Purpose: Detectors such as birdcage coils often consist of networks of coupled resonant circuits that must produce specified magnetic field distributions. In many cases, such as quadrature asymmetric insert body coils, calculating the capacitance values required to achieve specified currents and frequencies simultaneously is a challenging task that previously had only approximate or computationally inefficient solutions.
Theory and Methods: A general algebraic method was developed that is applicable to linear networks having planar representations such as birdcage coils, transverse electromagnetic (TEM) coils, and numerous variants of ladder networks. Unlike previous iterative or approximate methods, the algebraic method is computationally efficient and determines current distribution and resonant frequency using a single matrix inversion. The method was demonstrated by specifying irregular current distributions on a highly elliptical birdcage coil at 3 Tesla.
Results: Measurements of the modal frequency spectrum and transmit field distribution of the two specified modes agrees with the theory. Accuracy is limited in practice only by how accurately the matrix of self and mutual inductances of the network is known.
Conclusion: The algebraic method overcomes the inability of the existing inductance equalization method to account for all elements of the inductance matrix and the inability to accommodate modal currents that are not (co)sinusoidal.