Random Error Characterization of Nonsmooth Parabolic Reflector Antennas With Gore-Faceted or Discontinuous Surface

A generalized random error characterization method is proposed mainly to evaluate the effects of random error on radiation pattern for nonsmooth parabolic reflector antennas, which are synthesized by the gore-faceted or discontinuous surface. Based on the previous work of the second-order Taylor series expansion of the radiation integral, two matrix-form formulas of the generalized method are derived. With the assumed Gaussian distribution of the random surface error, the average power pattern can be easily calculated by the generalized method. The proposed method can overcome the drawbacks of the previous methods for nonsmooth parabolic reflector antennas and its computational accuracy can be guaranteed. The wide applicability of the generalized method is sequentially demonstrated by a smooth reflector antenna, a 0.5 m Ka-band gore-faceted rib reflector, and a 1 m Ka-band symmetric stepped reflector. Through the simulations on different types of nonsmooth parabolic reflector antennas, the versatility of the proposed method can be easily illustrated.