Low-cost integrated resistor networks can be used to implement a low-parts-count two-op-amp differential amplifier with low common-mode gain. Integrated onto a common substrate and processed together, resistors of integrated networks match well and are an alternative solution to discrete resistors, especially for amplifiers with a wide common-mode input voltage range. The amplifier circuit is shown below.

In some diff-amp applications such as high-side current sensing, where the sense resistor voltage to ground can have a large range, it is important that the op-amp differential amplifier (diff-amp ) reject the floating voltage of the sense resistor. In other words, the common-mode (CM) gain, A_CM of the diff-amp must be minimized. The above amplifier circuit is a two-op-amp diff-amp with half of an 8-R resistor network. Two parts (using a quad op-amp) can implement a dual diff-amp circuit with low error caused by CM gain.

Two sources for CM gain are the op-amps used in the diff-amp and the gain-setting resistors around the op-amps. Amplifier CM rejection is usually specified as the CM rejection ratio ,

where A_v is the (desired) differential gain,

and v_o = amplifier output voltage. The (undesirable) amplifier CM gain is

where the common-mode voltage is

and is the average of the voltages at the inputs. As the CM voltage changes, ideally no change in the output voltage of the diff-amp occurs, and only the difference voltage at the diff-amp inputs is amplified. For the above circuit with equal resistors in the network, the quasistatic gain is A_v0 = 2.

The derivation of A_¬CM caused by resistor mismatch is rather involved. (See Planet Analog articles, Seemingly Simple Circuits, Part 3: Effect of Resistor Tolerances on Diff-Amp Gains and Seemingly Simple Circuits, Part 4: Diff-Amp Common-Mode Rejection by this author for details.) However, it reduces to a rather simple approximate formula:

where ε = resistor tolerance. A +/-0.2 % resistor network matching tolerance has ε = 0.002.

Thick-film R-networks are low-cost and readily available from passive-components manufacturers. They typically are specified at 1 % to 2 % absolute inaccuracy. What matters for low A_-CM is how well the resistors match, and being made in a common process on a common substrate, they match typically to 0.2 % to 0.4 %. Thick-film TCR tracking is typically about 50 ppm/^o C, comparable to T2 1 % metal-film resistors.

Suppose that the resistors match to 0.33 %, or ε = 0.0033. Then the CM gain of the given diff-amp is

The CM error resolution is 6.83 bits and A_CM ≈ 8.8 mV/V. At a +/-0.2 % match, the error resolves to 1/187.5 = 5.33 mV/V, or about 7.55 bits. For many applications, this CM error is acceptably low. If so, a CM trimpot adjustment (of the bottom R of the string) is eliminated from the circuit. If it is not sufficient but close, such as for an 8- to 10-bit system, then software calibration can remove the CM error. (See Part 2 of the above-mentioned diff-amp article series for that.) Greater precision can be achieved using thin-film R-networks at greater cost – an alternative to discrete +/-0.1 % metal-film resistors.

A 16-pin SMT or DIP R-network has 8 matched resistors, usually of the same value. For a gain of up to 4, the extra resistors can be placed in series or parallel to modify A_v . Placing resistors of a given tolerance in either series or parallel results in the same tolerance for the combinations.