An Efficient 1-D Periodic Boundary Integral Equation Technique to Analyze Radiation onto Straight and Meandering Microstrip Lines

A modeling technique to analyze the radiation onto arbitrary 1-D periodic metallizations residing on a microstrip substrate is presented. In particular, straight and meandering lines are being studied. The method is based on a boundary integral equation, more specifically on a mixed potential integral equation (MPIE), that is solved by means of the method of moments. A plane wave excites the microstrip structure, and according to the Floquet-Bloch theorem, the analysis can be restricted to one single unit cell. Thereto, the MPIE must be constructed using the pertinent 1-D periodic layered medium Green´s functions. Here, these Green´s functions are obtained in closed form by invoking the perfectly matched layer paradigm. The proposed method is applied to assess the radiation onto 1) a semi-infinite plate, 2) a straight microstrip line, and 3) a serpentine delay line. These three types of examples clearly illustrate and validate the method. Also, its efficiency, compared to a previously developed fast microstrip analysis technique, is demonstrated.