| Summary: | A new representation of the external-Q (Q_{ext}) calculations for cavities coupled to waveguides is derived based on a circuit model. The Q_{ext} value is obtained by solving analytical equations of the input impedance of a cavity provided as a function of the frequency; large numerical simulations are not necessary. The derivation starts with a fundamental expression of the ratio of the stored energies of two loss-free circuits forming a parallel resonant circuit. By applying this expression to the input impedance of a cavity seen from the detuned-short-circuit plane, as well as to those of open- and short-end waveguides, a precise estimation of Q_{ext} is given. It is then explained that the result is almost independent of the choice of the cavity boundary. This method is an alternative to the electromagnetic representation of the Q_{ext} calculation [P. Balleyguier, in Proceedings of the XIX International Linac Conference, Chicago, Illinois, USA, edited by C. E. Eyberger, R. C. Pardo, and M. M. White (ANL-98/28, 1998), pp. 133–135.]. It is also shown why this estimation provides a good approximation when Q_{ext} is high. Formulas for the TEM, TE, and TM modes of waveguides are presented along with a simple example of a loop-coupled cavity.
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