Rational ABCD modeling of high-speed interconnects

Introduces a new numerical approximation technique, called the differential quadrature method (DQM), in order to derive the rational ABCD matrix representing the high-speed interconnect. DQM is an efficient differential equation solver that can quickly compute the derivative of a smooth function by estimating a weighted linear sum of the function values at few mesh points in the domain of the function. Using DQM, the s-domain Telegrapher´s equations of interconnect are discretized as a set of easily solvable algebraic equations, which lead to the rational ABCD matrix. The entries of ABCD matrix take the form of rational approximations with respect to s, rather than the conventional ABCD matrix whose entries are complex transcendental functions in s. Although the rationalization result is comparable with Pade approximation of AWE, DQM does not require moment-generating or moment-matching. For both uniform and nonuniform interconnects, DQM-based rational ABCD matrices lead to high accuracy as well as high efficiency for transient analysis of high-speed interconnects