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Transimpedance Operational Amplifier Simulation circuit help

  1. Jan 30, 2016 #1
    1. The problem statement, all variables and given/known data

    (a) Derive the relationship
    between the output voltage V and the input current I; i.e. if V = kI
    find k in terms of R1, R2 and Rf.

    (b) Calculate the current I if Rf = 10 MΩ, R1 = 90 kΩ, R2 = 10 kΩ
    and V –0.1 V.

    (c) Model the circuit using PSPICE [using an ideal opamp]
    and use the model to confirm the calculation made in (b).
    2. Relevant equations
    upload_2016-1-30_20-22-37.png

    3. The attempt at a solution
    (a) V= KI, K= R2/ R2+ (Rf*R1/Rf+R1)

    (b) I= V/K , I= -0.1/(10k/10k+(90k*10M/90k+10M), I= -0.992A (too big a current?)

    (c)
    upload_2016-1-30_20-38-24.png

    Im not sure how to complete this schematic, I need to check current calculation in (b). I dont kow what "Vin" is. Any help is greatly appreciated as I have no training on this software.
     
  2. jcsd
  3. Jan 30, 2016 #2

    gneill

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    Staff: Mentor

    In part (a) the syntax in your algebraic expression for K is ambiguous: the order of operations is not clear. Use parentheses to make the order of operations unambiguous. It also seems unlikely that the output voltage would be positive if ##I## is positive. Shouldn't K have a negative value? The input current ##I## should impose a potential drop across the feedback resistor, pushing the junction of R1 and R2 negative.

    Can you show your derivation of K?

    For part (b), yes, that current looks to be too big and of the wrong sign. Note that the given output voltage is negative.

    For part (c) you should be able to use a current source at the input. Set it to the value you calculate in part (b) and check the resulting output voltage V.
     
  4. Jan 31, 2016 #3
    Ok, for (a) my derivation of "K" is that Rf (feedback resistor) is in parallel with R2, so I have (Rf*R2)/(Rf+R2) = (10*10^6*10*10^3)/(10*10^6+10*10^3) = 1. Using the voltage divider rule I have -(R1/(R1+1)) = K (where 1= (Rf*R2)/(Rf+R2)). Thats my relationship for K, for (b) I have V=KI, I=V/K therefore -0.1/-(90*10^3/(90*10^3+1)) =0.1A which is positive but still too large considering it is a transimpedance circuit that measures very small currents.
     
  5. Jan 31, 2016 #4

    gneill

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    You should avoid plugging in numbers and rounding before the very end when you have values where small differences can be important to the behavior of the system. A purely symbolic derivation is safer. Also, I think you've lost several orders of magnitude in calculating the value of Rf || R2. It should be closer to 10 kΩ, not 1 Ω .

    By using the voltage divider rule you're ignoring the current ##I## that's injected into the junction of R1 and R2.

    I get a different value for K, one that is negative and quite large.

    Instead, try KCL node analysis at the junction of R1 and R2, and note that the voltage there is fixed by the potential drop across Rf (v1 in the image below).

    upload_2016-1-31_9-22-26.png
     
  6. Jan 31, 2016 #5
    KCL node analysis at the junction of R1 and R2, I have (V1-Vout)/R1 for I1 and for I2 I have (Vout-V1)/R2.
     
  7. Feb 1, 2016 #6

    NascentOxygen

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    And what's your related expression for I, the current through Rf?
     
  8. Feb 1, 2016 #7

    LvW

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    Ohms law for R2 results in I2=-V1/R2.
     
  9. Feb 1, 2016 #8
    Well according to KCL, I1+I2=I so V1/R1-V1/R2= I
     
  10. Feb 1, 2016 #9

    gneill

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    Nope and nope.

    Both I and i2 are shown flowing into the node, while only i1 flows out. So i1 = i2 + I. That means i1 - i2 = I. Also, R1 and R2 terminate at different nodes at different potentials (R1 terminates at the output node that has potential V), so you can't write V1/R1 - V1/R2 = I. You need to write the node equation that takes into account the nodes where the branches terminate.
     
  11. Feb 1, 2016 #10
    If R1 terminates at the output node then thats Vout/R1 and R2 terminates at the central node so thats -V1/R2, and for Rf is V1/Rf. Since I1=I+I2 then Vout/R1=-V1/R2+V1/Rf.
     
  12. Feb 1, 2016 #11

    gneill

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    No, in nodal analysis you write the current on a branch between two nodes as the potential difference between the nodes divided by the branch resistance. So for example if there was a resistance R between a node at potential Va and another node at potential Vb, then the current flowing from node A to node B through resistance R would be given by (Va - Vb)/R.
     
  13. Feb 1, 2016 #12
    Well for that I have (V1-Vout)/R1 + (V1-Vout)/R2 + (Vin-V1)/Rf assuming the reference node V1.
     
  14. Feb 1, 2016 #13

    gneill

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    R2 connects between v1 and ground (0V), not Vout. You already know the current coming from the Vin node as ##I##, so you don't need to know Vin. Nodal analysis uses a sum of current terms (it's KCL at a node), and ##I## is the known current in that particular branch.
     
  15. Feb 1, 2016 #14
    If I have- (V1-Vout)/R1+(0-V1)/R2 =0 for my nodal equation, where does Rf come in? As I need to find K in terms of all 3 resistors.
     
  16. Feb 1, 2016 #15

    gneill

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    There are three branches meeting at node v1. You need three currents.... which one's missing in your equation?
     
  17. Feb 1, 2016 #16
    Well its "I" flowing through Rf, Which is V1/Rf, So the three currents therefore are (V1-Vout)/R1+(0-V1)/R2 + V1/Rf =0
     
  18. Feb 1, 2016 #17

    gneill

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    True, but look at the diagram I posted in post #4. That current is a given quantity (well, a given symbolic quantity anyways).
     
  19. Feb 1, 2016 #18
    Are we talking about representing V1/Rf as simply "I" in our nodal equation? If so how is Rf represented for my derivation of K? Thanks for your patience.
     
  20. Feb 1, 2016 #19

    gneill

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    Yes, you need both an "I" and and "Rf" eventually. Since "I" is a given you can use it as though it were a constant. So plugging it into the node equation you have (summing currents leaving the node):

    ##\frac{v1 - 0}{R_2} + \frac{v1 - Vout}{R_1} - I = 0##

    Now since ##I## is a given quantity you can find a value for v1 separately. Just follow the path from the input to the v1 node. What potential drop can you see?
     
  21. Feb 1, 2016 #20
    The p.d is across the Rf resistor from the input to V1 node, and V1 represents the p.d.
     
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