Efficient Extraction of Frequency-Dependent Substrate Parasitics Using Direct Boundary Element Method

An efficient method based on a direct boundary element method is proposed for extracting frequency-dependent substrate coupling parameters. A frequency-independent real-valued linear equation system is first solved. Then, the solution is transformed into frequency-dependent parameters at a specified frequency with the Sherman-Morrison-Woodbury formula. The first step is performed only once for a given structure, and the method is very efficient for extraction with multiple frequencies. The proposed method is compared with the Green´s function-based method and the approach in our earlier paper for typical substrate structures. Numerical results demonstrate its accuracy, efficiency, and versatility.