Mixed-Mode ABCD Parameters: Theory and Application to Signal Integrity Analysis of PCB-Level Differential Interconnects

Abstract

The mixed-mode ABCD parameters are newly introduced and developed, where the definition and the connection are carefully established to have both the advantages of the mixed-mode S-parameters and the ABCD parameters, simultaneously. In addition, closed-form equations to model symmetric and asymmetric coupled transmission lines are derived. With the derived equations, the voltage transfer functions and the eye diagram of a variety of printed circuit board (PCB)-level differential interconnects are analytically attainable, which greatly enhances their applicability for signal integrity analysis. To verify the derived equations and to validate the proposed mixed-mode ABCD parameters, a series of microstrip-type differential lines on PCB test vehicles were fabricated and tested. The effectiveness of the proposed mixed-mode ABCD parameters was successfully confirmed through the comparison studies, in particular for the case of mode-conversion occurrence at the differential lines.