New Cosine-q Pattern Formulas for the Analysis of Elongated-Aperture Antennas

The cosine-q radiation pattern formulas allow one to create sidelobe-free patterns with easily controlled beamwidth and taper. These advantages make the cosine-q pattern an ideal feed source in the studies of reflectors, transmit-/reflect-arrays, and lens antennas. However, in this communication, it is shown that the original cosine-q formulas are limited to rotationally symmetric patterns and lose their effectiveness when an elliptical pattern (or a fan-beam) with highly unequal beamwidths in two principal cuts is desired. This limits the application of cosine-q sources in antennas with elongated apertures, which are of great interest in radar sensing and CubeSat applications. This communication proposes a set of new formulas that enable the use of cosine-q-type illumination for elongated-aperture antennas. The model is further improved by adding a phase function that accounts for the interleaved phase center locations, which can appear in practical feed sources. The effectiveness of the new cosine-q formulas is demonstrated by analyzing two representative antennas: a C-band linearly polarized 7 m
$\times1.5$
m aperture reflector antenna and a K-band circularly polarized 20 cm
$\times10$
cm reflectarray antenna.