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Orthogonal Relaxation

IP.com Disclosure Number: IPCOM000035824D
Original Publication Date: 1989-Aug-01
Included in the Prior Art Database: 2005-Jan-28
Document File: 3 page(s) / 27K

Publishing Venue

IBM

Related People

Cockerill, TJ: AUTHOR [+5]

Abstract

An orthogonal waveform relaxation algorithm is shown which, when integrated into a sub-network waveform relaxation program, allows certain tightly coupled circuits to be included in the waveform analysis.

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Orthogonal Relaxation

An orthogonal waveform relaxation algorithm is shown which, when integrated into a sub-network waveform relaxation program, allows certain tightly coupled circuits to be included in the waveform analysis.

A disturbing behavior during bit addressing of a memory chip was observed while performing hardware measurements (1), and was found to be a sensitivity to substrate distributed resistance. Normally a relaxation program like TOGGLE
(2), consisting of distributed resistance in series with the power supplies and ground, has difficulty partitioning and analyzing tightly coupled circuits. In order to rectify this problem, an orthogonal waveform relaxation algorithm was developed.

Because the distributed resistances are small, the sub-circuits are no longer loosely coupled and the waveform relaxation algorithm has difficulty partitioning this kind of large circuit into N sub-ciruits, since every sub-circuit is strongly connected to the others via the distributed resistances.

Referring to the figure, network N consists of three major sub-networks, i.e., Nr1, Ns and Nr2. Nr1 and Nr2 are the distributed resistance networks attached to the power supply and ground respectively. Ns = (Ns1, Ns2, Ns3,...., Nsm) is the original network
without these resistances.

Let Fsi(x(t),x(t),t) = 0, i = 1m be a set of a set of nonlinear differential equations representing the exact behavior of Nsi and fr1(x(t),t) = 0 fr2(x(t),t) = 0 be a set of linear algebraic equations representing the exact behavior of Nr1 and Nr2.

The sub-network Ns is analyzed with the original relaxation algorithm as before with the assumption that Vdi, Vgi, (i = 1,m) are known. Then the sub- network Nr1 and Nr2 is analyzed with the computed load currents from the sub- network Ns. This process is repeated until a convergence is obtained. A convergence is realized if the resistances are smaller than the resistance of devices connected to them and this condition is obviously satisfied.

Two distinct le...