Circuit-model representation of external-Q calculation

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.