Singularity cancellation and extraction techniques for precise evaluation of impedance integrals in thin-wire analysis

Various methods for numerical calculation of impedance integrals in thin-wire analysis are investigated. Two integration methods based on singularity extraction techniques and one based on singularity cancellation technique are considered for calculation of potential integrals. Five novel transformations for the singularity cancellation technique are compared for the second integration in evaluation of impedance integrals. Optimal choice of integration methods for the first and the second integration enable very efficient and accurate evaluation of impedance integrals. For example, accuracy to 15 significant digits can be achieved using Gauss-Legendre formulas of order 30. The significance of such accuracy is illustrated in the case of thin-wire antenna of 1m in maximum dimension, which is successfully analyzed in range from few Hz to 1 GHz.