Mutual Impedances of Parallel Wires

T V H E concept of the mutual impedance per unit length between two straight parallel filamentary conductors is well understood by engineers, and its calculation formula is simple. This mutual impedance is a pure reactance (directly proportional to the frequency), the induced electromotive force being in phase quadrature with the inducing current. In the case of open-wire circuits, even when operating with carrier currents of very high frequency, the mutual impedance can be calculated with high accuracy by regarding the wires as filamentary. For cable circuits, however, the foregoing statement is not true, because of the close juxtaposition of the wires. In such circuits the wires may be termed " t h i c k , " meaning t h a t their diameter is appreciable compared with their interaxial separation. Depending in a complicated manner on the conductivity, permeability, diameter, and interaxial separation of such wires, the frequency may easily be so high as to render the filamentary formulas for the mutual impedance of even straight wires quite inaccurate and unreliable. In such cases it is necessary to consider the current distribution over the cross-section * T h e two parts of this paper are distinct, though complementary. was written by Ray S. Hoyt, Part II by Sallie Pero Mead. Part I