Institute for Telecommunication Sciences
the research laboratory of the National Telecommunications and Information Administration

Kenneth P. Spies; 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

To request a reprint of this report, contact:

Lilli Segre, Publications Officer
Institute for Telecommunication Sciences
(303) 497-3572

Disclaimer: Certain commercial equipment, components, and software may be identified in this report to specify adequately the technical aspects of the reported results. In no case does such identification imply recommendation or endorsement by the National Telecommunications and Information Administration, nor does it imply that the equipment or software identified is necessarily the best available for the particular application or uses.

Back to Search Results