# Sidebands in AM Transmission

1. Jan 31, 2013

### Staff: Mentor

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?

2. Jan 31, 2013

### nsaspook

Last edited by a moderator: Sep 25, 2014
3. Jan 31, 2013

### Staff: Mentor

Thanks for the links, but I'm not seeing anything about where the sidebands come from.

Last edited by a moderator: Sep 25, 2014
4. Jan 31, 2013

### nsaspook

5. Jan 31, 2013

### Staff: Mentor

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:
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.

Last edited: Jan 31, 2013
6. Jan 31, 2013

### Staff: Mentor

7. Jan 31, 2013

### marcusl

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.

8. Jan 31, 2013

### Staff: Mentor

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"?

9. Jan 31, 2013

### cepheid

Staff Emeritus
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?

10. Jan 31, 2013

### cepheid

Staff Emeritus
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

11. Jan 31, 2013

### Staff: Mentor

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.

12. Jan 31, 2013

### cepheid

Staff Emeritus
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.

13. Jan 31, 2013

### cepheid

Staff Emeritus
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.

14. Jan 31, 2013

### Staff: Mentor

Ah ok, just like when you look at the spectrum on a spectrum analyzer and it shows the sidebands.

Nah, I'm good. The single frequency is just a "special case" I'm assuming.

15. Feb 1, 2013

### 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. 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.

16. Feb 1, 2013

### Staff: Mentor

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?

17. Feb 1, 2013

### rcgldr

It might help to note that components of a sine wave undergoing a change in amplitude appear similar to a higher or lower frequency sine wave of fixed gain (steeper or milder ramp rates near the crossover point). The rate of change in the gain determines the bandwidth consumed by the modulated signal. Morse code AM transmistters, which turn signals on and off, are designed to take 5 ms to switch the signal on and off, in order to reduce the bandwidth.

Last edited: Feb 1, 2013
18. Feb 1, 2013

### nsaspook

Signal Decomposition, used to analyze a signal.
http://users.ece.gatech.edu/~vkm/nii/node35.html [Broken]

Yes, the sideband frequencies are actually transmitted along with the carrier (the actual carrier average power does not change during AM modulation).

http://www.technology.heartland.edu/faculty/chrism/data comm/am modulation.ppt

Last edited by a moderator: May 6, 2017
19. Feb 1, 2013

### sophiecentaur

There is a parallel with vectors. You can 'decompose' a vector into two components along two arbitrary axes and that may make a problem easier to solve.

But the easiest way to show how AM produces sidebands is to start with a formula which describes Amplitude Modulating a carrier wave with angular frequency ωc with a cosine modulating signal of frequency ωm does:
A =A0Cos(ωct)(1+Bcos(ωmt))

A0 is the mean amplitude of the carrier and B is the Modulation Index - the depth of modulation.

This will give you the familiar picture of a carrier amplitude varying in level, as the modulation varies, and around its unmodulated amplitude. (The envelope picture). That expression can be transformed, using the basic multiple angle trig identities into
A = A(cos(ωc) + Bcos((ωmc)/2 + B((ωmc)/2)
which shows you that the AM signal can be described as a carrier and a pair of sidebands that have up to half the amplitude of the carrier.
You don't need to do any Fourier analysis for this - in the simple case, it's just a bit of simple trig. And, if you don't like trig, then steer clear of Fourier - it's harder still.

20. Feb 1, 2013

### Staff: Mentor

My god what have I gotten myself into!? This is why I don't ask questions! I get amazing answers that show me how ignorant I really am! I think I'll take some of the advice I see you give around the forum Sophie. I'll hold off on running until I can walk in this area. (Or in my case, roll over and crawl first)

Thanks guys! I don't quite understand, but I'm definitely better off than I was before.

21. Feb 1, 2013

### nsaspook

Fourier analysis is complex when looked at from the viewpoint of pure mathematics but it's how our ear/brain works so it's a natural way of analyzing complex events. The inner ear is an approximation of Fourier analysis as it separates the sound energy using nerve structure filters that each only respond to a narrow range of vibrations. The brain receives the Fourier Transform of the acoustical signal, phase and intensity information and then somehow generates the patterns that we recognize as sounds.

22. Feb 2, 2013

### sophiecentaur

It's a bit simplistic to say that our hearing receives the FT. The cochlea does a time varying frequency analysis. Both time and frequency domains are perceived. FT is just a mathematical process relating the two domains yet is often quoted in cases where it just isn't that straightforward. Windowing is very relevant in practice.

23. Feb 2, 2013

### nsaspook

Agreed, I did say it was an "approximation of Fourier analysis", our hearing is a blend of several methods.

http://clas.mq.edu.au/perception/psychoacoustics/hearing_theory.html

Last edited: Feb 2, 2013
24. Feb 2, 2013

### sophiecentaur

I think the big problem arises when we attempt to describe what the brain / sensor combination 'actually does' with its input, using the same terms that we use to describe how we would make a recording or perform signal analysis using technology.
The same difficulty arises when describing our visual perception, where the temptation is to think that the camera-like structure of the eye's hardware gives the remotest clue about how we make a conscious model of our surroundings in our heads.
I think this thread would be better to stick to the basics of signal processing, where we do have a chance of understanding what goes on. At least the Maths is appropriate and fits the evidence.

25. Feb 2, 2013

### nsaspook

Not always. :shy: