Dual op amp takes absolute difference

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Originally published in the August 6, 1992, issue of EDN

A traditional implementation of an absolute-difference function comprises a difference circuit followed by an absolute-value circuit; the entire circuit requires at least three op amps. The design problem is complicated in single-supply-only systems, which usually require an artificial ground, typically one-half of the supply. The circuit in Figure 1 takes the absolute value of the difference of two voltages using only two single-supply, ground-referenced op amps. The circuit is designed for dc or low-speed operation.


For the case where V₁>V₂, IC_1A is disabled because diode D₁ is off. IC_1B and its associated resistors form a classic difference circuit where V_OUT= (R₂/R₁)(V₁−V₂).

For the case where V₂>V₁, diode D₁ conducts, producing the composite amplifier system made up of both IC_1A and IC_1B, where V_OUT=(R₂/R₁) (V₂−V₁). Using these two equations, the overall function of the circuit for V₁ and V₂ greater than zero is as follows: V_OUT=(R₂/R₁)|(V₁−V₂)|.

The circuit was built and tested with R₁=10 kΩ and R₂=220 kΩ. For V₂>V₁, the composite amplifier system has poor phase margin and is unstable. Thus, the circuit compensates the loop with the dominant pole formed by R₃ and C₁. At a gain of 22 and a desired response time of about 300 μsec (the 10 to 90% rise time when V₂ becomes 0.1V greater than V₁), values of R₃=56 kΩ and C₁=850 pF produced the best empirical results. R₃ and C₁ will vary, depending on the required speed of the response and the closed-loop gain.

Also, when V₂>V₁, the output of IC_1A becomes a function of the factor 2V₂−V₁. Thus, IC_1A may saturate for large values of V₂. The factor’s upper limit is as follows, where V_SAT is the saturation voltage for IC_1A: (2V₂−V₁)<V_SAT(R₁+R₂)/R₂. For the LM2902 operating from 5V, V_SAT is approximately 3.5V. This last equation also implicitly sets a common-mode voltage (V_CM) limitation. You can see this limitation by setting V₁=V₂=V_CM and allowing the factor (2V₂−V₁) to reduce to V_CM.