Why do we run out of radio frequencies?

Well, we do have some ways to conserve the spectrum.

First, there’s AM, which takes up a nice, tidy 10 KHz with the carrier wave and the upper and lower sidebands. However, the fidelity is awful.

Or, if you’re feeling really conservation minded, you could use the upper, lower, upper-upper, or lower-lower sidebands and play four things at once in that same 10 KHz bandwidth. If you’ve ever listened to the stuff that goes out on those bands you’d realize that you either have to speak a foreign language, be a spy, or be a hellfire-and-brimstone fundie. But it’s an option.

FM takes up as much as it does because it requires that much for good fidelity. You can run an FM program with as little deviation as you like, but using limiters and filters makes it sound wooden and dull. If you’re gonna do that, you may as well use AM.

And thank you, GaryM, for correcting that faux pas. I explained that stuff to her in about two minutes on my way out the door to broadcast some AM/FM/sideband programs. Sorry I wasn’t clearer.

The noise reduction ability of FM depends to some extent on a factor called the Modulation Index. This is the ratio of the carrier frequency (the frequency to which you tune your receiver to get the station) shift divided by the modulating frequency. For example, it your audio signal contains frequencies up to 10 kHz and you shift the carrier frequency by 50 kHz, the Modulation Index is 5. Now, the act of shifting the frequency means that the frequency is accelerated, i.e. the frequency changes with time, which results in the generation of harmonics quite far beyond the 50 kHz by which the carrier frequency is shifted.

In addition, the stations are separated in your receiver by electrical filters. A filter with a frequency pass band from 10 mHz to 10.1 mHz does not give zero output for frequencies outside those limits. Rather, the filter attenuation (signal reduction) increases gradually starting at those pass band frequencies. Because of the inherent cussedness of nature, if you allow too much of the adjacent station signal into the pass band, the addition of that signal to the desired one combined with the fact that the receiver circuits are not precisely linear can also result in a phenomenon called intermodulation which results in all sorts of funny little background mutterings coming out of your speaker while you are trying to listen to Beethoven.

For all of these reasons and some others, a guard band in addition to the actual required signal bandwidth is provided between stations. The people who specify channel bandwidth are fully aware of the need for conservation of frequency spectrum and place the stations as close together in frequency as they can and still maintain a specified quality of broadcasting.