Analysis of nonlinear left-handed transmission lines using state space modelling

In this paper we demonstrate the use of state space modelling for analysing parametric generation in nonlinear composite right left handed transmission lines. The system natural frequencies are identified and found to be comparable to the dominant poles of the linearized system. With an input pump excitation, the structure generates parametric frequency components, and the state space analysis suggests that the values of the parametric frequencies are determined by the dominant poles of the linearized system. The growth of the parametric components depends on the net effect of the energy transfer from the pump and the dissipative nature of the structure. It is found that below a threshold value of the pump amplitude, the parametric components are inhibited. This threshold value is a function of the pump frequency and the structure losses. The numerical calculations are in good agreement with measurements. State space formulations allow the application of the mature and robust techniques of systems and control methodologies to analyse the behaviour of nonlinear right left handed transmission line systems.