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An exact method, which is more straightforward than those previously published, is derived for the calculation of the minimum radiation Q of a general antenna. This expression agrees with the previously published and widely cited approximate expression in the extreme lower limit of electrical size. However, for the upper end of the range of electrical size which is considered electrically small, the exact expression given here is significantly different from the approximate expression. This result has implications on both the bandwidth and efficiency limitations of antennas which fall into this category.