Balancing non-inverting opamp gain to minimize distortion

• The Experiment

Here is a common dual opamp configuration:

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?- ##### Gain Calculations

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:

$R1 = 2.7K\\Omega$ $R2 = 2.7K\\Omega$ $R3 = 10K\\Omega$

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:

$0.79 \\cdot 1.27 = 1$

• The Results

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:

R1	R3	U1A Gain	R2	R3	U1B Gain	Output Gain
2700	1000	0.27	2700	1000	3.70	1
2700	4700	0.64	2700	4700	1.57	1
2700	10000	0.79	2700	10000	1.27	1
2700	47000	0.95	2700	47000	1.06	1
2700	100000	0.97	2700	100000	1.03	1

• The Conclusion

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.