Closed Loop Voltage Gain Of An Instrumentation Operational Amplifier
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Closed Loop Voltage Gain Of An Instrumentation Operational Amplifier Figure 13.1 illustrates the instrumentation operational amplifier (IA).
Find the closed loop voltage gain of the instrumentation amplifier. Assume the op-amp is an ideal op-amp.

The strings: S7P5A51 (change - physical).

The math:
Pj Problem of Interest is of type change (physical - change).  Consider figures 13.1 and 13.2. In figure 13.2, R1 of figure 13.1 is halved and each of the first two operational amplifier is treated independently as a non-inverting operational amplifier. So, the output of each of the non-inverting op-amp with input V1 and V2 is an input to the second stage of the instrumentation amplifier. If the op-amp is an ideal op-amp then:
The voltage gain of each of the non-inverting operational amplifier = (1 + R2/(R1/2) = 1 + 2R2/R1.
The op-amp of the second stage is a differential amplifier and the inputs are:
(1 + 2R2/R1)V1 and (1 + 2R2/R1)V2.
So, for an ideal differential op-amp:
Output voltage, Vout = (RF/R)(1 + 2R2/R1)(V1 - V2)
So, closed loop gain of instrumentation amplifier = Av = Vout/(V1 - V2) = (RF/R)(1 + 2R2/R1)

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