Fractional-order Bandpass Filter Research Articles

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.

Further Generalization and Approximation of Fractional-Order Filters and Their Inverse Functions of the Second-Order Limiting Form

This paper proposes a further generalization of the fractional-order filters whose limiting form is that of the second-order filter. This new filter class can also be regarded as a superset of the recently reported power-law filters. An optimal approach incorporating constraints that restricts the real part of the roots of the numerator and denominator polynomials of the proposed rational approximant to negative values is formulated. Consequently, stable inverse filter characteristics can also be achieved using the suggested method. Accuracy of the proposed low-pass, high-pass, band-pass, and band-stop filters for various combinations of design parameters is evaluated using the absolute relative magnitude/phase error metrics. Current feedback operational amplifier-based circuit simulations validate the efficacy of the four types of designed filters and their inverse functions. Experimental results for the frequency and time-domain performances of the proposed fractional-order band-pass filter and its inverse counterpart are also presented.

Realization of fractional band pass filter on reconfigurable analog device

Abstract This paper presents a realization of fractional-order Band pass-filter (FOBF) based on the concepts of fractional order inductors and fractional order capacitors. The FOBF is designed and implemented using both simulation and hardware approaches. The proposed filter order is considered up to second order or less with any real positive number. One of the cases is considered when α ≤ 1 and β ≥ 1. In the second case, the filter is designed when β ≤ 1 and α ≥ 1. In order to calculate the optimal filter parameters, the modified Particle Swarm Optimization (mPSO) algorithm has been utilized for coefficient tuning. Also, a generalized approach to design any second order FOBF is discussed in this work. The realization and performance assessment have been carried out in simulation environment as well as in lab experiment with field programmable analog array (FPAA) development board. The experimental results indicate the value of efforts to realize the fractional filter.

Modeling and Performance Improvement of Fractional-Order Band-Pass Filter Using Fractional Elements

Fractional-order circuits are the emerging area for analyzing the parametric response of the filters and its performance improvement can be analytically observed by using an optimization technique. In this paper, the fractional-order band-pass filter, using fractional-order capacitor (FC) and fractional-order inductor (FI), is investigated. The characteristics of the filter with desired fractional-order of FC and FI bearing range from 0.1 ≤ α ≤ 1.0 to 0.1 ≤ β ≤ 1.0, respectively having a step change of 0.1, are simulated. The frequency parameters of the proposed band-pass filter having order with in this range of α and β resulted during simulation. The quality factor is optimized from the results of the fractional-orders α and β for the given FC and FI, respectively. The theoretical quality factor in this integer-order filter is compared with its optimized Q value in its fractional-order counterpart. The proposed filter is modeled by using the best orders of α = 0.4 and β = 1.0 for FC and FI, respectively with optimized Q-factor. Finally, the frequency parameters of the filter as modeled are obtained through simulation using MATLAB/Simulink R2011a.

Optimal design of a fractional order immittance in the second quadrant with wide CPZ

This paper presents a design technique to realize fractional order (FO) immittance in the second quadrant of the impedance plane, using Bruton’s generalized immittance converter (GIC). Design guidelines are developed based on a sub-optimal analysis of phase error resulted by non-ideal op amps. The analysis takes into account finite open-loop dc gain and finite unity-gain frequency of practical op amps and aim to maximize the constant phase zone for a given phase band specification. The fractance of the realized fractor can also be tuned to a desired value by varying one of the GIC resistances. Several simulations and experimental validations are demonstrated. Also, high Q, FO bandpass filter with wide tuning range is presented as an application of the designed obtuse angle fractor.

Implementation and analysis of tunable fractional-order band-pass filter of order 2α

This paper proposes a new design of a 2α-order fractional-order band-pass filter with tunability feature. The proposed filter is approximated with the Continued Fraction Expansion and Matsuda second-order approximations. The realized filter transfer function is based on the Inverse Follow the Leader Feedback configuration, with Operational Transconductance Amplifiers as active elements. As a result, the order of the proposed filter can be adjusted by changing a single parameter, which is the bias current Ibias. A comparison with the previous works is performed, showing the advantage of the electronic tuning feature using one bias current value in the proposed filter. Sensitivity analysis is conducted to investigate the effect of circuit parameters variation, such as capacitance and gain factors. Stability analysis is performed by studying the poles’ location and movement versus the filter parameters. Besides, the effect of transistor mismatch is evaluated using Monte Carlo analysis. Matlab and Cadence software, with UMC technology of 0.13 μm CMOS, are used for verifying the proposed implementation.

Optimal integer‐order rational approximation of α and α + β fractional‐order generalised analogue filters

A new approach to determine the integer-order transfer function approximation for α and α + β, where 0 <; α , β <; 1, fractional-order analogue filters is presented. Reported works deal with this design problem by using techniques which are non-optimal. The proposed designs with guaranteed stability are obtained by employing a global search optimisation algorithm called colliding bodies optimisation (CBO). The modelling error is iteratively minimised by CBO in the least-squares sense directly in the frequency domain. The improved accuracy in the magnitude response of the proposed fractional-order low pass filters, fractional-order high pass filters, and fractional-order band pass filters as compared to the designs based on the Matsuda and the continued fractions expansion-based techniques is demonstrated. The efficacies of the proposed filters are also validated in SIMULINK platform.

Fractional-order band-pass filter design using fractional-characteristic specimen functions

Two (α + β)-order transfer functions realizing fractional-order band-pass filter responses are presented and analysed, where 0 < α ≤ 1 and 0 < β ≤ 1. Generalizing the transfer functions from integer to fractional order offers continuous and independent control of the magnitude characteristic slopes both below and above the filter center frequency. The transfer function coefficients that minimize the magnitude error between the discussed fractional-order transfer functions and proposed fractional-characteristic specimen functions in a specified frequency band are determined using a numerical least squares optimization search routine. The relations for computing the transfer function coefficients as functions of α and β are given. The simulations show that the magnitude frequency characteristics of the transfer functions with the new coefficients are very well matched with the specimen functions. Further verification of these results was carried out using the Tow-Thomas filter topology with RC approximations of fractional-order capacitors. The computation of filter element parameters is demonstrated for selected values of α and β and the simulated and measured frequency characteristics of the filter are included to validate the fractional-order responses.

Emulation of current excited fractional-order capacitors and inductors using OTA topologies

A novel topology suitable for emulating fractional-order capacitors and inductors using current excitation is achieved using a fractional-order differentiator/integrator block and appropriately configured Operational Transconductance Amplifiers. The scheme is capable of emulating both fractional-order capacitors and fractional-order inductors without any modifications to its structure. This implementation allows for electronic tuning of the order, capacitance/inductance, and bandwidth of operation by modification of only the bias current. Post-layout simulation results of the impedance magnitude and phase confirm the correct emulated behavior of both fractional-order capacitors and inductors. Two examples highlight the applications of this topology in i) realizing a fractional-order bandpass filter and ii) emulating a Cole-impedance model for biological applications. For both examples the characteristics of each circuit are validated in simulation.