Modeling delay and noise in arbitrarily coupled RC trees

Closed-form equations for second-order transfer functions of general arbitrarily coupled resistance-capacitance (RC) trees with multiple drivers are reported. The models allow precise delay and noise calculations for systems of coupled interconnects with guaranteed stability and represent the minimum complexity associated with this class of circuits. Their accuracy is extensively compared against other relevant models and is found to be better or comparable to more expensive models. All results are derived from a theoretical approach, and their physical basis is examined. The simplicity, accuracy, and generality of the models make them suitable for use in early signal integrity analyses of complex systems and incremental physical optimization.