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Non-Ideal Op-Amp gain derivation

  1. Mar 5, 2014 #1

    Maylis

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    1. The problem statement, all variables and given/known data
    Problem statement is in the attachment HW 5, it is problem #1.


    2. Relevant equations



    3. The attempt at a solution
    I am just stuck with a whole bunch of variables and this just looks like a complete mess
     

    Attached Files:

  2. jcsd
  3. Mar 5, 2014 #2
    The best and the easiest way to solve this circuit is to use a matrix. And then use the math software and allow the computer to solve the matrix for us.
    See the example
     

    Attached Files:

  4. Mar 5, 2014 #3

    rude man

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    Your equations look right.

    I have 2 suggestions:
    1. Instead of R, use G=1/R for all resistances. Makes the math look cleaner by eliminating fractions in your two basic equations.
    2. Put your basic equations into math software. Don't try to solve them yourself; you are liable to make a mistake.
     
  5. Mar 5, 2014 #4

    Maylis

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    I'm plugging in the numbers in your equation Jony, and my gain is many orders of magnitude greater than Rf/Rs.

    I get -10^24 for the top part of the franction, then 10^16 on the bottom part, giving 10^6 as the gain. The gain for the ideal is 100.
     
    Last edited: Mar 5, 2014
  6. Mar 5, 2014 #5
    You must have made an error in your arithmetic. I get -99.9889 for the gain.
     
  7. Mar 5, 2014 #6

    Maylis

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    I do it over and over and get the same result, are you getting -9.99999E+24 on the top of the fraction, and 1.000E+17 on the bottom?
     
  8. Mar 6, 2014 #7
    Here's the result I get:

    attachment.php?attachmentid=67305&stc=1&d=1394099970.png
     

    Attached Files:

  9. Mar 6, 2014 #8
    Because I made a stupid mistake not in the matrix but in input 5. The gain is A times larger than is should. To correct this simply remove the first A in numerator

    correct numerator = Ri RL (-A Rf+Ro) = Ri RL (Ro - Rf A)

    Sorry for confusion.
     
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