大型電子封裝與系統之先進巨觀建模技術研究

In the design of chip-to-chip interconnect of modern high-speed electronic systems, engineers usually begin with extracting the frequency response (e.g., S parameters) of the packaging and printed circuit board (PCB) routing using fullwave electromagnetic simulation; the S parameters are then fitted with a rational function which can be synthesized into equivalent circuits; the equivalent circuits are then combined with the chip model to perform time domain simulation of the complete channel. The mathematical process of transforming the frequency response of a multiport circuit into an equivalent rational function is called macromodeling, which plays an important role in the whole design flow. The efficiency and accuracy of the macromodeling algorithm, as well as the order ofthe final rational model, will significantly influence the speed and reliability of the design of the electronic system.This project aims at studying three representative macromodeling algorithms in detail: the vector fitting method (VF), the Loewner matrix method (LM), and the adaptive Antoulas-Anderson method (AAA). The focus of VF is how to efficiently combine with the balanced truncation (BT) to reduce the model order? And can the final order of VF+BT be comparable to that of LM? The focus of LM is how to efficiently construct the matrices when the number of frequency samples is less than the actual required order of the underlying model? The focus of AAA is how to extend its original scalar version to the multiport case, such that it is still highly efficient as well as accurate? Finally, after answering these key questions, we expect to make a fair and comprehensive comparison between the three methods, when applied to large-scale (>200 ports) circuits.