Sidebands in AM Transmission

  1. Drakkith

    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. jcsd
  3. Last edited by a moderator: Sep 25, 2014
  4. Drakkith

    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
  5. Drakkith

    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.

    Edit: Whoops, just noticed the link. Reading it now.

    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. berkeman

    Staff: Mentor

  7. marcusl

    marcusl 2,120
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    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. Drakkith

    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. cepheid

    cepheid 5,193
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    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. cepheid

    cepheid 5,193
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    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. Drakkith

    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. cepheid

    cepheid 5,193
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    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. cepheid

    cepheid 5,193
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    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. Drakkith

    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. 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.

    [​IMG]
     
  16. Drakkith

    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?

    Are you asking me?
     
  17. rcgldr

    rcgldr 7,523
    Homework Helper

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

    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
     
  19. sophiecentaur

    sophiecentaur 13,705
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    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. Drakkith

    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.

    Nsaspook, thanks for the links, they were pretty helpful!
     
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