Authors: Cvetićanin, Stevan
Zorica, Dušan 
Rapaić, Milan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Frequency Characteristics of Two Topologies Representing Fractional Order Transmission Line Model
Journal: Circuits, Systems, and Signal Processing
Volume: 39
Issue: 1
First page: 456
Last page: 473
Issue Date: 1-Jan-2020
Rank: M22
ISSN: 0278-081X
DOI: 10.1007/s00034-019-01178-y
Classical telegrapher’s equation is generalized in order to account for the hereditary nature of polarization and magnetization phenomena of the medium by postulating fractional order constitutive relations for capacitive and inductive elements in the elementary circuit, as well as by the two topological modifications of Heaviside’s elementary circuit, referred as series and parallel, differing in the manner in which the effect of charge accumulation effect along the line is taken into consideration. Frequency analysis of generalized telegrapher’s equations is performed, with a particular emphasis on the asymptotic behavior for low and high frequencies. It is found that, like Heaviside’s elementary circuit, parallel topology leads to low-pass frequency characteristics, while the series topology leads to band-pass characteristics. It is also demonstrated that the logarithmic phase characteristics are linear functions of frequency, being suitable for determining some of the fractional differentiation orders in generalized telegrapher’s equations.
Keywords: Fractional order electrical elements | Frequency characteristics | Generalized telegrapher’s equation | Transmission line
Publisher: Springer Link
Project: Smart Electricity Distribution Grids Based on Distribution Management System and Distributed Generation 
Inteligent SCADA system for early fault detection and error compensation in processes and equipment in process industry 
Development of intelligent monitoring control system to increase energy efficiency in buildings 
Viscoelasticity of fractional type and shape optimization in a theory of rods 
Provincial Government of Vojvodina, Grant 142-451-2384/2018

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