Modelling of electrically thick cylindrical antennas

Abstract

AbstractHallen's integral equation has been used as the basis for the formulation of cylindrical antenna theories for many years. Being a Fredholm integral equation of the first kind, its solution is mathematically an ill‐posed problem. The stability of the numerical methods based on this integral equation is dependent on the singularity and the non‐smoothness of the kernel function. For electrically thick cylindrical antennas, the dominance of the singular part of the kernel (logarithmic) is weakened and the kernel function becomes relatively smooth. This observation implies possible deteriorations of the stability of the numerical methods based on Hallen's integral equation. This paper describes the development of an alternative formulation for the electrically thick cylindrical antennas based on the singular integral equation of the first kind with a Cauchy‐type kernel which eliminates the potential instability problem. A numerical method based on this formulation of the antenna problem has been implemented and case studies show that it is very stable and efficient for the numerical modelling of electrically thick cylindrical antennas.