Op-amp transfer function help

Aug 06, 2006 3 Replies
W

Hello Group,



I need some tips on the deviration of a transfer function for an op-amp circuit that is in "Troubleshooting Analog Circuits" by Bob Pease, pg.



  1. I do not want anyone to solve it for me; rather, I would like a sanity check on my loop equations that I am coming up with using Mesh Analysis to determine the transfer function...and...if there is an easier way. Once I get the loop equations, that leaves me with three equations and a big ass determinant to deal with. There must be an easier way and/or something that I am missing. A single resistor between the terminals shouldn't cause this much trouble :-(

I am assuming clockwise for all currents in each window and analyzing clockwise as well. The loop equations I am coming up with are:



Loop1: Vin - I1(R3+R4) + (I2*R3) + (I3*R4) = 0 Loop2: Vin + (I1*R3) - I2(R1 + Rb + R3) + (I3*Rb) = 0 Loop3: -(I1*R4) - (I2*Rb) + I3(R4 + Rb + R2) = Vo



Mr. Pease states that the transfer function is: Vout/Vin = (1 + R2/R1) + ((R2 + R4)/Rb)



Link to circuit:

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J

If you are simplifying by assuming an ideal opamp, you assume infinite gain, so Vin - must equal Vin +, in order to eliminate a saturated output.

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W

I would imagine the V+ and V- inputs would have to be (ideally) equal. I can pop the circuit into any Spice but I am more interested in figuring out the transfer fuction for personal glory :-). It has been a while since I had to sit down and derive the equations rather than using a book as a reference. If you don't use it, you lose it. I am trying not to lose it.

FYI, this link should work. I was foiled by Bravenet once again.

formatting link

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J

You have an equation for Vin- and another equation for Vin+ set them equal to each other. If you need the equation for the actual response with a non ideal opamp, you need another equation that tells how Vo is related to Vin + and Vin -.

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