Partial reluctance based circuit simulation is efficient and stable

Partial reluctance K, the inversion of partial inductance L, is proposed by Devgan et al. to capture the on-chip inductance effect (2000). Partial reluctance based circuit simulation is efficient and stable because it is believed that partial reluctance effect is local and partial reluctance matrix is positive definite, although it has not been proved or illustrated clearly. In this paper, we are going to prove that mutual partial reluctance effect between a completely shielded short conductor segment and a conductor segment outside the shield is zero, which implies that the partial reluctance effect is local. Also, an iterative cutting algorithm is proposed to guarantee the strong diagonal dominance of the partial reluctance matrix, which is a sufficient condition for the partial reluctance matrix to be positive definite. With these two characters of partial reluctance, the circuit simulation based on partial reluctance is efficient and stable.