Rapid time-domain simulation of fractional capacitors with SPICE

Fractional capacitors, commonly called constant-phase elements or CPEs, are used in modeling and control applications, for example, for rechargeable batteries. Unfortunately, they are not natively supported in the well-used circuit simulator SPICE. This manuscript presents and demonstrates a modeling approach that allows users to incorporate these elements in circuits and model the response in the time domain. The novelty is that we implement for the first time a particular configuration of RC elements in parallel in a Foster-type network with SPICE in order to simulate a constant-phase element across a defined frequency range. We demonstrate that the circuit produces the required impedance spectrum in the frequency domain, and shows a power-law voltage response to a step change in current in the time domain, consistent with theory, and is able to reproduce the experimental voltage response to a complicated current profile in the time domain. The error depends on the chosen frequency limits and the number of RC branches, in addition to very small SPICE numerical errors. We are able to define an optimum circuit description that minimizes error while maintaining a short computation time. The scientific value is that the work permits rapid and accurate evaluation of the response of CPEs in the time domain, faster than other methods, using open source tools.