A HYBRID PROCEDURE TO SOLVE HALLENS PROBLEM

The knowledge of the electromagnetic fields in the neighborhood of an antenna needs the accurate evaluation of the current distribution on E t. This is a subject which deserves a particular attention mainly for sensors, It is called Hallen's problem the one relevant to the current distribution on a cylindrical antenna. We have already shown [1] that this problem can be formulated as a Fredholm integral equation of the second kind with a continuous kernel, and that this integral equation can be solved by a transformation into a linear system of algebraic e quations. Even if this solution has a number of doubtless improvements with respect to previous approaches [2], [3], however it does not exp licit the logarithmic singularity of the current due to the infinite c apacitance of the infinitesimal gap, As a consequence the above expans ion requires more and more terms to obtain an assigned precision of th e solution, the closer we are to the gap. In this paper, we show that it is possible to extract the singular part of the current, and to obt ain a reasonable precision with a finite number of terms regardless of the distance from the gap, The method seems to be suitable for thick dipole antennas, The procedure has been defined hybrid because we firs t resort to a finite number of steps of the iterative solution, and th en the nth integral equation is solved by the Bubnov-Galerkin projecti on method.