Methods to generate state space models by closed forms and...

Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design

Reexamination Certificate

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C716S030000

Reexamination Certificate

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11037636

ABSTRACT:
There is provided a set of methods with the exact accuracy to effectively calculate the 2n-th order state space models of RLC distributed interconnect and transmission line in closed forms in time domain and transfer functions by recursive algorithms in frequency domain, where their RLC components can be evenly distributed or variously valued. The main features include simplicity and accuracy of the said closed forms of the state space models {A,B,C,D} without involving matrix inverse and matrix multiplication operations, effectiveness and accuracy of the said recursive algorithms of the transfer functions, dramatic reduction of the calculation complexity to O(n2) for the state space models, simulation methodology, and practice of various model reductions and their optimization. For evenly distributed RLC interconnect and transmission line, the said closed form of state space model has its computation complexity of only a fixed constant, i.e., O(1).

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Yu et al., “Explicit Formulas and Efficient Alogirithm for Moment Computation of Coupled RC Trees With Lumped and Distributed Elements,” IEEE, 2001, pp. 445-450.
Bobba et al., “Maximum Voltage Variation in the Power Distribution Network of VLSI Circuits With RLC Models,” IEEE, 2001, pp. 376-381.

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