AN EXACT FORMULATION FOR THE VECTOR POTENTIAL OF A CYLINDRICAL-ANTENNA WITH UNIFORMLY DISTRIBUTED CURRENT AND ARBITRARY RADIUS

This paper presents an exact formulation for the vector potential and corresponding electric fields associated with a uniform current cylindrical dipole antenna of arbitrary radius. A mathematically exact representation of the vector potential and electric fields has not previously been available for cylindrical wire antennas. The exact expressions given in this paper converge rapidly in the induction and near-field regions of the antenna. They are completely general and independent of the usual restrictions involving the wavelength, field point distance, dipole radius and length. The properties of these exact expressions allow them to be readily used for the efficient as well as accurate computational modeling of cylindrical wire antennas. The successful derivation of an exact expression for the uniform current vector potential, and ultimately the electric fields, depends upon finding an exact representation for the cylindrical wire kernel integral as well as a certain integral of this kernel. An exact expression for the cylindrical wire kernel will be presented which is analytically as well as numerically convenient to work with. It will be demonstrated that the integral of the kernel may be expressed in terms of a series which involves a generalized exponential integral and higher-order associated integrals. Several methods for evaluating the generalized exponential integral will be discussed including some useful asymptotic expansions. A numerically stable forward recurrence relation for the higher-order associated integrals will also be presented.