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Determining the gain of an op-amp with feedback?

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data

    8242017227_8bf9d9f51b_z.jpg

    2. Relevant equations

    I have two "golden rules" I was given which are "no current into the op-amp" and [itex]V_{-} = V_{+}[/itex]

    and the open loop gain is infinite

    Basically my notes and textbooks are leaving me with pretty much nothing though

    3. The attempt at a solution

    tried determining the currents like we did in other methods. tried figuring out the case when x=1 and x=0. I don't get how current can flow across the resistor if V_=V+. I'm basically completely lost. No Idea where to start.
     
  2. jcsd
  3. Dec 3, 2012 #2

    gneill

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    Staff: Mentor

    Using your "golden rules", given a voltage V_in at the input, what will be the voltage at the + terminal of the op-amp? (Hint: you're looking at a simple voltage divider).

    So, what then is the voltage at the "-" terminal?
     
  4. Dec 3, 2012 #3
    well I would say [tex]V_{+}=\frac{xR}{(1-x)R+xR}V_{in}[/tex][tex]V_{+}=x[/tex]
     
  5. Dec 3, 2012 #4
    and my golden rule says that V_=V+
     
  6. Dec 3, 2012 #5

    gneill

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    Staff: Mentor

    Well, ##x\,V_{in}##, right?

    Good. So what's the current through the input resistor, R?
     
  7. Dec 3, 2012 #6
    oops I meant V-=xV_in
     
  8. Dec 3, 2012 #7
    the current through the input resistor would be [tex]\frac{V_{in}-xV_{in}}{R}=\frac{(1-x)V_{in}}{R}[/tex]so[tex](1-x)V_{in}=xV_{in}-V_{out}[/tex][tex]1-x=x-\frac{V_{out}}{V_{in}}[/tex][tex]\frac{V_{out}}{V_{in}}=2x-1[/tex]?
     
  9. Dec 3, 2012 #8
    if my work is hard to follow I just said that the current through the input resistor must equal the current through the feedback resistor after the "so".
     
  10. Dec 3, 2012 #9
    this makes sense to me now so I hope it's correct haha.
     
  11. Dec 3, 2012 #10

    gneill

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    Staff: Mentor

    Looks good. For someone who started out with "no idea", you've carried it off nicely :smile:
     
  12. Dec 3, 2012 #11
    thanks a lot. I guess usually I just have "no idea where to start". sucks on exams!
     
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