Approximate formula for the phase of the aperture-reflection coefficient of open-ended rectangular waveguide

Expressions are derived for estimating the approximate values of the phase of the dominant mode reflection coefficient at the aperture of standard open-ended rectangular waveguides (OEGs). The derivation uses the principle of power conservation and is accomplished by equating net input power to total radiated power. Negligible resistive loss in the waveguide walls is assumed. The expressions compare favorably with the earlier 90° approximation and with measured data, and facilitate a fully theoretical (rather than semiempirical) estimation of the on-axis gain and far field of OEGs by using Yaghjian´s (1984) formulas.