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A solution of the broadside back-scattering cross section, , of a center-loaded cylindrical antenna with any load impedance, , is obtained by a variational method through a four-terminal network approach. A simple formula for , in terms of and the parameters , and associated with the antenna has been derived. The impedances , and are independent of the load and they are determined by using the variational principle. Numerical results of the first order approximation are presented, and they are in good agreement with some measured results available in the literature.