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Amplitude Modulation of a wave

  1. Dec 26, 2014 #1
    1. The problem statement, all variables and given/known data
    I am utterly confused. When I was reading my textbook , I found something unacceptable.


    While deriving an expression for a modulated wave,
    It's been given that
    "A sinusoidal carrier wave can be represented as c (t) = Ac sin
    (ωt + Φ)
    where c (t) is the signal strength of the carrier wave.
    Let m (t) = Am sinωmt represent the message or the modulating signal.
    The modulated signal cm (t) can be written as
    cm= (Ac+Amsin ωmt) sin ωct

    I wonder how's it possible! Shouldn't it be cm (t) = Acsin ωct + Am sinωmt ?

    But then I made an adhoc assumption - which was not satisfactory - but I thought it could be justified from a more rigorous application of mathematics. So, I continued reading

    On the next page, I found something in contrast to my "assumption".
    In the topic "Production of amplitude modulated wave" -
    According to my textbook "Here the modulating signal Am
    sinωmt is added to the carrier signal Acsinωt to produce the signal x (t). This signal x (t) = Am sinωmt + Ac sin ωct is passed through a square law device."

    Now this equation for x (t) is different from the one which was used (in the textbook) earlier.
    What even is happening?
     
    Last edited: Dec 26, 2014
  2. jcsd
  3. Dec 26, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    If the sum of two signals of different frequencies ω1 and ω2 is the input of a linear network, the output would be again the sum of two signals with the same frequencies.
    Using a nonlinear device, one, for example, that produces the square of the input, it will "mix" the frequencies. Expand (Asin(ω1t) + Bsin(ω2t ))2, what do you get? ( there will be components with frequencies of 2ω1, 2ω2, ω12, ω12).
    Semiconductor diodes, transistors have nonlinear characteristics, and can be used for "mixing frequencies"
     
  4. Dec 26, 2014 #3
    Ok.
    So, the problem lies in the arrangement of all that in my textbook..
     
  5. Dec 26, 2014 #4
    They mentioned the result before deducing the expression for the same.
    I got it!
    Thanks!!
     
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