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I think it's like the 4-diode rectifier principle, positive signal gets through, negative can't get through diode. Diode conducts on positive half of wave, doesn't conduct on negative half of wave.
Nice article that may help to explain rectification circuits:
This arrangement is a way to subtract the diode drop. It acts closer to an ideal diode. This is because it takes feedback voltage from the furthest end of the diode (rather than directly from the output as in opamp circuits we are used to seeing).
By having the diode inside the op amp negative feedback loop, the diodes forward drop is reduced by the open loop gain of the op amp.
Since most op amps have an open-loop gain of a 100,000 or more, the typical 0.7V diode forward drop is reduced to below 10µV (negligible for most practical purposes).
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