Resonant Modes of the Birdcage Coil

Abstract

This paper presents a small and complete set of analytic equations which can be used to design a birdcage coil and predict its resonant modesa prioribefore construction begins. The simple models used include full mutual coupling between all meshes and give the resonant spectrum for both unshielded and shielded coils. The equations are valid, in compact form, for lowpass, highpass, bandpass, and more general birdcage structures. The resonant-mode frequencies are shown to depend on the spatial discrete Fourier transforms of the vectors of electric and magnetic coupling around the coil, making obvious the connection between the resonant and the spatial frequencies of each mode. Inversion of the equations provides values of all of the mesh inductances and couplings from the measured resonance frequencies following coil construction, a result of considerable practical importance. Experimental results are presented which show that these methods regularly predict operating frequencies to a high degree of accuracy for both unshielded and shielded coils.