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The generalized (Fig. 1), representing a concatenation of flat waveguides A, B and C, filled by isotropic dielectric is considered. Such frame appears for convenient determination of parameters of the equivalent circuit of the multi-mode slotted radiator [1], covers practically all internal and external problems: the step changing of cross-section at ε_c → ∞; the radiation of aperture L → ∞ etc. Thus it is possible to take advantage of modern methods of an electrodynamics, which allows to use the previous results at finding out of the scattered field by each subsequent modification of the generalized wave-guide frame, that dramatically reduces a computing time for numerical calculations.