Second-Order Expansion Computation of Average Power Pattern of Cylindrical Reflector Antennas With Random Surface Errors

To consider the effects of random surface errors on the radiation pattern of cylindrical reflector antennas, a second-order expansion computation method is proposed to calculate the boresight gain loss and average power pattern. The additional phase error caused by random surface distortion is expanded into a second-order Taylor series expansion in radiation integral. Based on the probabilistic Gaussian distribution of phase errors, the boresight gain loss and average power pattern can be simplified into a second-order expression of a root-mean-square (rms) value of random surface errors. Simulation results on a Ku/Ka-bands parabolic cylindrical reflector illustrate that the second-order expansion can account for the boresight gain loss within a computational accuracy of 0.1 dB when the rms value of random surface errors is below $\lambda /22$ for the Ku-band, as well as $\lambda /24$ for the Ka-band. When the rms value of random surface errors is below $\lambda /50$ for the Ku-band, or $\lambda /100$ for the Ka-band, the second-order expansion can also account for the first sidelobe in an average power pattern.