The effects of parasitic reactances on nonlinear networks

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Abstract
This paper considers several of the problems caused by the presence of small parasitic capacitances and inductances in nonlinear network models. It first gives the condition for which the behavior of a network model can be approximated by the behavior of a simplified model recently with the parasitics removed. The condition is that the resistive subnetwork viewed from the terminals of the parasitics be strictly locally passive for a certain set of currents and voltages. This condition is independent of the relative magnitudes of the parasitics. The paper then considers networks whose equations cannot be put into normal form without the addition of a parasitic. In the case where two different choices of parasitics enable the network equations to be put into normal form, it gives conditions on the resistive subnetwork which ensure that the behavior of the two resulting networks is the same. It then exhibits a class of networks such that the networks resulting from the addition of any choice of parasitic which enables the network equations to be put into normal form have the same behavior. Finally, the paper shows how the behavior of this class of networks can be determined without the addition of parasitics. It formulates an inertia postulate and an explicit jump postulate to enable the multivalued normal form equations to be solved unambiguously.