Some little-known facts about transmission lines and some new results

Abstract

The study of transmission lines forms an integral part of any curriculum in electrical engineering. This paper presents some little-known but interesting facts about transmission lines, which are generally not found in textbooks, along with some new facts, which arose as extensions of these little-known ones. The facts highlighted in this paper are that: 1) the real part of the characteristic impedance is always greater than the magnitude of its imaginary part; 2) the real and imaginary parts of the characteristic impedance and the propagation constant are interrelated by four inequalities; 3) the magnitude of the load reflection coefficient $( vert Gamma _{L} vert )$ may exceed unity, even for a passive load; 4) the concepts of incident power and reflected power, as usually employed in dealing with lossless lines, are not, in general, valid in a lossy line; 5) the law of power conservation is not violated because of Fact 3; and that 6) the maximum value of $vert Gamma _{L} vert $ depends on whether the load or the characteristic impedance is variable and whether the load is active or passive.