4 - Transmission Lines

Abstract

This chapter deals with the explanation of transmission lines. A transmission line is a distributed circuit element. Unlike a conventional low-frequency circuit, the voltages and currents on a transmission line vary with longitudinal position because they experience a phase (or time) delay as the wave propagates from one end of the line to the other. A transmission line is used to transfer a signal from the generator to the load by guiding an electromagnetic (EM) wave between two conductors. This chapter is devoted to the fundamentals of frequency-domain analysis of transmission lines with an emphasis on physical concepts rather than detailed mathematical derivations. A distributed circuit model is employed to derive the transmission line equations, whose solution describes the wave behavior of voltages and currents along the line. This chapter considers an infinite line to emphasize the concepts of phase delay and spatial dependence, which account for the distributed nature of voltages and currents along a transmission line. The propagation characteristics of lossless and lossy lines are discussed, with the latter specialized to low-loss and distortionless cases. Properties of the standing waves along a terminated transmission line, such as impedance, reflection coefficient, voltage and current distribution, are discussed in detail. Mathematical expressions are derived for power flow, including power loss due to interference between incident and reflected waves on a lossy line and the condition of conjugate matching for maximum power transfer. Finally, the basic operations of the Smith chart to characterize standing waves on a terminated line are explained with an example.