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This paper presents a generalized variational method for calculation of equivalent-circuit parameters or scattering coefficients of any thin obstacle. The equivalent susceptance is obtained from an eigenvalue of a general-energy operator. The method is applied here to the scattering of a plane wave by a conducting screen containing a doubly-periodic array of square apertures. Previous variational formulations of analogous waveguide problems were largely restricted to cases in which only the dominant mode can propagate. In applying these methods to scattering problems, the ratio of aperture spacing to wavelength had to be restricted to less than unity at normal incidence so that no additional propagating modes were excited. The formulation presented here can be applied, however, for any number of propagating modes. Numerical results are presented for scattering by a periodically apertured screen, giving scattering coefficients as a function of wave number of the incident wave. The distribution of energy into higher-order diffraction lobes is evaluated.