Analysis on phase properties of a transmission line model with non-linear elements

The theme of this paper is to analyze phase response of a conventional transmission line (Tx line) unit cell with the presence of a non-linear element. In this analysis, a non-linear inductor and non-linear capacitor are used in two Tx line models, firstly, forward wave supporting structure (low pass in nature) and secondly composite right hand left hand meta-material (CRLH-MTM) structure (bandpass in nature) which supports both forward and backward waves. For the non-linearity, a quadratic constitutive relation is considered between charge and voltage for a capacitor. For an inductor it is between the flux and the current. This analysis is to investigate the possibility of producing the negative group delay in the unit cell of Tx model in the presence of a non-linear element. This implies the opposite phase velocity and group velocities in the dispersion relationship for the Tx line model.