A simple method for a digital readout of Randles impedances

Abstract

The Randles impedance model (RIM) characterizes a wide range of physical phenomena. The model comprises three elements: a resistor in series with a combination of a capacitor and another resistor arranged in parallel. This structure makes determining RIM component values particularly complex. Although such values can be found using Electrical Impedance Spectroscopy (EIS), this process requires a large number of measurements and complex hardware. Other time-based methods reduce the number of measurements, but the hardware involved is still excessive for a portable system, requiring complicated arithmetic calculations that may produce less than accurate results. This article presents a readout method based on time measurements that uses only a simple digital processor (DP) without analog-to-digital converters (ADCs), and two resistors of known value to estimate the RIM parameters in digital format. The method performs three Randles impedance capacitor charge-discharge processes to obtain five time measurements. The results are found by processing the time measurements in the DP using simple arithmetical operations. Despite the simplicity of both the hardware and the reading and calculation methods, errors in the estimates of a range of RIM parameter combinations are among the lowest in the literature, varying between 1.22% and 1.66%, depending on the parameter to be estimated.