Modal Network Representation for Broadband SI/PI-Analysis of Interconnection Structures in Multilayer PCBs

Abstract

A modal equivalent circuit for interconnection structures within multilayer PCBs including the rigorous incorporation of dissipation, dispersion and skin effect is presented for the first time. Based on the discrete field formulation of the three-dimensional boundary value problem an exact network representation is obtained from the corresponding eigenvalue problem employing the lossless modes. In contrast to a recently published general approach, the mutual coupling of the modes can be neglected, such that the network complexity is minimized. The modal network includes the physical-based rational approximation of the intrinsic system dynamic, which is independent of the port positions. These in turns determine the excitation of the individual modes and can be simply accounted for by a transducer network. The model order is safely estimated in advanced and significantly reduced by the approximation of all sub-resonant (higher) modes by lumped elements. The accuracy and advantages of the proposed SPICE-compatible equivalent circuit are demonstrated and compared to the conventional overall vector fitting approach in frequency and time-domain examples including non-linear terminations.