Nonlinear Membrane Circuit Loaded on a Lossy Transmission Line without the Heaviside’s Condition

The paper deals with transmission lines terminated by a nonlinear circuit describing a simplified model of membrane. This means that all elements of the membrane circuit are nonlinear ones as follows: in series connected LR-loads parallel to C-load. Using the Kirchhoff’s laws we formulate boundary conditions. For lossy transmission lines systems with the Heaviside’s condition, the mixed problem is considered in previous papers. The main goal of the present paper is to investigate the same problem for lossy transmission lines without the Heaviside’s condition. We reduce the existence of solution of the more complicated mixed problem for such a system to the existence of fixed point of an operator acting on a suitable function space. Then by ensuring the existence of this fixed point we obtain conditions for existence of a generalized solution of the mixed problem. The obtained conditions are easily verifiable. We demonstrate the advantages of our method by a numerical example.

Analysis of Lossy Transmission Lines Terminated by Schottky Diode Circuit

In the present paper we consider a lossy transmission line terminated by a circuit corresponding to a Schottky diode. On the base of Kirchhoff’s law boundary conditions are derived. Then a mixed problem for the lossy transmission line system is formulated. We reduce the mixed problem for the hyperbolic transmission line system to an initial value problem for a system of differential equations with delays on the boundary. We prove existence-uniqueness theorem for oscillatory solution. The paper ends with numerical example with real values of the Schottky diode parameters.

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

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.