Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 456–473 | Cite as

Frequency Characteristics of Two Topologies Representing Fractional Order Transmission Line Model

  • Stevan M. CvetićaninEmail author
  • Dušan Zorica
  • Milan R. Rapaić
Short Paper


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.


Generalized telegrapher’s equation Transmission line Fractional order electrical elements Frequency characteristics 


Compliance with ethical standards

Conflict of interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and publication of this article.


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Authors and Affiliations

  1. 1.Department of Power, Electronic and Telecommunication Engineering, Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia
  2. 2.Mathematical InstituteSerbian Academy of Arts and SciencesBelgradeSerbia
  3. 3.Department of Physics, Faculty of SciencesUniversity of Novi SadNovi SadSerbia
  4. 4.Department of Computing and Control Engineering, Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

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