VCO start-up and stability analysis using time varying root locus

The oscillator circuit is one of the key components of the communication systems. It is necessary for an oscillator to provide the proper oscillations in order to confirm the stable operation of a communication circuit. There are many different analysis methods of analyzing the start-up and frequency stability of a system, but mostly it fails to analyze properly due to the parasitics involved. Somehow if any of them manages to compute the analysis it would be very complex, difficult and time consuming. The time varying root locus (TVRL) approach can be utilized to analyze the start-up and frequency behavior of different oscillator designs. It is a theoretical based technique that can provide further insights into a circuit designer for oscillator operation. To analyze the start-up behavior, a semi-symbolic TVRL approach can be used with the help of the numerical QZ (Generalized Schur Decomposition) algorithm. By finding the time varying roots of polynomials, TVRL can help to estimate the undesired operating points. A symbolic TVRL analysis is capable of computing the system roots during an oscillation with the help of Muller algorithm. Different numerical and the CAD (Computer Aided Design) tool are involved to implement this theoretical approach. Cadence 45nm CMOS General Process Design Kit (GPDK) helps to design the required schematic and SpectreRF simulator computes the time varying periodic solutions. Maple script can form an admittance matrix which is later used in MATALB to compute the final TVRL trajectories of dominant poles. The corresponding results are then analyzed to detect the failure mechanism which is responsible for relaxation oscillations. In this thesis, an active inductor quadrature voltage controlled oscillator and five stage ring oscillator circuits are proposed to analyze thoroughly with the help of TVRL approach. The above mentioned techniques along with some extra computations have been implemented to verify whether the proposed circuits can overcome the relaxation oscillations and can produce the proper sinusoidal waveforms or there is a need to devise some modifications

Influence of the Mass ratio on the fluid-elastic instability of a flexible cylinder in a bundle of rigid tubes

Several linear lumped-parameter models were proposed in the past to identify the main mechanisms underlying the cross-flow instability of a single flexible cylinder in tube bundles. Basing on such models, we analyze the influence of the mass ratio when the cylinder vibrates in the transverse direction, without structural damping (corresponding to a zero Scruton number). For two selected mass ratios, we focus on this linear interaction plotting the poles of the fluid–structure system as a function of the reduced velocity (root locus). This asymptotic approach allows a better understanding of the combined influence of the transient fluidelastic coupling and the mass ratio

Delay-dependent Stability of Genetic Regulatory Networks

Genetic regulatory networks are biochemical reaction systems, consisting of a network of interacting genes and associated proteins. The dynamics of genetic regulatory networks contain many complex facets that require careful consideration during the modeling process. The classical modeling approach involves studying systems of ordinary differential equations (ODEs) that model biochemical reactions in a deterministic, continuous, and instantaneous fashion. In reality, the dynamics of these systems are stochastic, discrete, and widely delayed. The first two complications are often successfully addressed by modeling regulatory networks using the Gillespie stochastic simulation algorithm (SSA), while the delayed behavior of biochemical events such as transcription and translation are often ignored due to their mathematically difficult nature. We develop techniques based on delay-differential equations (DDEs) and the delayed Gillespie SSA to study the effects of delays, in both continuous deterministic and discrete stochastic settings. Our analysis applies techniques from Floquet theory and advanced numerical analysis within the context of delay-differential equations, and we are able to derive stability sensitivities for biochemical switches and oscillators across the constituent pathways, showing which pathways in the regulatory networks improve or worsen the stability of the system attractors. These delay sensitivities can be far from trivial, and we offer a computational framework validated across multiple levels of modeling fidelity. This work suggests that delays may play an important and previously overlooked role in providing robust dynamical behavior for certain genetic regulatory networks, and perhaps more importantly, may offer an accessible tuning parameter for robust bioengineering

Studies in predictor display technique Final report

Predictor display technique for manual altitude control, and automatic pitch axis performanc

The Focus-Center-Limit Cycle Bifurcation in Symmetric 3D Piecewise Linear Systems

The birth of limit cycles in 3D (three-dimensional) piecewise linear systems for the relevant case of symmetrical oscillators is considered. A technique already used by the authors in planar systems is extended to cope with 3D systems, where a greater complexity is involved. Under some given nondegeneracy conditions, the corresponding theorem characterizing the bifurcation is stated. In terms of the deviation from the critical value of the bifurcation parameter, expressions in the form of power series for the period, amplitude, and the characteristic multipliers of the bifurcating limit cycle are also obtained. The results are applied to accurately predict the birth of symmetrical periodic oscillations in a 3D electronic circuit genealogically related to the classical Van der Pol oscillator.Ministerio de Ciencia y Tecnología DPI2000-1218-C04-04Ministerio de Ciencia y Tecnología BFM2001-2668Ministerio de Ciencia y Tecnología BFM2003-00336Junta de Andalucía TIC-13

Unified volterra series analysis of injection locked oscillators.

by Fan Chun-Wah.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 90-[91]).Abstract also in Chinese.Chapter CHAPTER 1: --- INTRODUCTION --- p.1Chapter CHAPTER 2: --- BACKGROUND OF INJECTION LOCKING --- p.3Chapter 2.1 --- Basics of Injection Locking --- p.3Chapter 2.2 --- Analytical Methods for Injection Locking --- p.6Chapter 2.2.1 --- Analysis of Fundamental Mode Injection Locking --- p.6Chapter 2.2.2 --- Analysis of Ha rmonic/Subharmonic Injection Locking --- p.9Chapter 2.4 --- Numerical Methods --- p.11Chapter CHAPTER 3: --- THE VOLTERRA SERIES METHOD FOR NONLINEAR CIRCUIT ANALYSIS --- p.13Chapter 3.1 --- Volterra Expansion --- p.14Chapter 3.2 --- Evaluation of Nonlinear Transfer Function --- p.16Chapter 3.2.1 --- Probing Method --- p.16Chapter 3.2.2 --- Nonlinear Current Method --- p.17Chapter 3.2.3 --- Higher order nonlinear current --- p.20Chapter 3.2.4 --- Voltage response by using nonlinear transfer function --- p.20Chapter 3.3 --- Advantage of Volterra Series --- p.21Chapter 3.4 --- Volterra Series Simulator(VSS) Implementation --- p.22Chapter 3.4.1 --- Admittance Matrix Formulation --- p.22Chapter 3.4.2 --- Evaluation of Nonlinear Response --- p.26Chapter 3.4.3 --- Local Cache and Global Cache --- p.26Chapter 3.4.4 --- Components Library --- p.27Chapter 3.4.5 --- Verification of Simulator --- p.27Chapter CHAPTER 4: --- VOLTERRA SERIES GENERAL INJECTION-LOCKED OSCILLATOR FORMULATION --- p.28Chapter 4.1 --- Volterra Series Approach to Analysis of Autonomous System --- p.29Chapter 4.1.1 --- Chua and Tang's work --- p.29Chapter 4.1.2 --- Cheng and Everard's work --- p.29Chapter 4.1.3 --- Huang and Chu 's work --- p.30Chapter 4.2 --- A Novel Approach --- p.33Chapter 4.3 --- Derivation of Determining Equation --- p.35Chapter 4.4 --- Injection Lock vector and circuit synthesis --- p.38Chapter 4.5 --- Modification to Volterra Series Simulator (VSS) --- p.40Chapter CHAPTER 5: --- CIRCUIT MODELING AND PARAMETER EXTRACTION --- p.42Chapter 5.1 --- Forward-Bias Gate Measurement --- p.42Chapter 5.2 --- Low FREQUENCY S-PARAMETER MEASUREMENT --- p.50Chapter 5.3 --- Parameter Extraction from High Frequency S-Parameter Data --- p.52Chapter 5.3.1 --- Direct Extraction Method --- p.52Chapter 5.3.2 --- Estimation of lead inductance --- p.56Chapter 5.4 --- Large Signal Characterization and Extraction --- p.59Chapter 5.4.1 --- Large Signal Model --- p.59Chapter 5.4.2 --- Extraction of g2 and g3 --- p.60Chapter 5.5 --- Equivalent circuit model for inductor and capacitor --- p.67Chapter CHAPTER 6: --- APPLICATION TO 1/3 ANALOG FREQUENCY DIVIDER --- p.68Chapter 6.1 --- Oscillator design by negative resistance approach --- p.68Chapter 6.2 --- Simulation of Free Running Oscillation by VSS --- p.73Chapter 6.3 --- Simulation of injection locked oscillator by VSS --- p.75Chapter 6.4 --- Injection Locking Experiment --- p.77Chapter 6.5 --- Injection Lock Vector --- p.80Chapter CHAPTER 7: --- CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK --- p.85Chapter 7.1 --- Conclusions --- p.85Chapter 7.2 --- Recommendations for Future Work --- p.86APPENDIX 1: REFERENCES --- p.87APPENDIX 2: PUBLICATION --- p.9

Feasible Computation in Symbolic and Numeric Integration

Two central concerns in scientific computing are the reliability and efficiency of algorithms. We introduce the term feasible computation to describe algorithms that are reliable and efficient given the contextual constraints imposed in practice. The main focus of this dissertation then, is to bring greater clarity to the forms of error introduced in computation and modeling, and in the limited context of symbolic and numeric integration, to contribute to integration algorithms that better account for error while providing results efficiently. Chapter 2 considers the problem of spurious discontinuities in the symbolic integration problem, proposing a new method to restore continuity based on a pair of unwinding numbers. Computable conditions for the unwinding numbers are specified, allowing the computation of a variety of continuous integrals. Chapter 3 introduces two structure-preserving algorithms for the symbolic-numeric integration of rational functions on exact input. A structured backward and forward error analysis for the algorithms shows that they are a posteriori backward and forward stable, with both forms of error exhibiting tolerance proportionality. Chapter 4 identifies the basic logical structure of feasible inference by presenting a logical model of stable approximate inference, illustrated by examples of modeling and numerical integration. In terms of this model it is seen that a necessary condition for the feasibility of methods of abstraction in modeling and complexity reduction in computational mathematics is the preservation of inferential structure, in a sense that is made precise. Chapter 5 identifies a robust pattern in mathematical sciences of transforming problems to make solutions feasible. It is showed that computational complexity reduction methods in computational science involve chains of such transformations. It is argued that the structured and approximate nature of such strategies indicates the need for a higher-order model of computation and a new definition of computational complexity

Millimetre-wave optically injection-locked oscillators for radio-over-fibre systems

Theoretical analysis and experimental results for millimetre-wave optically injection-locked oscillators are presented in this thesis. Such oscillators can be employed to replace conventional photodiode plus amplifier receivers for local oscillator signal reception in millimetre-wave radio-over-fibre systems. The theories for electrical injection-locked oscillators are reviewed in detail. Three differences between Adler’s and Kurokawa’s equations for locking bandwidth are highlighted for the first time. These differences are the absence of l/cos# factor in Adler’s equation, larger bandwidth predicted by Kurokawa’s equation, and a difference in definition of Q factors. Locking bandwidth equations for optically injection-locked oscillators are developed based on the theories of electrical injection-locked oscillators and are then used to design optically injection-locked oscillators. A novel millimetre-wave indirect optically injection-locked oscillator is presented. An edge-coupled photodiode is used to detect the optical signal. Negative resistance and computer simulation techniques were used for predicting the free running oscillation frequency. The maximum output power of the oscillator is 5.3 dBm, and the maximum locking bandwidth is measured to be 2.6 MHz with an output power o f-12 dBm. Results from a comparison with conventional optical receivers show that the gain of the optically injection-locked oscillator is more than 10 dB higher than that of a photodiode plus amplifier receiver, that the oscillator output power remains constant with input signal power variations whereas the output power of the photodiode plus amplifier receiver changes (linearly) with the input signal power, and that, at high-offset frequencies, the phase noise of the optically injection-locked oscillator is much lower than that of the photodiode plus amplifier receiver. These advantages make the optically injection-locked oscillator an ideal replacement for the photodiode plus amplifier receiver in radio-over-fibre systems. An improved wide-band design for millimetre-wave optically injection-locked oscillators is presented for future work