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It is shown that the eigenvalues, which are derived in a closed form from a simpler solution, associated with balanced hybrid modes in conical scalar horns are close (within 4%) to the exact values obtained numerically by Clarricoats for the first ten modes. It is verified that the simpler expressions obtained for the far-field radiation patterns of conical scalar horns, supporting the balanced HE11 mode, closely follow the available experimental results for several values of α0 (half the flare angle), including the case α0 = 90°. From a study of the variation of the on-axis gain with the significant dimensions of the horn, an empirical relation for determining the dimensions of optimum scalar horns is obtained.
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Narasimhan et al. (1972) studied this question.
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