This paper presents a small and complete set of analytic equalength show that the model calculations can usefully predict tions which can be used to design a birdcage coil and predict its birdcage performance, can aid in choosing dimensions and resonant modes a priori before construction begins. The simple capacitor values before construction begins, and can minimodels used include full mutual coupling between all meshes and mize or eliminate the iterative tuning/rebuilding which has give the resonant spectrum for both unshielded and shielded coils. often accompanied practical birdcage construction.
The equations are valid, in compact form, for lowpass, highpass,
To this end, a solution for the resonant modes of the bandpass, and more general birdcage structures. The resonantbirdcage using the mesh eigenvalue approach of Tropp ( 7) mode frequencies are shown to depend on the spatial discrete and Joseph and Lu (8) is presented which makes clear the Fourier transforms of the vectors of electric and magnetic coupling dual transform nature of the solution. Although portions of around the coil, making obvious the connection between the reso-
this treatment have appeared elsewhere, the presentation here nant and the spatial frequencies of each mode. Inversion of the equations provides values of all of the mesh inductances and cou-is rigorous, and the results are of wider scope than previous plings from the measured resonance frequencies following coil contreatments and motivate new results. The inversion procestruction, a result of considerable practical importance. Experidure of the second section is one such new result and shows mental results are presented which show that these methods reguhow all the inductance values can be derived from the resolarly predict operating frequencies to a high degree of accuracy nant frequencies measured for a birdcage coil. This result is for both unshielded and shielded coils. α§ 1997 Academic Press used to check the accuracy of the inductance calculations presented in the third section, which, for the practicalminded reader interested in predicting coil behavior, contains 51