A Graphical Theory of Traveling Electric Waves Between Parallel Conductors

The analytical theory of simple traveling waves along parallel conductors is well known. Its disadvantage is that the relationships among the incoming, reflected, transmitted, and absorbed currents and voltages are expressed by a number of simulaneous equations difficult to grasp, from a physical point of view, in their entirely. For this reason, a graphical theory has been developed according to which all the quantities involved are represented in a so-called star diagram and the whole phenomenon conveyed to the eye quantitatively. The star diagram is then applied to the following practical cases of a simple rectangular-front non-attenuated long traveling wave: (a) Reflection from and absorption in a non-inductive terminal resistance; (b) Reflection from an open-circuited and from a short-circuited end of a line; (c) The case of critical resistance; (d) Repeated reflections from the ends of a line; (e) Discharge of a wave to the ground, directly or through a resistance; (f) Passage of a wave through the junction point of two conductors having different values of surge impedance; (g) Same as (f), only the junction provided with a series or shunted resistance, (h) Effect of a lumped series inductance or shunted capacitance in reducing the steepness of a wave front. In each case, the results agree with those deduced analytically, for example by R. Rüdenberg in his book ``Elektrische Schaltvorgänge.'' Some reciprocal relationships are pointed out at the end and further problems suggested to which the star diagram may be applied.