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Amplifiers - Voltage gain of a current controlled voltage source and current source.

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data

    I've been reviewing my electrical theory and I'm having trouble trying to calculate an expression for the voltage gain for these two specific circuits. (Images c and d of the question.png attachment). I already know the answers, however I am unable to derive the same solution. Answers are given with my solution attempt.



    2. Relevant equations
    Kirchoff's loop law and current junction law.

    Voltage gain = Output voltage/Input Voltage

    R_s is source resistance, R_L is load resistance.
    r_o is amplifier output resistance and r_i is amplifier input resistance.


    3. The attempt at a solution
    I've attached my solution for b if it's unclear what I am asking. I'm pretty sure I've misunderstood something while working it out but haven't been able to figure out the correct steps. Any help is appreciated.

    Edit: Attachments are now there.
     

    Attached Files:

    Last edited: Sep 13, 2012
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  3. Sep 13, 2012 #2

    berkeman

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    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    I'm not seeing any attachments. Try again?
     
  4. Sep 13, 2012 #3

    rude man

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    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    Part (c): well, the input voltage is Vin and the output voltage is what if the controlled current source is μVin feeding an output impedance of ro?

    What function, if any, does ri have?
     
  5. Sep 13, 2012 #4
    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    r_i is a constant but I'll see where I get with your suggestions on C for now. It's just late here right now but I'm going back to it in the morning. Thank you very much.
     
    Last edited: Sep 14, 2012
  6. Sep 14, 2012 #5

    rude man

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    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    Yeah, ask yourself if ri has any significance at all ....
     
  7. Sep 14, 2012 #6
    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    I thought r_i would have mattered as it is used in the voltage divider rule to figure out the input voltage of the amplifier and from there mu*v_in would have been the output voltage of the amplifier.

    If I considered the first loop in C then we have:

    Vs = VSource Resistance + VAmp input resistance.
    Vs = I(Rs + ri)
    I = Vs/(Rs + ri)

    then multiply by r_i to get
    VAmp input resistance = riVs/(Rs + ri)

    The diagrams also aren't too clear on the symbols but I believe by vin and Iin is referring to the voltage/current across/through the amp. input resistor. I'll post the full picture for B that is given as a text example.
     

    Attached Files:

  8. Sep 14, 2012 #7

    rude man

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    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    Now that you've included the entire circuit - yes, it matters. It's a voltage divider as you said.

    You're on the right track.
     
  9. Sep 14, 2012 #8
    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    For C:

    Then if I know the vin voltage, the amp. output voltage would just be μvin. But then by Kirchoff's loop law, since the load is in parallel with the amplifier output voltage, this would imply the load voltage, amplifier output resistor voltage and the amplifier voltage are equal.

    vL = μvin = μriVs/(Rs + ri)

    I just realized I forgot to put in Av for part C so:

    And so gain is Av = vL/vs = ri/(Rs + ri)

    However my text has the solution as Av = μrirsRL/[(ri + Rs)(ro + RL)] so I'm off by a factor of RL/(ro + RL).

    The textbook seems correct only if the load ,amp. output resistance and amp. were in series since I'd be able to use voltage divider again to multiply in the extra factor I'm missing mentioned above or unless I've misunderstood something for the second part of the solution.
     
    Last edited: Sep 14, 2012
  10. Sep 14, 2012 #9

    vk6kro

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    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    The input voltage is given by the input current times the input resistance. Just like Ohms Law.

    The output voltage is given by the output current (hfe* iin) times the parallel combined resistance of the load and the output z of the transistor.



    If you keep the input current as your only variable, it will cancel when you calculate the voltage gain, which is just the ratio of the two calculations above.

    Voltage gain = output voltage / input voltage
     
  11. Sep 14, 2012 #10
    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    Gotcha, so referring to C:

    Av = vL/vs

    where:

    By Ohm's Law:
    vs = IRtotal = I(Rs + ri)

    So far then I have:

    Av = vL/I(Rs + ri)

    Then vL = μvin = μIinReq

    Where Req = RLro/(ro + RL)

    Then vL = μIin*RLro/(ro + RL)

    And now Av = μIin*RLro/vin[(ro + RL)(Rs + ri)]

    But vin/Iin = ri by Ohm's Law thus:

    Av = μri*RLro/[(ro + RL)(Rs + ri)]

    Thanks so much for your help. Let me know if I had followed any of the above steps incorrectly. I'll try to work through D with what I now know.
     
  12. Sep 14, 2012 #11
    Re: Amplifiers - Voltage gain of a current controlled voltage source and current sour

    Bah ignore this...I thought I had D right for a moment...


    For D:

    For Av = vL/vs

    vs = iin(ri + Rs)

    μiin = μvin/Req

    where Req = RL + Ro

    μiin = μvin/(RL + Ro)

    Since the right loop of D is a series circuit, multiplying the output current on both sides by RL will yield vL on the left.

    vL = RLμiin = μvinRL/(RL + Ro)

    Av =
     
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