Abstract
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.
Highlights
Horns are among the simplest and most widely used microwave antennas
This paper provides a set of simple polynomial approximations that adequately describe the gain reduction factors of pyramidal and sectoral horns
We presented a set of nth-order polynomial approximate expressions for the gain reduction factors of pyramidal and sectoral microwave horns
Summary
Horns are among the simplest and most widely used microwave antennas. They occur in a variety of shapes and sizes and find application in areas such as wireless communications, electromagnetic sensing, radio frequency heating, and biomedicine. The formula includes the geometrical optics of the radiated field and the singly diffracted fields of the aperture edges and represents the monotonic gain component It omits multiple diffraction and diffractted fields reflected from horn interior; it is adequate for pyramidal horns but calculates erroneously the gain of sectoral ones [4]. We provide improved approximate polynomial expressions for the gain reduction factors of a rectangular horn These formulas were obtained from the application of least squares polynomial fitting over the range of aperture phase error parameters from zero to one (typical values for practical applications [19,20]).
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