Equivalent mixed-mode characteristic impedances for differential signal vias

Differential signal via structures in multi-layer printed circuit boards (PCBs) and packages are studied using an equivalent coupled multi-conductor transmission-line model. Thus, easy-to-understand transmission-line concepts, such as mixed-mode characteristic impedances and propagation constants, can be used to characterize the performance of differential signal via structures in a signal path. The closed-form expressions of per-unit-length parameters in the equivalent coupled multi-conductor transmission-line model are derived based on a physics-based via circuit model with parallel-plane impedances and via-plate capacitances. Mode conversions are discussed for different via structures. Effects of geometrical parameters on equivalent differential via impedances are studied in the paper as well. The proposed method provides a straightforward approach to design differential via structures for better signal integrity.