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In this document, we derive the formula for the circuit gain of a non-inverting amplifier using a finite op-amp gain of a=1.0. We apply the golden rule #1, which states that the input voltages at the positive and negative input terminals are equal, but note that this rule no longer holds due to the finite gain of the op-amp. Instead, we use the voltage difference between the input and output terminals to find the circuit gain.
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Problem T
Consider the usual non-inverting amplifier op-amp circuit, shown below.
You will recall that, for an ideal op-amp, the circuit gain is
Vout /Vin = 1 + (R 2 /R 1 ).
This can be arbitrarily large, depending on your choice of resistors. Now assume that the op-amp has a gain of A=1.0 (instead of infinity) and derive the formula for the circuit gain V (^) out /Vin. Can Vout /Vin still be arbitrarily large?
Hint: Golden Rule #1, which says that V (^) + =V (^) – , can no longer hold. Instead V+ – V (^) – = V (^) out.