Convergence behavior and acceleration of the Berenger and leaky modes series composing the 2-D Green´s function for the microstrip substrate

The Green´s functions G_A and G_V are calculated for a two-dimensional microstrip substrate by placing the substrate into a closed perfectly-matched-layer waveguide and by performing a modal expansion in Berenger and leaky modes. It is shown that each series composing G_A and G_V has a particular convergence behavior when considering small lateral distances between the excitation and the observation points. It is then demonstrated that, by applying the Shanks transform to accelerate each series separately, a more efficient calculation for the Green´s functions can be obtained than by direct computation of the series. The theory is illustrated by means of a representative example