Generalized time-fractional telegrapher’s equation in transmission line modeling

Cvetićanin, Stevan M.; Zorica, Dušan; Rapaić, Milan R.

doi:10.1007/s11071-016-3322-z

Cited by 32 publications

(14 citation statements)

References 27 publications

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“…Anomalous di®usion has been characterized in both space and time using a rich variety of fractional order derivatives when the line or skin e®ect is described by fractional di®erential equations. 34 In recent decades, scientists and engineers recognize that the fractional di®erential equations provide a better approach to describe the complex phenomena in nature such as the skin e®ect, dielectric relaxation and chaos. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

R‐Smith

Kartci

Brančík

2018

J CIRCUIT SYST COMP

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The paper presents a computationally e±cient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of e®ective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of°exibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are e®ectively algorithmized.

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Section: Introductionmentioning

confidence: 99%

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

R‐Smith

Kartci

Brančík

2018

J CIRCUIT SYST COMP

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“…The aim is to reconsider fractional telegrapher's equation in the setting of heat conduction phenomena, as well as to obtain its solution on semi-infinite domain in the integral form for all values of the orders of fractional derivatives, using the approach presented in [11] and extending the results of [3], and to examine the features of such obtained solutions.…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

Fractional telegrapher’s equation as a consequence of Cattaneo’s heat conduction law generalization

Zorica

Cveticanin

2018

Theor appl mech (Belgr)

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Fractional telegrapher's equation is reinterpreted in the setting of heat conduction phenomena and reobtained by considering the energy balance equation and fractional Cattaneo heat conduction law, generalized by taking into account the history of temperature gradient as well. Using the Laplace transform method, fractional telegrapher's equation is solved on semi-bounded domain for the zero initial condition and solution is obtained as a convolution of forcing temperature on the boundary and impulse response. Some features of such obtained solution are examined.

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“…Advancement in VLSI technology offers very high scale of integrated circuits in a system-on-chip. Indeed, with the continuous scaling of technology, the interconnect delay becomes the dominant source of delay [1,2]. Hence, the interconnect performance becomes a vital factor in determining the circuit performance in both timing and power.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, the interconnect performance becomes a vital factor in determining the circuit performance in both timing and power. One way to model the interconnect response is to use accurate interconnect models and signal propagation characterization to simulate the response of interconnects [1,3] . This is done by using RLC models in the tree model to simulate the different nodes response [4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Elmore delay in the fractional order domain

Soltan

Radwan

Yakovlev

2017

2017 European Conference on Circuit Theory and Design (ECCTD)

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Interconnect design has recently become one of the important factors that affect the circuit delay and performance especially in the deep submicron technology. The modelling of interconnects is typically based on using Elmore definitions of the delay time and rise time. So, a general formula for Elmore delay time and rise time in the fractional order domain are presented in this work. It is found from the new formulas of the delay time and rise time that these timing values could be controlled or tuned by the fractional orders. Hence, the fractional order can compensate for the components value. Furthermore, a case study of shunt compensation circuit is studied here to show the impact of the fractional orders on the delay time. The impact of the component values along with the fractional order on the new timing definition is studied using MATLAB analysis.

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Generalized time-fractional telegrapher’s equation in transmission line modeling

Cited by 32 publications

References 27 publications

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

Fractional telegrapher’s equation as a consequence of Cattaneo’s heat conduction law generalization

Elmore delay in the fractional order domain

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