Cameras

How do you find the CMRR of a single op-amp differential amplifier?

The differential amplifier circuit has 1 matched resistor pair and 1 mismatched resistor pair.

Ignoring the CMRR and PSRR of the op-amp itself because it is expected to be much better.
Also for simplification ignore the bias current, and offset voltage and current of the amplifier.
Consider the case where both inputs are the same. This is the common mode voltage. There is no difference signal (differential mode). The output is zero, ideally.

The CMRR is due to the difference in gain between the + and the – inputs. If there was no difference the output is zero, and the CMRR is infinite.

Looking at the link below…
Mismatch of the single pair of resistors. That means the gain of one side is incorrect Say the gain mismatch was 100 and 101, and should be 100. The ratio to the signal gain is 100:101/100.
Expressed in dB..
20(log(ratio)) = 20 x Log (0.99/100) = 40dB. A 1% error is 40dB CMRR.

If the formula given in the first link is broken down you will see that it is just (the non-inverting gain – the inverting gain), considering the input voltages, so that would give an output voltage for any input voltages considering all the resistors and both voltages. If both the inputs are the same there is some voltage, due to mismatch. With a difference, the differential gain shows up. This ratio between difference gain and common mode gain is CMRR (at DC).

Operational Amplifier Tutorial – Basic Non-Inverting Op Amp (Part 2)

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