Circuit theory of periodically driven nonlinear systems

The systems under discussion are nonlinear, but driven by a strong periodic "carrier." Examples of such systems are oscillators, frequency multipliers, limiters, modulators, and periodically driven feedback systems. It is of interest to inquire how small perturbations on the periodic driving are propagated throughout the system, and to this end a circuit theory for these perturbations is developed. In different Contexts these perturbations could be desired or undesired modulation, noise, hum, or synchronizing signals. In general the random processes in such a system will, because of the periodic driving, be nonstationary; but various representations are developed that are stationary, and hence can be described by spectral analysis. The concept of impedance is developed for the small perturbations, and the validity of Kirchhoff's Laws is examined. Specific problems are not treated in detail; instead, a general framework is set up within which a variety of problems can be analyzed. Problems of this sort include the theory of noise in oscillators, propagation of noise and modulation in nonlinear systems, the noise theory of frequency multipliers, and synchronization of oscillators.