Chapter 1 - Transmission Line Equations and Properties

Abstract

This chapter presents general properties of the transmission-line equations mutuated from the theory of Maxwell's equations. The link between the transmission-line equations and Maxwell's equations is shown by the fact that the structure of the line equations strongly resembles that of Maxwell's equations. The chapter deals with the Poynting theorem for transmission lines with frequency-independent parameters and extends it to the frequency domain and then discusses the more general case of transmission lines with frequency-dependent parameters. This theorem is important not only for its physical significance but also because it makes it possible to tackle other important questions, such as the problem of the uniqueness of the solution and the reciprocity properties. By using the Poynting theorem, it is possible to establish conditions that, once satisfied, ensure that the solution of the transmission-line equations is determined and unique. The problem of the uniqueness of the solution is fundamental to the characterization of two-conductor lines as two-ports and, more widely, of multiconductor lines as multiports. Some properties of two-ports and, more generally, of multiports that represent the terminal behaviors of transmission lines are a direct consequence of another fundamental property of line equations, common to many linear systems: the property of reciprocity. By using Poynting theorem in the Laplace domain, various forms of the property of reciprocity for transmission lines are demonstrated in the chapter.