Pseudo-Differential (2 + α)-Order Butterworth Frequency Filter

Abstract

This paper describes the design of analog pseudo-differential fractional frequency filter with the order of (2 + α), where 0 < α < 1. The filter operates in a mixed-transadmittance mode (voltage input, current output) and provides a low-pass frequency response according to Butterworth approximation. General formulas to determine the required transfer function coefficients for desired value of fractional order α are also introduced. The designed filter provides the beneficial features of fully-differential solutions but with a less complex circuit topology. It is canonical, i.e. employs minimum number of passive elements, whereas all are grounded, and current conveyors as active elements. The proposed structure offers high input impedance, high output impedance, and high common-mode rejection ratio. By simple modification, voltage response can also be obtained. The performance of the proposed frequency filter is verified both by simulations and experimental measurements proving the validity of theory and the advantageous features of the filter.

A Review of Recent Advances in Fractional-Order Sensing and Filtering Techniques

“…Reference [55] presents the design of a fractional-order analog pseudo-differential frequency filter with order 2 + α, where α ∈ (0 1). The resulting filter is a low-pass Butterworth that employs a minimum number of passive components and current conveyors as active elements.…”

FPAA-Based Realization of Filters with Fractional Laplace Operators of Different Orders

“…step #2: Approximation of the obtained data, based on the fitfrd built-in function, which forms the state-space model of the data for a given order of approximation (n). step #3: Conversion of the model to an integer-order transfer function of the form in (3) using the ss2tf built-in function.…”

“…Due to the absence of commercial availability of such elements, they are approximated by RC schemes, such as the Foster and Cauer networks. The price paid for the offered quick design procedure is the absence of on-the-fly tuning of the filter's characteristics, making it suitable only for cases of filters with pre-defined type and frequency characteristics [3][4][5]. (b) Approximation of the fractional-order Laplace operators in (1) using appropriate tools, such as Continued Fraction Expansion, Oustaloup, Matsuda and Carlson [6], and then substitution of the resulting rational function approximations of these operators.…”

Versatile Field-Programmable Analog Array Realizations of Power-Law Filters

“…Non-integer order signal processing has received significant research interest in the following fields [1][2][3][4][5][6]. The first field is electrical engineering, for implementing filters and oscillators [5,[7][8][9][10][11][12][13][14][15], chaotic systems [16], sensor systems [17], and control systems [2,[18][19][20][21]. This originates from the fact that both filters and oscillators offer additional degrees of freedom due to the non-integer order, which opens the door for scaling the characteristic frequencies of the filters/oscillators, as well as for precisely controlling the gradient of the transition from the pass-band to the stop-band.…”

“…Considering (1a) and (1b), this can be done through the substitution operation s → s α , with 0 < α < 1 being the order of the operator. The resulting filters are denoted in the literature as fractional-order filters [7,8,15].…”