Fundamentals of Thin-Wire Integral Equations With the Finite-Gap Generator—Part I

We discuss certain fundamental properties of Hallén´s and Pocklington´s equations with the finite-gap generator (FGG), which has long been used as a feed model for cylindrical antennas. For the case of the exact kernel, we focus on whether important quantities are finite or infinite and compare to corresponding quantities obtained using the delta-function generator (DFG). For the approximate kernel, we focus on the unsolvability of the two equations and the relation of unsolvability to the important phenomenon of unphysical oscillations. We also extend to the FGG the so-called effective-current method; this is an easy-to-apply remedy for the oscillatory solutions that allows one to obtain reasonable answers for important quantities such as current distributions and the input impedance. It is shown here that these answers are close to those obtained with the exact kernel. We show that, in a certain sense, the method is more advantageous to apply in the present (FGG) case than in the DFG case. Our discussions-especially in Part II of this paper-bring out similarities to: 1) the phenomenon of superdirectivity, and 2) recently discussed numerical phenomena occurring within the Method of Auxiliary Sources.