The all-minors VCCS matrix tree theorem, half-resistors and applications in symbolic simulation

The matrix tree theorem for directed graphs is generalized to cover all minors of nodal formulations of all linear circuits with voltage controlled current sources. The term signs are readily evaluated from linking-cycle-arborescence: configurations in a common generalization of Maxwell´s and Coates´ rules. All minors are treated with the same formalism. The formulation introduces half-resistors which are transposed unistors. Their use for intuitive description of circuit operation based on approximation, nodal impedance conditions and backward error analysis is described for BJT amplifiers and the switch model for digital MOS circuits