State-Space Randles Cell Model for Instrument Calibration

Abstract

It is desirable to calibrate electrochemical impedance spectroscopy (EIS) instrumentation using a Randles circuit. This presents a challenge as realistic loads, simulated by this circuit, contain theoretical components (Warburg elements) that are difficult to model. This thesis proposes a state-space solution to this problem and explores the process of realizing a digital high-accuracy approximation of a Randles circuit for the purposes of verifying and calibrating EIS instrumentation. Using Valsa, Dvo{\v r}{\'a}k, and Friedl's network approximation of a Warburg element, a collection of state-space relations describing the impedance of a Randles circuit are derived. From these equations the process of realizing a digital system is explored; this includes a discussion on methods of discretization, an overview of the challenges of realizing digital filters, and an analysis of the effects that finite word-length has on the accuracy of the model when using fixed-point hardware.