An absolute value circuit produces at its output a voltage equal to the absolute value of the input voltage.
Figure below shows the diagram of an absolute value circuit.
Absolute value circuit
As we can see from the figure, it is a dual half-wave rectifier circuit discussed earlier followed by a difference amplifier.
When the applied input is of positive polarity (say +V), diode D1 is forward-biased and diode D2 is reverse-biased. Assuming ideal diodes, the equivalent circuit in this case is shown below. The output (Vo) in this case is equal to +V.
Equivalent absolute value circuit with positive input
When the applied input is of negative polarity (say –V), diode D1 is reverse-biased and diode D2 is forward-biased. Assuming ideal diodes, the equivalent circuit in this case is shown in figure below. By applying Kirchhoff’s current law (KCL) at the inverting terminal of the first opamp, we can determine voltage (Vx) to be equal to (2/3)V. Also, Vx = (2/3)Vo. Therefore, Vo = V. Thus, the output always equals the absolute value of the input.
Equivalent absolute value circuit for negative input