A High-Precision Circuit-Simulator-Compatible Model for Constant Phase Element Using Rational Function Approximation

Constant phase elements (CPEs) are commonly used in bioelectronic systems, to model the impedance of bioelectrodes and electrode-electrolyte interfaces. To simulate the systems with an electronic design automation tool, a circuit-simulator-compatible model of the CPE is required to use bioelectrodes in circuit simulation. This paper applies rational function approximation to the impedance of CPEs as a function of frequency, which is able to be implemented with Verilog-A language. In comparison to previously published works which simply approximate a CPE into several serially connected RCs, our work illustrates the theoretical basis behind the approximation with RCs and provides a method perform the approximation, thus resulting in a smaller relative root mean square error of impedance magnitude and phase (4 orders of magnitude lower using 25 RCs) within a bounded frequency range. To validate the model accuracy, it is applied to the modeling of human cochleae, with the simulated results correlating well with the measured results. Furthermore, this model is implemented in a circuit that includes a bioelectrode and a thin-film transistor switch, showing the capability for circuit simulation with CPEs.