Analytical Equivalent Circuit Modeling for BGA in High-Speed Package

The ball grid array (BGA) structure is the interconnection between package to printed circuit board and the discontinuity from BGA affects the performance for the whole link path in the high-speed digital system. So, it is important to accurately model the BGA structures. In current methods, the current distribution of conductors is treated as isotropic. However, the pitch size of solder balls is comparable to the diameter. The current is no longer uniformly distributed. In this paper, a fast modal-based approach is developed to accurately and efficiently capture the proximity effect. Image theory is also applied in the proposed approach to reduce the computational domain from 3-D structure to 2-D. The matrix reduction approach is applied to obtain the physical loop inductance. The lumped capacitance is obtained in [1] . A $\pi $ topology equivalent circuit model for the BGA structure is built. Good agreement between the equivalent circuit model and full-wave simulation can be achieved up to 40 GHz.