A compact model of the ZARC for circuit simulators in the frequency and time domains

Equivalent-circuit models containing fractional-order elements are often employed to make use of fractional-order calculus in the frequency and time domains in a variety of applications. Many of these circuits contain constant-phase elements that appear in parallel with a resistor in a configuration called ZARC. But to avoid fractional order derivatives and include it in circuit simulators, the ZARC itself can also be replaced by equivalent circuit models that only contain integer order elements, such as resistors and capacitors. In this article, a novel compact model is presented to substitute the ZARC by a multiple-RC network. This model is valid for a continuous value of the order exponent and is applicable over a very wide range of frequencies, making it useful in both the frequency and time domains. Since it uses only basic functions and operators, it has been easily implemented as a subcircuit in circuit simulators. The validity of the model has been verified and it has been compared with some previously proposed passive circuit models. The model has also been discussed in relation to the initialization problem, which is an often overlooked challenge in fractional-order circuits.