A combined complex image and contour integral method for rapid solution of patch resonators

The resonator structure is divided into interior and exterior regions. For the interior region, the standard 2-D Okoshi formulation of magnetic current (electric voltage) on the patch perimeter is used. For the exterior region, a 3-D complex image formulation of magnetic current is used. The tangential electric and magnetic fields of the exterior and interior formulations are then matched over the patch perimeter to form a moment method matrix equations. Numerical results are provided for rectangular and circular patch resonators of direct microstrip feed over a wide frequency range. These numerical examples demonstrate the versatility, speed, and accuracy of the method.<
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