Mutual coupling analysis of a conformal array of elements on a cylindrical surface

The analysis of multiport antennas may be approached by resorting to the powerful concept of eigenexcitations of the structure. They may be defined as the eigenvectors of the admittance matrix, i.e., those sets of voltages and currents at the antenna terminals which are related simply by a proportionality factor (eigenvalue of the admittance matrix). Similarly, the eigenexcitations may be alternatively defined as the eigenvectors of the scattering matrix. The analysis for this special kind of excitation is sometimes relatively easy. The general case may then be treated by utilizing superposition principle. An array of infinitely long longitudinal slots equispaced on a conducting cylinder is analyzed in detail. The eigenvectors of the admittance and scattering matrices are easily found because of the symmetry of the structure. Expressions for the eigenvalues of these matrices, and for the radiation patterns due to the array eigenexcitations, are found in the form of infinite series rapidly convergent (even for cylinders of large radius). By using linearity an expression for the radiation pattern of the single excited element in the array environment (the main result of this paper) is then established. Expressions are also given for the coupling (or scattering) coefficients. A number of numerical examples with different cylinder radii are discussed in detail.