Abstract
The paper presents a computationally efficient 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 effective 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 flexibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are effectively algorithmized.
Highlights
Numerical inverse Laplace transform (NILT) methods are ranked among the potential methods for the analysis of transient behavior of linear dynamical systems
The hyperbolic NILT method[8] is used to get the 2D results, whereas, the FFT NILT method generalized to be able to invert Laplace transforms in matrix forms is used for the 3D results[5]; both methods are accelerated via the qd algorithm
A second approach to solve the multiconductor TLs (MTLs) system equations can be performed by further applying another Laplace transform with respect to the geometric coordinate x,53 while considering fractional-order MTL elements, which leads to the following matrix equation in the ðs; qÞ domain:
Summary
Numerical inverse Laplace transform (NILT) methods are ranked among the potential methods for the analysis of transient behavior of linear dynamical systems. Fractional calculus, the branch of mathematics regarding di®erentiations and integrations to noninteger orders, is aeld that was introduced 300 years ago.[9] Inspired by the fractal models in the environment, integer to noninteger models were explored. The main reason for using integer-order models was the absence of solution methods for fractional di®erential equations. 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.
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