Electronically Controlled Power-Law Filters Realizations

Abstract

A generalized structure that is capable of implementing power-law filters derived from 1st and 2nd-order mother filter functions is presented in this work. This is achieved thanks to the employment of Operational Transconductance Amplifiers (OTAs) as active elements, because of the electronic tuning capability of their transconductance parameter. Appropriate design examples are provided and the performance of the introduced structure is evaluated through simulation results using the Cadence Integrated Circuits (IC) design suite and Metal Oxide Semiconductor (MOS) transistors models available from the Austria Mikro Systeme (AMS) 0.35 μm Complementary Metal Oxide Semiconductor (CMOS) process.

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

“…It is demonstrated that the PLFs reported in [20][21][22][23] are also a small subset of the class of filters proposed in this work; 2.…”

“…Two FO elements-based band-stop filter of the form (s p + k 1 s q + k 2 )/(s p + k 3 s q + k 2 ), where, p = 1 + β 1 + β 2 , q = 1 + β 2 , and β 1 , β 2 ∈ (0, 1), was presented in [29], which is also unlike the proposed fractional-order band-stop filter (FBSF) model. Note that the transfer function of the PLF reported in [20][21][22][23] can be obtained from (4) by setting α = 1. Therefore, the proposed FO filter transfer function also provides a further generalization of the PLF models.…”

“…As reported in [21], the frequency-domain-based curve-fitting using the Sanathanan-Koerner least-squares method presented in [20,22,23] can lead to unstable inverse LP and inverse HP type PLFs for some design cases. The proposed approach to formulate the constraints, which is different from the method adopted in [21], helps convert the stable filter into its stable inverse counterpart also through a simple inversion.…”

“…Two techniques exist in the literature for conversion of the FTF into its integer-order counterpart: (a) substitution of the rational approximation of the s α operator [17] in the FTF, as reported in [18], or further optimizing the obtained integerorder model to enhance the design bandwidth [14], and (b) direct determination of the ITF which approximates the magnitude and phase-frequency characteristics of the FO filter. For this purpose, either optimization techniques or curve-fitting procedures have been employed for the design of FO transitional filter [19], power-law filter (PLF) [20][21][22][23], etc.…”

Plant Tissue Modelling Using Power-Law Filters

“…Here, denotes the mother function of the standard filter. The methods efficient for approximating power-law filters are either frequency response curve fitting or padé approximations [ 33 ]. Single and double dispersion impedance models were represented by power-law filters in [ 34 ].…”