1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

    IMG_0042.JPG


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

    Here is the solution:

    IMG_0041.JPG


    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

    gneill

    User Avatar

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted