Abstract: The matching theory based on an equivalent circuit model is outlined that self-consistently determines the modulation of a klystron output cavity for arbitrary coupling of the output waveguide to the cavity and arbitrary cavity and/or electron beam parameters. An equivalent circuit model including a mutual inductance and the induced current for the output cavity is established, the output power and the reflected power are discussed. For the cases where the complex coupling coefficient equals 1 and does not equal 1, we respectively determined expressions for the reflected power. We derived an expression for the output power corresponding to the gap voltage for the case when the coupling is perfectly matched to the output waveguide, and also for the case of arbitrary coupling. We worked out expressions for the resonant frequency of the output cavity and externally-loaded Q leading to the matching conditions. If the matching conditions are satisfied, the output power corresponding to the new theory equals approximately the output power corresponding to the traditional theory.