Use a Self Powered Op Amp to Create a Low Leakage Rectifier
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You can combine a carefully chosen op amp, a low-threshold P-channel MOSFET, and two feedback resistors to make a rectifier circuit with less forward drop than a diode. The rectified output voltage powers the active circuitry, so no additional power supply is necessary. The circuit's quiescent current is lower than most Schottky diodes' reverse-leakage current. This circuit provides active rectification at voltage drops as low as 0.8V. At lower voltages, the MOSFET's body diode takes over as an ordinary diode.