Circuit-model representation of external-Q calculation

Abstract

A new representation of the external-Q (Qext) calculations for cavities coupled to waveguides is derived based on a circuit model. The Qext 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 Qext 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 Qext calculation. It is also shown why this estimation provides a good approximation when Qext is high. Formulas for the TEM, TE, and TM modes of waveguides are presented along with a simple example of a loop-coupled cavity. © 2006 The American Physical Society.