The most common CPE is a constant phase angle capacitor where the phase angle is between 0 and -90 degrees. This circuit element is used for modeling physical properties in e.g. bioimpedance and electrochemistry. It also describes a super capacitor. The CPE is to some degree also related to a memristor. Many ordinary real-life capacitors are in practice constant phase angle elements also with a phase angle just slightly less in absolute value than 90 degrees, see YouTube video referred to below.
Circuit realizations have been proposed based on passive networks of RC-circuits, and active circuits based on op-amps. These circuits vary in how large bandwidth they will be valid for, but the larger bandwidth, the better. In 2021 we proposed a time-varying circuit and it is of special interest to study how that can be implemented, for instance with gyrators.
This MSc thesis consists in studying this phenomenon, look at possible ways of implementing it using more or less standard circuit elements (probably analog), and build and characterize prototypes of CPE circuits.
This thesis work will give plenty of opportunity to demonstrate that you are able to analyze a new and unknown problem, and understand it enough to realize it in a concrete circuit. Although the problem stated here may not be directly applicable to a specific job, the skills learned will still be applicable.
References:
- Valsa, J., & Vlach, J. (2013). RC models of a constant phase element. International Journal of Circuit Theory and Applications, 41(1), 59-67
- Elwakil, A. S., Allagui, A., Maundy, B. J., & Psychalinos, C. (2016). A low frequency oscillator using a super-capacitor. AEU-International Journal of Electronics and Communications, 70(7), 970-973.
- S Holm, T Holm, Ø G. Martinsen, Simple circuit equivalent for the constant phase element, PLOS ONE, March 2021
- S Holm, Time domain characterization of the Cole-Cole dielectric model, J Electr. Bioimpedance 11.1: 101-105, Dec. 2020
- S. Holm, Waves with Power-Law Attenuation, Springer, 2019, Ch. 5.8
- Capacitor with fractional derivative characteristics, also called capacitor soakage or dielectric absorption, YouTube video