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Finding impedance that is unit step function

  1. May 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider the following circuit which uses ideal components. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the impedance [itex]Z_{2}[/itex] such that the system output is a unit step function of voltage. Be certain to show all components used to construct [itex]Z_{2}[/itex] and their connections along with component values of your design.
    Z1 is Given
    circuit:
    9.jpg

    2. Relevant equations

    KVL, KCL, V=IR,

    3. The attempt at a solution

    Nothing yet. Just wanted to get this up here for now.
     
    Last edited: May 4, 2013
  2. jcsd
  3. May 4, 2013 #2

    rude man

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    The output will not be a UNIT step function unless the input voltage is > 1V.

    The solution furthermore is not unique. You can say pick any R2, then X2 is defined as is the voltage gain < 1.
    Where Z1 = R1 + jX1 and Z2 = R2 + jX2.
     
  4. May 5, 2013 #3
    Ok I understand why the input voltage has to be > 1V. So how should I start this out? Can I connect the two grounds and do a loop equation?
     
  5. May 5, 2013 #4

    rude man

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    The two grounds are already connected, by definition.

    Let Z1 = R1 + jX1, Z2 = R2 + jX2, then you have a voltage divider Vout/Vin = Z1/(Z1 + Z2). In terms of the real vs. the imaginary components of that transfer function, what has to be true to make the transfer function independent of frequency?
     
  6. May 5, 2013 #5
    real and imaginary must be equal?
     
  7. May 5, 2013 #6
    or reactance is 0?
     
  8. May 6, 2013 #7

    rude man

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    Much better! Come up with a Z2 such that the transfer function Z1/(Z1 + Z2) has no frequency sensitivity.
     
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