Balancing non-inverting opamp gain to minimize distortion

U1A is an attenuator configuration while U1B is a positive gain configuration. Here R3 is just a resistor to ground, but in practice R3 might represent a sub-circuit consisting of an active filter.

What is the relationship between the two opamps regarding their gain and distortion levels?

The formula for U1A gain is a simple voltage divider:

{\large \frac{R3}{(R1 + R3)} }

The formula for U1B gain is the standard non-inverting gain formula

{\large \frac{R2}{R3} } + 1

For example, take the following resistor values:

Then the gain of the individual opamps can be caluclated:

{\small U1A} = {\large\frac{10000}{(2700+ 10000)} } = 0.79

{\small U1B} = {\large\frac{2700}{10000} } + 1 = 1.27

The final output gain of the series opamps can be found with the product of the U1A attenuation and U1B gain factors:

0.79 \cdot 1.27 = 1

Assuming that series resistor R1 and feedback resistor R2 are equal then the final gain – the product of U1A and U1B gain – will always equal unity:

Note that a lower value of R3 will increase signal attenuation in U1A which will in turn require a higher gain in U1B to compensate.

Higher gain will cause higher distortion in the form of increased noise floor. Therefore, care should be taken to choose a suitably high value of R3 so that distortion requirements can be met.