Generating sparse partial inductance matrices with guaranteed stability

• Published in: Computer-Aided Design, International Conference on (ICCAD '95) pp. 45 - 52
• Main Authors: Krauter, Byron, Pileggi, Lawrence T.
• Format: Conference Proceeding
• Language: English
• Published: Washington, DC, USA IEEE Computer Society 01.12.1995
• Series: ACM Conferences
• Subjects: Computing methodologies > Symbolic and algebraic manipulation > Symbolic and algebraic algorithms > Linear algebra algorithms; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on matrices; partial inductance; partial inductance matrices; magnetic vector potential
• ISBN: 9780818672132; 0818672137
• DOI: 10.5555/224841.224857

This paper proposes a definition of magnetic vector potential that can be used to evaluate sparse partial inductance matrices. Unlike the commonly applied procedure of discarding the smallest matrix terms, the proposed approach maintains accuracy at middle and high frequencies and is guaranteed to be positive definite for any degree of sparsity (thereby producing stable circuit solutions). While the proposed technique is strictly based upon potential theory (i.e. the invariance of potential differences on the zero potential reference choice), the technique is, nevertheless, presented and discussed in both circuit and magnetic terms. The conventional and the proposed sparse formulation techniques are contrasted in terms of eigenvalues and circuit simulation results on practical examples.