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Homework Help: Simple High Pass Filter Problem

  1. Feb 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Given a simple RC high pass filter, I need to find the value of C that will give the output as shown on a scope capture.

    Input Voltage: [tex]2.5 + 10.01cos(\omega t)[/tex] (10.01V wave shifted up 2.5V)
    Output Voltage: [tex]3.46cos(\omega t - 60^\circ)[/tex]
    R = 5k
    [tex]\omega = 2\pi 100[/tex]

    2. Relevant equations

    [tex] V_O = \frac {V_I}{1 + \frac {1}{j\omega RC}}[/tex]

    3. The attempt at a solution

    I'm not sure how to take into account the DC component of the input voltage. I know it will be filtered out in the end, but I would think that it would be needed for the computations. Ignoring the DC component and using phasor notation, I come up with a phase angle of -19.9 equal to a phase angle of -30:

    [tex]3.46\angle60 + \frac {3.46}{(628.32)(5k)C}\angle-30 = 10.01\angle0[/tex]

    [tex]\frac {3.46}{(628.32)(5k)C}\angle-30 = 8.81\angle-19.9[/tex]

    Where'd I go wrong?
  2. jcsd
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