A Switched-Capacitor CVC and CFC for Capacitive Sensors Representable using $\pi$-Model

In this paper, a new Capacitance-to-Voltage Converter (CVC) and Capacitance-to-Frequency Converter (CFC) for capacitive $\pi$-model are presented. A simple and effective closed-loop mechanism is proposed that provides the output voltage and frequency proportional to the sensor capacitances in the $\pi$-model. The proposed feedback mechanism ensures that the linearity performance of the converter is not affected by the non-linearity of the elements in the forward path. A $\pi$-model capacitor comprises of three capacitances, $C_{x2}$: the capacitance formed between the electrodes and $C_{x1}$ and $C_{x3}$: capacitance between each electrode and ground. Such $pi$-model representation is very effective in sensing the relative position of the measurand (by measuring $C_{x1}$ and $C_{x3}$) in addition to the measurand detection (from capacitance $C_{x2}$). The proposed switched-capacitor based converter uses only DC source for excitation and hence achieve high accuracy measurements. A prototype has been developed and verified the practicality of the converter for sensor capacitance ranges from 20 pF to 200 pF. The worst-case linearity error of 3.5% was observed when operated in open-loop configuration, and the error reduced to 0.28% when operated in the proposed feedback configuration. The developed prototype exhibited negligible cross-sensitivity between the capacitance measurement in the $\pi$-model and can provide the best measurement rate compared to the existing architectures of capacitive $\pi$-models.