Analysis of Multiconductor Transmission Lines, 2nd Edition

10

LITERAL (SYMBOLIC) SOLUTIONS FOR THREE-CONDUCTOR LINES

The general solution of the transmission-line equations for a two-conductor line considered in Chapters 6 and 8 is simple enough that it can be obtained in literal form, that is, in terms of symbols for the line terminations and the line parameters such as characteristic impedance Z_C and the line one-way time delay T_D. For example, see Eqs. (6.39) and (6.70) of Chapter 6 and (8.14) of Chapter 8. This literal or symbolic solution gives considerable insight into how the various parameters affect the terminal voltages and currents. This advantage is similar to a transfer function that is useful in the design and analysis of electric circuits and automatic control systems [A.2]. In order to obtain the same insight from the numerical solution, we would need to perform a large set of computations with these parameters being varied over their range of anticipated values.

Chapters 7 and 9 have examined the solution of the MTL (multiconductor transmission line) equations for a general (n + 1)-conductor line. This is so complex that it is not feasible to generate literal solutions, and the solution process must be accomplished with digital computer programs, that is, a numerical result is obtained. This numerical process does not reveal the general behavior of the solution. In other words, the only information we obtain is the solution for the specific set of input data, for example, line length, terminal impedance levels, source ...