# RLC parallel circuit; fourier components

mathman44

## Homework Statement

In my lab we did an experiment using an RLC parallel circuit, with the L and C in parallel. The voltage source was set at square waves. I am being asked to explain why there are frequencies, beyond the resonance, at which there is a peak voltage drop across the capacitor.

For example, in my circuit the resonance is at 9.382khz, and then there are subsequent peak voltage drops across C at:

1.878 khz, 1.342 khz, 1.043 khz... each resonant peak with a lesser voltage drop than the previous.

I have a feeling this has to do with the fourier components of the square wave, but I can't wrap my head around this. Any hints? Thanks in advance.

Staff Emeritus
Homework Helper
You have the right idea. What is the Fourier series for a square wave?

mathman44
A very large number of sine waves. :s

mmmboh
$$V(t) = \frac{4V_0}{\pi}\left(\sin(wt) + \frac{1}{3}\sin(3wt) + \frac{1}{5}\sin(5wt) + \dots \right)$$

Now what Staff Emeritus
Homework Helper
Actually, I may have misinterpreted your original post. What exactly did you do in this experiment?

mathman44
Basically, why are there frequencies (of square waves) other than the fundamental frequency that give voltage peaks across a capacitor, in parallel with an inductor, in an RLC circuit?

Staff Emeritus
Homework Helper
I know, but your statement is ambiguous. Are you varying the frequency of the input signal and seeing the response peak at different frequencies, or do you have a fixed-frequency input signal and see a bunch of peaks in the spectrum?

mathman44
The first.

Staff Emeritus
Homework Helper
Heh, I was betting on the latter based on what you wrote. Good thing I asked.

Try dividing those frequencies into the resonance frequency of your circuit. Notice anything about the results and how they might relate to the Fourier decomposition of the square wave mmmboh gave above?

mathman44
Great, thanks!

Zsiegel