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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The station frequency is what the tuning circuit in your radio locks on to and that’s called the carrier wave. The audio information ends up being broadcast on one or both sides of that carrier wave frequency because of how it is modulated (basically mixing the audio wave into/onto/with the carrier wave).
Depending on the quality of the broadcast, the bandwidth required to transmit the audio might be higher or lower. If there was no audio information at all modulated onto the carrier wave there would be a single narrow precise frequency with nothing either side.
If you have a good enough radio you can tune to the carrier frequency and adjust the bandwidth to hear what difference it makes. A narrow bandwidth reduces the higher frequency audio information, again because of how it’s modulated onto the carrier wave.
You can try it out here : http://websdr.ewi.utwente.nl:8901/
Scroll in and out and left and right on the waterfall view. It’s showing you a very wide spectrum of frequencies that the radio can tune into. Frequency is horizontal axis and time is vertical axis. Strong signals will show up as orange lines. Drag the yellow tuning thingy over to one of those lines. Then choose USB for upper side band (bandwidth to the right of the station frequency), or LSB for lower side band (to the left), or AM (both sides), or CW for just the carrier wave. Then play with the width of the filter.
You’ll see that some stations are broadcasting using different bandwidths. Ones that need a lot of audio fidelity like music stations use more bandwidth than something like a CB radio where it’s just speech that needs to be understood.
And that is the key thing to understand about bandwidth. Our hearing goes up to about 20khz, but to encode that wide of a frequency range onto a carrier wave would require 20khz of room either side of the carrier wave. And there’s only so much of the radio spectrum to go around. If each station required 40khz of bandwidth, plus some separation, we’d have far fewer stations.
The way things work now, AM stations get half of that to themselves. They get exclusive use of whatever frequency they’re transmitting their carrier wave on, plus 10khz either side. That’s the standard and law that we have settled on.
That might not be answering your specific question but I think it’s beyond an ELi5 answer to explain how radio wave modulation works. The thing to know is that the more audio information you want to broadcast – the more bandwidth you need – because it’s more information.
And AM radio is analog. The information is contained in constantly varying electrical voltages. It’s not broken up into packets that can be re-assembled at your leisure. It has to all be broadcast at the same time, received at the same time, and demodulated at the same time. So it always needs the full amount of bandwidth, whatever that might be.
Like you’re 5. Similar to a wave on the ocean, when the wave stands taller (in height) it must get wider to support that height. There’s maths that can be used to explain the height:width relationship.
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.
AM is something you can [experience in real life](https://youtu.be/b9UO9tn4MpI?si=PWaLv98qpzs38T95).
All sounds can be represented as a set of frequencies and intensities that vary over time. When you speak and make sound, the lowest frequency is centered at 0 Hz. We call this “baseband”, as it’s the fundamental signal itself.
AM is one of the simplest ways to represent sound, where it is essentially a way to shift baseband up to a very high frequency. Instead of 0 Hz, we instead have a powerful reference point, called a carrier. That’s all it really is, you mix your voice with some powerful pure tone RF signal, and that sends it up to effectively be transmitted by an antenna.
AM works off a phenomenon called heterodyning. Despite the complicated name, you experience it all the time. When you hear two tones that are really close (say, 445 Hz and 440 Hz), you can hear the difference as a 5 Hz wobble. That’s how you recover the signal from the carrier.
About that video, the cool thing about it is that the electric arcs themselves produce a carrier, and a sidebar. Imagine them as a ton of constituent waves with pure frequencies, each being decoded back to baseband by mixing with the strongest component: the carrier wave.
Now, we still haven’t answered your question. Why does it take bandwidth? If you look at the waveform itself, it “looks” like it’s a constant frequency, right? But! The caveat is that to change the intensity of that carrier, you need other frequencies. Adjust the volume means adding more constituent waves in a precise manner. Or, more simply put, “modulating with the baseband”. Those frequencies just so happen to shape the wave so that it’s overall appearance (called the “envelope”) looks like baseband. In reality, you can think of AM as just disguised baseband, which already requires bandwidth (as you know).
Have a look at the Fourier Analysis, and you will quickly understand why you cannot have a single frequency when you modulate a sine wave.
I think the piece of information you are missing is, a single, precise frequency only describes an infinite sine wave with no change in amplitide ever. The moment you change the amplitude even a little, you have added other frequencies in.
Imagine a guitar playing some notes. If you strum one string that’s a single frequency. If we strum three strings we get a chord, which is made up of three frequencies.
The note A, (when you hear an orchestra tuning up, it’s the note they play at the beginning) is 440 hertz, which means it’s a wave that goes up and down 440 times per second. If you took a slow-mo image of a guitar string playing an A, you’d see it go up and down 440 times per second.
In AM radio, we transmit the “A” by changing the strength of the “carrier wave” which is the number you tune on the radio, 440 times per second. So you tune into AM570, well, if it’s playing an A, that 570 carrier frequency is getting louder and softer 440 times a second, which your radio decodes into an A and plays it.
Back to our guitar chord. We have three frequencies, A 440 Hz, C# at 555 Hz, and E at 660 Hz (these are all just musical notes, doesn’t matter too much which notes we pick). We then need to vary the carrier signal by a combination of all those frequencies, which leads us to have to have increased bandwidth. The more frequencies we add (like by a lot of people talking, an entire orchestra) then you need more bandwidth.
Interestingly, Morse code is great because it doesn’t need a lot of bandwidth, just the single tone it’s transmitting at, which is why a lot of ham radio operators (like me) use it still, as it can easily cut through interference, and you need less power to transmit longer distances.
hope that helps! Radio is tons of fun!
The transmission of AM is actually on quite narrow band. Technically, it can’t be exactly a single frequency because the modulation of the carrier — even if it only varies the amplitude — can also be understood as linear combination of frequencies around the carrier waveform, even if the bandwidth is quite narrow relative to the carrier frequency.
It comes from trigonometric identities such as this: sin(a + b) = sin(a)*cos(b) + cos(a)*sin(b). If a is the carrier and b is the signal waveform, and you can interpret modulation as sin(a + b) + sin(a – b) = sin(a) * cos(b). The right hand side of the equation is actually the modulation of carrier waveform a with signal b, and it looks indistinguishable from linear combination of two frequencies, a+b and a-b. Thus to carry 10 kHz signal you’d need 20 kHz bandwidth to do it around the carrier frequency — can’t escape the math.
Also, nobody is going to place radio stations 20 kHz apart even if they only had to carry up to 10 kHz sounds. In order to receive one station, you’d require incredibly good filter that hears exactly the very narrow bandwidth around the center frequency and that is practically hard. It might be doable digitally using modern technology, I guess, but not analog crap equipment of yore.
When you change the amplitude at different times, you *make* different frequencies. Take a pure frequency, AM-modulate it, then in the output of the modulation, analyze the frequencies, and you will discover there’s more than one frequency in it.
Fourier theorum says that any wave shape can be recreated as a combination of pure frequencues.
With AM radio, you vary the amplitude of a single pure carrier frequency. With Fourier theorum you could also create the same wave shape by mixing several frequencies together.
The fact is, they are equivalent. If you put a spectrum analyser on the signal you would see all those frequencies appear. The range between the min and max frequency is the bandwidth.
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