# Sidebands in AM Transmission

by Drakkith
Tags: sidebands, transmission
 PF Patron P: 10,397 Say you are transmitting AM radio signals. You input an audio signal of 1khz which is used to modulate a signal of 1 mhz. The heterodyning process outputs 4 different frequencies, the audio, carrier, sum, and difference. But where are the sum and difference? If I look at a graph of the modulated waveform, I can see the carrier and the audio (as amplitude variation in the carrier), but where are the other two? The sidebands as they are also known. I'm not seeing how you add and subtract the frequencies if you are using the audio signal to modify the amplitude of the carrier. When you transmit the signal from your antenna, are you sending power through the two sidebands as well, or only on the main carrier frequency?
 P: 386 When you measure a modulated waveform there are several ways to picture the changes. If you only look at the time vs level domain it's hard to see the changes. What you need is a way to see the other domains of the signal. http://www.naic.edu/~phil/hardware/M...r_basis_of.pdf https://www.youtube.com/watch?v=Lp6sT-n55N4 With today's electronics some pretty cool stuff can be made for cheap. http://www.youtube.com/watch?v=ZuRcaxpbYCw
PF Patron
P: 10,397
 Quote by nsaspook When you measure a modulated waveform there are several ways to picture the changes. If you only look at the time vs level domain it's hard to see the changes. What you need is a way to see the other domains of the signal. http://www.naic.edu/~phil/hardware/M...r_basis_of.pdf https://www.youtube.com/watch?v=Lp6sT-n55N4
Thanks for the links, but I'm not seeing anything about where the sidebands come from.

P: 386

## Sidebands in AM Transmission

 Quote by Drakkith Thanks for the links, but I'm not seeing anything about where the sidebands come from.
http://www.home.agilent.com/owc_disc...%20103-104.pdf

You can't normally see side-band signals with a time-domain display.
PF Patron
P: 10,397
 Quote by nsaspook http://www.home.agilent.com/owc_disc...%20103-104.pdf You can't normally see side-band signals with a time-domain display.
I think there's a misunderstanding. I don't want to "see" the sidebands, I want to understand how they are created when mixing two signals together.

Ok, that's interesting. According to the link:
 An AM signal is really a composite signal formed from several components: the carrier sine wave is added to the upper and lower sidebands, as the equation indicates.
That makes sense. However I think I'm failing to understand how changing the amplitude of the carrier creates two different frequencies in addition to the original two. It's just not "clicking" I guess.
 Mentor P: 37,668 See if post #4 in this thread by the_emi_guy helps: http://www.physicsforums.com/showthread.php?t=606315 .
 PF Patron Sci Advisor P: 1,998 An ideal mixer multiplies two signals. Use trig identities to write cos(fm)*cos(fc) = cos(fm+fc) + cos(fm-fc)] / 2 A real mixer is non-ideal and allows some of fc to leak through to the output. (Leakage of fm is far away and is filtered out). Real mixers also produce harmonics and high-order mixing products, which again are filtered away.
 PF Patron P: 10,397 Maybe this is a bad question, but are the sidebands actually propagating outwards from the antenna along with the modulated carrier? Or is this just something that happens when you "do the math"?
Mentor
P: 5,194
 Quote by Drakkith Maybe this is a bad question, but are the sidebands actually propagating outwards from the antenna along with the modulated carrier? Or is this just something that happens when you "do the math"?
A sideband of a modulated signal is a feature of the frequency spectrum of that signal. So, it is something that exists in the frequency domain (also sometimes called "Fourier space") not in the time domain, or real space. Are you familiar with Fourier analysis?
Mentor
P: 5,194
 Quote by Drakkith That makes sense. However I think I'm failing to understand how changing the amplitude of the carrier creates two different frequencies in addition to the original two. It's just not "clicking" I guess.
It's not just that you're creating two different discrete frequencies.

The modulating signal (the one that contains the actual information content) already contains a whole continuous spectrum of frequencies. It's a theorem from Fourier analysis that you can represent an arbitrary time-variable signal as a sum* of sinusoids of different frequencies and amplitudes. So that information signal contains a continuum of frequencies, from 0 up to some maximum frequency (that defines the bandwidth). You would see this if you were to look at the frequency spectrum of the signal (which you do by taking its Fourier transform). Anyway, what multiplying this signal by the carrier does is simply to shift the frequency spectrum so that instead of one spectrum being centred on zero, there are now two identical such spectra centred on +carrier frequency and -carrier frequency. To see why this is, you'd need to understand more about Fourier transforms and convolution.

*I use the term "sum" loosely, it's actually an integral called an inverse Fourier transform
PF Patron
P: 10,397
 Quote by cepheid A sideband of a modulated signal is a feature of the frequency spectrum of that signal. So, it is something that exists in the frequency domain (also sometimes called "Fourier space") not in the time domain, or real space. Are you familiar with Fourier analysis?
Barely. I don't know any details on it and I've never had to work with it.

You say it doesn't exist in real space? Could you elaborate? I'm unfamiliar with frequency domain as well. If this is too complicated without understanding both frequency domain and fourier analysis just say so.
Mentor
P: 5,194
 Quote by Drakkith Barely. I don't know any details on it and I've never had to work with it. You say it doesn't exist in real space? Could you elaborate? I'm unfamiliar with frequency domain as well. If this is too complicated without understanding both frequency domain and fourier analysis just say so.
The frequency spectrum of the signal is just a plot in which the y-axis is power and, and x-axis is frequency, so that the plot is telling you how much power your signal contains at each frequency. (Just like when you look at a plot of the spectrum of a source of EM radiation).

A sideband is a feature on this plot. The upper sideband is the portion of the spectrum that lies above the carrier frequency, and the lower sideband is the portion of the spectrum that lies below the carrier frequency.
 Mentor P: 5,194 I just read the OP and saw that you were considering a simpler case where the modulating (information-containing) signal is also just a sinusoid at a single frequency. Sorry, I hope I haven't confused things by talking about a more general case with a broadband spectrum.
PF Patron
P: 10,397
 Quote by cepheid The frequency spectrum of the signal is just a plot in which the y-axis is power and, and x-axis is frequency, so that the plot is telling you how much power your signal contains at each frequency. (Just like when you look at a plot of the spectrum of a source of EM radiation). A sideband is a feature on this plot. The upper sideband is the portion of the spectrum that lies above the carrier frequency, and the lower sideband is the portion of the spectrum that lies below the carrier frequency.
Ah ok, just like when you look at the spectrum on a spectrum analyzer and it shows the sidebands.

 Quote by cepheid I just read the OP and saw that you were considering a simpler case where the modulating (information-containing) signal is also just a sinusoid at a single frequency. Sorry, I hope I haven't confused things by talking about a more general case with a broadband spectrum.
Nah, I'm good. The single frequency is just a "special case" I'm assuming.
 P: 386 One way to look at the creation of sideband frequencies is to work the problem in reverse. A function (signal) can be decomposed into purely sinusoidal components. You want to create a AM single frequency modulation time-domain display on your oscilloscope display. To create this display you have RF frequency generators and a summing network. What set of frequencies would you have to set the RF generators to recreate the AM modulation display.
PF Patron
P: 10,397
 Quote by nsaspook One way to look at the creation of sideband frequencies is to work the problem in reverse. A function (signal) can be decomposed into purely sinusoidal components.
I understand most of that, however what exactly does "decomposed" mean? Is this something that you do when the signal gets to the receiver, or are there actually two different frequencies in addition to the carrier that are being transmitted from the antenna which interfere and cause the carrier to vary in amplitude?

 You want to create a AM single frequency modulation time-domain display on your oscilloscope display. To create this display you have RF frequency generators and a summing network. What set of frequencies would you have to set the RF generators to recreate the AM modulation display.