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

Exact formulas are derived for the quality factor
Q
of strip and line source antennas. Contrary to popular opinion, none of them is equal to Taylor's superdirectivity ratio
\gamma
or to
\gamma - 1
. But in the case of
E
-plane strip sources (the complement of the type of strip source treated by Woodward and Lawson) the value of
Q
is precisely equal to
\gamma_{\alpha}^{-1/2}- 1
, where
\gamma_{\alpha}^{\beta}
is a generalized superdirectivity ratio that reduces to Taylor's
\gamma
when the edge exponent
\alpha
and the pattern weighting exponent
\beta
are both zero. In the case of
H
-plane strip sources the value of
Q
is approximately equal to
\gamma_{\alpha}^{1/2} - 1
, and for
H
-plane line sources of vanishing width
a
it is approximately equal to
[(2/\pi) \ln (2.516\lambda/\pi a)]\gamma_{\alpha}^{1}
.