Harmonic analysis of oscillators through standard numerical continuation tools

In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard continuation package - without modification - such as AUTO, which we used. Our technique works for any kind of oscillator, including electronic, mechanical and biochemical systems. We provide two case studies. The first study concerns itself with the autonomous electronic oscillator known as the Colpitts oscillator, and the second one with a nonlinear damped oscillator, a non-autonomous mechanical oscillator. As shown in the case studies, the proposed technique can aid both the analysis and the design of the oscillators, by following curves for which a certain constraint, related to harmonic analysis, is fulfilled.Comment: 20 pages, 4 figure

Analysis and simulation methods for free-running, injection-locked and super-regenerative oscillators

RESUMEN: En los últimos años, muchos esfuerzos han sido dedicados al desarrollo de técnicas complementarias para el análisis de circuitos autónomos de microondas. Estas técnicas están pensadas para su uso en combinación con balance armónico, ampliamente usado para el análisis a frecuencias de microondas. De hecho, balance armónico sufre de restricciones cuando se utiliza para el análisis de circuitos autónomos, en su mayoría debidos a su falta de sensibilidad a las propiedades de estabilidad de la solución que se genera o se extingue mediante bifurcaciones. En esta tesis doctoral se presentan nuevos métodos de simulación y análisis para la caracterización y modelado de osciladores libres, sincronizados y superregenerativos. Todos los resultados obtenidos mediante los nuevos métodos de simulación y análisis han sido comparados satisfactoriamente con otras técnicas de simulación y con medidas.ABSTRACT: In the last years, numerous efforts have been devoted to the development of complementary analysis tools for autonomous microwave circuits. They are intended to be applied in combination with the harmonic-balance (HB) method, widely used at microwave frequencies. In fact, HB suffers from a number of shortcomings when dealing with autonomous circuits, mostly due the fact that it is insensitive to the stability properties of the solution, generated and extinguished through bifurcation phenomena. Here, new simulation and analysis methodologies for the characterization and modeling of free-running, injection-locked and super-regenerative oscillators have been proposed to overcome these problems when using commercial software. Results from the different new analysis methodologies have been successfully compared with independent simulations and with measurements

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

Analysis of superregenerative oscillators in nonlinear mode

Superregenerative oscillators in a nonlinear mode are investigated in detail using methodologies based on envelope transient, complemented with additional algorithms. A maximum-detection technique is applied to obtain the input-power threshold for nonlinear operation under different implementations of the quench signal. A mapping procedure enables the prediction of hangover and self-oscillation effects. It is based on the detection of the sequence of local maxima in the envelope amplitude after the application of a single input pulse. Using a contour-intersection method, and depending on the analysis time interval, it is possible to quantify the hangover effects and obtain the oscillation boundary, in terms of any two significant parameters. Then, a compact time-variant behavioral model is derived, valid in the absence of hangover and self-oscillation effects. It consists of a single time-variant Volterra kernel and is applicable provided that the amplitude transitions occur outside the sensitivity interval. Various methodologies are tested in a practical FET-based oscillator at 2.7 GHz. The prototype has been manufactured and measured, obtaining good agreement with the analysis results.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under the research project TEC2017-88242-C3-1-R

Event-Driven Simulation Methodology for Analog/Mixed-Signal Systems

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 김재하.Recent system-on-chip's (SoCs) are composed of tightly coupled analog and digital components. The resulting mixed-signal systems call for efficient system-level behavioral simulators for fast and systematic verifications. As the system-level verifications rely heavily on digital verification tools, it is desirable to build the mixed-signal simulator based on a digital simulator. However, the existing solutions in digital simulators suffer from a trade-off between simulation speed and accuracy. This work breaks down the trade-off and realizes a fast and accurate analog/mixed-signal behavior simulation in a digital simulator SystemVerilog. The main difference of the proposed methodology from existing ones is its way of representing continuous-time signals. Specifically, a clock signal expresses accurate timing information by carrying an additional real-value time offset, and an analog signal represents its continuous-time waveform in a functional form by employing a set of coefficients. With these signal representations, the proposed method accurately simulates mixed-signal behaviors independently of a simulator's time-step and achieves a purely event-driven simulation without involving any numerical iteration. The speed and accuracy of the proposed methodology are examined for various types of analog/mixed-signal systems. First, timing-sensitive circuits (a phase-locked loops and a clock and data recovery loop) and linear analog circuits (a channel and linear equalizers) are simulated in a high-speed I/O interface example. Second, a switched-linear-behavior simulation is demonstrated through switching power supplies, such as a boost converter and a switched-capacitor converter. Additionally, the proposed method is applied to weakly nonlinear behaviors modeled with a Volterra series for an RF power amplifier and a high-speed I/O linear equalizer. Furthermore, the nonlinear behavior simulation is extended to three different types of injection-locked oscillators exhibiting time-varying nonlinear behaviors. The experimental results show that the proposed simulation methodology achieved tens to hundreds of speed-ups while maintaining the same accuracy as commercial analog simulators.ABSTRACT I CONTENTS III LIST OF FIGURES V LIST OF TABLES XII CHAPTER 1 INTRODUCTION 1 1.1 BACKGROUND 1 1.2 MAIN CONTRIBUTION 6 1.3 THESIS ORGANIZATION 8 CHAPTER 2 EVENT-DRIVEN SIMULATION OF ANALOG/MIXED-SIGNAL BEHAVIORS 9 2.1 PROPOSED CLOCK AND ANALOG SIGNAL REPRESENTATIONS 10 2.2 SIGNAL TYPE DEFINITIONS IN SYSTEMVERILOG 14 2.3 EVENT-DRIVEN SIMULATION METHODOLOGY 16 CHAPTER 3 HIGH-SPEED I/O INTERFACE SIMULATION 21 3.1 CHARGE-PUMP PHASE-LOCKED LOOP 23 3.2 BANGBANG CLOCK AND DATA RECOVERY 37 3.3 CHANNEL AND EQUALIZERS 45 3.4 HIGH-SPEED I/O SYSTEM SIMULATION 52 CHAPTER 4 SWITCHING POWER SUPPLY SIMULATION 55 4.1 BOOST CONVERTER 57 4.2 TIME-INTERLEAVED SWITCHED-CAPACITOR CONVERTER 66 CHAPTER 5 VOLTERRA SERIES MODEL SIMULATION 72 5.1 VOLTERRA SERIES MODEL 74 5.2 CLASS-A POWER AMPLIFIER 79 5.3 CONTINUOUS-TIME EQUALIZER 84 CHAPTER 6 INJECTION-LOCKED OSCILLATOR SIMULATION 89 6.1 PPV-BASED ILO MODEL 91 6.2 LC OSCILLATOR 99 6.3 RING OSCILLATOR 104 6.4 BURST-MODE CLOCK AND DATA RECOVERY 109 CONCLUSION 116 BIBLIOGRAPHY 118 초 록 126Docto

Awakened oscillations in coupled consumer-resource pairs

The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables respectively and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.Comment: 31 pages, 8 figures 2 tables, 48 reference

Noise analysis of super-regenerative oscillators in linear and nonlinear modes

A rigorous analysis of noise effects in super-regenerative oscillators (SROs), operating in both linear and nonlinear modes, is presented. For operation in the linear mode, two different analysis methods are presented. One is based on the calculation of linear-time variant (LTV) transfer function with respect to the input signal and the noise sources. The second method is based on a compact semianalytical formulation of the pulsed oscillator under the effect of the quench signal. The compact formulation also enables the analysis of the SRO in the nonlinear mode. It constitutes a fully new mathematical description of SROs, with general applicability, as it is not restricted to a particular oscillator topology. It relies on a numerical nonlinear black-box model of the stand-alone free-running oscillator, extracted from harmonic-balance simulations. This model is introduced into an envelope-domain formulation of the SRO at the fundamental frequency. Both the method based on LTV transfer functions and the semianalytical formulation take into account the cyclostationary nature of the SRO response to the noise sources. In the nonlinear mode, the variances of the amplitude and phase are calculated linearizing the formulation of the pulsed steady-state solution. The particular time variation of the phase variance is explained in detail and related to the onset and extinction of the oscillation in the presence of an RF input signal. The new analysis methods have been validated with both independent circuit-level simulations and measurements.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under Project TEC2017-88242-C3-1-R

Analysis and design of wideband voltage controlled oscillators using self-oscillating active inductors.

Voltage controlled oscillators (VCOs) are essential components of RF circuits used in transmitters and receivers as sources of carrier waves with variable frequencies. This, together with a rapid development of microelectronic circuits, led to an extensive research on integrated implementations of the oscillator circuits. One of the known approaches to oscillator design employs resonators with active inductors electronic circuits simulating the behavior of passive inductors using only transistors and capacitors. Such resonators occupy only a fraction of the silicon area necessary for a passive inductor, and thus allow to use chip area more eectively. The downsides of the active inductor approach include: power consumption and noise introduced by transistors. This thesis presents a new approach to active inductor oscillator design using selfoscillating active inductor circuits. The instability necessary to start oscillations is provided by the use of a passive RC network rather than a power consuming external circuit employed in the standard oscillator approach. As a result, total power consumption of the oscillator is improved. Although, some of the active inductors with RC circuits has been reported in the literature, there has been no attempt to utilise this technique in wideband voltage controlled oscillator design. For this reason, the dissertation presents a thorough investigation of self-oscillating active inductor circuits, providing a new set of design rules and related trade-os. This includes: a complete small signal model of the oscillator, sensitivity analysis, large signal behavior of the circuit and phase noise model. The presented theory is conrmed by extensive simulations of wideband CMOS VCO circuit for various temperatures and process variations. The obtained results prove that active inductor oscillator performance is obtained without the use of standard active compensation circuits. Finally, the concept of self-oscillating active inductor has been employed to simple and fast OOK (On-Off Keying) transmitter showing energy eciency comparable to the state of the art implementations reported in the literature