SOME THEOREMS ON DYNAMIC RESPONSE OF NONLINEAR TRANSISTOR NETWORKS

Relative to the huge body of theory of linear time‐invariant systems, very little of a general and ‘precise nature is known about the network‐theoretic properties of transistor circuits operating under large‐signal conditions. One basic property P which a transitor network might have is that if the input approaches a constant, then the output approaches a constant which is independent of the initial conditions. In this paper we prove a stability theorem concerning a nonlinear differential equation that governs the behavior of a large class of networks. A corollary of this theorem asserts that if a certain condition is satisfied, then property P holds. We consider also the problem of estimating the rate of decay of transients in transistor networks and we prove theorems which allow us to make some often quite conservative, but definite, statements concerning limitations on switching speeds. A practical example considered shows that in some cases the bounds, which are frequently very easy to evaluate, can be quite useful. The proofs depend in an interesting way on the relationship between the static diode characteristic and the nonlinear capacitance associated with a semiconductor junction. © 1969 The Bell System Technical Journal