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Both a new approximate characteristic equation and closed-form expressions for the amplitudes of the space harmonics (SH) are presented for the transverse electric modes of periodic magnetron-type cavities. Contrary to the narrow-slot approximation (NSA), which is often used in practical calculations, our approximate model takes the angular dependence of the field in the resonators (slots) into account and, hence, allows to more accurately calculate the electromagnetic characteristics (EM-C) of the cavity. Comparing to the results obtained from numerically rigorous approaches, the necessity of taking this dependence into account is shown. The potentials of the suggested model are outlined for improving the accuracy of the EM-C calculations for parameter combinations which are typical for some microwave vacuum tubes.