Capturing Oscillator Injection Locking via Nonlinear Phase-Domain Macromodels

Autoparametric Vibrations of a Nonlinear System with a Pendulum and Magnetorheological Damping, by Jerzy Warminski and Krzysztof Kecik: Introduction to Autoparametric Vibrations. - Model of the Nonlinear Oscillator with an Attached Pendulum. - Approximate Analytical Solutions and Their Stability. - Regular and Chaotic Dynamics Near the Main Parametric Resonance. - Experimental Setup of the System with Active MR Damper. - Dynamics of an Autoparametric System with MR Damper. - Influence of a Nonlinear System's Suspension on the InstabilityRegions. - Conclusions and Remarks. - References. - On the Dynamics of Pedestrians-Induced Lateral Vibrations of Footbridges, by Stefano Lenci and Laura Marcheggiani: Introduction and Literature Review. - A Continuous-Time Model: the SAMEO Model. - A Discrete-Time Model. - Conclusions. - References. - Applications for Shape Memory Alloys in Structural and Machine Dynamics, by Matthew P. Cartmell, Arkadiusz J. Z ak and Olga A. Ganilova: Review of the Literature and Introduction. - Modelling of the Shape Memory Effect. - Dynamics of Composite Beams and Plates with Integrated SMA Elements. - Applications to Flexible Rotors. - Antagonistic Actuation Control of Vibration in Plates. - Conclusions. - References. - Theoretical and Experimental Nonlinear Vibrations of Sagged Elastic Cables, by Giuseppe Rega: Introduction. - Cable Modelling and Theoretical Analysis. - Nonlinear Phenomena in Forced Dynamic Response. - Experimental Characterisation of Cable Nonlinear Dynamics. - Further Developments and Research Topics. - References. - Engineering Applications of Non-Smooth Dynamics, by Marian Wiercigroch and Ekaterina Pavlovskaia Non-Smooth Dynamical Systems in Engineering Dynamics. - Drifting Oscillator as an Effective Model of Vibro-Impact Moling. - Nonlinear Dynamics Caused by Fatigue Crack Growth. - Regular and Chaotic Dynamics of a Rotor System with a Bearing Clearance. - Conclusions. - References.

A dicone moving on a pair of cylindrical rails can be considered as a simplified model of a railway wheelset. Taking into account the non-linear friction laws of rolling contact, the equations of motion for this non-linear mechanical system result in a set of differential-algebraic equations. Previous simulations performed with the differential-algebraic solver DASSL, [2], and experiments, [7], indicated non-linear phenomena such as limit-cycles, bifurcations as well as chaotic behaviour. In this paper the non-linear phenomena are investigated in more detail with the aid of special in-house software and the path-following algorithm PATH [10]. We apply Poincare sections and Poincare maps to describe the structure of periodic, quasiperiodic and chaotic motions. The analyses show that part of the chaotic behaviour of the non-linear system can be fully understood as a non-linear iterative process. The resulting stretching and folding processes are illustrated by series of Poincare sections.

Timing jitter is a concern in high frequency oscillators; the presence of timing jitter will degrade system performance in many high speed applications. In the first part of the paper, the authors have simulated the timing jitter due to CMOS device noise in a nine-stage CMOS differential ring oscillator, and a methodology to efficiently simulate timing jitter has been developed. Simulation results show that the variation of absolute jitter due to flicker noise has t-dependence while for white noise it has t/sup 0.5/-dependence; these are consistent with accepted theory. Two important parameters, cycle jitter and cycle-to-cycle jitter, used to describe jitter performance can be obtained from simulation. Simulation results are also compared with measurement results, and it is shown that simulation results are very close to measurement results. All these serve to verify the validity of this technique. In the second part of the paper, the authors have employed this methodology and investigated the timing jitter in silicon BJT/or SiGe HBT ECL ring oscillators, and they have shown that BJT/or SiGe HBT oscillators have lower jitter compared to their CMOS counterparts. The methodology described in the paper is also applicable to other types of clock generator and oscillators such as LC oscillators, as well as other kinds of noise source such as power supply and substrate noise.

This work reports a modified regulated cascode (RGC) transimpedance amplifier (TIA) with tolerance to the ultra-high photodiode capacitances encountered in visible light communication systems. The new design is proposed to ameliorate internal miller capacitance limiting effects, inherent in traditional RGC designs through the use of a cascode circuit within the RGC. The paper introduces the design principle of the proposed RGC and presents derivation of tractable mathematical equations for describing the operation. The bandwidth advantage of the new design is shown through comparing the operation of the modified circuit to the traditional one using full circuit simulations. The paper presents full circuit designs, based on discrete components and printed circuit board (PCB) construction of both circuits and contrasts their operation, experimentally demonstrating bandwidth advantage for different values of photodiode capacitances and amplifier transimpedance gain values. Measurements show that using the modified RGC TIA results in a bandwidth improvement of over 200 &#x0025; relative to the conventional RGC design, achieving a bandwidth of 200 MHz at <tex>$2\ \mathrm{K}\Omega$</tex> transimpedance gain with a 300 pF photodiode capacitance. As such, this is one of the highest bandwidths reported for such high capacitances, to-date.

On-chip clock generation is an attractive alternative to external quartz oscillators for low-power sensing systems. LC and ring oscillators typically use less power, and can start and stop much faster than traditional quartz oscillators, allowing systems to spend more time in low-power sleep states. A hybrid on-chip clocking scheme is evaluated in which a ring oscillator is used as the reference clock for digital processing, and an LC oscillator is used when a more stable, accurate reference is needed for digital communication. Simulations show that the fast wakeup capabilities of the hybrid clock system lead to as much as 80% reduced power in interrupt-driven applications compared to a system using a crystal reference clock source. The on-chip clock generators of the WIMS series of microsystems are described to demonstrate the concept of the hybrid clock scheme.

Many of today's applications require that a phase-locked loop (PLL) operate at high speeds, while maintaining reasonable phase noise and jitter performance. Voltage-controlled oscillators (VCO) are important building blocks in PLLs. More importantly, the VCO is the major contributor of phase noise in a PLL. The noisy environment, mainly due to the switching noise generated by the digital portion of these systems. imposes stringent constraints on the design of VCOs, especially phase noise or timing jitter. The switching noise originated in the digital portion of the systems are coupled to the supply and ground rails of the VCO of PLLs. Another important block of a PLL is the charge-pump, a block that is responsible for generating the control voltage to be applied to the VCO. The stability or fluctuation of the control voltage, can severely affect the phase noise performance of the VCO. The research in this thesis, centered on (i) the design considerations of CMOS charge-pumps, (ii) the timing jitter of the delay-cells of low-voltage CMOS ring-VCOs and (iii) the design of a high-speed ring oscillator. A PLL was designed using a new active inductor 6.3-GHz ring oscillator, with a tuning range of +/- 15% was designed in 0.18um CMOS technology. The ring oscillator employed active inductor loads that resulted in an improvement of about 42% in oscillation frequency when compared to the conventional resistor loaded ring oscillator.

Supply and ground noise sensitivity of a wide variety of ring and LC oscillators has been analyzed based on the perturbation projection vector (PPV) technique. The resulting PPV provides an understanding of how specific frequency content of supply/ground noise is converted to oscillator phase noise. Based on this analysis oscillators that are tolerant of supply/ground noise can be identified and used for low noise oscillator design.

Thermal deformation is a nonlinear dynamic phenomenon and is one of the significant factors for the accuracy of machine tools. In this study, a dynamic feed-forward neural network model is built to predict the thermal deformation of machine tool. The temperatures and thermal deformations data at present and past sampling time interval are used train the proposed neural model. Thus, it can model dynamic and the nonlinear relationship between input and output data pairs. According to the comparison results, the proposed neural model can obtain better predictive accuracy than that of some other neural model.

Real systems inevitably include some kind of nonlinearities. Power system is a typical nonlinear system with a huge scale. The steady state stability and the transient stability of power systems result from the intrinsic nonlinearities. Bifurcation theory tells us various kinds of nonlinear structure. In this article periodic orbits and chaotic behaviors detected from the view point of nonlinear system analysis are explained. Some engineering applications are also described.

Voltage instability as a nonlinear dynamic phenomenon is investigated, by introducing a dynamic load flow (LF) Jacobian matrix as a specific index to assess the nonexistence of a stable new equilibrium point in response to perturbations. Reference is made to the Lyapunov exponent and bifurcation theories to provide extension of steady-state based indices for voltage stability, this time taking care of system differential equations, to a continuous monitoring of system distance from collapse during transients caused by step perturbations. Theoretical results are validated on the IEEE 30-node test network, accounting for the effect of typically committed components and regulation loops, such as synchronous generators, and voltage dependent loads under load tap changing transformers. Comparison with traditional modal analysis is also provided for sake of completeness.

Kymographic imaging is a modern method for displaying and evaluating vibratory behaviour of the vocal folds which is crucial for voice production. This review summarizes the state of the art of this method, and focuses on the progress in this area within the last 5 years. Videokymography, using a special videocamera, offers high-speed (video)kymographic images in real time, which is advantageous in daily clinical practice. Two other methods use software to create kymograms retrospectively: digital kymography processes high-speed videolaryngoscopic recordings and offers numerous research possibilities, whereas strobovideokymography processes videostroboscopic recordings, and its use is limited to regular vibration patterns. Current studies reveal that high-speed kymographic images allow more reliable visual evaluation of vibrations than by watching video recordings. Image analysis procedures have been advanced to quantify the vibration properties of the vocal folds. New information has been obtained on asymmetry, mucosal waves, irregularities, phonation onset, and nonlinear dynamic phenomena in voice disorders, as well as in singing. High-speed kymography visualizes vibratory features which are not simply observable via traditional methods. It shows large potential in better understanding the functional origin of hoarseness and unsteady phonatory states. Further research in this area is envisioned.

We develop a continuous time model with heterogeneous fundamentalists, imitators, and discrete time delays. We show that nonlinear dynamic phenomena, such as coexistence of attractors and local and global bifurcations, occur due to the existence of a time gap in the process of adjustment of market prices.

Damage detection and prediction is essential for structural health monitoring. Vibration based methods have been used in health monitoring. In this work damage is proposed to be a nonlinear dynamical phenomenon and can be analyzed by utilizing the bifurcation theory. A methodology for predicting failure is proposed which utilizes the concepts of distance to stability boundary as estimated by bifurcation analysis. The proposed methodology is illustrated by developing bifurcation boundary for a two degree of freedom nonlinear mass-spring-damper system. Two damage models are investigated to illustrate the utility the proposed methodology in capturing and estimating the evolution of damage phenomenon.

Spatially localized excitation of a one-dimensional magnetic system in an external high-frequency field is studied analytically (collective variable method) and numerically. The dependences of the amplitude of local quasi-soliton states on the amplitude of this field for different frequencies and damping in the system are found for the case of direct application of a localized magnetic field. The field dependence is found to have hysteresis and “instability windows” in the stationary states. Within these instability regions, the excitations become nonstationary: they are accompanied by additional periodic nutation of the magnetization vector. Here such nonlinear dynamics phenomena as period doubling and transitions to chaos are observed.

Rub-impact and fatigue crack are two important rotor faults. Based on the crack theory, an improved switching crack model is presented. Dynamic characteristics of a rotor-bearing system with imbalance, rub-impact and transverse crack are attempted. Various nonlinear dynamic phenomena are analyzed using numerical method. The results reveal that unstable form of the rotor system with coupling faults is extremely complex as the rotating speed increases and there are some low frequencies with large amplitude. The influence of crack depth and angle on the dynamic behavior of a cracked rotor is important insomuch as the quasi-periodical and chaotic motions in system response will occur along with different parameters. It is indicated that this study can contribute to a further understanding of the nonlinear dynamics of such a rotor system with coupling faults of crack and rub-impact.