Effects of spurious modes in resonant cavities

General theory of two reactively coupled interacting resonant modes is presented in terms of normalized equivalent circuit parameters. For the first time analytical equations are derived that explain the effects on the mode frequencies, Q factors and couplings as a function of detuning for two coupled resonant modes. All equations are verified experimentally by observing a mode interaction while tuning a tunable sapphire-loaded superconducting cavity resonator. This work enables theoretical analysis of the effect of a spurious mode on an operational mode in a resonant cavity. The extent that the spurious mode can translate its inferior frequency stability and Q factor is investigated. The impact of utilizing a high-Q whispering gallery resonator with a high spurious mode density for low-noise signal generation is discussed.