Kenneth P. Spies and Eldon J. Haakinson

Abstract: This report describes methods for calculating, under certain simplifying assumptions, footprints (contours of constant power density) for idealized models of several common types of transmitting antennas (circular aperture, elliptical aperture, rectangular aperture, and helical beam antennas), and for antenna beams of specified but rather arbitrary shape. The transmitter is mounted on a satellite at a prescribed location in the geostationary orbit and has its main-lobe axis directed toward a given aim point on the earth. Formulas are first derived for calculating the intersection of the earth with a ray emanating from a given geostationary satellite and having a prescribed direction in space. For each idealized antenna type, procedures are next discussed for finding those directions in space where the relative power density has a specified constant value; intersection formulas are then applied to locate the corresponding footprint. Far-field patterns are approximated for aperture antennas by evaluating Fourier transforms of assumed aperture illumination distributions, and for the helix by assuming it radiates in the axial mode. Owing to gross discrepancies between actual and ideal side-lobe patterns, the analysis is confined to the main lobe of idealized antenna models.

Keywords: antenna patterns; footprints; geostationary satellite; power density contours

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