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Finding gain with opamps

  1. Jan 25, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-1-25_12-11-49.png
    I need to find the gain in this question.

    2. Relevant equations


    3. The attempt at a solution
    I know gain will be Vo/Vs. I did many calculations to end up with Vs being 0. Would this be logical? I know ideal op amps will have infinite voltage gain, so if you divide by 0 then it will go towards infinity? So I'm not sure if that would be correct for this question.
     
  2. jcsd
  3. Jan 25, 2017 #2

    berkeman

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    Staff: Mentor

    You should find Vo/Vs as you say, you don't "find" Vs.

    Write the KCL equations for the nodes, and use the properties of an ideal opamp to help simplify the problem. Please show us the KCL equations, and your work toward solving them. :smile:
     
  4. Jan 25, 2017 #3
    upload_2017-1-25_12-25-16.png

    upload_2017-1-25_12-25-42.png

    I'm not really sure what to do in these problems but that was what I tried
     
  5. Jan 25, 2017 #4

    berkeman

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    Sorry, I'm not able to read that. Can you try scanning the pages to see if they are more readable that way?
     
  6. Jan 25, 2017 #5

    gneill

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    You might want to simplify the resistor network first, since it looks like there are parallel and series opportunities to exploit. You'll have fewer nodes and equations that way!
     
  7. Jan 25, 2017 #6

    CWatters

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    Can I suggest you take a good look at the circuit and see it you can simplify it before starting with equations.

    Oh bother gneil beat me too it.
     
  8. Jan 25, 2017 #7
    Ok, I will try to simplify that first. But do I have the right idea, would I use the same methods once I simplify?
     
  9. Jan 25, 2017 #8

    gneill

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    Let's see your reduced circuit first. It may not be worth writing equations for it :wink:
     
  10. Jan 25, 2017 #9
    upload_2017-1-25_20-50-3.png
     
  11. Jan 25, 2017 #10

    gneill

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    Looks like you can still simplify it a bit more.
     
  12. Jan 25, 2017 #11
    upload_2017-1-25_21-3-35.png
     
  13. Jan 25, 2017 #12

    gneill

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    No, you've lost the path from the output to the "-" input. When you combined the 60 kΩ and 30 kΩ, the resulting 20 kΩ should still be connected to the 80 kΩ resistor.
     
  14. Jan 25, 2017 #13
    upload_2017-1-25_21-27-40.png

    like this? I don't know how to connect the op amp. After do I write equations?
     
  15. Jan 25, 2017 #14

    gneill

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    The 80 kΩ and 20 kΩ resistors are in series and can be reduced to a single 100 kΩ resistor. But the circuit layout is fine. The op-amp is connected as it was in the original circuit and will behave the same.

    You should be able to spot the problem with this circuit without writing any equations, and in fact you were on the right track in your early posts where you recognized that the magnitude of the gain would be the full gain of the ideal op-amp (infinite).
     
  16. Jan 25, 2017 #15
    I'm not sure what the problem is.

    Is what I did in my first posts correct or completely wrong?
     
  17. Jan 25, 2017 #16

    gneill

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    Ask yourself if there is any effective feedback that will limit the gain of the circuit. Can any amount of current fed back from the output through the 100 kΩ change the voltages that the op-amp sees at its inputs?
    It was a bit off track since you were solving for Vs, which should be an independent variable and not dependent on the circuit operation. It's an input. However, you did recognize that there was some kind of problem since it appeared that infinities were springing up.
     
  18. Jan 25, 2017 #17
    Isn't the current entering the op amp supposed to be 0A? for both inputs
     
  19. Jan 25, 2017 #18

    gneill

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    Yes, but feedback is supposed to cause changes in potential differences on components leading to those inputs. Can any amount of current through the "feedback" path make any difference in the potentials at the op-amp inputs in this circuit?
     
  20. Jan 25, 2017 #19
    If it is too big? I'm not sure I understand, my professor never mentioned feedback in his notes.
     
  21. Jan 25, 2017 #20

    gneill

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    Feedback is what sets the gain of an op-amp circuit. The so-called open-loop gain of an (ideal) op-amp is infinite. Feedback "closes the loop" and controls the overall gain of the circuit, limiting it to some finite value.

    Effectively in this circuit the 100 kΩ resistor does nothing to control the op-amp's gain.
     
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