Wave modulations in the nonlinear biinductance transmission line

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 Glinzburg Landau (CGL) equation. The modulational instability criterion for sinusoidal waves has been recovered. Furthermore, numerical simulations show that the theoretical predictions are well reproduced.