181 research outputs found
Computing the Synchronization Regions of Injection-Locked Strongly Nonlinear Oscillators for Frequency Division Applications
No full textUnified Computation of Parameter Sensitivity and Signal-Injection Sensitivity in Nonlinear Oscillators
No full textIn this paper, two relevant computational aspects related to the design of nonlinear oscillators are considered: sensitivity to electrical parameter variation and sensitivity to small-amplitude injected signals. First, the analysis of the perturbation induced by parameter fluctuation is theoretically investigated, and a set of formal equations is deduced that allows us to correctly decompose amplitude and period variations. Second, the analysis of the perturbation induced by a generic weak signal is considered. This analysis is based on a well-consolidated approach that employs the Floquet eigenvector v1 (t) to project perturbation into the phase domain. It is shown that the same system of equations that formalizes the parameter-sensitivity problem can be exploited to calculate the v1 (t) projection vector. An efficient and reliable numerical implementation of a formal perturbation analysis is then proposed that allows the oscillator designer to evaluate both parameter sensitivity and signal-injection sensitivity in a homogeneous frame
Stochastic Analysis of Switched-Capacitor Circuits for Sampled Data Converters
No full textThis paper describes an original simulation-based method to derive the stochastic properties of the output noise of switched-capacitor circuits which are used in sampled-data converters. The method relies on a linear time-varying approximation of the large-signal transient response of the switched circuits. It is shown how switched-capacitor-circuit noise and quantization noise, due to the presence ofharsh comparators, can be analyzed in a unified frame where the data converter is modeled as a discrete-time system
An Experimental Method to Extract the Phase-Sensitivity of Oscillators to Noise Perturbations
No full textThis paper describes an original experimental procedure to extract the phase sensitivity of oscillators to noise perturbations. The proposed method relies on measuring the width of the locking ranges over which the oscillator's response synchronizes with injected small-amplitude signals. It is shown that this sensitivity function can be employed to accurately predict how inner noise sources are transferred to output phase-noise and jitter. The extraction procedure is applied to a relaxation oscillator that exhibits a strongly nonlinear behavior
Nonlinear Phase-Domain Macromodeling of Injection-Locked Frequency Dividers
No full textThis paper describes an original nonlinear phase-domain macromodel of Injection-Locked Frequency Dividers which are driven by a nonlinear input device that produces heavy harmonic distortion. These non-harmonic frequency dividers can provide wide lock ranges, however their analysis is complicated by the strong nonlinear behavior for which the hypothesis of weak injection does not apply. The proposed approach consists in adopting a nonlinear model for the input section of the divider and in combining it with a Perturbation-Projection Vector-based macromodel for the linear-time-varying section of the oscillator. The proposed macromodel is employed to predict the synchronization regions of an ILFD driven by several types of injected waveforms. In addition, closed-form expressions for the output phase-noise spectrum are also provided
Synchronization Analysis of Two Weakly Coupled Oscillators Through a PPV Macromodel
No full textThis paper adopts a phase-domain macromodel based on perturbation projection vector to study the synchronization effects that take place between two weakly coupled oscillators. Original closed-form expressions for the locking region of the coupled oscillators and for the common locking frequency are derived. The route to synchronization is described analytically by predicting the oscillation frequency shifts, which are induced by mutual pulling as a function of the interaction strength. Under the assumption of a weak coupling, the proposed approach can be applied to a wide class of oscillator topologies
Versatile Time-Domain Approach to Simulate Oscillators in RF Circuits
No full textThis paper presents a versatile simulation technique for the time-domain analysis of RF oscillators. The method blends the superior accuracy and robustness of implicit RungeKutta integration formulas with the high efficiency of a particular envelope-following technique. The method can be applied to study both transient and steady-state responses of autonomous and nonautonomous circuits and can also be applied to the case of harsh nonlinear oscillator topologies
Frequency-Shift Induced by Colored Noise in Nonlinear Oscillators
No full textThis brief employs a perturbation phase-domain model to numerically investigate the phenomenon of frequency- shift induced by colored-noise in nonlinear oscillators. It is shown that colored-noise with frequency decaying spectrum tends to induce a frequency-shift phenomenon both in almost-linear oscillators and in nonlinear topologies such as ring oscillators. It is also shown that the relevance of the phenomenon depends linearly on the noise variance
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