# How can an RF coil emit at 3 different frequencies at the same time during Amplitude Modulation?

This image shows how an AM wave is generated and emitted:

This comment explains how 3 separate waves are sent at once to represent an AM wave:

the transmitter does not transmit one pure sine wave at one single frequency, it transmits a narrow spread of different frequencies with the unmodulated carrier at the center of the range and the sidebands flanking it.

My question is, if there is a single RF coil oscillating at a certain frequency (let's say 50Hz to keep things simple), how can it also create side bands at different frequencies? It just seems physically not possible.

Electrons are moving up and down the transmitter antenna 50 times a second and emit a wave in space, but there is also a signal at 51 and 49Hz? How are they being generated at the same time? The coil is not oscillating at those frequencies. I can't wrap my head around it.

• Basically, the world is much more complex than just a single sine wave. You hear multiple frequencies at once with music, why not with radio waves too? I feel the above diagram needs a nice animation showing the frequencies all being added in. Feb 22, 2022 at 6:00
• I had exactly the same questions (ham.stackexchange.com/questions/12029/…) and I found it difficult to find a suitable "intuitive" explanation. I find the usual trig identities answers unsatisfying. Some good answers on that page (my rambling in-cohesive one isn't one of them!) I think I understand it better now, but it's still hard to explain it in "plain English"!! Feb 22, 2022 at 12:58
• It's also a problem to assume that the universe might fit your requirements for having a personally "intuitive" explanation. Try quantum mechanics, or string theory, or the "curved" space-time required by general relativity, to convince you otherwise. More than one Nobel prize winner has said the equivalent of "shut up and calculate". "Use the trig, Luke." Feb 22, 2022 at 17:50

First off, an RF coil does not oscillate. It can have an oscillating current in it, but it is just one part of an oscillator circuit.

In an AM transmitter, the sidebands are not generated in the oscillator. The oscillator generates a single frequency, this frequency is then mixed with the audio frequencies in a non-linear device such as a diode or transistor. This is where the sidebands are generated.

• Right, but the "combined" signal should be running on one frequency, i.e after they are mixed I would expect a single signal on a single frequency is being emitted form the antenna. I can't get how the other 2 frequencies are being generated. Math formulas aren't helping.
– Dan
Feb 22, 2022 at 14:17
• @Dan The combined or mixed signal can't be running on one frequency. If there was one frequency how would you transmit any "intelligence"? I think you are able to visualize the AM carrier with it's amplitude varying up and down (as per your image). What you may not understand is that this variation in amplitude gives rise to sideband frequencies. So, if you analyze this amplitude modulated signal, you'll actually find a carrier and sidebands. That's what the image you posted is trying to tell you. Feb 22, 2022 at 14:35
• Well I would assume the "amplitude" change happens on the same carrier frequency. Why would it generate a separate frequency, maybe the answer is "that's how nature works" ? still can't picture it tho.
– Dan
Feb 22, 2022 at 15:23
• @Dan: don't think of what's being generated. Think of what's being received. Feb 22, 2022 at 16:48
• Now with quantum mechanics, you might ask what frequency RF photons are being emitted by the antenna. But the QM uncertainty principle probably says that you can't statistically tell the difference between 3 slightly different energies of photons, sometimes cancelling each other out, due to phase, and 1 energy of photon coming at a varying rate. Likely, the electrons in your antenna are similarly confused. Feb 22, 2022 at 17:36

It's a mathematical equivalence. One of the trigonometric identities. If you amplitude modulate a sine wave, or sum 3 pure sinewaves of certain frequencies and amplitudes together, you get exactly the same result. Exactly the same mathematical result, or exactly the same electron motion (or EM field deltas).

So you just can't tell any difference between whether the coil is or isn't oscillating at 3 different frequencies summed together, versus what seems to be just 1 amplitude modulated frequency, if both produce exactly the same measurable result, due to the mathematical equivalence. It's like asking if 1 + 1 is really 2 or not.

Which isn't back and forth by exactly the same amount each and every cycle. So any single frequency pure sine wave (identical in amplitude each cycle) can't be the correct mental model.

If it makes your brain hurt less, you can say that the transmitter isn't really transmitting 3 different frequencies, but since the transmitted result is mathematically identical to one that is, any receiver, spectrum analyzer, or FFT display is free to "choose" to display the resulting signal as 3 sine waves, even if your brain "chooses" the alternate representation.

Or: Don't think of the 3 frequencies as being generated by the transmitter. Think of them as what is being received thought 3 extremely narrow filters, due to the changing effects of the modulation. The peaks of the resulting modulation will tickle a receiver filter at the carrier frequency. But the modulation peaks will also tickle a receiver filter one cycle too fast, and a filter that is one cycle too slow (a frequency that has one cycle less between modulation peaks). The troughs, being smaller won't cancel out the peaks (unlike with a completely orthogonal frequency filter). So the peaks of the amplitude modulated signal will tickle 3 filters of different frequencies, and look to those 3 filters exactly like as if 3 transmitters were transmitting on 3 slightly different frequencies.

• but here's the question. If I only sample the centre frequency (AKA the carrier wave) using GQRX or any other software, will I see a a constant amplitude or not? if it's constant then how is the transmitter sending multiple frequncies at once? this is so weird. In FM, the frequencies change but they are transmitted in different time slots, but AM is tramissitng all separate frequencies at once. Just doesn't make sense.
– Dan
Feb 22, 2022 at 16:56
• Constant or not? Depends on the time period over which you average each observation (e.g. the length of the FFT used, and whether the FFT results are averaged, or individually reported). Averaging hides a lot of detail. Feb 22, 2022 at 16:58
• e.g. if you use short FFTs, and us a debugger on GQRX, and log or print out the result of each individual FFT, you won't see a constant at the center frequency, but the display will mush all those different and changing FFT results into one constant looking blur (actually 3 constant looking blurs). Feb 22, 2022 at 17:02
• @Dan to "only sample the center frequency" you would need a zero-width filter, which would have an infinite delay and thus never tell you anything. A real filter has a bandwidth. And a filter that's able to react on the timescale of the modulating signal will have a bandwidth wide enough to include the sidebands. Feb 22, 2022 at 17:03
• Yup. The computer running GQRX does not have enough memory to run an infinite length FFT (e.g. how may exabytes^Inf is required to fit more than the lifetime of the known universe). Not possible. So filter width has to be finite. Feb 22, 2022 at 17:05

In the real world, there is no such thing as a zero width wall. Similarly, you can't have a radio transmission with zero bandwidth.

Let's say, hypothetically, that you have a transmitter that is only putting out a sine wave. However, if this is a real (i.e., practical) transmitter, it has instabilities that cause its frequency to wobble a teeny bit, so that "single frequency" actually varies around a center frequency and causes the signal to have a bandwidth.

Now, if you want to also transmit information along with this sine wave, you have to modulate the information into the signal. In order for that signal to contain the information, its bandwidth must increase. A transmission with no bandwidth can't contain any information.

This increased bandwidth results in the signal now covering a range of frequencies. The terms "Amplitude modulation" and "Frequency modulation" might imply that the frequency doesn't change, or the amplitude doesn't change, but that's not how it works. Amplitude modulation works by using the audio amplitude to drive the transmission amplitude -- but the frequency also shifts. Frequency modulation uses the audio amplitude to adjust the frequency offset from a center frequency, but the amplitude also changes.

Consider that a transmitter puts a sine wave on an antenna by introducing a sinusoidal varying voltage. When you change the amplitude, you change that voltage from something different from the original sine wave. When you vary the voltage at some frequency (related to the audio signal), you are adding those new frequencies to the sine wave and giving it more bandwidth -- it is no longer just one sine wave at one frequency.

Amplitude, frequency, and phase are all related; when you modulate a signal, you vary all of them through some mathematical relationship, and exactly what that math is depends on the modulation type.

Along with the varying voltage is a corresponding current which may or may not be in phase. The antenna, like all physical things, has a frequency response. The range of frequencies over which the frequency response of the antenna is favorable to transmission is what we call the "bandwidth" of the antenna. As long as the bandwidth of the antenna is greater than the bandwidth of our signal, the antenna will convert our current and voltage waves into radio waves and they will radiate out of the antenna.

You can think of the antenna like a filament in a light bulb. You put power into it and it radiates. Except that the size of the typical radio antenna is a lot closer to the wavelength of the radio wave it radiates than it is with a light bulb.

• "A transmission with no bandwidth can't contain any information" But I thought all you need in case of AM is to change the frequency of a wave itself. Why won't that work? You are literally transmitting alternating data. Same can be used for binary transmission, something like ASK?
– Dan
Feb 22, 2022 at 23:36
• When you change the frequency, the bandwidth will be the range of frequencies that are covered. Feb 22, 2022 at 23:40
• Ok so applying more voltage to my AM signal, by shouting in a microphone or just applying more power to the signal, I am introducing more frequencies into my final signal. That I can now understand. Now the remaining part of my question is, how does the antenna actually transmit a signal with a bunch of frequencies packed into it? The only way I can imagine it is, some electrons are moving faster or slower than other electrons in the antenna hence different frequencies are being emitted at the same time.
– Dan
Feb 22, 2022 at 23:56
• Would you agree with the above comment?
– Dan
Feb 23, 2022 at 0:34
• Added a section on antennas. The antenna barely cares what frequencies are in the signal fed into it. The electrons don't move faster or slower from your signal. Their speed is constant within a medium, and within most conductors, it is near (but slower than) the speed of light in a vacuum. Feb 23, 2022 at 0:39

The wave form is complex. It can be thought of as an infinite number of sine waves that when added together, form a complex wave.

Imagine a sheet of rubber, a vibrating membrane. This membrane can have a single sine wave going down it's X axis, and at the exact same time another frequency and amplitude across it's Y axis.

If you observe the membrane along one side, you'll see a complex wave create from the two frequencies and their amplitudes. There will be constructive and destructive interference which creates the wave form.

A wave is ANY recurring pattern not just sine waves. That means square, triangle and ANY combination of them.

Research the Fourier Series. The Fourier Series says that any series of orthogonal functions can be used to create any function the exception being at the boundaries of the function. That exception doesn't matter here.

• I've asked this question on the physics site which is more specific to what i'm trying to learn, but not many answers yet: physics.stackexchange.com/questions/696066
– Dan
Mar 2, 2022 at 13:26
• Ok, I see the question now. I've worked for a particle accelerator and I have had similar questions. Let me think if I know anything about it still.
– wbg
Mar 2, 2022 at 16:56
• The electrons do not move at different speeds. They bunch up. Those bunches have limit on density b/c same polarity 1/2 spin cannot exist adjacent to each other. Wires have pretty slow velocity factor so there's no real corrections.
– wbg
Mar 2, 2022 at 17:03