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Homework Help: Expression for closed loop gain of differential amplifier

  1. Dec 21, 2017 #1
    1. The problem statement, all variables and given/known data
    The question is

    Derive an expression for the closed loop gain of the differential amplifier.


    I have solutions for these questions but the solution for this question is quite vague.

    Here is the solution:


    I understand part 1 and part 3, but part 2 I don't.

    So looking at part 2, it starts by doing a voltage divider to find the voltage at V* by doing V1 x R4/R3xR4

    The rest of the step in part 2, I don't understand.

    How does it go from from V* = V1 x R4/R3xR4 then to = V1/(R1 + R3/R4)
    then to = (V1 x R4/R3)/(1 + R4/R3)

    Is there some steps that should be in between to show more clearly what is happening because I can't follow it. Can someone explain how to get from each step to the next?
  2. jcsd
  3. Dec 21, 2017 #2


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    Staff: Mentor

    Unless there's some special relationships between the resistor values that we haven't been told about I don't see how the derivation makes sense. certainly the final result is rather dubious, depending as it does upon only two of the four resistor values.
  4. Dec 21, 2017 #3
    [tex] \frac {V_1} {R_1 + \frac {R_3} {R_4} } [/tex] is a mistake, it should be
    [tex] \frac {V_1} {1+ \frac {R_3} {R_4} } [/tex]

    For the rest, isn't there some assumption like R1/R2 = R3/R4 ?
  5. Dec 21, 2017 #4
    Yes, R1/R2 = R3/R4, it says that in the solutions.

    and yes, that is a mistake.

    i'm confused about where the 1 comes from, why does it just appear?
  6. Dec 21, 2017 #5
    [tex] \frac{ R_4} {R_3+R_4} [/tex] divide the numerator and the denominator by R4
  7. Dec 21, 2017 #6
    ok, thanks. can you explain how it goes from

    V1/(1 + R3/R4) then to = (V1 x R4/R3)/(1 + R4/R3)
  8. Dec 21, 2017 #7
    I also get that from the leftmost expression by dividing numerator and denominator by R3. (So the middle expression seems to have no point)
  9. Dec 21, 2017 #8
    yea, i see that. i understand all the steps now, thanks for your help
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