Mode extinction effect on printed transmission lines when the thickness of lossy conductors is decreased

Printed transmission lines have been extensively examined so far, but results obtained there are all concerned with the waveguiding conductors with no loss and zero thickness, except very few results. We have recently studied the transmission characteristics of printed transmission lines in detail, when the waveguiding conductors have finite conductivity and thickness, and we have found an unexpected affect that we call "the mode extinction effect." This effect results in significant changes in the dispersion behavior of the printed-transmission-line fundamental mode. For a critical thickness, it may turn out that such transmission line can not use in open structural configuration, but must always be used by putting into a packaging box. In this paper, we discuss thoroughly this important effect and related results from the standpoints of both the dispersion behavior and the vector field plots.