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A two-dimensional mixed-potential integral equation formulation is used to analyze the eigenmodes of microstrip lines. The new method involves a fast evaluation scheme for the space domain Green's functions of the substrate by using perfectly matched layers to obtain closed-form expressions as a series of leaky and Berenger modes. Efficient summation of these series is performed by means of the Shanks transform. The modal series can be applied to calculate all field interactions analytically, except for the selfpatch and the nearest neighbor contributions. Examples show an important reduction in CPU time for the new perfectly matched layers approach, as compared to the classical evaluation of the continuous Sommerfeld integrals.