When a vector terminal describes a certain locus on its plane, the square root value of that vector will also trace another correspondingly the latter may be called the square root or radical figure of the former. Thus, the radical figures of a straight line, a circle passing the origin, a circle in general position and a parabola having its axis on the abscissa are respectively shown to be a rectangular hyperbola, a lemniscate, a casinian curve or oval and a radical parabola, the last being so named for a while.
The loci of square vectors of the propagation constant or vector attenuation and the vector surge impedance, when one of the line constants or the angular velocity of the current is varied, are easily seen to be either one of a straight line, a circle or a parabola. Thus, their radical vectors or the propagation constant and the surge impedance themselves trace one of the radical figures, mentioned above. Each case is discussed in details.
As a numerical example, the loci for the standard telephone cable are traced, when the linear inductance, leakance or the angular velocity is varied.
View full abstract