Analysis of a three-component impedance using two sine waves

A common method to identify several components modeling complex impedance is by impedance spectroscopy. The unknown impedance is measured by applying several sine waves and the impedance components are determined by curve-fitting to the results obtained at each measurement frequency. This paper presents a novel method able to determine three independent impedance components by using only two sine waves instead of the customary three sine waves that would be required in impedance spectroscopy. Each sine wave yields two measurement results: one in phase with the injected signal and another one in quadrature (90° phase shift) with that signal. Using two sine waves yields four measurement results and solving the corresponding equation system would permit us to calculate up to four independent impedance components. We have derived the equations needed to calculate three independent components and tested the method by measuring an impedance network consisting of three components using a commercial impedance analyzer. The resulting error is less than 1.3% for each component. The proposed method outperforms common impedance spectroscopy in measurement time, calculation power required, and instrumentation simplicity.