Stochastic analysis of cycle slips in injection-locked oscillators and analog frequency dividers

A detailed investigation of cycle slips in injection-locked oscillators (ILOs) and analog frequency dividers is presented. This nonlinear phenomenon gives rise to a temporal desynchronization between the injected oscillator and the input source due to noise perturbations. It involves very different time scales so even envelope-transient-based Monte Carlo analyses may suffer from high computational cost. The analysis method is based on an initial extraction of a reduced-order nonlinear model of the injected oscillator based on harmonic-balance simulations. This model has been improved with a more accurate description of oscillation dependence on the input source either at the fundamental frequency or, in the case of a frequency divider, at a given harmonic frequency. The reduced-order model enables an efficient stochastic analysis of the system based on the use of the associated Fokker-Planck equation in the phase probability density function. Several methods for the solution of the associated Fokker-Planck equation are compared with one of them being applicable under a wider range of system specifications. The analysis enables the prediction of the parameter-space regions that are best protected against cycle slips. The technique has been applied to two microwave ILOs and has been validated through commercial software envelope simulations in situations where the computational cost of the envelope simulations was acceptable, and through measurements. The measurement procedure of the cycle slipping phenomenon has been significantly improved with respect to previous work.This work was supported by the Spanish Ministry of Economy and Competitiveness under Contract TEC2011-29264-C03-01

Stability analysis with Pole-zero Identification: unveiling the critical dynamics of microwave circuits

The term pole-zero identification refers to obtaining the poles and zeros of a linear (or linearized) system described by its frequency response. This is usually done using optimization techniques (such as least squares, maximum likelihood estimation, or vector fitting) that fit a given frequency response of the linear system to a transfer function defined as the ratio of two polynomials [1], [2]. This kind of linear system identification in the frequency domain has numerous applications in a wide variety of engineering fields, such as mechanical systems, power systems, and electromagnetic compatibility. In the microwave domain, rational approximation is increasingly used to obtain black-box models of complex passive structures for model order reduction and efficient transient simulation. An extensive bibliography on the matter can be found in [3]-[6]. In this article, we focus on a different application of pole-zero identification. We review the different ways in which pole-zero identification can be applied to nonlinear circuit design, for power-amplifier stability analysis, and more. We provide a comprehensive view of recent approaches through illustrative application examples. Other uses for rational-approximation techniques are beyond the scope of this article.This work was supported in part by the French Space Agency (CNES) under projects R-S10/TG-0001-019 and R-S14/TG-0001-019; by a joint Ph.D. research grant from CNES and Thales Alenia Space, France; by project TEC2015-67217-R (MINECO/FEDER); and by the Basque Country Government through project IT1104-16

Periodically Disturbed Oscillators

By controlling the timing of events and enabling the transmission of data over long distances, oscillators can be considered to generate the "heartbeat" of modern electronic systems. Their utility, however, is boosted significantly by their peculiar ability to synchronize to external signals that are themselves periodic in time. Although this fascinating phenomenon has been studied by scientists since the 1600s, models for describing this behavior have seen a disconnect between the rigorous, methodical approaches taken by mathematicians and the design-oriented, physically-based analyses carried out by engineers. While the analytical power of the former is often concealed by an inundation of abstract mathematical machinery, the accuracy and generality of the latter are constrained by the empirical nature of the ensuing derivations. We hope to bridge that gap here. In this thesis, a general theory of electrical oscillators under the influence of a periodic injection is developed from first principles. Our approach leads to a fundamental yet intuitive understanding of the process by which oscillators lock to a periodic injection, as well as what happens when synchronization fails and the oscillator is instead injection pulled. By considering the autonomous and periodically time-varying nature that underlies all oscillators, we build a time-synchronous model that is valid for oscillators of any topology and periodic disturbances of any shape. A single first-order differential equation is shown to be capable of making accurate, quantitative predictions about a wide array of properties of periodically disturbed oscillators: the range of injection frequencies for which synchronization occurs, the phase difference between the injection and the oscillator under lock, stable vs. unstable modes of locking, the pull-in process toward lock, the dynamics of injection pulling, as well as phase noise in both free-running and injection-locked oscillators. The framework also naturally accommodates superharmonic injection-locked frequency division, subharmonic injection-locked frequency multiplication, and the general case of an arbitrary rational relationship between the injection and oscillation frequencies. A number of novel insights for improving the performance of systems that utilize injection locking are also elucidated. In particular, we explore how both the injection waveform and the oscillator's design can be modified to optimize the lock range. The resultant design techniques are employed in the implementation of a dual-moduli prescaler for frequency synthesis applications which features low power consumption, a wide operating range, and a small chip area. For the commonly used inductor-capacitor (LC) oscillator, we make a simple modification to our framework that takes the oscillation amplitude into account, greatly enhancing the model's accuracy for large injections. The augmented theory uniquely captures the asymmetry of the lock range as well as the distinct characteristics exhibited by different types of LC oscillators. Existing injection locking and pulling theories in the available literature are subsumed as special cases of our model. It is important to note that even though the veracity of our theoretical predictions degrades as the size of the injection grows due to our framework's linearization with respect to the disturbance, our model's validity across a broad range of practical injection strengths are borne out by simulations and measurements on a diverse collection of integrated LC, ring, and relaxation oscillators. Lastly, we also present a phasor-based analysis of LC and ring oscillators which yields a novel perspective into how the injection current interacts with the oscillator's core nonlinearity to facilitate injection locking.</p

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

Layout-accurate Ultra-fast System-level Design Exploration Through Verilog-ams

This research addresses problems in designing analog and mixed-signal (AMS) systems by bridging the gap between system-level and circuit-level simulation by making simulations fast like system-level and accurate like circuit-level. The tools proposed include metamodel integrated Verilog-AMS based design exploration flows. The research involves design centering, metamodel generation flows for creating efficient behavioral models, and Verilog-AMS integration techniques for model realization. The core of the proposed solution is transistor-level and layout-level metamodeling and their incorporation in Verilog-AMS. Metamodeling is used to construct efficient and layout-accurate surrogate models for AMS system building blocks. Verilog-AMS, an AMS hardware description language, is employed to build surrogate model implementations that can be simulated with industrial standard simulators. The case-study circuits and systems include an operational amplifier (OP-AMP), a voltage-controlled oscillator (VCO), a charge-pump phase-locked loop (PLL), and a continuous-time delta-sigma modulator (DSM). The minimum and maximum error rates of the proposed OP-AMP model are 0.11 % and 2.86 %, respectively. The error rates for the PLL lock time and power estimation are 0.7 % and 3.0 %, respectively. The OP-AMP optimization using the proposed approach is ~17000× faster than the transistor-level model based approach. The optimization achieves a ~4× power reduction for the OP-AMP design. The PLL parasitic-aware optimization achieves a 10× speedup and a 147 µW power reduction. Thus the experimental results validate the effectiveness of the proposed solution

Macromodeling and demonstration of the LT6600 amplifier and lowpass filter

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (leaves 100-101).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The goal of this thesis is to demonstrate the abilities of the Sevastopoulos-LaPorte active low-pass filter topology in Linear Technology Corporation's LT6600 integrated circuit (IC). The thesis is split into two parts, representing two facets of how engineers will evaluate the LT6600: by simulation and in the laboratory. The LT6600-10 macromodel and its design methodology is presented, as well as comparisons of macromodel characteristics with measured characteristics of the LT6600-10 IC. For the lab demonstration portion, the LT6600-2.5 was integrated into a digital code-division multiple access (CDMA) communications system, complete with transmit and receive sections. The performance of the LT6600 in this system was shown to be as good as or better than most conventional filtering approaches. When implemented in a communications system., the LT6600-10 required up to 13 less components than other reasonable filtering options and provided 4th-order signal attenuation with only 14 nV/[square root]Hz of voltage noise spectral density.by Cheng-Wei Pei.M.Eng

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Optimal Control and Synchronization of Dynamic Ensemble Systems

Ensemble control involves the manipulation of an uncountably infinite collection of structurally identical or similar dynamical systems, which are indexed by a parameter set, by applying a common control without using feedback. This subject is motivated by compelling problems in quantum control, sensorless robotic manipulation, and neural engineering, which involve ensembles of linear, bilinear, or nonlinear oscillating systems, for which analytical control laws are infeasible or absent. The focus of this dissertation is on novel analytical paradigms and constructive control design methods for practical ensemble control problems. The first result is a computational method %based on the singular value decomposition (SVD) for the synthesis of minimum-norm ensemble controls for time-varying linear systems. This method is extended to iterative techniques to accommodate bounds on the control amplitude, and to synthesize ensemble controls for bilinear systems. Example ensemble systems include harmonic oscillators, quantum transport, and quantum spin transfers on the Bloch system. To move towards the control of complex ensembles of nonlinear oscillators, which occur in neuroscience, circadian biology, electrochemistry, and many other fields, ideas from synchronization engineering are incorporated. The focus is placed on the phenomenon of entrainment, which refers to the dynamic synchronization of an oscillating system to a periodic input. Phase coordinate transformation, formal averaging, and the calculus of variations are used to derive minimum energy and minimum mean time controls that entrain ensembles of non-interacting oscillators to a harmonic or subharmonic target frequency. In addition, a novel technique for taking advantage of nonlinearity and heterogeneity to establish desired dynamical structures in collections of inhomogeneous rhythmic systems is derived

Stability analysis of RF power amplifiers through MIMO pole-zero identification techniques.

163 p.El amplificador de potencia es un componente clave en la arquitectura de los transmisores de comunicaciones inhalámbricas. La complejidad de las señales de los sistemas de comunicación actuales impone unas especificaciones exigentes en el diseños de los mismos. Es por ello que los ciclos de concepción de los circuitos de microondas son en general lentos y muy costosos.Desafortunadamente, la aparición indeseada de oscilaciones al medir las prestaciones de los amplificadores de potencia de radio-frecuencia y microondas es un problema muy común al que se enfrentan los diseñadores. Un amplificador de potencia diseñado sin llevar a cabo análisis rigurosos de estabilidad puedes ser inestable, y ello puede llevar a la generación de oscilaciones que impiden el correcto funcionamiento del amplificador y pueden incluso llegar a destruirlo completamente o quemarlo