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Works OK, but you *do* need an op-amp that'll go right down to the negative supply rail - many don't.
If the centre line of your scope picture is 0V then the input appears to have a slight positive offset. This would contribute to the ve half cycle conducting longer than the -ve half and tend to give the output shown.
I ran some Spice simulations of this FW rectifier configuration with op amps which are capable of input and output at the negative rail (such as the CA3140), and they worked fine. I even found a behavioral model of CA3140 (the model had no strobe or offset pins), and it also worked fine in your circuit. The principle presumably is that on the negative side, the op-amp is putting out a positive signal; and on the positive side, the op-amp can't produce an output (and the diode can't conduct) so the op-amp resistors and the variable resistor on the output just form a potential divider.
The potential divider will drop the voltage to something between 0.4 and 0.57 of the input value. I strongly suspect that you've got a DC offset, as the others have said.
Surely the output of the poor IC is needing to swing below ground, to make up for the diode drop? Ian This application note may be useful in understanding why you have the waveforms shown, just may be down to the frequency applied or the op amp characteristics. Seems like I've had that problem myself before.
HTH Armadillo Maybe the AC input waveform has a significant DC offset. Adding AC coupling is problematic because the input impedance of this circuit is 30k for ve half cycles and 10k for -ve half cycles, so I guess using an AC coupling capacitor would cause a DC offset.
I spent almost one day trying this circuit with CA 3140, single supply, to get a reasonable full wave rectification (absolute vale) but only got what is shown in the picture. I think I might start by tying the input to ground and working out why the output isn't ground. Also, I can't see the reason for connecting pin 8 (Strobe) to pin 1 (apart from the datasheet telling you to). Hola Rob, Sorry, I forgot to tell that to focus in the rectification I had left the offset adjustment for later (with pin 8, open).