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Novel explicit formulas are introduced in this paper for the prediction of peak voltages and amplification factors in stepped-impedance coaxial and waveguide low-pass filters. Based on a coupling-matrix model and a simplified electromagnetic (EM) formulation, voltages in the filter critical areas are calculated analytically, without need of any 3-D EM simulations. Only filter prototype parameters are required in this method, which is therefore fast and considerably simplifies the power-handling analysis of corrugated filtering structures. The accuracy of the formulas is verified via commercial finite-difference time-domain software and multipactor breakdown test.