A scheme is described to switch the power supply to the MEMS microphone on and off in a cyclic manner that is synchronized with the associated ADC sampling rate. In this way the MEMS microphone amplifier, whether it is a J-FET transistor or an operational amplifier, is off most of the cycle time, and is turned on only for a few micro-seconds prior to the sample-and-hold timing of the ADC device. By this method, the average power consumption of an existing analog MEMS microphone can be reduced by a factor of 10 or more.