On the quality factor of strip and line source antennas and its relationship to superdirectivity ratio

Exact formulas are derived for the quality factorQof strip and line source antennas. Contrary to popular opinion, none of them is equal to Taylor's superdirectivity ratio toγ - 1. But in the case ofE-plane strip sources (the complement of the type of strip source treated by Woodward and Lawson) the value ofQis precisely equal toγα-1/2- 1, whereγαβis a generalized superdirectivity ratio that reduces to Taylor's the edge exponent the pattern weighting exponent both zero. In the case ofH-plane strip sources the value ofQis approximately equal toγα1/2 - 1, and forH-plane line sources of vanishing widthait is approximately equal to[(2/π) ln (2.516λ/π a)]γα¹.