# RLC parallel circuit; fourier components

1. Mar 27, 2010

### mathman44

1. The problem statement, all variables and given/known data

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.

2. Mar 28, 2010

### vela

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

3. Mar 28, 2010

### mathman44

A very large number of sine waves. :s

4. Mar 28, 2010

### mmmboh

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

Now what

5. Mar 28, 2010

### vela

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

6. Mar 28, 2010

### 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?

7. Mar 28, 2010

### vela

Staff Emeritus
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?

8. Mar 28, 2010

### mathman44

The first.

9. Mar 28, 2010

### vela

Staff Emeritus
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?

10. Mar 28, 2010

### mathman44

Great, thanks!

11. Aug 24, 2011