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