Modeling of Distributed RLC Interconnect and Transmission Line via Closed Forms and Recursive Algorithms

• Published in: IEEE transactions on very large scale integration (VLSI) systems 2010-01, Vol.18 (1), p.119-130
• Main Authors: WANG, Sheng-Guo, BEN WANG
• Format: Article
• Language: English
• Subjects: Applied sciences; Circuit properties; Closed form; Design. Technologies. Operation analysis. Testing; Distributed computing; distributed RLC circuit; Electric, optical and optoelectronic circuits; Electronic circuits; Electronic equipment and fabrication. Passive components, printed wiring boards, connectics; Electronics; Exact sciences and technology; Frequency domain analysis; Integrated circuit interconnections; Integrated circuits; interconnect; Kirchhoff's Law; Miscellaneous; modeling; recursive algorithm; Reduced order systems; RLC circuits; Runtime; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Transfer functions; transmission line; Transmission line matrix methods; Transmission lines
• ISSN: 1063-8210; 1557-9999
• DOI: 10.1109/TVLSI.2008.2008439

This paper presents the closed forms of the state-space models and the recursive algorithms of the transfer function models for fast and accurate modeling of the distributed RLC interconnect and transmission lines, which may be evenly or unevenly distributed. Considered models include the distributed RLC interconnect lines with or without external source and load connection. The effective closed forms and recursive algorithms do not involve any matrix inverse, LU matrix factorization, or matrix multiplication, thus reducing the computation complexity dramatically. Especially, the computation complexity of the closed forms for any evenly or unevenly distributed RLC interconnect line circuits is only O (1) or O ( m ), respectively, in sense of the scalar multiplication times, where m ¿ N of the system order. The features of new recursive algorithms are two recursive s-polynomials and the low computation complexity. Examples illustrate the new methods in both time and frequency domains. Comparing with the PSpice, the new methods can dramatically reduce the runtime of the time responses and the Bode plots by 25% - 98.5% in the examples. The results can be applied to the RLC interconnect analysis and model reduction as a key to new approach.