Multiple Resonant Multiconductor Transmission Line Resonator Design Using Circulant Block Matrix Algebra
In this thesis, a new design procedure to determine resonant conditions for a multiconductor transmission line (MTL) resonator is proposed. The MTL is represented as a multiport network using its port admittance matrix. Closed form solutions for different port resonant modes are calculated by solving the eigenvalue problem of the admittance matrix using the block matrix algebra. A port admittance matrix can be formulated to take one of the following forms depending on the type of MTL structure: i) a circulant matrix, ii) a circulant block matrix (CB), or iii) a block circulant circulant block matrix (BCCB). A circulant matrix can be diagonalized by a simple Fourier matrix, and a BCCB matrix can be diagonalized by using matrices formed from Kronecker products of Fourier matrices. For a CB matrix, instead of diagonalizing to compute the eigenvalues, a powerful technique called “reduced dimension method” can be used. Application of block matrix algebra helps reduce the computational complexity and also simplifies the formulation of the analytical solutions.
To demonstrate the effectiveness of the proposed methods (2n port model and reduced dimension method), a two-step approach was adopted. First, a standard published Radio Frequency (RF) coil is analyzed using the proposed models. The obtained resonant conditions are then compared with the published values and are verified by full-wave numerical simulations. Second, two new dual-tuned RF coils for magnetic resonance (MR) imaging, a surface coil design using the 2n port model and a volume coil design using the reduced dimensions method, are proposed, constructed, and bench tested. Their validation is carried out by employing 3D EM simulations as well as undertaking MR imaging in clinical scanners. Imaging experiments were conducted on phantoms, and the investigations indicate that these RF coils achieve good performance characteristics and a high signal-to-noise ratio in the regions of interest.
Prof. Reinhold Ludwig
Research Committee Members: