The theory of the bird-cage resonator

Abstract

Circuit equations for the low-pass bird-cage resonator are solved to yield a two-parameter expression for the resonant frequencies; good agreement with experiment is shown for a bird cage of eight meshes. A theory of the driven bird-cage coil is given, which describes capacitive or inductive drive schemes, neglecting perturbations of coil symmetry due to the drive reactance. The theory shows how the polarization plane of the B field of a perfectly symmetrical bird cage can be rotated arbitrarily about the resonator's cylinder axis. Deviations from ideal symmetry, due to imperfect construction or trimming reactances, are then treated by perturbation theory. It is shown that in first order, the perturbation does not disturb the sinusoidal current distribution of the bird cage, although it does polarize that distribution along a direction fixed by the positions of the perturbing elements. The measured and calculated polarization directions are shown to agree to within experimental error; the measured frequency shifts due to perturbation are within 10% of those calculated. It is shown that two identical perturbations in space quadrature produce eigenstates with no spatial polarization, i.e., circularly traveling current waves.