Magnetic-resonance-imaging (MRI) systems for medical and scientific applications require a high-performance, high-power inductor capable of establishing a uniformly strong magnetic field. The transverse-electromagnetic (TEM) resonator¹ has received a great deal of attention recently as a superior replacement for standard birdcage coils² in MRI applications requiring magnetic field levels of 4.7 to 9.4 T. For example, at operating frequencies of 200 and 400 MHz,³ a TEM resonator can achieve better magnetic field homogeneity and a higher quality factor (Q) than an equivalent birdcage coil resulting in improved MRI image quality. In support of the analysis and design of a highQ TEM resonator for MRI applications based on coupled microstrip lines, the authors developed an effective approach based on the use of the finite-element method (FEM).

The primary difference between a TEM resonator and a birdcage coil is the cylindrical shield. The shield functions as an active element of the system, providing a return path for currents in the inner conductors. In a birdcage coil, the shield is a separate entity, disconnected from the inner elements, and only reflecting the fields inside the coil to prevent excessive radiation loss. Because of its shield design, a TEM resonator behaves like a longitudinal multiconductor transmission line that can support standing waves at high frequencies.⁴ Unlike a birdcage coil, the TEM resonator's inner conductors do not possess connections to their closest neighbors, but instead connect directly to the shield through capacitive elements. Resonance mode separation is accomplished though mutual coupling between the inductive inner conductors. Since all the conductors connect to the shield with tunable capacitive elements, the field distribution can be adjusted to achieve the best homogeneity.

In ref. 5, the authors successfully adapted the numerical tool used in ref. 6 to analyze and design an n-element unloaded coupled-microstrip-line TEM resonator. This adapted numerical tool allows the determination of the primary parameters: the inductive and capacitive matrices, [L] and [C], respectively, with respect to the geometrical parameters of the TEM resonator by FEM analysis. A comparison of these FEM results with those obtained in ref. 4 by the boundary element method (BEM) show good correlation in the case of a 12-element unloaded coupled-microstrip-line TEM resonator. To demonstrate this adapted numerical method, an eight-element unloaded coupled-microstrip-line TEM resonator will be designed and analyzed. The resonator has –63.33 dB minimum reflection and an unloaded quality factor (Q_o) of 400 at 200 MHz.

The unloaded TEM resonator is schematically shown in Fig. 1. The functional elements of the TEM resonator are n inner-coupled microstrip conductors, distributed in a cylindrical pattern and connected at the ends with capacitors to the cylindrical outer shield.⁴

The cross section of the coupled microstrip line TEM resonator is presented in Fig. 2. It is formed by an outer shield of radius rB and n microstrip conductors w wide and t thick which constitute the cylindrical pattern of radius rR.

The EM properties of the coupled microstrip line TEM resonator can be described in terms of its primary parameters [L], [C] and its secondary parameter, the unloaded quality factor Q_o :

The coefficients for these matrices are obtained by solving a two-dimensional static field problem based on Laplace's equation:^4-7

where:

V = 1 V on the ith conductor's surface, and

V = 0 on all others conductors.

In this article, the solution of Eq. 1 is found by using FEM analysis. This solution represents the distribution of potential V at the different mesh nodes of the structure.