Floquet theory and non-linear perturbation analysis for oscillators with differential-algebraic equations

Oscillators are key components of electronic systems. In RF communication s ystems, they are used for frequency translation of information signals and for channel selection, and in digital electronic systems, they are used as a time reference, i.e. a clock signal, in order to synchronize operations. Undesired perturbations in practical electronic systems adversely affect th e spectral and timing properties of oscillators, which is a key performance limiting factor, being a major contributor to bit-error-rate (BER) of RF c ommunication systems, and creating synchronization problems in clocked and sampled-data systems. Characterizing how perturbations affect oscillators i s therefore crucial for practical applications. The traditional approach to analysing perturbed nonlinear systems (i.e, linearization) is not valid fo r oscillators. In this paper, we present a theory and efficient numerical m ethods? for non-linear perturbation and noise analysis of oscillators descr ibed by a system of differential-algebraic equations (DAEs). Our techniques can be used in characterizing phase noise and timing jitter due to intrins ic noise in IC devices, and evaluating the effect of substrate and supply n oise on the timing properties of practical oscillators. In this paper, we a lso establish novel results for periodically time-varying systems of linear DAEs, which we rely on in developing the above theory and the numerical me thods. Copyright (C) 2000 John Wiley & Sons, Ltd.