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2 years ago in Electrical Engineering By Raman

When designing a pyramidal horn, are King’s optimum aperture phase error rules still the definitive guideline for balancing gain, beamwidth, and horn length?

I'm designing a standard gain horn and came across the classical papers by King which define "optimum" horns based on maximizing gain for a given length by allowing a specific phase error across the aperture. In the age of EM optimization, are these analytical rules still the best starting point, or have they been superseded? If they are valid, what are the specific phase error criteria (e.g., 0.25λ path difference) for the E- and H-plane, and how are they used to calculate the flare dimensions?

ApertureSizing KingsRules E-Plane h-plane FlareAngle HornAntenna

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By Nazia Answered 1 year ago

 King's rules remain an excellent and physically insightful starting point. They are based on allowing a maximum phase error of π/2 radians (90°) at the aperture edge relative to the center, which strikes a balance between gain, beamwidth, and length. For a given desired gain and frequency, these rules give you the optimum aperture dimensions and horn length. I still use them to generate my initial model before any EM optimization. The formulas dictate different phase errors for E- and H-planes due to the different field distributions, leading to different flare angles. Modern solvers can then fine-tune these dimensions, often for sidelobe suppression or specific pattern shape, but they rarely deviate far from King's optimum. For a standard gain horn, starting with King will save significant optimization time. 

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