Small-signal behavior of nonlinear lumped networks

This paper develops two theorems concerning the small-signal behavior of nonlinear time-varying networks whose state equations are of the form x^·= f(x, u, t). The conclusions of the theorems are supported by experiments. The input is of the form U(t) + u(t), where the bias U(t) is allowed to be time-varying (typically, slowly varying) and u(t) is the small signal. The bias induces a moving operation point X(t). Given some simple assumptions concerning the linearized small-signal equivalent circuit it is shown that provided u(t) is sufficiently small on [0, ∞), the state trajectory about the operating point is bounded on [0, ∞) and tends to zero as u → 0. The method of proof also shows that this result applies to some distributed circuits. The second theorem shows that the push-pull connection reduces the distortion due to the nonlinearities of both resistors and energy storing elements. The third part of the paper describes numerical experiments that support the conclusions of the theory and a design procedure for nonlinear networks to be operated in the small-signal mode.