Novel Methods for Modeling of Multiple Vias in Multilayered Parallel-Plate Structures

This paper presents novel modeling methods for accurate and efficient analysis of coupling of multiple vias in finite-sized multilayered parallel-plate structures. The new modeling methods address two open problems related to the modal expansion with the T-matrix method for the analysis of via coupling. First, a novel boundary modeling method, called the frequency-dependent cylinder layer (FDCL), is proposed to resolve the open problem of boundary modeling. In the FDCL, virtual cylinders with dynamic radii are postulated to approximate the original finite-sized boundary of parallel-plate structures. Second, a generalized T-matrix model, which is derived by the mode-matching technique, is created to characterize the coupling effect for vias penetrating more than one layer in a multilayered structure. With the two open problems successfully solved, the modal expansion with the T-matrix method incorporating the FDCL boundary modeling method and the generalized T-matrix model can now be fully utilized for efficient and accurate analysis of finite-sized multilayered parallel-plate structures with a large number of vias. Both numerical and experimental verifications are presented to validate the new modeling methods.