Fractional-order Capacitor Research Articles

CNTFET-Based Single-Ended Fractional Order Colpitts Oscillator: Design, Simulation and Comparative Analysis

In this paper, we design and simulate a Single-Ended Colpitts Oscillator (CO) in integer and fractional order domains. The oscillators are realized in 32[Formula: see text]nm node conventional MOSFET and carbon nanotube field effect transistor (CNTFET) technologies. Therefore, four COs have been designed, simulated and rigorously compared. These include integer order conventional MOSFET-based CO, fractional order MOSFET-based CO, CNTFET-based integer order CO and CNTFET-based fractional order CO, all based on 32-nm technology nodes. The fractional order approach has been used as it results in better control over the phase and frequency of the oscillator. Herein, fractional order capacitors of various orders, used in realizing the fractional order COs, are realized and their frequency responses are studied. This is being done to ensure whether the designed pseudo-capacitances have fractional behavior or not in the desired frequency and phase spectrum. It has been observed that the variation of fractional order [Formula: see text] from 0.4 to 0.81 has resulted in a slight reduction of oscillation frequency from 1.68[Formula: see text]GHz ([Formula: see text]) to 1.351[Formula: see text]GHz ([Formula: see text]) keeping the pseudo-capacitance same at 0.3[Formula: see text]nF in MOS-based topology. Since the fractional order realization increases the circuit complexity and power consumption, therefore, CNTFET-based integer order as well as fractional order COs have been designed. The CNTFET-based fractional order CO retains the advantages of the fractional order domain as well as the power efficiency of CNTFETs. Further, it has been observed that integrating fractional-order capacitor (FOC) with the CNTFET CO results in a much larger constant phase zone (CPZ), an important performance measuring parameter. A rigorous comparative analysis of the four COs designed in this work has been performed.

Optimized coordinated control method with virtual inertia based on fractional impedance model for charging stations

Due to the EV (Electric Vehicles) charging stations are characterized by weak damping and low inertia, the EV with a high degree of uncertainty can easily have an impact on the stability of the charging station system. Therefore, this paper proposes an optimization control method to improve the system inertia effect based on the fractional order impedance model of the charging station. This paper presents a study on establishing a fractional impedance model for charging stations, using the deviation between theoretical impedance spectra and actual measurements as a criterion. The goal is to enhance system inertia and optimize the parameters of the fractional-order controller to improve the supporting capacity of the charging station system and enhance its dynamic response. Initially, considering the fractional characteristics of the EV load, a fractional impedance model of the charging station is established. The analysis demonstrates that the fractional-order capacitor provides inertia to the system, enhancing its inertia support capability. In addition, a virtual inertia control strategy based on fractional-order PID (FOPID) is designed. Finally, an improved particle swarm optimization algorithm is utilized to optimize the control parameters. Through experimental verification under different operating conditions, it has been demonstrated that the fractional-order control strategy can achieve a dynamic response time of approximately 0.025s and limit the voltage deviation within 5%. Furthermore, the rotational inertia can rapidly increase to the maximum value satisfying the objective function within 0.05s. The results indicate that this control method effectively suppresses the DC voltage and power oscillations in the distribution grid.

Modeling and Control Research of Fractional-Order Cascaded H-Bridge Multilevel STATCOM

Abstract: This paper introduces fractional-order capacitors and fractional-order inductors into the conventional integer-order cascaded H-bridge multilevel static compensator (ICHM-STATCOM), thereby constructing the main circuit of the fractional-order cascaded H-bridge multilevel static compensator (FCHM-STATCOM). Mechanism-based modeling is employed to establish switching function models and low-frequency dynamic models for the FCHM-STATCOM in the three-phase stationary coordinate system (a-b-c). Subsequently, fractional-order rotating coordinate transformation is introduced to establish the mathematical model of the FCHM-STATCOM in the synchronous rotating coordinate system (d-q). Additionally, a fractional-order proportional-integral (FOPI)-based fractional-order dual closed-loop current decoupling control strategy is proposed. Finally, this paper validates the correctness of the established mathematical models through digital simulation. Moreover, the simulation results demonstrate that by appropriately selecting the order of fractional-order capacitors and fractional-order inductors, the FCHM-STATCOM exhibits superior dynamic and static characteristics compared to the conventional ICHM-STATCOM, and the FCHM-STATCOM provides a more flexible reactive power compensation solution for power systems.

On the Influence of Fractional-Order Resonant Capacitors on Zero-Voltage-Switching Quasi-Resonant Converters

This paper focuses on the influence of the fractional-order (FO) resonant capacitor on the zero-voltage-switching quasi-resonant converter (ZVS QRC). The FO impedance model of the capacitor is introduced to the circuit model of the ZVS QRC; hence, a piecewise smooth FO model is developed for the converter. Numerical solutions of the converter are obtained by using both the fractional Adams–Bashforth–Moulton (F-ABM) method and Oustaloup’s rational approximation method. In addition, the analytical solution of the converter is obtained by the Grünwald–Letnikov (GL) definition, which reveals the influence of the FO resonant capacitor on the zero-crossing point (ZCP) and resonant state of the converter. An experimental platform was built to verify the results of the theoretical analysis and numerical calculation.

MO-CCCII-Based Single-Input Multi-Output (SIMO) Current-Mode Fractional-Order Universal and Shelving Filter

This study introduces an innovative filter topology capable of providing simultaneous positive and negative gain outputs for one-fractional order LP, with high-pass, all-pass, and fractional-order shelving filter responses. The circuit, utilizing multi-output second-generation current-controlled conveyors, stands out as the first to deliver ten outputs, incorporating both integer and fractional-order filter responses, without requiring additional components. Its current-mode design simplifies the process, employing minimal active and grounded passive elements, making it appropriate for low-voltage/low-power applications. The filter utilizes fifth-order Oustaloup approximation and Foster type-I RC networks for fractional-order capacitors, providing enhanced control over the transition slope. PSpice simulations confirmed a 1 kHz cut-off, showcasing low power consumption, minimal noise, and a wide dynamic range, positioning the filter as suitable for sensors, control, and acoustic applications.

Fractional-Order LCL Filters: Principle, Frequency Characteristics, and Their Analysis

The fractional-order LCL filter, composed of two fractional-order inductors and one fractional-order capacitor, is a novel fractional-order π-type circuit introduced in recent years. Based on mathematical modeling, this article comprehensively studies the principles and frequency characteristics of fractional-order LCL filters. Five critical properties are derived and rigorously demonstrated. One of the most significant findings is that we identify the necessary and sufficient condition for resonance in fractional-order LCL filters when the sum of the orders of the fractional-order inductors and the fractional-order capacitor is equal to 2, which provides a theoretical foundation for effectively avoiding resonance in fractional-order LCL filters. The correctness of our theoretical derivation and analysis was confirmed through digital simulations. This study reveals that fractional-order LCL filters exhibit more versatile operational characteristics than traditional integer-order LCL filters, paving the way for broader application prospects.

Fractional-Order Modeling of Arterial Compliance in Vascular Aging: A Computational Biomechanical Approach for Investigating Cardiovascular Dynamics.

Goal: The goal of this study is to investigate the application of fractional-order calculus in modeling arterial compliance in human vascular aging. Methods: A novel fractional-order modified arterial Windkessel model that incorporates a fractional-order capacitor (FOC) element is proposed to capture the complex and frequency-dependent properties of arterial compliance. The model's performance is evaluated by verifying it using data collected from three different human subjects, with a specific focus on aortic pressure and flow rates. Results: The results show that the FOC model accurately captures the dynamics of arterial compliance, providing a flexible means to estimate central blood pressure distribution and arterial stiffness. Conclusions: This study demonstrates the potential of fractional-order calculus in advancing the modeling and characterization of arterial compliance in human vascular aging. The proposed FOC model can improve our understanding of the physiological changes in arterial compliance associated with aging and help to identify potential interventions for age-related cardiovascular diseases.

An electronically tunable fractional order inductor employing VD-EXCCII

An electronically tunable Fractional Order Inductor (FOI) for both grounded as well as floating circuits is designed using a Voltage Differencing Extra-X Current Conveyor (VD-EXCCII), grounded MOS resistor, and grounded Fractional Order Capacitor (FOC) with four MOS switches. The grounded positive and negative fractional order functionality can be easily executed by using the gate voltage (VG) of an MOS transistor. Ideal as well as the non-ideal port characteristics of VD-EXCCII are also studied in the presence of the parasites available in the active block VD-EXCCII. The verification of the proposed FOI is first simulated through PSPICE in which the VD-EXCCII uses 0.18 μm TSMC CMOS parameter. In addition to traditional impedance verification of the proposed FOI, an application of the FOI is translated for the design of sixth order High-Pass Filter (HPF), sixth order Low-Pass Filter (LPF), and a voltage mode Multiple Input Single Output Universal Filter (MISO-UF) design. Moreover, the performance of the proposed negative FOI circuit is also demonstrated through a Fractional Inductance Cancellation Circuit (FICC).

Design of a Fractional Order Low-pass Filter Using a Differential Voltage Current Conveyor

In this paper, an active implementation of a differential voltage current conveyor (DVCC) based on a low-pass filter operating in the fractional order domain is presented. The transfer function for a fractional order system is dependent on the rational approximation of sα. Different methods used for calculating the rational approximation, including Carlson, Elkhazalil, and curve fitting, are evaluated here. Finally, to validate the theoretical results, a fractional order Butterworth filter is simulated in the Pspice environment using the 0.5 micrometer CMOS technology with an R-C network-based fractional order capacitor. Additionally, using the Monte Carlo analysis, the impact of current and voltage faults on DVCC response is investigated. It has been inferred that realization with a wider bandwidth is possible.

Frequency and temperature-dependence ZnO based fractional order capacitor using machine learning

This paper investigates the fractional order behavior of ZnO ceramics at different frequencies. ZnO ceramic was prepared by high energy ball milling technique (HEBM) sintered at 1300 °C to study the frequency response properties. The frequency response properties (impedance and phase angles) were examined by analyzing through impedance analyzer (100 Hz - 1 MHz). Constant phase angles (84 °-88 °) were obtained at low temperature ranges (25 °C-125 °C). The structural and morphological composition of the ZnO ceramic was investigated using X-ray diffraction techniques and FESEM. Raman spectrum was studied to understand the different modes of ZnO ceramics. Machine learning (polynomial regression) models were trained on a dataset of 1280 experimental values to accurately predict the relationship between frequency and temperature with respect to impedance and phase values of the ZnO ceramic FOC. The predicted impedance values were found to be in good agreement (R2 ∼ 0.98, MSE ∼ 0.0711) with the experimental results. Impedance values were also predicted beyond the experimental frequency range (at 50 Hz and 2 MHz) for different temperatures (25°C - 500°C) and for low temperatures (10 °C, 15 °C and 20 °C) within the frequency range (100 Hz - 1 MHz).

Fractional-Order MOS Capacitor: Experimental Results and Monte Carlo Analysis

In this work, an experimental implementation of a Fractional-order MOS capacitor using a fractal tree structure in discrete circuits was carried out in order to validate the theoretical results obtained of the simulations. In addition, a Monte Carlo analysis was performed to determine the sensitivity of the electrical circuit to the variation of some parameters.In these analyzes were observed that for a tolerance of 20% in the device values and for 2σ above and below the median values(for both, width, and initial frequency value of fractal zone) it is noticed a deviation of 18% and -14%, respectively, which is areasonable deviation for a group that contains more than 90% of the samples.

Fractional-Order-Based Low-Order Harmonic Current Suppression Method Considering Asymmetrical Capacitor Parameters

The problem of the second harmonic current (SHC) on the dc bus side of the single-phase inverter system has attracted widespread attention. The active power decoupling method based on dual capacitors can suppress SHC effectively. However, the asymmetrical capacitor parameters will deteriorate the SHC suppression performance and lead to the first-order harmonic current. To eliminate these low-order harmonic currents, this article proposes a SHC suppression method based on the fractional-order capacitor (FOC), where no power supply is employed and little loss is incurred. The capacitance and the order of the proposed FOC can, both, be adjusted. The principle and operating mode of the FOC are analyzed, and the control strategy of adjustment is given. The method can realize the SHC suppression with the advantages of a simple control strategy, hot-swappable, and high flexibility. Most importantly, the method can effectively suppress the first-order harmonic current caused by the asymmetrical parameters of the capacitors. Finally, an 800 W prototype based on the proposed method is built, and the simulation and experimental results both verify the effectiveness of the proposed method.

Passive realization of the fractional‐order capacitor based on fractional‐order inductor and its application

SummaryThis paper investigates a new implementation of a passive fractional‐order capacitor (FOC) based on a single‐component fractional‐order inductor (FOI). The significance of this approach lies in providing the fractional‐order passive circuit to synthesize an FOC, which avoids the approximation that only depends on the integer‐order transfer function and reflects truly the infinite‐dimensional nature of fractional‐order impedance characteristic. For this purpose, the realizable conditions of this passive FOC are obtained and the main ideas of the proposed method are described by examples. The sensitivity of the impedance magnitude and phase angle on required components parameters is also analyzed in order to facilitate the design of the FOC emulator. Furthermore, the bandwidth is extended by modular structures connected in series, and the proposed approach shows an improvement over some previous methods in terms of accuracy. Also, based on the fractional calculus Grünwald–Letnikov definition, a single‐component FOI circuit element is packaged to build simulation circuit in Matlab/Simulink, and the effectiveness of the proposed method are validated by simulated and experimental results. In the application of an FOC, the results from in the series–parallel fractional‐order RLCβ bandreject filter circuit indicate that the fractional‐order counterpart can reduce the ripple and improve the suppression level at a certain frequency, and the peak amplitude and the overshoot decrease initially with decreasing order. Moreover, under the fixed inductance, capacitance, and resistance, the rise time varies almost inversely with order, whereas the setting time is on the decrease as the order is decreasing.

Packaged Flexible Planar Copper Foil Fractional-Order ‘0.61–0.87’ Capacitors: Series/Parallel Combinations

The fabrication of packaged, flexible, and planar fractional-order capacitors (FOCs) using copper foil electrodes and thin films of PVDF polymer nanocomposite dielectric is presented in this paper. An extensive comparison of FOC properties is made by using two separate conductive fillers, i.e., graphene nanosheets (GNS) and reduced graphene oxide (rGO). Similar fractional-order is observed at a particular filler loading in both types of FOCs; however, differences in the pseudocapacitance values and width of the constant phase (CP) zone exists. Fractional order α (alpha) is reported to vary in the range 0.61–0.87 in impedance measurements made on individual samples of rGO/PVDF and GNS/PVDF FOCs and series/parallel connections of two identical-order FOCs. For series/parallel connection of arbitrary-order FOCs, α varies from 0.61 to 0.83. Phase angle variation ranges from − 56.2° to − 79° for standalone pure FOC samples, whereas, for series/parallel connection of identical or arbitrary order FOCs, phase ranges from − 54.94° to − 77.75°. Phase ripple varies between ± 1.1° and ± 4.8°, and a maximum CP zone of 4 decades (1 kHz to 10 MHz) for the fabricated samples is reported. Industrial manufacturing of large-value capacitors demands materials to be flexible to enable rolling of large-area electrodes into a miniature device. FOCs fabricated in this work match the design specifications of commercial standard thin film capacitors and show high-value capacitances as well as flexibility of materials and structure.

Implementation and Experimental Verification of Resistorless Fractional-Order Basic Filters

Novel structures of fractional-order differentiation and integration stages are presented in this work, where passive resistors are not required for their implementation. This has been achieved by considering the inherent resistive behavior of fractional-order capacitors. The implementation of the presented stages is performed using a current feedback operational amplifier as active element and fractional-order capacitors based on multi-walled carbon nano-tubes. Basic filter and controller stages are realized using the introduced fundamental blocks, and their behavior is evaluated through experimental results.

Implementation of Carlson Approximation-Based Fractional Order Universal Filter Using MO-CCCII

In this paper, a new current mode fractional order filter is presented using multi-mode second generation current controlled current conveyors (MO-CCCII).in this method consists of two resistors and grounded capacitors using 3MO-CCCII. This is accomplished with a fractional-order capacitor, also known as a stationary phase element, to form a fractional-order filter. The proposed filter is designed as fractional 0.2, 0.4 orders. The fractional order capacitor was obtained using reduced integer-order models of fractional differentiators using the Carlson method18 using third order Foster I RC network circuit. The filter is simulated using BJT-based MO-CCCII using LTSPICE Simulation for the filter to verify the theory and show its performance of it.

Electronically tunable positive and negative fractional order inductor circuit using single topology

This article presents electronically tunable grounded and floating fractional order inductor circuits. The proposed circuits employ two operational transconductance amplifiers (OTAs), one fractional order capacitor, one inverter and four MOS switches and are capable to work in positive mode and negative mode without change in topology. The behaviour of the proposed circuit is also analyzed in presence of parasites that may appear in the practical circuit. The functional verification is done via pre and post layout simulations at 90 nm CMOS technology parameter. The usefulness of the proposed positive fractional inductor circuit is demonstrated through fractional order band pass filter and fractional order high pass ladder filter. The performance of the proposed negative fractional inductance circuit is demonstrated through a fractional inductance cancellation circuit.

Implementation of a fully analog feedback loop with a Carbon-Black-based fractional order controller

Fractional calculus is a mathematical framework that has attracted considerable interest from mathematicians, physicists, and engineers. Among its applications, the use of fractional calculus in the automatic control field has led to interesting results, such as more robust controllers, compared to their integer-order counterparts. The proposed work utilizes the physical realization of a solid-state fractional-order capacitor for the implementation of a fractional-order lead compensator. The proposed capacitor is realized using a carbon black-based dielectric. Therefore, a fully analog closed-loop system implementation is realized. A suitable case study is conducted to validate the controller performance, both from simulations and experimentally. The obtained results further confirm the possibility of realizing and applying a fully analog fractional-order controller.

Optimized fractional-order Butterworth filter design in complex F-plane

This paper introduces a new technique to optimally design the fractional-order Butterworth low-pass filter in the complex F-plane. Design stability is assured by incorporating the critical phase angle as an inequality constraint. The poles of the proposed approximants reside on the unit circle in the stable region of the F-plane. The improved accuracy of the suggested scheme as compared to the recently published literature is demonstrated. A mixed-integer genetic algorithm which considers the parallel combinations of resistors and capacitors for the Valsa network is used to optimize the frequency responses of the fractional-order capacitor emulators as part of the experimental verification using the Sallen–Key filter topology. The total harmonic distortion and spurious-free dynamic range of the practical 1.5th-order Butterwoth filter are measured as 0.13% and 62.18 dBc, respectively; the maximum and mean absolute relative magnitude errors are 0.03929 and 0.02051, respectively.

Extraction of Cardiac Cell Membrane Fractional-Order Capacitance from Current Response to Voltage Step

The aim of the article is to examine the possibilities of modeling electrical properties of cardiac cell membrane using the Cole impedance model containing a fractional-order capacitor. A method is presented to determine the parameters of the model based on the current transient response to a voltage step applied to the membrane. The method is based on the numerical minimization of the least squares error between the recorded and calculated transient response of the model using the MATLAB function fminsearch. The use of a fractional-order capacitor in the membrane model is found to result in a reduction in the modeling error compared to that of the classic capacitor.