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Frequency Characteristics of Two Topologies Representing Fractional Order Transmission Line Model

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Abstract

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.

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Authors and Affiliations

  1. Department of Power, Electronic and Telecommunication Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21000, Serbia

    Stevan M. Cvetićanin

  2. Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, Belgrade, 11000, Serbia

    Dušan Zorica

  3. Department of Physics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia

    Dušan Zorica

  4. Department of Computing and Control Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića, 6, Novi Sad, 21000, Serbia

    Milan R. Rapaić

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  1. Stevan M. Cvetićanin
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  2. Dušan Zorica
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Correspondence to Stevan M. Cvetićanin.

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This work was partially supported by Serbian Ministry of Science, Education and Technological Development, under Grants III42004 (SMC), TR32018, TR33013 (MRR), and 174005 (DZ), as well as by Provincial Government of Vojvodina under Grant 142-451-2384/2018 (DZ).

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Cvetićanin, S.M., Zorica, D. & Rapaić, M.R. Frequency Characteristics of Two Topologies Representing Fractional Order Transmission Line Model. Circuits Syst Signal Process 39, 456–473 (2020). https://doi.org/10.1007/s00034-019-01178-y

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  • DOI: https://doi.org/10.1007/s00034-019-01178-y

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