Programmable constant phase element realization with crossbar arrays

Constant Phase Elements (CPEs) have been widely used in many applications due to the extra degree of freedom, which offers new responses and behaviors.

This paper proposes a new programmable CPE realization using resistive crossbar arrays. By programming the resistive devices, different CPEs can be obtained.

The proposed realization can be approximated as a weighted sum of low and high pass filters having the same cut-off frequency (i.e., Lapicque model). The closed-form approximation expression is derived, and then the Flower Pollination Algorithm (FPA) is used to find the optimal values of the network components.

Different design examples are given over the frequency range of 10^6-10 rad/sec to prove the ability of this realization achieving any fractional order with less than 5% relative error in both phase and pseudo-capacitance. Monte-Carlo simulations are performed to evaluate the sensitivity of the proposed realization against device variability. In addition, multiple CPEs can be designed at the same time by utilizing the multiple ports of the crossbar array. The proposed realization is compared with two other state-of-art realizations showing comparable results as standalone realization and within fractional-order relaxation oscillator application.

The proposed crossbar realization has proven its ability to realize any CPE with acceptable error. In addition, this multiple-port design offers high flexibility and on-the-fly switching of the CPE.