Solution of Hallen's Integral Equations by Means of Nystrom Method

To solve Hallen's integral equations accurately, Nystrom method is applied in this paper. To obtain an exact and finite solution, both the exact kernel and a finite gap width must be taken into consideration in the case of a gap feed. A modification function that converts the approximate kernel to the exact kernel is derived. As the modification function is singular, a one-point correction method is proposed, as a singularity subtraction method. Using a step function source, we can use various quadrature rules to solve the problem. The results show small difference between them. The validity of this theory is confirmed by comparing the measured results and the calculated results. The effect of the feed system is shown to be strong.