A simple method for fabricating a constant phase element (CPE) has been discussed. Dependence of the phase angle on several physical parameters have also been elaborated. Finally, a fractional-order differentiator circuit has been constructed using the CPE, and its performance has been compared with the simulated results

This paper reports the fabrication of a fractional order element (FOE) with predefined specifications. The FOE is a circuit element similar to resistance, capacitance, and inductance generally used in electrical network. The specifications of integer order elements, i.e., inductance, resistance, and capacitance, are defined by the magnitude only as their exponents are of fixed value, namely, - 1, 0, and +1, respectively. The specialty of FOE is that both its magnitude and exponent value have to be defined, where the value of the exponent dictates the behavior. This paper elaborately discusses the methodology of realizing a fractional order capacitor named here as FOE (or, in general, FOE). It has been found that a FOE can be realized by dipping a capacitive-type probe, coated with a porous film of polymer of particular thickness, into a polarizable medium. The thickness, uniformity, and stability of the porous film, on the electrode, are responsible for different exponent values.

This paper introduces a tunable fractional order parallel resonator (FOPR) whose resonating frequency can be tuned by the coefficient of a fractional order (FO) element (fractor). At the same time, its Q-factor can be set very high (theoretically infinite) by varying its resistor. Using this FOPR circuit, two simple FO filters (FO bandpass and FO notch) are also developed. The paper includes detail sensitivity analyses of these circuits for various circuit parameters and describes how different design parameters of proposed FOPR and FO filters are chosen accordingly. Proposed FOPR and FO filters are simulated in MATLAB and realized in hardware. The hardware circuits are tested practically, and detail experimental results are provided. It is found that the experimental data are in good agreement with the simulation data. In hardware, the realized FOPR has achieved a Q-factor up to 360, and the realized FO notch filter has Q > 10 when its attenuation is more than 30 dB. Different practical aspects of filter tuning are also described in detail.

Here, we propose the fabrication of a solid state fractional capacitor for which constant phase (CP) angles were attained in different frequency zones: 110 Hz–1.1 kHz, 10 kHz–118 kHz, and 230 kHz–20 MHz. The configuration makes use of epoxy resin as the matrix in which multi-walled carbon nanotubes (MWCNTs) are dispersed. Adhesive nature of the epoxy resin is utilized for binding the electrodes, which avoids the extra step for packaging. The fractional capacitive behavior is contributed by the distribution of time constants for the electron to travel from one electrode to the other. The distributive nature of the time constant is ensured by inserting a middle plate which is coated with a porous film of polymethyl-methacrylate in between the two electrodes. The phase angle trend for the configuration is studied in detail, and it is observed that as the % of carbon nanotubes (CNTs) loading increases, the CP angle increases from $-85°$ to $-45°$ in the frequency zones above 100 Hz. The developed device is compact and it can be easily integrated with the electronic circuits.