Generating sparse partial inductance matrices with guaranteed stability

This paper proposes a definition of magnetic vector potential that can be used to evaluate sparse partial inductance matrices. Unlike the commonly applied proce-dure of discarding the smallest matrix terms, the proposed approach maintains accuracy at middle and high frequen-cies and is guaranteed to be positive definite for any degree of sparsity (thereby producing stable circuit solu-tions). While the proposed technique is strictly based upon potential theory (i.e. the invariance of potential differ-ences on the zero potential reference choice), the tech-nique is, nevertheless, presented and discussed in both circuit and magnetic terms. The conventional and the pro-posed sparse formulation techniques are contrasted in terms of eigenvalues and circuit simulation results on practical examples. 1