Fast impedance measurements at very low frequencies using curve fitting algorithms

The method for reducing the time of impedance measurements at very low frequencies was proposed and implemented. The reduction was achieved by using impedance estimation algorithms that do not require the acquisition of the momentary voltage and current values for at least one whole period of the excitation signal. The algorithms were based on direct least squares ellipse and sine fitting to recorded waveforms. The performance of the algorithms was evaluated based on the sampling time, signal-to-noise (S/N) ratio and sampling frequency using a series of Monte Carlo experiments. An improved algorithm for the detection of the ellipse direction was implemented and compared to a voting algorithm. The sine fitting algorithm provided significantly better results. It was less sensitive to the sampling start point and measured impedance argument and did not exhibit any systematic error of impedance estimation. It allowed a significant reduction of the measurement time. A 1% standard deviation of impedance estimation was achieved using a sine fitting algorithm with a measurement time reduced to 11% of the excitation signal period.