Note on Cavity Perturbation Theory

A criterion is presented for the applicability of cavity perturbation theory for measuring permeabilities and dielectric constants of materials. In the literature, the perturbation criterion is usually stated as: the rf fields in the cavity with and without the sample are approximately equal. This is the same as stating that changes in the stored energy in the cavity, upon introduction of the sample, are small. This criterion is shown to be too strong, and usually violated in experiments. A weaker but sufficient criterion, for all commonly encountered Q values, is that changes in the over-all geometrical configuration of the rf fields must be small upon introduction of the sample. Experimentally, this means that for small sample measurements only the percentage change in the real part of the frequency must be small. Data are presented to demonstrate the above ideas.