Abstract:
A study of the electrically thick solid cylindrical antenna as a boundary value problem using the integral equation approach is presented. The conventional magnetic field integral equation, which can be identified as a Fredholm integral equation of the second kind, is extensively used as the oo.sis of the solution methods although the conventional electric field integro-differential equation is also employed when its transformation to a singular integral equation is possible. The limitation of the conventional magnetic field integral equation due to the possible coupling between the exterior radiation problem and the interior complementary cavity problem is emphasized. The detection and elimination of - the coupling problem are also discussed. Apart from the usual transverse magnetic mode considered in cylindrical antenna theory, the transverse electric and the hybrid modes are also discussed. It is found that for an electrically thick solid cylindrical antenna, efficient solution methods based on the conventional magnetic field integral equation can be readily formulated to study the different modes of field. The solid cylindrical antennas _with a flat end cap and a hemispherical end cap are chosen to illustrate the methods of solving the boundary value with and without the edge singularity. The presence of the edge singularity imposes a further constraint to the problem and frequently requires suitable modifications to the original problem formulation. When the solid cylindrical antenna with a flat end cap is excited in the transverse magnetic mode, two methods of solving the edge singularity problem are found to be satisfactory: the collocation method of solving the magnetic field integral equation using a series of expansion functions which possess the correct analytic behaviour satisfied by the induced surface current density in the neighbourhood of the edges and the method based on a simultaneous application of the conventional magnetic field integral equation and the conventional electric field integro-differential equation to the cylindrical region and the end disk respectively of the antenna surface. Basically this latter method involves the choice of suitable expansion functions to satisfy the edge condition also but it permits a more elegant treatment of the kernel function singularity and an analytical development of the asymptotic form of the current density near the feed-point. The solid cylindrical antenna with a flat end cap and excited in the transverse electric mode presents other problems not encountered in the corresponding case of excitation in the transverse magnetic mode due to the singularity of the induced surface current density at the edges. A modification of the conventional magnetic field integral equation using a co-ordinate transformation technique is found to be satisfactory. Further it is shown that this modification to the problem formulation eliminates the coupling problem which exists in the conventional formulation.