Analytical transfer function for the simulation of the frequency-domain and time-domain responses of the blocked-diffusion Warburg impedance

Abstract

In this study, an analytical transfer function has been developed to simulate the frequency impedance spectrum and the time-domain potential response of the blocked-diffusion Warburg (BDW) impedance. Fundamental electrode and diffusion theories are considered for the derivation of the analytical transfer function representing the BDW impedance. The validation of the analytical transfer function is carried out using parameters extracted from the electrochemical impedance response of a Li-ion battery electrode comprised of silicon nanowires. A Simulink model is developed considering the architecture of the Randles electrical circuit and the new analytical transfer function of the BDW impedance to simulate the frequency impedance spectrum and the dynamic voltage of modern batteries. The Simulink model requires parameters extracted from electrochemical impedance measurements for the simulation of the dynamic voltage of a Li-ion battery electrode and a NiMH battery. The Simulink model comprising the analytical transfer function of the BDW impedance could be a valuable tool for the simulation of the voltage of modern batteries for different applications.