Comprehensive electromagnetic approach for modeling of on-chip power grid switching.

摘要

A methodology is presented for on-chip power grid modeling with uncompromised electromagnetic accuracy. The proposed methodology avoids the painstaking and error-prone process of power grid inductance extraction. It is the purpose of this research to develop and demonstrate a methodology for on-chip power grid modeling based on Maxwell's equations, which will provide the electromagnetic rigor and computational flexibility and efficiency needed for accurate and expedient prediction of both on-chip power supply switching noise as well as power supply-induced noise coupling.;At the heart of the proposed methodology is the development of a discrete electro-magnetic model for the on-chip power grid directly from the physical geometry in chip design. More specifically, the primitive system of Maxwell's equations for the rotation of the electric and magnetic fields is discretized over a finite-difference grid that encompasses the power grid. The resulting discrete model is in a state-space form that resembles the popular modified nodal analysis (MNA) formalism used for large circuit analysis in SPICE but with one very important difference. It is extremely sparse. Thus, despite the very large dimensions of the generated discrete model, its transient analysis is carried out most efficiently. Finally, the proposed methodology is unique in that, in addition to providing for on-chip power switching modeling with electromagnetic accuracy, computational flexibility and efficiency, it also enables the direct modeling of distributed power-grid induced electromagnetic interference.