Exact solution of Hall é n´s integral equations by Numerical Integral Equation Method

Hallén´s integral equation is widely used to calculate the current distribution and input- impedance of dipole antennas. There are two problems. One is that Hallén´s integral equation using an approximate kernel has no solution. The other one is that Hallén´s integral equation using the exact kernel with a δ function feed has also no solution. In this paper Numerical Integral Equation Method (NIEM) is proposed to solve these problems. A modification function which converts the approximate kernel to the exact kernel is derived. As the modification function diverges, three points correction method is also proposed. Using the solution of offset feed by a δ function source, a problem with a finite gap feed is solved. The validity of this theory is confirmed comparing the measured result and the calculated result.