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Circuit Analysis with VCCS and VCVS

  1. Aug 26, 2012 #1
    1. The problem statement, all variables and given/known data
    For the circuit in Figure P1.42, suppose R3 = 2*R2, and R2 = 10 * R1. Find the resistor values so that Gv = Vout/Vin = 1000.

    question42-1.jpg

    2. Relevant equations

    V = IR

    for Voltage Controlled Current Source - i(t) = gm * vx
    for Voltage Controlled Voltage Source - v(t) = μ * vx



    3. The attempt at a solution

    Everytime I try to figure out the resistor values I get R3 = 500. The answer is R3 = 5 k ohms which the book gives us.
     
  2. jcsd
  3. Aug 26, 2012 #2

    lewando

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    Unless I'm losing my mind, it looks like Vout = 5V2, which is independant of the value of R3.

    How do you come up with your answer?
     
  4. Aug 26, 2012 #3
    I said that
    Vin = Iin*R1

    V2 = .8*Vin * R2
    = .8 (Iin*R1) * R2

    Vout = 5*V2
    = 5 * (.8 (Iin*R1) * R2)
     
  5. Aug 26, 2012 #4

    CWatters

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    I think R3 is only needed to calculate Iout not Vout.

    Rest deleted as I made a mistake.
     
  6. Aug 26, 2012 #5

    lewando

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    Those look fine. If you combine

    V2 = .8*Vin * R2

    and

    Vout = 5*V2

    you can get an expression for Vout/Vin as a function of R2 only.

    Using your stated constraint for R3 = 2R2, I also come up with R3 = 500 ohms.
     
  7. Aug 26, 2012 #6
    Is it possible that we are a factor of ten off?
     
  8. Aug 26, 2012 #7

    lewando

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    I think it is more likely that your book is off by a factor of 10. Are you sure that R3 = 2*R2? Maybe an additional set of eyes on this problem might build the case against your book.
     
  9. Aug 26, 2012 #8
    This is the question from the book:

    2012-08-26200101.jpg
     
  10. Aug 28, 2012 #9
    As it turns out, the book was off. It was supposed to say .5 k Ω and not 5.
     
  11. Aug 28, 2012 #10

    lewando

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    That's great! Thanks for the closure.
     
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