# FM spectrum questions

1. Mar 28, 2007

### Firefox123

I have a few questions regarding the spectrum of FM....

1. What is the equation that predicts where the sidebands will occur in an FM signal given a certain FM rate and deviation?

2. If I have an FM signal with a rate of 16 KHz and a deviation of 5 KHz and I look at the signal on a spectrum analyzer I am seeing a signal at the carrier frequency and then the largest sidebands are occuring at +16 KHz and - 16 KHz away from the carrier. I am not understanding why.

3. Assume an FM signal of 200 MHz with a deviation of 5 KHz and a rate of 4 KHz. On the spectrum analyzer I see a signal at 200 MHz and the largest sidebands occur at 200 MHz + 4KHz and 200 MHz -4KHz. If I create a CW wave at either 200 MHz + 4KHz or 200 MHz - 4KHz, it seems to cause alot of interference to the point that the receiver is not able to correctly receive the transmitted information. What is going on here?

Thanks for any input.

2. Mar 28, 2007

### antoker

Pretty good explanation about FM is done http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm".

Hmm, all your questions are arising from not knowing how fm is created. You can actually get all the info from deriving equations. Just start with some carrier frequency $$f(\omega (t)) = A\cdot sin((\omega _{c}+\omega (t) )+ \phi)$$ where $$\omega (t)$$ is a signal that is being transmitted, then, when you rewrite your equation in term of the $$e^{x}$$ function, you'll understand why and where sidebands occurs (hint $$FT(e^{x}) = \delta$$). Same goes for frequency deviation. Or you can do a FT on the equation, same results will appear. I'm guessing that you'll understand it better, when the mathematical fundamentals has been provided.

Last edited by a moderator: Apr 22, 2017
3. Mar 28, 2007

### Firefox123

Ive read that before...its a pretty good explanation.

I have already seen the mathematical explanation before...I was just throwing the first 2 questions out there to see if maybe someone had a different way of looking at it besides just doing an FT on the FM signal.

As far as the third question is concerned though...

Imagine I am representing a signal by using a 4 KHz tone to modulate the carrier to represent a digital '1' and using the unmodulated carrier to represent a digital '0'.

What kind of interference would a signal at + or - 4KHz from the carrier cause in the receiver?

Last edited by a moderator: Apr 22, 2017
4. Mar 28, 2007

### antoker

That's looks like an frequency/amplitude shift keying scheme to me. The answer depends on what you're modulating, are you modulating an amplitude of the carrier, or are you modulating a frequency?

Only carrier present, will result in one spike on a spectrum analyzer at the carriers frequency.
Carrier, amplitude modulated by a 4kHz tone, will result in typical spectral representation of a AM signal, i.e carrier spike +/- two lobes at 4kHz
Carrier, frequency modulated by a 4kHz tone, will result in FM spectra, looking much like a sinc function, check out this http://www.algomusic.com/jmsl/tutorial/FMSpectrumApplet.html" [Broken] for better explanation.

http://ccrma.stanford.edu/~jos/mdft/FM_Spectra.html" [Broken]

Last edited by a moderator: May 2, 2017
5. Mar 28, 2007

### Averagesupernova

I assume you are wondering why when you set a signal generator to deviate a carrier at 5 Khz with a 16 Khz modulating signal why do you see signals past 5 Khz. After all, if we are deviating only 5 Khz then why should we see anything past that right? The reason is that when we frequency modulate a carrier we ALWAYS generate sidebands above and below the carrier at the modulating frequency and all harmonics of it out to the frequency we are deviating at. This works out nicely when we have a high modulation index. The modulation index is the deviation/modulating frequency. Suppose we frequency modulate a carrier at 500 hertz. We set the deviation at 10 Khz. We will have sidebands every 500 hertz going out away from the carrier (above and below) all the way out to 10 Khz away from the carrier. We will have a total of 20 sidebands on each side of the carrier. As the modulating freqency goes up, the number of sidebands drops. A common mistake is to assume that the bandwidth of the whole affair is the deviation x 2. This works out ok with a high modulation index, but as the modulating frequency gets closer to the deviation, the bandwidth increases. There are certain combinations of modulating frequencies and deviation that cause certain sidebands to disappear completely and also cause the carrier to completely disappear. I forget what the ratio is, and the link posted earlier in the thread probably explains it, but what is known as a bessel null is when these sidebands or carrier goes away.