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This paper presents a high-precision capacitive angular position sensor (CAPS). The CAPS is designed to be excited by a single voltage to eliminate the matching errors of multi-excitations, and it is mainly composed of excitation electrodes, coupling electrodes, petal-form sensitive electrodes and a set of collection electrodes. A sinusoidal voltage is applied on the excitation electrodes, then the voltage couples to the coupling electrodes and sensitive electrodes without contact. The sensitive electrodes together with the set of collection electrodes encode the angular position to amplitude-modulated signals, and in order to increase the scale factor, the sensitive electrodes are patterned in the shape of petal-form sinusoidal circles. By utilizing a resolver demodulation method, the amplitude-modulated signals are digitally decoded to get the angular position. A prototype of the CAPS is fabricated and tested. The measurement results show that the accuracy of the sensor is 0.0036°, the resolution is 0.0009° and the nonlinearity over the full range is 0.008° (after compensation), indicating that the CAPS has great potential to be applied in high-precision applications with a low cost.