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.

小数电容器通常称为恒定相位元件或 CPE，用于建模和控制应用，例如可充电电池。不幸的是，常用的电路模拟器 SPICE 本身并不支持它们。本手稿提出并演示了一种建模方法，允许用户将这些元件合并到电路中并在时域中对响应进行建模。新颖之处在于，我们首次使用 SPICE 在 Foster 型网络中并行实现 RC 元件的特定配置，以便在定义的频率范围内模拟恒定相位元件。我们证明该电路在频域中产生所需的阻抗谱，并在时域中显示对电流阶跃变化的幂律电压响应，与理论一致，并且能够重现对复杂的实验电压响应时域中的当前轮廓。除了非常小的 SPICE 数值误差之外，误差还取决于所选的频率限制和 RC 分支的数量。我们能够定义一个最佳电路描述，在保持较短的计算时间的同时最大限度地减少错误。科学价值在于，这项工作允许使用开源工具快速、准确地评估 CPE 在时域中的响应，比其他方法更快。