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This paper presents an energy-efficient capacitive-sensor interface with a period-modulated output signal. This interface converts the sensor capacitance to a time interval, which can be easily digitized by a simple digital counter. It is based on a relaxation oscillator consisting of an integrator and a comparator. To enable the use of a current-efficient telescopic OTA in the integrator, negative feedback loops are applied to limit the integrator's output swing. To obtain an accurate ratiometric output signal, auto-calibration is applied. This eliminates errors due to comparator delay, thus enabling the use of a low-power comparator. Based on an analysis of the stability of the negative feedback loops, it is shown how the current consumption of the interface can be traded for its ability to handle parasitic capacitors. A prototype fabricated in 0.35 μm standard CMOS technology can handle parasitic capacitors up to five times larger than the sensor capacitance. Experimental results show that it achieves 15-bit resolution and 12-bit linearity within a measurement time of 7.6 ms for sensor capacitances up to 6.8 pF, while consuming only 64 μA from a 3.3 V power supply. Compared to prior work with similar performance, this represents a significant improvement in energy efficiency.