Real axis integration of Sommerfeld integrals with applications to printed circuit antennas

Printed circuit antennas are becoming an integral part of imaging arrays in microwave, millimeter, and submillimeter wave frequencies. The electrical characteristics of such antennas can be analyzed by solving integral equations of the Fredholm first kind. The kernel involves Sommerfeld integrals which are particularly difficult to solve when source and field points lie on an electrical discontinuity, as it occurs in the determination of the characteristics of printed circuit antennas. An analytic-numeric real axis integration technique has been developed for such integrals and it is combined with piece-wise sinusoidal expansions to solve the Fredholm integral equation for the unknown current density.