Mutual Inductance in the Bird-Cage Resonator

Formulas are derived to account for the effect of the mutual inductances, between all meshes, upon the electrical resonance spectra bird-cage resonators, and similar structures such as the TEM resonator of P. K. H. Roschmann (United States Patent 4,746,866) and J. T. Vaughan et al. (Magn. Reson. Med. 32, 206, 1994). The equations are parameterized in terms of isolated mesh frequencies and coupling coefficients, and ought therefore apply not only to simple magnetic couplings used in the derivation, but to electromagnetic couplings as well. A method for measuring the coupling coefficients-applicable to shielded as well as unshielded resonators-is described, based upon the splitting of frequencies in pairs of coupled resonators; and detailed comparisons are given between calculated and measured resonance spectra: for bird-cage resonators, with and without shields, and for the TEM resonator.