A Handy Formula for Estimating the Effects of Random Surface Errors on Average Power Pattern of Distorted Reflector Antennas

A handy formula is presented to evaluate the effects of random surface errors on average power pattern for distorted reflector antennas. Based on the previous work of Rahmat-Samii on average power pattern degradation for random surface errors, the surface distortioninduced phase error is expanded into a second-order Taylor series expansion in radiation integral. With the probabilistic distribution of phase errors, the closed-form expressions of average power pattern and variance on boresight gain and sidelobe levels are demonstrated by this handy formula. To show the effectiveness of this formula, its applicability region is derived. The derivation clearly shows that when the root-meansquare amplitude of surface distortion is below λ/30, the handy formula presents a good agreement with the exact one in boresight gain within a 0.1 dB computational accuracy. Comparing with the previous work, this formula can estimate the boresight gain loss by hand quickly without the exponential calculation, which will benefit the antenna design.