SUMMARYThe 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.