Application of subspace projection approaches for reduced-order modeling of electromagnetic systems

The requirements for fast switching speeds, low voltage, low power, tightly integrated, and mixed analog-digital circuits, have brought the need for electromagnetic computer-aided design capability to integrated circuit design, especially for packaging and interconnect design. For clock frequencies in the GHz regime and rise times of a few tens of ps, full wave electromagnetic analysis may be required for packaging design and interconnection simulation. Subspace projection approaches, including the Pade via Lanczos (PVL), Krylov, and rational Krylov algorithms, have been used for reduced-order modeling of wide-band electromagnetic systems. A frequency segmentation technique has also been used with the Lanczos algorithm to obtain benchmark data and for scattering parameter extraction from the electromagnetic system. From the various techniques, the combined PVL/frequency segmentation technique is the most promising for efficient and accurate modeling of electromagnetic systems.