This paper proposes a novel design criterion for optimal pyramidal horns. According to it, the optimal aperture phase error parameters of a pyramidal horn are determined from the minimization of the horn's lateral surface area. We present two families of curves that illustrate the optimal aperture phase error parameters for frequency and directivity values in the area of practical interest. We also discuss two simple approximate design methods for the calculation of the optimal horn parameters. Comparisons with well-known design methods demonstrate the efficacy of our approach. The proposed criterion produces the lightest horn for a given directivity; as a result its fabrication requires less material compared to other structures. Moreover, the designed horns have smaller aperture area and occupy less space. The present approach is a useful design tool when the size and weight of a pyramidal horn or its manufacturing cost are of concern.
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