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Homework Help: A simple waveform help please

  1. Jul 16, 2005 #1
  2. jcsd
  3. Jul 16, 2005 #2

    OlderDan

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    As an absolute value of something, or as a piecewise definition for each of the intervals that has a continuous derivative.
     
  4. Jul 16, 2005 #3
    I'm sorry i do not follow. I understand if it was just a ramp function it would just be (Vm/T) t but i still dont know
     
  5. Jul 16, 2005 #4

    OlderDan

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    The last waveform is called a Full-wave rectified sine. It is a sine function with all the negative regions flipped to positive. It is the absolute value of the sine function

    [tex] f(x) = \left| {A\sin 2\pi \frac{t}{T}} \right| = A\left| {\sin 2\pi \frac{t}{T}} \right| [/tex]

    or you could write separate functions for the separate intervals with alternating plus and minus signs in front of the sine function.
     
  6. Jul 16, 2005 #5
    i see.. so am i correct to say that the equation for f(x) for the third waveform would be Asin(4pi/T)?
     
  7. Jul 16, 2005 #6

    OlderDan

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    No. For one thing you need a variable, t, in the argument of the sine function (T is a constant) and you need to define the function to be zero in the intervals where the waveform is zero. One way to do that would be to take 1/2 times your second waveform and add A/2 so that the square wave is between 0 and A; then use that in place of the A in the sine function you have.
     
  8. Jul 17, 2005 #7
    for the full rectified sine wave, the equation for f(t) from 0 to T/2. can it not have a sin in the equation maybe something like A(1-t^2)? (i know that's incorrect)
     
  9. Jul 17, 2005 #8
    anyone? :(
     
  10. Jul 18, 2005 #9

    OlderDan

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    I'm not sure what you are asking. For the full-wave rectified sine the function is a sine function from 0 to T

    [tex] f(x) = A\sin \pi \frac{t}{T}} [/tex]

    Between T and 2T it is

    [tex] f(x) = -A\sin \pi \frac{t}{T}} [/tex]

    There is no 1-t^2 involved
     
  11. Jul 18, 2005 #10

    OlderDan

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    CORRECTION!

    Sorry, I misinterpreted the T as being the period of the sine function. In fact 2T is the period in the figure. This should have been

    [tex] f(x) = \left| {A\sin \pi \frac{t}{T}} \right| = A\left| {\sin \pi \frac{t}{T}} \right| [/tex]
     
  12. Jul 18, 2005 #11

    OlderDan

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    From 0 to T/2 or from nT to (n+1/2)T this should be

    [tex] f(x) = {A\sin 2\pi \frac{t}{T}} [/tex]

    From T/2 to T or from (n+1/2)T to (n+1)T f(x) is zero.
     
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