Demonstrating AM sidebandsPieter-Tjerk de Boer, PA3FWM email@example.com
(This is an adapted version of part of an article I wrote for the Dutch amateur radio magazine Electron, April 2017.)
Amateur radio courses teach that in amplitude modulation, sidebands arise. This can be proven mathematically, and nowadays with an SDR one can easily see them. When I had written my first SDR program with a waterfall display, back in 2004, I fascinatedly listened and watched the AM sidebands of, back then, Radio 10 Gold on 1008 kHz for quite a while.
Recently I built the setup sketched in the figure, consisting of an amplitude-modulated signal generator, a resistor, a quartz crystal, and an oscilloscope. Such a crystal has a very low impedance on its series resonant frequency. Together with the series resistor this forms a sharp notch filter: that single frequency is short-circuited. If we now modulate the signal generator's amplitude with a tone of say 1 kHz and change its carrier frequency, we can one after the other notch out one sideband, the carrier itself, and the other sideband. The effect of this is also shown in the figure. First the "undisturbed" spectrum and corresponding oscilloscope image. Then the same picture with one sideband notched out: we see on the oscilloscope that the amplitude modulation is still there, but less deep, because the contribution from one of the sidebands is no longer there. (Leaving only one sideband also introduces phase modulation, but that is not visible on the oscilloscope here.)
The last picture shows the situation where the carrier itself has almost entirely been notched out. The oscilloscope picture now looks very different. If we feed this signal to a simple envelope detector, then we get something that looks more like 2 kHz than 1 kHz: there are twice as many amplitude peaks per second than in the original signal. And indeed, if one holds a portable radio near this setup, tuned to the signal generator's frequency, one suddenly hears a twice as high tone when the carrier is notched.
In fact, this was exactly the reason why I did this experiment: I wanted to know whether the digital kitchen radio discussed previously has an envelope detector in its software, or a so-called synchronous detector. The latter would only need a very small amount of remaining carrier to still produce undistorted audio (i.e., the 1 kHz tone). But no, we heard a 2 kHz tone, so there's an envelope detector in the kitchen SDR.