# Fundamental and harmonics of a square wave

1. Jan 25, 2012

### lcr2139

1. The problem statement, all variables and given/known data
Measurements taken of a square-wave signal using a frequency-selective voltmeter (called a spectrum analyzer) show its spectrum to contain adjacent components (spectral lines) at 98kHz and 126kHz of amplitudes 63mV and 49mV, respectively. For this signal, what would direct measurement of the fundamental show its frequency and amplitude to be? What is the rms value of the fundamental? What are the peak-to-peak amplitude and period of the originating square wave?

2. Relevant equations
none given, and only proportions used so far.

3. The attempt at a solution
I know that the fundamental frequency is the first harmonic, and that the relationship between two frequencies represent the ratio of harmonics. Using this knowledge, I created a proportion of 98kHz/126kHz and found that it equaled 7/9, so the 98kHz part was the 7th harmonic and that the 126 kHz was the 9th harmonic. Then I created a ratio of the frequency and the harmonic, finding that 14kHz was correct for both trials. However, I do not think that this is correct because it is such a small number compared to the other frequencies. I tried the same thing with the amplitudes, but they failed. I do not understand what the rms value of the fundamental means- is it the frequency? amplitude? How do you find the originating wave if you do know know what harmonic the original wave is?

2. Jan 25, 2012

### MisterX

It should be that much smaller. I think 14 kHz is correct. But you actually shouldn't have to do any math if you have the spectrum analyzer in front of you. The fundamental for a square wave should have the largest amplitude of any harmonic and should be the lowest frequency with any significant amplitude. It would be the lowest frequency "spike" on the magnitude plot.

In this case RMS is related to amplitude. Doing an internet search for "RMS" or "root mean square" may be worth your time. Any harmonic is itself essentially a sine wave, and there is a constant conversion factor to convert from peak amplitude to RMS amplitude for a sine wave.

Last edited: Jan 25, 2012
3. Jan 27, 2012

### lcr2139

Thank you very much! This helped a lot.