There are several different types of precision rectifier, but it is necessary to explain what a precision rectifier actually is. In its simplest form of circuit, a half wave precision rectifier is implemented using an op amp, and includes the diode in the feedback loop. This is the figure of the circuit.
For a low frequency positive input signal, 100% negative feedback is applied when the diode conducts. The forward voltage is effectively removed by the feedback, and the inverting input follows the positive half of the input signal almost perfectly. When the input signal becomes negative, the op amp has no feedback at all, so the output pin of the op amp swings negative as far as it can. Assuming 15V supplies, that means perhaps -14V on the op amp output.
For a low frequency positive input signal, 100% negative feedback is applied when the diode conducts. The forward voltage is effectively removed by the feedback, and the inverting input follows the positive half of the input signal almost perfectly. When the input signal becomes negative, the op amp has no feedback at all, so the output pin of the op amp swings negative as far as it can. Assuming 15V supplies, that means perhaps -14V on the op amp output.
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