Elo Model Reduction and Case Study of Evenly Distributed Rc Interconnect

Abstract

This paper presents state space closed forms and transfer function recursive algorithms for evenly distributed RC interconnect models and their even length-order (ELO) model reduction. The closed-forms have a computation complexity O(1). The characteristics of the ELO model simplification to its original model are revealed. It is shown that extremely high-order RC interconnects can be accurately approximated only by a tenth or higher order ELO model. The order may be reduced further when external ports are included and dominated. The results are useful to VLSI interconnect model reduction and design, and to control systems with a distributed transmission line.

Modeling of DistributedRLCInterconnect and Transmission Line via Closed Forms and Recursive Algorithms

“…Here, the authors' motivation is to tackle the problem step by step; hence, move toward their overall goal of solving the aforementioned tree or net interconnects. On the other hand, the results developed here also can contribute to modeling tree and net interconnects by providing simple line models for the tree or net, similar to the methods in [2]and [24]. It is feasible to extend the proposed models to cover more complex interconnect structures (trees), as we comment in Section III.…”

“…Wang et al [22] excellently review projection-based algorithms for model order reduction, and further present algorithms based on generalized orthonormal basis functions in Hilbert and Hardy space. Recently, Wang et al [2], [24] presented an even-length order (ELO) model simplification methods for RC interconnects. Clearly, the BTM, ELO, other state-space equation-based methods (e.g., [15]), and some projection-based algorithms need to start from the state-space model in the time domain.…”

“…On the other hand, the transfer function in s-domain has been widely used for analysis and model reduction, such as direct transfer function truncation (DTT) method by Ismail and Friedman [12] that directly truncates the transfer function for model reduction with a nice approach to the tree structure. It is noted that the state-space model closed forms and the transfer function recursive algorithms of the RC-distributed line circuits have been investigated by the authors [2], [23], [24].…”

An example of balanced truncation method and its surprising time domain performance

“…The 2nd order non-scaled BTM model is: They are the BTM reduced models of the original system model (12) under the original time system. VI.…”

“…Hence, an effort of providing high quality model reduction is then necessary in order to evaluate the circuit performance and characteristics in a reasonable time period as required by real design practice. Many methods have been developed for this issue, such as the asymptotic waveform evaluation (AWE) [9], the Padé approximation via Lanczos process (PVL) in the Krylov space [2], the projection-based algorithms with generalized orthonormal basis functions in Hilbert and Hardy space [13], the even-length-order model simplification method (ELO) [11,12], the BTM as mentioned above, and others. Due to the large size of the systems, the computation cost is a significant challenge to many methods.…”