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# Algorithm for Solving Linear Sparse Complex Simultaneous Equations in APL for Circuit Analysis

IP.com Disclosure Number: IPCOM000088759D
Original Publication Date: 1977-Jul-01
Included in the Prior Art Database: 2005-Mar-04
Document File: 2 page(s) / 44K

IBM

## Related People

Ho, CW: AUTHOR [+2]

## Abstract

In a computer-aided circuit analysis and design program, a set of complex linear equations has to be solved for doing frequency domain (AC) circuit analysis. There are two existing approaches for this problem. The first one is to separate the real part and the imaginary part of the equation, and solve these two parts of equations simultaneously by using real arithmetic. By doing so, this increases the dimension of the sparse matrix so that a new matrix ordering step is required if, in addition to the AC analysis, DC or transient analysis is required. It is therefore not very efficient. The alternative approach is to use a complex arithmetic complier to preserve the dimension of the equation and its sparse pattern. However, the complex arithmetic complier is not available in APL program language.

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Algorithm for Solving Linear Sparse Complex Simultaneous Equations in APL for Circuit Analysis

In a computer-aided circuit analysis and design program, a set of complex linear equations has to be solved for doing frequency domain (AC) circuit analysis. There are two existing approaches for this problem. The first one is to separate the real part and the imaginary part of the equation, and solve these two parts of equations simultaneously by using real arithmetic. By doing so, this increases the dimension of the sparse matrix so that a new matrix ordering step is required if, in addition to the AC analysis, DC or transient analysis is required. It is therefore not very efficient. The alternative approach is to use a complex arithmetic complier to preserve the dimension of the equation and its sparse pattern. However, the complex arithmetic complier is not available in APL program language.

A simple and efficient algorithm has been developed and implemented for solving complex linear equations in doing frequency domain analysis for linear circuits or small signal nonlinear circuits. The data structure of the complex equations is similar to that of the real equation case. After the matrix ordering, as shown in Fig. 1, the nonzero data are stored in the order labelled as I, II, III and IV in Figs. 2A and 2B. In the complex case, one more row of the same length containing the values of the imaginary part of the matrix is added to the row containing the values of the r...