In this work the possibilities of three‐ and four‐stage Bennett‐type aperiodic rf mass spectrometers with energy modulators of 5 and 7 grids have been explored. The expressions for the energy gain, resolving power, harmonics, and their relative peak heights have been obtained. The oscillatory behavior of the energy‐modulating functions has been analyzed using an IBM 1620 Computer, and graphical representations are given which permit the determination of the energy interval over which the analyzer can be operated. Resolution for the most favored combinations of stage separations has been calculated atVr1and 90&percent; values of the retarding voltage level, A grid with improved microoptics and relatively higher ionic transmission coefficient has been developed for use in rf mass analyzers.