The aperture phase taper due to quadratic phase errors in the principal planes of a rectangular horn imposes signifi-cant constraints on the on-axis far-field gain of the horn. The precise calculation of gain reduction involves Fresnel integrals; therefore, exact results are obtained only from numerical methods. However, in horns’ analysis and design, simple closed-form expressions are often required for the description of horn-gain. This paper provides a set of simple polynomial approximations that adequately describe the gain reduction factors of pyramidal and sectoral horns. The proposed formulas are derived using least-squares polynomial regression analysis and they are valid for a broad range of quadratic phase error values. Numerical results verify the accuracy of the derived expressions. Application examples and comparisons with methods in the literature demonstrate the efficacy of the approach.
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