Spherical Coordinate Systems For Defining Directions And Polarization Componets In Antenna Measurements

Author: Allen C. Newell

The results of theoretical calculations or measurements for 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 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, and propose a terminology that is useful to distinguish between them, and define the mathematical transformations between them. These concepts are essential when the results of different measurements or calculations are compared or when an antenna’s orientation is changed. Both mathematical and graphical representations will be presented.



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