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Find V_out given V_in

  1. Apr 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose Vin(t) = 4cos(2pi*t + 20*) + 3cos(4pi*t + 30*) +5sin(5pi + 50*)V and Vin(t) passes through a system with the following transfer function characteristic H(f):
    |H(f)| = 10f + 1 (magnitude response with f in Hz)
    <H(f) = (5*)f (phase response)

    Find V_0(t) of this system as Vin(t) is passed through it.

    2. Relevant equations

    H(f) = Vout(t) / Vin(t)
    H(f) = 1 / (1+j(f/f_b))
    |H(f)| = 1 / sqrt(1 + (f/f_b)^2)
    <H(f) = -arctan(f/f_b)

    3. The attempt at a solution

    I broke Vin(t) into 3 separate terms and found the polar form of each, as well as the particular value for f

    V1 = 4<20*, f1 = 2pi/2pi = 1
    V2 = 3<30*, f2 = 4pi/2pi = 2
    V3 = 1.31<0*,f3 = 0/2pi = 0

    From how I interpret the problem, the statement has a typo and is actually asking for Vout(t). So,

    Vout(t) = H(f)*Vin(t)
    Vout(t) = H(f1)*V1 + H(f2)*V2 + H(f3)*V3

    My problems seems to be that I can not get H(f) from |H(f)| and <H(f). No graph is given. Any advice? Thanks in advance!
  2. jcsd
  3. Apr 8, 2010 #2

    careful: you can't compare apples and oranges. You just need to put Vin in the frequency domain. You have H(f) though:

    H(f) = 1 / (1+j(f/f_b))

    now Vout(f) = H(f)*Vin(f) becomes a problem of doing the inverse transform back to the time domain.
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