RC models of a constant phase element

Abstract

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.

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

“…Unfortunately, these elements are not yet commercially available [17][18][19] and, therefore, they have to be approximated by appropriate integer-order networks. A possible solution for approximating fractional-order capacitors is the employment of an RC network, [20][21][22] but this su®ers from the requirement for re-designing the network in order to change the characteristics of the fractional-order element. The behavior of fractional-order inductors is approximated through the combination of a fractional-order capacitor emulator and a Generalized Impedance Converter (GIC).…”

First-order adjustable transfer sections for synthesis suitable for special purposes in constant phase block approximation

“…In addition, other drawbacks limit utilization of solution in [18], see Table 1. Demanded transfer function has form: K(s) = (s ± g m2 /C)/(s + g m1 /C) or K(s) = (s ± g m1 /C)/(s + g m2 /C), which is required for synthesis with bilinear systems [1,4]. All intentionally designed AP/bilinear sections in this paper have this form of transfer function.…”

“…Therefore, the main aim of this paper is simple utilization of signal-flow graphs (SFG) [8,9] to the design of electronically controllable AP (circuit with non-minimal argument) and pseudo AP sections (circuits with minimal argument) and their application. A substantial attention is given to separated control of zero and pole frequency of AP sections that could be very useful in some cases for diverse forms of adjusting and control in the circuit synthesis (circuits with minimal and non-minimal argument for so-called CPEs [1], blocks and special types of transfer characteristics in fractional-order applications [2][3][4]). All circuits discussed in this paper offer commonly required benefits: (I) Grounded capacitors.…”

“…On the other hand, rest of the most known filtering systems such as low-pass, high-pass, band-pass, and band-reject transfer functions are so-called minimal argument circuits wherein zeros and poles are in the left-half-plane. In recent years, an important attention was given to circuit systems with constant phase character [1] (and references cited therein) and systems with special type of transfer characteristic in fractional-order applications [2][3][4]. Synthesis of some from these specific active circuits requires building blocks similar to AP sections [4].…”

An ultra-broadband single-component fractional-order capacitor using MoS2-ferroelectric polymer composite

“…The resulting circuit's overall impedance yields a transfer function with a non-integer order. [27][28][29] However, oftentimes, the number of resistors and capacitors in the RC network is very high (adding an extra weight/cost to the system) and/or their resistance and capacitance values are impractical. To alleviate these bottlenecks, a method, which realizes the response of the RC network, using a microscale structure consisting of polyvinylidene fluoride (PVDF) ferroelectric polymer composites embedding carbon-based nanomaterials, particularly reduced graphene oxide (rGO) sheets and multi-walled carbon nanotubes (MWCNTs), has been employed.…”