Antenna Spherical Coordinate Systems and Their Application in Combining Results from Different Antenna Orientations

The results of theoretical calculations or measurements on antennas are generally given in terms of the vector components of the radiated electric field as a function of direction or position. Both the vector components and the direction parameters must be defined with respect to a spherical coordinate system fixed to the antenna. Along the principal planes there is no ambiguity about the terms such as vertical or horizontal component, but off the principal planes the definition of directions and vector components depends on how the spherical coordinate system is defined. This paper will define four different spherical coordinates that are commonly used in measurements and calculations, suggest a terminology that is useful to distinguish between them, and define the mathematical transformations between them. One important application of these concepts arises when comparing or combining measurement results from two antenna orientations. In this case, the axis of rotation dictates the preferred coordinate system and vector components. Measured results will be shown to illustrate the proper choice of coordinates for each situation.