A new dispersive, hybrid phase-pole macromodel for frequency-dependent lossy transmission lines

The need for rapid designs in the IC industry makes signal integrity analysis an important issue in the design cycle. Transmission line modeling for interconnect structures plays an important part in the signal integrity analysis. With system clock frequencies now in the multi-gigahertz range, traditional transmission line models, which assume constant frequency-independent RLGC parameters, no longer provide accurate results in many cases since the RLGC parameters vary with respect to frequency at high frequencies. In this paper we develop a new macromodeling method for lossy transmission lines with frequency dependent RLGC parameters. The basic idea is to represent the frequency-domain transfer function in terms of a series of analytical expansion functions with known inverse Laplace transform representations. If the analytical form of the expansion functions properly models the physical phenomenology of the signal dispersion and time delay, then only a small number of expansion functions will be required in the macromodel. Such a macromodel would have fewer terms than classical macromodel. Furthermore, since it accurately models the dispersion, it provides more accurate results than previous generalized Method of Characteristics (MOC) macromodals.