A stochastic algorithm for solving linear RC networks : pruning the transition-diagram tree

Authors
Lenahan, Russell Eugene
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Other Contributors
Le Coz, Yannick L.
Zhang, Tong
Hella, Mona Mostafa
Issue Date
2013-05
Keywords
Computer Systems engineering
Degree
MS
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This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
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Abstract
RC circuit evaluation is important for many applications in electrical design; particularly for high-end, digital IC-interconnect CAD. Such circuits are often too large to solve efficiently with traditional methods. Le Coz et al. have developed a method for solving these kinds of circuits at low frequencies. They used stochastic random walks based on a Taylor Series state-diagram approximation. Their method neglected high-order impulse-response moments. Thus, it is unsuitable at elevated frequencies comparable to inverse RC-circuit time constants. We have developed a state-diagram "pruning algorithm" for higher-frequency application, eliminating any need for a Taylor Series approximation. This is accomplished by altering the circuit's transition diagram to limit the number of weight factors that can cause non-convergent growth in stochastic evaluation. Preliminary trials of our new algorithm were performed. The trials achieved less than 4% error at a normalized characteristic frequency ω = 0.2. A third order Taylor Series approximation, on the other hand, yielded close to 150% error. Opportunities for future research include self- and mutual- inductance effects, and parallel software and hardware acceleration.
Description
May 2013
School of Engineering
Department
Dept. of Electrical, Computer, and Systems Engineering
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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