State Space Models of RLGC Interconnect with Super High Order in Time Domain and Its Research

In interconnect modeling, an exact original model is needed, whether in considering frequency-dependent or process variation or in model reducing. An exact original model is not only a precise start-point in model reducing, but also is the basis of evaluating the performance of the reduction models. This paper presents three types of exact interconnect RLGC state space models in time domain with super high order and computation complexity of O(N) by closed forms, where N is the total system order. They are the fundamental elements to construct interconnect trees or a special interconnect tree. The forms of these models are simpler than which in literature. Low order models are compared with 2000th order model. Low order models cause quite big errors in respect of the descriptions of oscillation characteristic and rise time. It has a risk when modeling branches in interconnect trees using lower order original interconnect models.