Why does an AM radio channel require any bandwidth at all? Why can’t it just transmit on a single, precise frequency?
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I spent about an hour digesting the answers on this post while also reading up on it myself. Every single post here is giving great info, but they all seem to be assuming a relatively advanced prior understanding of the principles. Allow me, someone who knows very little about this topic, try to offer a small rickety footstool to help you reach up and catch the helping hands that actually know what they’re talking about.
Amplitude modulation, as I’m sure you understand from the name, is, in its simplest form, taking a single pure frequency wave (the “carrier frequency”) and shifting the amplitude of the waves up and down to encode data (the “message signal”).
Generally, your carrier frequency needs to be a lot higher than the frequency of your message singal. This because the carrier frequency is going to “fill out” the waveform of your message singal. In essence, think of a graph of the carrier frequency sine wave, and then imagine “fencing it in” by the waveform of the message you want to send. The result will look [something like this](https://upload.wikimedia.org/wikipedia/commons/f/fb/DSBSC_Modulated_Output.png). You can perhaps think of it as sort of like the graph you’d get if you played a high-pitch tone on a speaker, and then you took the message you’re trying to encode and hooked its waveform directly to the volume slider to make the carrier wave louder or quieter as the encoded wave goes up and down. I think this is already the picture you have in your head of what AM radio is based on your follow-up questions in other comment threads.
So, the obvious thinking here is, “So what, this is still just a single-frequency wave, I’m just making it louder and softer”. And that’s true, that’s exactly what you’re doing. (Although “louder” and “softer” aren’t really the appropriate terms here, it would be “higher power” and “lower power”, since these are radio waves, not sound waves.)
Thing is though, that everyone is doing their best to explain to you, is that doing this *just so happens* to be the exact same recipe as what you’d get if you took two or more pure sine waves of slightly different frequencies close to the carrrier frequency and mushed them together.
For example, if your carrier frequency is, say, 800 kHz (a typical US AM radio station frequency) and you used the above method to encode sound data in to that wave, what you’ll have is a recipe for a complex waveform that, by pure mathematical coincidence, creates the same result as a completely different recipe made from other sine waves in, say, the 600 kHz to 1000 kHz range, all mushed together. The exact component frequencies being used at any given snapshot of time will vary in real time with the message you are trying to send, so unless you’re trying to send other pure sine waves as your encoded message, it only makes sense to talk about these component frequencies as sweeping out a range rather than any specific one.
The key insight here is that, no, you’re *not* actually beaming these component frequencies from your antenna. At least, not intentionally. You still very much are “just” doing the amplitude modulating thing. But because your wave recipe happens to be identical in result to that other recipe, it means any radio equipment sensitive to frequencies in that other recipe *are going to sense your broadcast anyway*. You can think of it sort of how like your computer screen only emits three specific colors of light, none of which are yellow, but if they happen to mix in just the right way, your eyes will detect yellow light anyway, exactly the same as it would if actual yellow light was entering your eye.
In essence, you are polluting those other frequencies with noise, because the wave math of your encoding just happens to exhibit identical wave math to those other frequencies. *That’s* why your signal has a bandwidth. It’s the width of all the other frequencies you happen to be polluting with this mathematical equivalence. These are the so-called “side bands” of your signal. If you do it the way shown in the above diagram, you’ll end up creating two identical side bands, one above your carrier frequency, and one below you carrier frequency. Each side band on its own will be as wide as your initial message signal is, so you will be taking up twice the bandwidth of your message with this method.
Here’s where things get interesting. When you do this modulation, you will develop two side bands, but there will also be a strong background “hum” of your original carrier frequency. This carrier frequency hum actually carries no information. It’s just a constant hum. And I don’t mean that this is your modulating up-and-down version of this wave. The modulation part is where the side band comes from; this hum is just a constant droning leftover component frequency. Since it’s not doing anything for your message signal, it’s actually wasting antenna power to include it in your broadcast, and it’s best to completely filter it out and send *only* the side bands. So, in a funny twist, it’s actually most efficient to transmit on every frequency in your allotted band *except* your actual carrier frequency. They call this [double-sideband suppressed carrier (DSB-SC)](https://en.wikipedia.org/wiki/Double-sideband_suppressed-carrier_transmission) modulation. That’s “double-sideband” because you are creating two side bands, and “suppressed carrier” indicating that you filter out that useless background hum.
A further refinement is realizing that your two side bands are actually identical mirrors of each other, and that you really only need one. So, with some clever signal filtering techniques, you can eliminate one whole side band to get [single-sideband suppressed carrier (SSB-SC)](https://en.wikipedia.org/wiki/Single-sideband_modulation) modulation. A detector listening for your broadcast will need to do some extra legwork to decode this, but you cut both the power emitted from the station and the bandwidth taken up by the signal in half from DSB-SC for the same exact transmission.
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