressions using the usual rules for series and parallel combinations of impedances.

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You must use Kirckhoff laws for alternate circuits. So, the tranfer function that you'll find can be used for any input signal, with Fourier Transform (because transfer function is the output of the system for a delta signal input in frequency domain).

We obtain:

\left\{\begin{aligned} &V_I e^{i\omega t}= R (I_1(t)+I_2(t)) + j \omega L (I_1(t)+I_2(t))+ R I_1(t) \\ &V_I e^{i\omega t}= R (I_1(t)+I_2(t)) + j \omega L (I_1(t)+I_2(t))+ \frac{1}{j \omega C} I_2(t) \\ \end{aligned}\right. or, if you aren't interested to know $I_1$ and $I_2$ in separated rings you can consider the parallel of R2 and C:

$$V_I e^{i\omega t}= RI(t) + j \omega L I(t) + \frac{1}{\frac{1}{j\omega L}+ j\omega C}I(t)$$

Now, you haven't sayed where is Vout...but with these approach, you can easily calculate current and tension in every point of circuit.

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