Why is Donald Duck on the Radio? Math Behind Single Sideband Explained

AM, or amplitude modulation, was the earliest way of sending voice over radio waves. That makes sense because it is easy to modulate a signal and easy to demodulate it, as well. A carbon microphone is sufficient to crudely modulate an AM signal and diode — even a piece of natural crystal — will suffice to demodulate it. Outside of broadcast radio, most AM users migrated to single side band or SSB. On an AM receiver that sounds like Donald Duck, but with a little work, it will sound almost as good as AM, and in many cases better. If you want a better understanding of how SSB carries audio, have a look at [Radio Physics and Electronics] video on the subject.

The video covers the math of what you probably already know: AM has a carrier and two identical side bands. SSB suppresses the carrier and one redundant side band. But the math behind it is elegant, although you probably ought to know some trigonometry. Don’t worry though. At the end of the video, there’s a practical demonstration that will help even if you are math challenged.

Dealing with signals as math equations are a staple if you seriously study electrical engineering. For example, you can model a pure sine wave with the equation: S(t) = A sin(2*pi*F*t) where A is amplitude, F is the frequency in Hertz, and t is time. Try it. In that example, the frequency is 1 kHz and the amplitude is 20, but you can tweak the values and see what happens. If you add something to the argument to the sin function, you’ll change the phase of the wave. If you followed that, you should have no problem with the video.

This math isn’t just good for working homework problems. It is the same math you need to do synthesis with a computer or digital signal processor. If you want to dig in, we talked about phase angle mathematics, earlier.

But wait, what’s with that screwy title? Have you ever heard an SSB signal on an AM radio? Most people describe it as sounding like Donald Duck. Listen at about the 20 second mark of this mp3 file and just after that, too where it is Upper Side Band (the other kind of USB) but off frequency and you’ll hear that famous voice. If all of this is unfamiliar, you need to explore the speech transmission origins of AM.

 

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