Parallel OpAmp configuration
The Wikipedia Instrumentation amplifier article explains it reasonably well using the theory. Let's use some diagrams instead to make this a bit more intuitive.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. \$ R_{GAIN} \$ removed.


With the gain resistor omitted we simply have two voltage followers.
In (a) we have a differential input of 1 V and a differential output of 1 V.
In (b) we have a common-mode input of 1 V and a differential output of 0 V.


The problem occurs with this circuit that if we want to increase the gain in the normal non-inverting amplifier way we would add resistors from IN- to ground on OA1 and OA2. The problem is that the common mode signal gets amplified too and this may cause overload for the following stage - particularly if the common mode signal is high relative to the signal of interest.







simulate this circuit

Figure 2. \$ R_{GAIN} \$ reinstalled.

To keep the maths simple I've set Rgain = 20 kΩ.


In (a) we know from our non-inverting amplifier theory that the op-amp will settle with V- = V+. Therefore with a 1 V input OA1 will have 1 V on IN-.
Similarly OA2 will have 0 V on V-.
Now there is 1 V across Rgain so 0.05 mA must flow through R1, Rgain and R2. From this we can work out the op-amp output voltages. We see that we have doubled the differential signal output to 2 V.
In (b) we can see that the common mode signal goes through with a gain of one.


So, by adding Rgain = 20 kΩ we have increase the differential gain by a factor of 2 without increasing the common mode gain. As we increase Rgain the benefits improve further.

Read paragraph 3 of the Wikipedia article in the light of this and see if it helps.