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In this paper, an explicit expression of the peak electric-field strength in the cavities of Chebyshev direct-coupled-cavity waveguide filters is derived. It is shown that the electric-field strength can be predicted from the analysis of the time-averaged stored energy in the lumped low-pass prototype, from which the cavity filter was derived. This simplifies the analysis and study of the power-handling capability of these types of filters considerably, as the stored energy in the prototype filters is easily computed. The analysis of the field distribution in the cavities of an example third-degree Chebyshev direct-coupled-cavity filter shows that the explicit expression for the peak electric-field strength derived in this paper agrees closely with results obtained from a TE10 circuit model of the filter, from a full-wave electromagnetic solver and from measurements.