Distributed parametric effect in long lines and its applications

Abstract

The article considers a parametric effect which takes place when the velocity of signal propagation in a long line changes. We found the analytical solution describing the form of the transformed signal for a line with losses, when line parameters change symmetrically. We also considered lines without losses, with asymmetrical change of parameters. Our theoretical results comply with experimental data. In certain conditions, such a line can be used as an amplifier. The parametric effect in optics is described by Maxwell's equations, while in case of a long line, the analysis is based on telegrapher's equations. However, it turns out that in the end, both in optics and electronics, the parametric effect is described by wave equations that are mathematically similar. This is because fundamentally, the parametric effect is physically based on energy interchange between the controlling (pump) signal and the transformed one, when the parameters of the propagating medium change. So, the obtained results can be used for analysis of parametric effects in optics and electronics.

Method for Finding Metabolic Properties Based on the General Growth Law. Liver Examples. A General Framework for Biological Modeling

“…The laws are presented by mathematical apparatuses, whose generality and completeness are sufficient to consistently and efficiently handle discipline’s problems within such naturally developed frameworks. For creating a framework for biological modeling, we will exploit such implicit exemplary frameworks used for solving problems in optics [28] , electronics [29] , remote sensing [30] , electromagnetic theory [31] . Some useful insights can be gained considering explicit development frameworks, which exist in more abstract disciplines, such as applied and financial mathematics [32] .…”

“…Based on experience in other disciplines, like physical sciences, software system development, etc. [28][29][30][31][32][33], as well as results of analysis of available integral models [34][35][36][37], ''vertical'' integration should be of higher priority. It should not be a complete model first, but rather a model's skeleton ''vertically'' piercing all scale levels.…”