The driving-point immittances of infinite cascades of nonlinear three-terminal networks: II-Nonuniform cascades

That nonuniform infinite cascades of linear resistive three-terminal networks can have driving-point immittances has been known for a long time, but this has not been established for nonlinear networks. This work does so. It thereby extends a prior analysis that established the existence of nonlinear characteristic immittances for uniform cascades. For the special case of nonuniform infinite ladder networks, it is shown herein that, when the nonlinear shunting conductances and series resistances are continuous, positive for positive arguments, negative for negative arguments, zero at the origin, monotonic near the origin, and uniformly bounded away from zero on any compact interval not containing the origin, then the ladder network possesses driving-point immittances, which are nonlinear curves in the voltage-current plane. Our results for nonuniform cascades of three-terminal networks employ generalizations of these monotonicity and boundedness requirements.