Why do we need the first stage of the two Operational Amplifiers? Couldn't we just input V1 and V2 into the differential amplifier?
The 3 op-amp design has three main advantages over a single op-amp differential amplifier.
- The input impedance is much higher, since the inputs drive directly into an op-amp input rather than into a resistive divider.
- The gain can be set by changing a single resistor, so the critical parts can be easily integrated on to one chip (maximizing symmetry) with a single external resistor for setting the gain.
- In high gain configurations the common mode rejection is much better because the gain of the first stage effectively multiplies the common mode rejection of the second stage.
Note that in general it is better to use a specific instrumentation amplifier chip than to try to build it yourself out of separate parts. Having everything on one chip improves symmetry and hence common mode rejection.
One of the biggest benefits of the 3 op amp INA is the equal and high input impedance. The op amp's non-inverting pins' input impedance can be up in the \$T\Omega\$ range. I'll leave it as an exercise for you, but if you look at the difference amplifier circuit, the input impedance of the negative input varies with the positive input.
In addition to input impedance concerns, gain in two stages offers better frequency response.
There is a single stage, high input impedance, differential amplifier.
Without Rg, this has a gain of (f+1). Rg can be used to increase the gain.
However it has performance compromises over the 3 amplifier version.
a) It has less open loop gain, so very high gains are not as stable
b) The two signal paths have different phase shift, so common mode rejection only works to low frequencies. You can improve this a bit with a strategically placed capacitor though
c) At low gains, common mode range is limited by the power supply headroom
d) It's more complicated to draw correctly than the 3 amplifier version. It's only recently that I've created a mnemonic to get the resistors in the right places from memory.
But, if you have only 2 amplifiers left, then it does work. It does allow you control of the gain with a single variable resistor, just like the 3 amplifier version, but unfortunately, just the 3 amp version, this resistor is floating.
When a person wants to vary the amplifier gain (for instance to exploit the maximum resolution of ADC) the 2 resistors with value K⋅R must be adjusted perfectly synchronously, via electromechanical adjustable resistors so an slight runout or wearing of these resistors results in imbalance between the value of this two resistors then it results in not to be neglected common mode factor. Usually the common mode in the previous stage (Wheatstone bridge for example) is way bigger than differential mode then it results in false measurements.