Transmission-Line Theory and Its Application

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Abstract
In Part I several forms of the solution of the transmission‐line equations are discussed including, in particular, a completely hyperbolic one in which the over‐all attenuation and phase shift of the terminal impedances are expressed in a form involving terminal functions which simplify the analysis of many complex problems. Formulas for the input resistance, reactance, conductance, and susceptance of a section of line of any length and terminated in an arbitrary impedance are given in completely general terms. Curves computed from these formulas for four typical terminations are shown. A general circle diagram for determining the input impedance and admittance as well as the terminal functions is described. It consists of circles of constant over‐all attenuation and circles of constant over‐all phase shift. The distribution of current is represented in general terms suitable for a line driven at one end or by a generator coupled loosely at any point along the line. In Part II the general formulas described in Part I are applied to practical problems. A simple and completely general formula is derived for determining the transfer of power and the efficiency of transmission for a line of any length terminated in an arbitrary load. An equally simple and general formula for the standing wave ratio is given. Application of the formulas for input impedance and admittance to the problem of bead spacing on resonant and non‐resonant lines and to series and shunt impedance transforming or matching sections is outlined. The experimental determination of attenuation and phase constants and of ``Q'' for the line and for the terminations is discussed. The application of formulas and experimental methods to include hollow pipe transmission lines or wave guides is considered briefly in Part III. A method for defining and measuring terminating impedances for hollow pipes is described.