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Analyzing a Circuit with an Op-Amp

  1. Mar 7, 2014 #1
    1. The problem statement, all variables and given/known data
    http://i.imgur.com/TBrFMIT.png


    2. Relevant equations



    3. The attempt at a solution
    So I basically start with node voltages at the positive terminal of the op-amp, and I label that node E, so the node voltage goes:

    VE/80 + (VE - VD)/20 = 0 (I labelled the node at the bottom of the diamond D)

    Continuing from this equation, I then analyze the circuit at node D, and I know the left node in the diamond is 10V, because it is connected to a voltage source which is connected to the ground. I also know the right node is 0V, because it's directly connected to the ground, so then I get the equation:

    (VD - 10)/40 + (VD - VE)/20 + VD/60

    From the node voltage equation at node E, I learn that VE = 0.8 VD, which means I can then substitute that value into my equation to solve for VD. Skipping the calculations, I get that VD = 4.84V.

    From there, I analyze the node on the right of the diamond, which I know to be 0V, this gives me the equation:
    -VD/60 + (-VC)/30 = 0 (I name the top node C)
    Simplifying this equation and substituting in the number for VD gives me a VC value of -2.42V
    I can also solve for VE using the equation I had earlier, VE = 0.8VD, so I get that VE = 3.87V.

    With these values, I use the summing point constraints, and I know that the voltage in the node connected to the negative terminal of the op-amp is the same as the voltage in the node connected to the positive terminal, giving me VE' = 3.87V (Naming the negative terminal E')

    Doing node voltage analysis on the node E' gives me an equation to solve for Vo, but I get a ridiculously high number when I try this. Could someone identify where I am going wrong with my work? Thank you in advance.
     
  2. jcsd
  3. Mar 8, 2014 #2

    gneill

    User Avatar

    Staff: Mentor

    Your value for the potential at the V+ input of the op-amp looks okay.

    Can you show your work for the node voltage analysis to determine Vo?
     
  4. Mar 8, 2014 #3
    Nevermind, I figured out why I was wrong, it's because I can't use the 0V node for node analysis, because there's an unknown current coming out of the ground.
     
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