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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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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Anonymous 0 Comments

Broadcasting on a very specific and narrow range means the receiver must be on *exactly* that specific and narrow range. This would be a pain in the ass.

Broadcasting on a slightly larger range means the receiver only needs to be within that slightly larger range. This is easier.

Anonymous 0 Comments

The only way to transmit on a single, precise frequency is to emit a perfect sine wave of constant amplitude. If the signal changes in amplitude, as required by AM radio transmission, then the signal is a no longer a single frequency, but a mixture of frequencies. The more rapidly the amplitude changes, the wider the range of frequencies that are mixed to produce the final signal.

The math that shows how this works is complex, but the result is simple. If you want to modulate an AM carrier wave with a 10Hz signal, you will need at least 10Hz of bandwidth. (Note that the simplest way to amplitude modulate a carrier wave with a 10Hz signal will use of 20 Hz of bandwidth.)

Anonymous 0 Comments

Take a look at this: it’s the sum of two sine waves very closely spaced in frequency:

https://www.wolframalpha.com/input?i=sound+sin%282+pi+200+t%29+%2B+sin%282+pi+204+t%29

(You can look at the graph or click “play sound” to hear it.)

As time goes on, the two waves move in and out of phase, creating a [“beat frequency”](https://www.physicsclassroom.com/class/sound/Lesson-3/Interference-and-Beats): the sine wave’s amplitude changes over time.

So, two closely-spaced frequencies are mathematically identical to an amplitude-modulated sine wave. And this goes both ways: all amplitude-modulated waves must be constructed from two or more pure frequencies.

So modulating the amplitude of a sine wave inevitably “spreads out” its frequency distribution into nearby frequencies. You can prove mathematically that the rate of information transfer in your amplitude-modulated wave is proportional to the width of the frequency band it occupies.

https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem

Anonymous 0 Comments

Let’s say you want to transmit speech via AM. You take that audio signal and modulate it onto the “single, precise frequency” which is your carrier frequency. By doing that, which is adding the actual information you want to transmit to the carrier, you modify the waveform. The resulting waveform will look different from the unmodulated carrier if you “draw” it on paper, and that’s true for both a time diagram as for a frequency diagram. The resulting signal contains a range of frequencies depending on the frequency range of the audio signal transmitted. While it’s not the full mathematical picture, imagine modulating a 1000 Hz sine wave onto the carrier with AM: you’ll see the faster carrier changing amplitude in a sinusoidal fashion with the frequency of 1000 Hz. If you go look at the signal in the frequency domain, you don’t have only the carrier’s frequency, the 1000 Hz also need to show up in some form.

A single, precise frequency does not carry any information, or the other way around, transmitting information requires bandwidth.

Anonymous 0 Comments

Because one single frequency cannot transmit any information.

The signal would only contain a single frequency, if that frequency does not change in any way – the same amplitude, the same phase. Of course, unchanging signal cannot carry information.

If you change the signal in any way – it will create sidebands: frequencies slightly above or below the base frequency. The faster you change the signal – the wider the sidebands will be. Switching the signal on/off also counts: the faster you switch – the wider the sidebands will be.

Those sidebands are not some side effect that can be filtered out – they are fundamental to the change. If you filter them out – all the change in the signal (and all information) disappears.

Anonymous 0 Comments

A single, precise, continuous signal contains no information or, at best, a single bit of information. Even morse code, which is just turning the carrier signal on and off at short intervals, uses a small amount of bandwidth. The reason is that, as a signal transitions from zero to a pure sine wave, it consists of other frequencies; an instant transition means an infinite range of frequencies are generated.

For morse, it’s necessary to limit the rate at which the signal goes from off to on to limit the spread of frequencies used. Faster morse needs faster transitions which uses more bandwidth. In the same way, the higher frequency audio you mix with a carrier wave, the more bandwidth the signal will occupy.

AM is the multiplication of the carrier wave with the audio signal. One piece of maths that can help understand what happens is the formula for multiplying two different frequencies:

sin(*a*)×sin(*b*)=0.5[cos(*a*−*b*)−cos(*a*+*b*)].

Now cosine is just sine with a phase change of 90° so this formula tells you that multiplying two frequencies generates a signal with both the sum and difference of the original frequencies. You send a 1 kHz tone over a 1 MHz AM transmitter and you’ll generate both a 999 kHz and 1001 kHz signal.

Anonymous 0 Comments

What any broadcast system is going to have trouble with is that is it not possible to filter one single frequency from the other broadcasts next to it on the dial. This is because the frequency filters in a radio receiver can not be that accurate as the environment around the radio receiver changes capacitance and the transmitted signal changes frequency slightly when it bounces off surfaces on the way to the receiver.

Anonymous 0 Comments

I think most answers here just complicate things instead of getting to the root of the question.

>Why does an AM radio channel require any bandwidth at all?

The simple answer would be: because the information you’re trying to transmit (generally voice or music) is, even without modulation, a waveform made of a lot of different frequencies. For example, you need at least a bandwidth of 4 kHz (from around 20 Hz to 4000 Hz) for voice to be intelligible.

You can, in fact, transmit a SINGLE continuous tone using AM modulation. That would require essentially no bandwidth (at least, mathematically speaking it would be infinitesimal), but that transmission would be useless because the whole point of communications is to transmit a *random*, *varying* piece of information.

Anonymous 0 Comments

If you transmitted a CW (continuous wave) sine wave it would be a single precise frequency. But as you start modulating it, you are deforming the sine wave and that introduces side band frequencies.

Anonymous 0 Comments

It can! You have discovered CW or continuous wave transmission! You can key the signal on and off to transmit your message.

A hello might look a little something like this:

-.-. –.- -.-. –.- -.-. –.-