Browse Prior Art Database

# Semi-Direct METHOD of Modular Analysis Using a Variation of the Modified Nodal METHOD of Formulating the Network Equations With No Auxiliary Variables

IP.com Disclosure Number: IPCOM000047862D
Original Publication Date: 1983-Dec-01
Included in the Prior Art Database: 2005-Feb-08
Document File: 3 page(s) / 25K

IBM

## Related People

Odeh, FM: AUTHOR [+2]

## Abstract

Large circuits that cannot otherwise be computer-analyzed by conventional circuit algorithmic methods are analyzed by a semi-direct method consisting of an inner Newton and an outer relaxation loop. A large circuit is partitioned into smaller circuits, the ith one of which has a set of internal variables, xi, and external (or connection) variable, u, which is common to all sub-circuits. The solution is obtained iteratively: First, a convergence solution (X*)n of the nth sub-circuit is obtained by setting u constant and iterating on Xn, (using only the equations of the nth sub-circuit). Having done that for all n = 1,2,...N = no. of sub-circuits, a convergence solution u* is obtained by setting (X*)1, (X*)2, ..., (X*)n constant and iterating on u, using the connection equations (i.e.

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 56% of the total text.

Page 1 of 3

Semi-Direct METHOD of Modular Analysis Using a Variation of the Modified Nodal METHOD of Formulating the Network Equations With No Auxiliary Variables

Large circuits that cannot otherwise be computer-analyzed by conventional circuit algorithmic methods are analyzed by a semi-direct method consisting of an inner Newton and an outer relaxation loop. A large circuit is partitioned into smaller circuits, the ith one of which has a set of internal variables, xi, and external (or connection) variable, u, which is common to all sub-circuits. The solution is obtained iteratively: First, a convergence solution (X*)n of the nth sub-circuit is obtained by setting u constant and iterating on Xn, (using only the equations of the nth sub-circuit). Having done that for all n = 1,2,...N = no. of sub-circuits, a convergence solution u* is obtained by setting (X*)1, (X*)2, ..., (X*)n constant and iterating on u, using the connection equations (i.e., the equations that connect all sub-circuits). The above process is one iteration, where the inner loop is Newton and the outer is relaxation. The process is repeated until Wui = ui+1 - ui <e (e=.0002+.002 u* ). The network partitioning occurs in a natural manner without using auxiliary variables, if the variables of each subcircuit are arranged as follows: (Xn)T = (Vn, in, en, yn)T,
.... (1) where vn: internal node voltages of the nth sub-circuit in: internal response current variables of the

sub-circuit

en: interface or connection node voltages

yn: interface or connection branch currents THE METHOD In equation (1), define (Xn)T = (vn, in)T .... (2)

u = (en, yn)T The superscript, T, indicates transpose. Then the nonlinear equations of the nth mode...