Effective High-Speed Via Model Considering Equivalent High-order Mode Inductance

A high-speed via model considering equivalent high-order mode inductance for frequencies above 70 GHz is proposed in this paper. The proposed via model, which considers the equivalent high-order mode inductance, is a high-accuracy and high-bandwidth via model, improved from the previously proposed mode-decomposition-based equivalent via (MEV) model. The equivalent high-order mode inductance is an inductance produced by the magnetic fields of high-order modes in the via domain. By including the empirical equivalent highorder mode inductance, the proposed via model accurately predicts the insertion and return losses of the via with a large anti-pad size up to the frequency of 150 GHz, which expand the the application range of the previously proposed MEV model. In the paper, the limitation of the previously proposed MEV model is analyzed by comparing the input impedance extracted from the MEV model and the full-wave simulation. An empirical closed-form formula is proposed to calculate the equivalent highorder mode inductance at high frequencies to improve the accuracy of the previously proposed model. In addition, the proposed single high-speed via model was expanded to a differential via pair model. The proposed high-speed via model was verified using simulation and measurement results