Simple formulas for the gain and far-field of open-ended rectangular waveguides

Simple formulae are presented for estimating the on-axis gain and far-field of open-ended rectangular waveguides (OEG). The on-axis gain formula is derived by incorporating in an approximate way the contribution of fringe currents at the shorter edges of the OEG into Schelkunoff´s classical gain formula. By comparing this formula with Yaghjian´s (1984) fringe current-based gain formula for the OEG, an explicit factor is arrived at to represent the effects on the H-plane pattern of the fringe current and reflection coefficient. Subsequently, a simple formula results for the H-plane pattern, which in turn makes the far-field estimation easier. Neither of these formulas need measured values of the aperture reflection coefficient of the OEG, unlike the approximate formulas by Yaghjian, and are simpler than these. The two sets of formulae compare very well with each other