RC models of a constant phase element

• Published in: International journal of circuit theory and applications Vol. 41; no. 1; pp. 59 - 67
• Main Authors: Valsa, Juraj, Vlach, Jiri
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2013; Wiley Subscription Services, Inc
• Subjects: Capacitors; constant phase element; fractance; fractional control system; Input impedance; Mathematical models; nanotechnology; Networks; Oscillators; Reproduction; Resistors; Ripples; Warburg diffusion element
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.785

SUMMARY The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between −90° and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright © 2011 John Wiley & Sons, Ltd. The described models consisting of several resistors and capacitors approximate an ideal constant phase element. Their input impedance phase is reasonably constant over several decades of frequency and can have any value between −90° and 0°. The models are much simpler and at the same time much more accurate than any other models of constant phase elements described so far.