A Parameterization Scheme for Lossy Transmission Line Macromodels With Application to High Speed Interconnects in Mobile Devices

We introduce a novel parameterization scheme based on the generalized method of characteristics (MoC) for macromodels of transmission-line structures having a cross section depending on several free geometrical and material parameters. This situation is common in early design stages, when the physical structures still have to be finalized and optimized under signal integrity and electromagnetic compatibility constraints. The topology of the adopted line macromodels has been demonstrated to guarantee excellent accuracy and efficiency. The key factors are propagation delay extraction and rational approximations, which intrinsically lead to a SPICE-compatible macromodel stamp. We introduce a scheme that parameterizes this stamp as a function of geometrical and material parameters such as conductor-width and separation, dielectric thickness, and permittivity. The parameterization is performed via multidimensional interpolation of the residue matrices in the rational approximation of characteristic admittance and propagation operators. A significant advantage of this approach consists of the possibility of efficiently utilizing the MoC methodology in an optimization scheme and eventually helping the design of interconnects. We apply the proposed scheme to flexible printed interconnects that are typically found in portable devices having moving parts. Several validations demonstrate the effectiveness of the approach