This paper presents two general topologies of fractional order oscillators. They employ Current Feedback Op-Amp (CFOA) and RC networks. Two RC networks are investigated for each presented topology. The general oscillation frequency, condition and the phase difference between the oscillatory outputs are investigated in terms of the fractional order parameters. Numerical simulations and P-Spice simulation results are provided for some cases to validate the theoretical findings. The fractional order parameters increase the design flexibility and controllability which is proved by the provided experimental results. © 2018 IEEE.
Frational Order Inverse Filters Based on CCII Family
This paper proposes two generalized topologies of fractional order inverse filters (FOIF). All possible realizations of each topology are investigated using the second generation current conveyor (CCII) family. Inverse fractional highpass (IFHPF), inverse fractional bandpass (IFBPF), and inverse fractional lowpass (IFLPF) filters are realized using the same topology based on the generalized admittances. Numerical and P-Spice simulation results are presented for selected cases to approve the theoretical findings. The fractional order parameters increase the design flexibility and controllability which is validated experimentally. © 2019 IEEE.
A Universal Fractional-Order Memelement Emulation Circuit
This paper proposes a current-/voltage-controlled universal emulator that can realize any fractional-order memelements (FOME). The proposed emulator consists of second-generation current conveyors (CCII) block, two switches, and a multiplier/divider block. The first switch controls the emulator mode (voltage or current), while, the other controls the type of the emulated FOME. The influence of the fractional-order capacitor (FOC) on the pinched hysteresis loop (PHL) area, is discussed which increases the controllability on the double loop area and the working frequency range. Numerical and PSPICE simulations are presented for selected cases to prove the theoretical findings. © 2019 IEEE.
On Series Connections of Fractional-Order Elements and Memristive Elements
This paper proposes a current-controlled fractional-order memristor emulator based on one active building block. The emulator consists of a multiplication mode current conveyor (MMCC) block with three passive elements. Additionally, the series connection of fractional-order inductor (FOI) and fractional-order capacitor (FOC) with memristive elements in the i-v plane is demonstrated numerically for different cases. Changing the order of the FOC or FOI and its effect on the pinched hysteresis loop area are investigated, which improve the controllability of the double loop area, the location of the pinched point, and the operating frequency range. Numerical, PSPICE simulation results, and experimental verification are investigated for different cases to approve the theoretical findings. Moreover, a sensitivity analysis using Monte Carlo simulations for the tolerance of the discrete components of the memristor emulator is investigated. © 2020 IEEE.
Generalized family of fractional-order oscillators based on single CFOA and RC network
This paper presents a generalized family of fractional-order oscillators based on single CFOA and RC network. Five RC networks are investigated with their general state matrix, and design equations. The general oscillation frequency, condition and the phase difference between the oscillatory outputs are introduced in terms of the fractional order parameters. They add extra degrees of freedom which in turn increase the design flexibility and controllability that is proved numerically. Spice simulations are introduced to validate the theoretical findings. © 2017 IEEE.
Butterworth passive filter in the fractional-order
In this paper, the generalized analysis of the first Butterworth filter based on two passive elements is introduced in the fractional-order sense. The fractional-order condition of the Butterworth circuit is presented for the first time where it will lead us back to the known condition of the integer-order circuit when the two fractional-orders equal one. Therefore, the conventional behavior of the integer-order circuit is a narrow subset of the fractional-order ones. The circuit is studied under same and different order cases, and verified through their numerical simulations. Stability analysis is also introduced showing the poles location in the fractional-order versus integer order cases. © 2011 IEEE.
General procedure for two integrator loops fractional order oscillators with controlled phase difference
This paper studies the fractional order two integrator loop based sinusoidal oscillators with two fractional order elements of different orders. Two general cases have been discussed and closed forms for the oscillation frequency and oscillation condition are driven. In addition, the effect of the fractional orders on the phase difference between the two oscillatory outputs is also presented. Design procedure for the two general cases is illustrated with numerical examples and validated through circuit simulations for three examples of oscillators based on two integrator loops. © 2013 IEEE.
CCII based KHN fractional order filter
This work aims to generalize the analysis of the fractional order filter to work for the low-pass, band-pass and high-pass responses. So, general expression for the maximum and minimum frequency points and the half power frequency points will be derived. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced. Besides, the effect of the fractional orders on the frequency response will be presented. Finally, to verify the numerical analysis and the proposed design procedure, circuit simulation will be used. © 2013 IEEE.
Current feedback operational amplifier (CFOA) based fractional order oscillators
This paper presents a study of fractional order oscillators based on current feedback operational amplifiers (CFOA). Two general cases have been discussed for the oscillation frequency and condition with the use of two fractional order elements of different orders. Design procedure for the two general cases is illustrated with numerical discussions. Circuit simulations for some special cases are presented to validate the theoretical findings. The simulations have been done using Ad844 commercial CFOA model © 2014 IEEE.
Fractional order oscillators with single non-zero transmission matrix element
This paper presents a study of fractional order oscillator design based on a matrix. The presented oscillator consists of a general two port network and three impedances. Only two port with single element in its transmission matrix is discussed which gives four possible networks. Different combinations for one element have been investigated. The impedances associated with the studied networks are series or parallel connection of resistors in addition to fractional order capacitors. The characteristic equation, oscillation frequency and condition for each combination are introduced. Numerical discussions of the presented oscillators with Spice simulations are presented to validate the theoretical findings. © 2015 IEEE.