On the Precision of Impedance Argument Estimation in the Presence of Additive Noise

Abstract

Estimating the argument of an electrical impedance is an important task in many engineering fields. Modern systems usually employ data acquisition systems to sample and digitize the voltage and current signals obtained by stimulating the unknown impedance with a sinusoidal signal. The presence of nonideal phenomena in signal generation or signal measurement inevitably leads to an increased uncertainty in impedance argument estimation. This work focuses on the effect of additive noise and proposes an analytical expression that can be easily used to compute the impedance argument standard deviation as a function of additive noise precision, number of samples, stimulus signal amplitude, current sampling resistance value, and nominal impedance modulus value. It specifically considers the presence of additive noise on both the voltage and current measuring channels. The analytical expression given is important when designing the measurement system to determine the minimum number of samples that should be acquired as well as in computing the confidence intervals for the estimations made using this method.