Compressive sensing-based wideband capacitance measurement with a fixed sampling rate lower than the highest exciting frequency

In this paper, an under-sampling method for wideband capacitance measurement was proposed by using the compressive sensing strategy. As the excitation signal is sparse in the frequency domain, the compressed sampling method that uses a random demodulator was adopted, which could greatly decrease the sampling rate. Besides, four switches were used to replace the multiplier in the random demodulator. As a result, not only the sampling rate can be much smaller than the signal excitation frequency, but also the circuit's structure is simpler and its power consumption is lower. A hardware prototype was constructed to validate the method. In the prototype, an excitation voltage with a frequency up to 200 kHz was applied to a capacitance-to-voltage converter. The output signal of the converter was randomly modulated by a pseudo-random sequence through four switches. After a low-pass filter, the signal was sampled by an analog-to-digital converter at a sampling rate of 50 kHz, which was three times lower than the highest exciting frequency. The frequency and amplitude of the signal were then reconstructed to obtain the measured capacitance. Both theoretical analysis and experiments were carried out to show the feasibility of the proposed method and to evaluate the performance of the prototype, including its linearity, sensitivity, repeatability, accuracy and stability within a given measurement range.