Addendum to "Measurement of short time changes of cavity Q and resonant frequency"

Abstract

Summary form only given. Formulas for the Q-factor and the resonant-frequency shift of a perturbed reflectiontype cavity have been derived recently and presented in the above-mentioned paper [ibid., vol. MTT-17, pp. 339-344, June 1969]. For the assumption that the external Q-factor, Qext is the same for the unperturbed and the perturbed cavity, a quadratic equation (14) for the unloaded Q-factor has been formulated. It has been pointed out that two values of Q, are obtained which are, respectively, smaller and greater than Q0, the unloaded Q-factor of the unperturbed cavity. However, by inspection of (14) it may be seen that one of the roots of the quadratic equation is always equal to this Q0. The other root is Q1 which is given by a formula where Ω01, and Ω02 are the values of the tuning parameter at which the resonant curves of the reflection coefficients of the unperturbed and the perturbed cavity intersect. This result shows that there is no ambiguity in the evaluation of the Q-factor of cavities when no change of the external Q-factor, Qext occurs during perturbation.