New PDF release: Computer Design Aids for VLSI Circuits (NATO ASI (Advanced

By P. Antognetti, Donald O. Pederson and Hugo De Man (Editors)

ISBN-10: 9028627014

ISBN-13: 9789028627017

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Extra resources for Computer Design Aids for VLSI Circuits (NATO ASI (Advanced Science Institutes) Series E Applied Sciences - No. 48)

Example text

3) [i where Ki and Kv are bxb submatrices containing the coefficients of the branch equations and S is the vecThe tor of indipendent current and voltage sources. coefficient matrix of the STA equations has dimensions b KVL (2b+n)x(2b+n) since we have n node equations, equations and b branch equations in 2b+n unknowns (b branch currents,b branch voltages and n node voltages). The main advantages of STA are : 1-STA can be applied to any circuit containing all basic resistive ideal elements listed in Table 1.

Therefore, since the solution of the two triangular systems require n 2 multiplications, the total computation involved in solving Ax=b by using LU decomposition is the same as GE. The similarity between LU decomposition and GE carries further. e. n, (k)) , j = k k + 1, n. 10) Moreover, the entries of L are equal to the multipliers ljk: ajk/a~kkused in GE. n, a(k)is different from zero. Therefore, before applying the LU decomposition method we have to reorder the rows and columns of A to obtain a matrix A' such that a'(k) different from zero.

About 115 days, to solve the system of equations. However, in the evaluation of the computer time needed, the sparsity of the coefficient matrix was not considered. It turns out that the solution of a system of linear algebraic equations assembled by a circuit simulator such as SPICE, requires only an average of n 1 - 5 multiplications to solve the system. In our previous example the computer time needed to solve the system would be only I sec. Also, in the previous example we considered that all the data needed to perform GE or LU decomposition fit in core.

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Computer Design Aids for VLSI Circuits (NATO ASI (Advanced Science Institutes) Series E Applied Sciences - No. 48) by P. Antognetti, Donald O. Pederson and Hugo De Man (Editors)

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