The Stability of Pumped Nonlinear Reactance Circuits

Abstract

In a mixer, modulator or parametric amplifier the quiescent state (no signal) is a driven state, for the local oscillator, carrier, or pump is always on. Thus asymptotic stability in the sense used by control engineers is not applicable. The usual linear circuit stability criterion-every bounded input gives a bounded output-is also unsatisfactory for physical circuits containing nonlinear elements because we know that there are bounded inputs that can burn out the nonlinear element. Consequently this paper begins with the stability criteria: 1) operation is always within the allowable dynamic range of the nonlinear element; 2) a periodic steady state with the same period as the pump (LO or Carrier) is approached asymptotically. The class of circuits discussed consists of a single nonlinear element in an arbitrary linear, time-invariant circuit. For this class a set of conditions that guarantees stability is derived. Special emphasis is placed on circuits where the nonlinear element is reactive because these elements present additional mathematical problems. An example is given to show the applicability of the conditions to a specific circuit.