A Geometrical and Highly Generalized Interpretation of Two-Element-Kinl One-Port Driving Functions

Abstract

This paper presents in terms of a three-dimensional surface a technique for a visual as well as mathematical treatment of broad generality of the RL, RC and LC one-ports. An examination of the partial fraction terms of all the two-element series and parallel components which make up the canonic one-ports indicates that seven different types of terms are all that occur. The real and imaginary parts of all such functions for s = ? + j? may be represented geometrically by a surface in three-space. It is found that all the real and imaginary part functions are geometrically 1) a plane parallel or inclined to Aar the a, o plane; 2) the basic surface, given by 2 + 2' A > O, located in various positions with respect to the axes; or 3) a combination of the plane and basic surface. The driving function of any two-element-kind one-port is the sum of some combination of the real and imaginary part functions and so is represented by a sum of some combination of the canonic surfaces.