Circuit Modeling of Nonlinear Lumped Element Transmission Lines Including Hybrid Lines

摘要

A nonlinear lumped element transmission line (NLETL) that consists of an $LC$-ladder network can be used to convert a rectangular input pump pulse into a series of RF oscillations at the output. The discreteness of the $LC$ sections in the network contributes to the line dispersion while the nonlinearity of the $LC$ elements produces the nonlinear characteristics of the line. Both of these properties combine to produce wave trains of high frequency. This paper describes an NLETL circuit model that is used to simulate RF generation for a given input pump pulse and the experiments used to validate the simulated results. The circuit model is used to study a nonlinear capacitive line that comprises nonlinear $C$ but linear $L$ and a nonlinear inductive line that comprises nonlinear $L$ but linear $C$. Extensive and comprehensive parametric studies were carried out for the various NLETLs to understand the behavior and characteristics of these lines. Interesting observations were made, and explanations were given for their occurrence. A hybrid line that comprises both nonlinear elements $L$ and $C$ was also investigated using the circuit model with the goal of better matching to a resistive load. Simulations of the hybrid line indicate promising results.