There are numerous circuits that perform an absolute value function using an op-amp. Many textbook examples start with a single op-amp half-wave circuit and simply add another op-amp to make a full-wave version. Among the various books I have, only one in my collection has the circuit shown here. It was originally published in Electronics magazine1 in 1969, and I have not come across it in other books on op-amp theory.
How it works
During the positive half-cycle D1 conducts and presents a voltage on the non-inverting input equal to the input voltage minus the D1 drop, divided by two. Since D2 is cut off, the op-amp is a standard non-inverting configuration with a gain of two.
During the negative half-cycle D1 is cut off, which effectively puts the non-inverting input at zero volts via R2. Since the inverting input is also at zero volts, the op-amp is now an inverting configuration with the input one diode drop lower. R4 has zero volts and therefore zero current, which effectively makes it transparent in this configuration.
In both half-cycles, since D3 is in the feedback loop, it compensates for the drops across D1 and D2. In my measurement the output can be loaded without affecting operation. The measurement shown used a 4 V pk-pk, 1 kHz sine input, and the IC was a general-purpose LM2904 running from ±15 V.
1 Spani, Wayne. “Absolute Value Circuit Needs Only One Op Amp.” Electronics, 20 Jan. 1969, p. 87.