Wave Modulations in the Nonlinear Biinductance Transmission Line

Abstract

Adding dissipative elements to a discrete biinductance transmission line which admits both low frequency (LF) and high frequency (HF) modes, dynamics of a weakly nonlinear modulated wave is investigated theoretically and numerically. In the semidiscrete approximation using a proposed decoupling ansatz for the voltage of the two different cells, it is shown that the original differential-difference equation for this transmission line can be reduced to the complex Ginzburg-Landau (CGL) equation. The modulational instability criterion for sinusoïdal waves has been recovered. Furthermore, numerical simulations show that the theoretical predictions are well reproduced.