Effect of a non-linearity on delays and velocities in a CRLH-MTM transmission line model

Abstract: The theme of this paper is to analyze the effect of a non-linearity (second order constitutive relationship between voltage and current in resistor, inductor and capacitor)) on phase delay and group delay for a unit cell of a conventional transmission line model and then by analyzing the phase and group velocities in a Composite Right Hand Left Hand Meta-material (CRLH-MTM) structure which is being used very extensively in the Transmission line (TL) theory for negative refractive index material realization. The complex propagation constant is determined for the non- linear transmission line model and it is observed that the non-linearity in the unit cell is producing the negative resistance which can be used in different electronic circuits, if the same non-linear devices are possible to be modelled from existing devices. Along with this, it is also observed that in order to remove the guard band that exists in the CRLH-MTM for supporting forward and backward waves, there has to be some non-linearity in the transmission line model which is a new finding after the study.

Keywords: Transmission line model, dispersion, complex propagation constant, phase velocity and group velocity.