In the Section 1, the improved Root-Omega method for extracting dielectric properties from fabricated multilayer printed circuit boards is proposed. Based on the electrical properties of fabricated transmission lines, the improved Root-Omega method applied to cases with smooth and rough conductors is validated using simulations. Error sensitivity analysis is performed to demonstrate the potential errors in the original Root-Omega procedure and the error sensitivity is significantly reduced by the proposed improvements.
In the Section 2, 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 3D structure to 2D. The matrix reduction approach is applied to obtain the physical loop inductance. The lumped capacitance is obtained. A π 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 40GHz.
In the Section 3, the proximity effect for BGAs between parallel plates is carefully considered. A modal-based cavity method is proposed to extract the partial inductance of two parallel plates. The modal basis function is used to count for the non-uniformly distributed current density. The physical loop inductance is further obtained from the matrix reduction approach. The extracted physical loop inductance is validated with a commercial finite element method-based tool. The boundary effect is demonstrated in the inductance extraction. The proposed method is used to optimize for the power distributed network design --Abstract, page iii
