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Starting from the radiation characteristics of a differential current element, the vector potential produced by a single-turn circular loop antenna is formulated in terms of a general loop current by a direct integration process. Evaluation of the resulting integrals for a limited number of specific loop current distributions leads to generalized expressions for both the standing-wave and traveling-wave cases. Radiation fields can be found from the integrated vector potential expressions. This technique represents only a slight modification of the one used by Sherman, but it extends his work in such a way that the results are equivalent to those obtained by Knudsen in a somewhat different manner.