Graphical-vector solution and study of the coil-loaded line

The paper describes a simple method of obtaining the single frequency steady-state solution of a coil-loaded line, including mid-coil and mid-section impedances and propagation constant by a graphical construction combined with ordinary slide-rule operations. The following advantages are suggested:¿ (a) It is fundamentally as rigorous as Campbell´s formulae. (b) It requires no special charts or tables of complex functions. (c) Apart from simple drawing instruments it requires only a log-log slide rule, or alternatively a table of simple exponentials plus an ordinary slide rule or log table. (d) Considerable errors are unlikely, as a check is afforded on the accuracy of the graphical construction and the calculations are in simple steps. (e) There is no conversion necessary between polar and rectangular co-ordinates. (f) The vector diagram and method of treatment lead to a clearer understanding of the loading phenomena than is given by most methods. Examples are given for a typical line with varying coil values and varying spacings at a single frequency, and graphs are included of results obtained. Certain tentative conclusions are drawn regarding cut-off phenomena.