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Magnitude detection, such as envelope detection or RMS estimation, is needed for many low-power signal-analysis applications. In such applications, the temporal accuracy of the magnitude detector is as important as its amplitude accuracy. We present a low-power audio-frequency magnitude detector that simultaneously achieves both high temporal accuracy and high amplitude accuracy. This performance is achieved by rectifying the signal with a high-ripple peak detector and then averaging this rectified signal with an adaptive-time-constant filter. The time constant of this filter decreases with increasing amplitude, enabling the filter to quickly respond on a short time scale to transients, while steady-state ripple is averaged on a longer time scale. The circuit has been fabricated in a 0.18 μm CMOS process and consumes only 1.1 nW-1.08 μW when tuned for operation from 20 Hz-20 kHz. It exhibits a dynamic range of 70 dB across typical speech frequencies.