1

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

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.

Dan
  • 311
  • 1
  • 8
  • 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. – user10489 Feb 22 '22 at 06:00
  • 1
    I had exactly the same questions (https://ham.stackexchange.com/questions/12029/finding-an-intuitive-explanation-of-mixer-theory/12040) 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"!! – Buck8pe Feb 22 '22 at 12:58
  • 1
    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." – hotpaw2 Feb 22 '22 at 17:50

4 Answers4

2

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.

GodJihyo
  • 252
  • 1
  • 2
  • 5
  • 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 '22 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. – Buck8pe Feb 22 '22 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 '22 at 15:23
  • @Dan To understand it you really need to understand the math, otherwise you just have to accept that that's how it is. Here is the math: https://en.wikipedia.org/wiki/Amplitude_modulation#Analysis – GodJihyo Feb 22 '22 at 15:47
  • The right hand image on the link you provided shows the AM signal as ONE signal with a fixed frequency, only its amplitude is changing. If I sample this frequency at it's centre (sample the carrier wave itself), will I see a fixed amplitude or will I see it changing? – Dan Feb 22 '22 at 16:33
  • @Dan It's a tough subject to understand and a difficult one to visualize, so I understand your confusion. But, when "only the amplitude is changing" then the signal is composed of the carrier frequency at a fixed amplitude and two separate sideband frequencies (above and below the carrier) at a lower amplitude. And it isn't some mumbo-jumbo mathematical abstraction, the signal actually contains energy at those frequencies. – Buck8pe Feb 22 '22 at 16:46
  • 1
    @Dan: don't think of what's being generated. Think of what's being received. – hotpaw2 Feb 22 '22 at 16:48
  • @Buck8pe Assume we have a carrier signal at a fixed frequency. I mix it with my voice and output a final signal. I send this final signal to my antenna. At any given time the electrons of the antenna go up and down the antenna at a certain frequency and amplitude based on the final signal. But at any given time there can only be a unique wave emitted at a certain frequency, how can there be 3 separate waves at 3 different frequencies at the same time? I'm not sure if I'm getting my confusion across. – Dan Feb 22 '22 at 17:07
  • @Dan Your assumption that an antenna can only radiate one frequency at a time is incorrect. We use combiners to put multiple transmitters using different frequencies on one antenna all the time. Repeaters receive on one frequency and transmit on another simultaneously using the same antenna. Even in audio there are multiple frequencies coming out of the speaker at the same time. – GodJihyo Feb 22 '22 at 17:23
  • @Dan : your assumption still appears to be that you (or the electrons) can tell the difference between 1 modulated wave, and 3 unmodulated waves mixed/summed. With AM modulation you can't. Neither can the electrons. – hotpaw2 Feb 22 '22 at 17:31
  • 1
    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. – hotpaw2 Feb 22 '22 at 17:36
  • @hotpaw2 Right, so wether it's a single mixed signal, or 3 unmixed signals, the electrons in the antenna are going up and down together, at a certain amplitude/frequency at a given time. It's not like half the electrons go at one frequency and the other half move differently, that's just impossible (i think). The antenna is sending a single wave, the receiver however can distinguish between the waves central carrier frequency and the extra data added to it as "side band". But it's all one wave from the sender to the receiver, not 3 waves on 3 separate frequents. Is that right? – Dan Feb 22 '22 at 17:46
  • It's not "not" if the transmitter electrons can't tell the diff between 1 varying force, and 3 forces that sum to the same (varying) electron acceleration. They are clueless. Same with the reception of the RF EM photons by the electrons in the receiver antenna. – hotpaw2 Feb 22 '22 at 17:53
  • "*that sum to the same electron acceleration*" that's the key sentence. Then it can't be 3 separate waves being emitted at once, its' just that the "separate waves" can be distinguishable by the receiver. – Dan Feb 22 '22 at 18:01
  • If you are an electron, how, at a modulation peak, can you tell whether you were hit with 2 Volts of EMF, or the sum of a 1 Volt field plus two 0.5 Volt fields at the same time? Or at the modulation trough, hit with nothing, or a 1 Volt field going one way, plus two half Volt fields going the other way? So how can you, the electron, say you weren't hit by one combo, but were by the other possible combo ??? – hotpaw2 Feb 22 '22 at 18:02
  • Im agreeing with you on your point :D all i'm saying is that, based on your comment, there can only be a single single (as the electrons are all moving together). – Dan Feb 22 '22 at 18:07
  • Due to both QM and a non-zero temperature, the electrons are not moving together. Their motions average together to the same as 3 types of motions, or one changing type motion, which statistically look the same to any observer. e.g. at any given time, some percentage of electrons are probably going the "wrong" way. – hotpaw2 Feb 22 '22 at 18:10
  • You can't say there aren't 3 waves (in superposition) being emitted if no physical experiment (or mathematical calculation) can tell the difference. Similar to special relativity or General Relativity. – hotpaw2 Feb 22 '22 at 18:24
  • Does this "phenomena" happen when every type of frequency and modulation? i.e AM/FM or even an unmodulated signal, do all have sidebands like this? If you emit just the AM carrier wave without mixing it with anything will it still have a sideband? – Dan Feb 22 '22 at 18:27
  • Any finite duration signal (less than the lifetime of the universe and beyond) has sidebands (it's part of the mathematics of the support of distributions, and of transforms). The shorter the signal (even a "pure" sine wave), the wider the sideband support. – hotpaw2 Feb 22 '22 at 21:51
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/134362/discussion-between-hotpaw2-and-dan). – hotpaw2 Feb 22 '22 at 23:22
1

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.

hotpaw2
  • 13,116
  • 6
  • 40
  • 72
  • 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 '22 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. – hotpaw2 Feb 22 '22 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). – hotpaw2 Feb 22 '22 at 17:02
  • 2
    @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. – hobbs - KC2G Feb 22 '22 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. – hotpaw2 Feb 22 '22 at 17:05
  • @Dan : An AM transmitter doesn't have to transmit on 3 frequencies at once. It only has to modulate 1 single frequency. Which then produces in a receiver the identical effect of 3 frequencies when the spectrum is averaged by an FFT or demodulator filter. – hotpaw2 Feb 22 '22 at 17:11
  • ahh there we go, so then it does NOT emit 3 separate frequencies, it emits a SINGLE mixed frequency (mix of carrier wave and my voice lets say), however if you sample it on the receiver side it could be as if it was sent with 3 different frequencies? – Dan Feb 22 '22 at 17:13
  • Whether it emits or not, 2 **identical** types of signals is a question for philosophy ( Is 1+1 really the same as 2 ?). In DSP, if you have a hammer (Fourier math or an FFT), every thing is a nail (spectrum with sidebands). – hotpaw2 Feb 22 '22 at 17:17
1

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.

user10489
  • 5,496
  • 1
  • 9
  • 22
  • "*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 '22 at 23:36
  • When you change the frequency, the bandwidth will be the range of frequencies that are covered. – user10489 Feb 22 '22 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 '22 at 23:56
  • Would you agree with the above comment? – Dan Feb 23 '22 at 00:34
  • 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. – user10489 Feb 23 '22 at 00:39
  • But going back to my original question which started this post, the signal has multiple frequencies packed into it and then you feed that to an antenna. Now I freeze time and look at the electrons in the antenna. At this very moment of frozen time, are multiple frequencies being emitted from that antenna? Remember we had multiple frequencies in that signal. Comparing them with time, how are they being emitted into air? that's what I keep asking here. If all electrons are moving at the same speed in that antenna given a slice of time then how can different frequencies get emitted at once? – Dan Feb 23 '22 at 00:51
  • When you freeze time, there is no signal anymore. For there to be a signal, there must be time. At best, you could sample the voltage on a receive antenna. One sample gets you nothing. You have to take multiple samples at at least 4x the frequency you want to observe to see anything. – user10489 Feb 23 '22 at 00:53
1

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.

Complex wave and Fourier Components

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.

wbg
  • 301
  • 1
  • 10
  • 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: https://physics.stackexchange.com/questions/696066 – Dan Mar 02 '22 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 02 '22 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 02 '22 at 17:03