# Differential Amplifier with Unity Gain Source vs Instrumentation Amplifier

I have two circuits. One is a differential amplifier with unity gain amplifiers for voltage control, and another is a instrumental amplifier. "Right" and "Left" are two 1V sine waves 180 degrees out of sync, with an offset of 2.5V.

I've noticed these two are very similar with the only difference being R12 connecting the two input op-amps. I am wondering what is the significance of this resistor between the two op-amps, what difference does it make in terms of performance. I know that the gain calculations are different, but I don't understand how it affects other performances such as response time.

To Less Determined Readers: Why would anyone build an instrumentation amplifier when a differential amplifier with separated unity gain amplifiers as inputs seem to do the job well enough?

• Getting differential gain in the first stage is superior in terms of noise Dec 16, 2023 at 12:43

Two factors:

• Easier to set the total gain
• Easier to achieve high common-mode (CM) rejection with high differential gains

Without R12, the bottom circuit will turn into pretty much the same thing as the top one (except for the gain factor of course): Two channels are buffered and fed to the diff amp.

In the circuit on top, you can set the entire circuit's gain by playing with at least two of the gain set resistors of the post-diff amp. However, this increases the risk of having increased common-mode (CM) gain because of the potentially mismatched resistors.

With the circuit at the bottom, once you set (or calibrated?) the post diff amp for the minimum CM, you can set (increase) the total gain by playing with only one resistor, R12, without touching the rest.

Therefore, with only one resistor, you can increase the differential gain whilst keeping the CM gain the same.

Circuit 1 is easier to set the gain, you only need 4 precision resistors. Circuit 1 also needs fewer resistors in total.

Both circuits are identical in terms of CMRR and input impedance.

Circuit 2 (instrumentation amp) is superior im terms of noise.

what is the significance of this resistor [R12] between the two op-amps, what difference does it make in terms of performance.

1. In circuit 2, Input Common Mode rejection occurs right at the input. The current through R12 is determined entirely by the differential input voltage. All the common mode voltage subtracts to zero here. This means that subsequent amplification will not be influenced by input common mode voltage. This reduces the CMRR demands placed on the differential amplifier in Circuit 1.
2. Noise is reduced in two ways: 1) The high value resistors in circuit 1 are sources of thermal noise. Circuit 2 uses significantly lower value resistors. 2) The differential amp in circuit 2 has unity gain, so noise generated by the input amplifiers is not amplified.
3. The lower resistance values in curcuit 2 will allow faster response with circuit capacitances.
4. The differential amplifier in Circuit 1 will have a reduced bandwidth due to gain-bandwidth product (GBW) than the differential amplifier in Circuit 2. The input amplifiers have a wide unity gain bandwidth in Circuit 1, but a GBW restricted bandwidth in Circuit 2. How this affects time response depends on the chosen amplifiers.
5. Of course changing gain with one resistor (R12) is easier than changing gain with 2 matched precision resistors.

Why would anyone build an instrumentation amplifier when a differential amplifier with separated unity gain amplifiers as inputs seem to do the job well enough?

If a differential amplifier with separated unity gain amplifiers as inputs does the job well enough, then there is no reason to do anything else.

If a differential amplifier with separated unity gain amplifiers as inputs does not do the job well enough, then use the instrument amp.