Error Analysis of Sommerfeld Integrals for Microstrip Antenna Problems

Accuracy of computation for Sommerfeld integrals is examined for applications to microstrip geometries. In a numerical approach proposed earlier, the influence of the singularities in the integrand is obviated by deforming a small portion of the contour from the real axis to the 1 ^st quadrant, thus avoiding the branch point and surface wave pole singularities in the $4^{\mathrm{t}\mathrm{h}}$ quadrant of the complex plane. The overall computational strategy comprises of numerical integration across the finite, deformed contour followed by a closedform evaluation of the tail part of the Sommerfeld integral. Given a specified a-priori error bound, a criterion for assessing the computational errors is developed here that restricts the maximum height of the deformed contour in the 1 ^st quadrant. Preliminary numerical results included here suggest the validity of the method while also indicating that there is scope for augmenting this criterion for large values of lateral separations between the source and observation locations.