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

Mathematical Modeling of Electronic Systems: From Oscillators to Multipliers

The ubiquity of electronics in modern technology is undeniable. Although it is not feasible to design or analyze circuits in an exhaustively detailed fashion, it is still imperative that circuit design engineers understand the pertinent physical tradeoffs and are able to think at the appropriate level of mathematical abstraction. This thesis presents several mathematical modeling techniques of common electronic systems. First, we derive, ab initio, a general analytical model for the behavior of electrical oscillators under injection without making any assumptions about the type of oscillator or the size or shape of the injection. This model provides novel insights into the phenomena of injection locking and pulling while subsuming existing theories found in the literature. Next, we focus on the familiar scenario of an inductor-capacitor (LC) oscillator locked to a sinusoidal signal. An exact analysis of this circuit is carried out for an arbitrary injection strength and frequency, a task which has not been executed to fruition in the existing literature. This analysis intuitively illuminates the fundamental physics underlying the synchronization of electrical harmonic oscillators, and it generalizes the notion of the lock range for such oscillators into separate necessary and sufficient conditions. We then turn to the classical estimate of the bandwidth of a linear time-invariant (LTI) system via the sum of its zero-value time constants (ZVTs), and we show that this sum can actually be used to tightly bound the bandwidth—both from above and from below—in addition to simply estimating it. Finally, we look at a natural generalization of the Gilbert cell topology: an analog multiplier for an arbitrary number of inputs; we then analyze its large- and small-signal characteristics as well as its frequency response. Throughout, we will demonstrate how infusing physical intuition with mathematical rigor whilst seeking a balance between detailed analysis and abstract modularity results in models that are conceptually insightful, sufficiently accurate, and computationally feasible.</p

Injection locked ring oscillator design for application in Direct Time of Flight LIDAR

Diplomová práce přibližuje systémy LIDAR přímo měřící čas průletu a časově digitální převodníky určené k použití v těchto systémech. Představuje problematiku distribuce hodinových signálů napříč soubory časově digitálních převodníků v LIDAR systémech a věnuje se jednomu z nových řešení této problematiky, které je založené na injekcí zavěšených oscilátorech. Technika injekčního zavěšení oscilátorů je důkladně matematicky popsána. V programu Matlab byl vytvořen simulační model injekcí zavěšeného kruhového oscilátoru, který potvrzuje správnost uvedených analytických predikcí. Ve výrobní technologii ONK65 byl navržen injekcí zavěšený kruhový oscilátor stabilizovaný pomocí smyčky závěsu zpoždění, určený pro implementaci časově digitálního převodníku pro systém LIDAR. Navržený injekcí zavěšený kruhový oscilátor byl verifikován počítačovými simulacemi zohledňujícími vliv procesních, napěťových i teplotních variací. Oscilátor poskytuje specifikované časové rozlišení 50 pikosekund a dosahuje dvakrát nižší hodnoty fázového neklidu než ekvivalentní volnoběžný oscilátor v dané technologii.The diploma thesis provides an introduction to Direct Time of Flight LIDAR systems and Time to Digital Converters used in these systems. It discusses the problem of clock distribution in LIDAR Time to Digital Converter arrays, and examines one of the possible solutions to this problem based on injection locked oscillators. The injection locking phenomenon is thoroughly mathematically described and a Matlab model of an injection locked ring oscillator is presented, confirming the analytic predictions. In ONK65 processing technology, an injection locked ring oscillator biased by a delay locked loop meant specifically for application in Time to Digital Converters for LIDAR systems has been designed. The designed oscillator has been verified by computer simulations taking process, voltage and temperature variations into account and offers specified time resolution of 50 picosecond as well as two times less clock jitter than an equivalent free-running oscillator in the given processing technology.

LOW-POWER FREQUENCY SYNTHESIS BASED ON INJECTION LOCKING

Ph.DDOCTOR OF PHILOSOPH

A Low-Power BFSK/OOK Transmitter for Wireless Sensors

In recent years, significant improvements in semiconductor technology have allowed consistent development of wireless chipsets in terms of functionality and form factor. This has opened up a broad range of applications for implantable wireless sensors and telemetry devices in multiple categories, such as military, industrial, and medical uses. The nature of these applications often requires the wireless sensors to be low-weight and energy-efficient to achieve long battery life. Among the various functions of these sensors, the communication block, used to transmit the gathered data, is typically the most power-hungry block. In typical wireless sensor networks, transmission range is below 10 meters and required radiated power is below 1 milliwatt. In such cases, power consumption of the frequency-synthesis circuits prior to the power amplifier of the transmitter becomes significant. Reducing this power consumption is currently the focus of various research endeavors. A popular method of achieving this goal is using a direct-modulation transmitter where the generated carrier is directly modulated with baseband data using simple modulation schemes. Among the different variations of direct-modulation transmitters, transmitters using unlocked digitally-controlled oscillators and transmitters with injection or resonator-locked oscillators are widely investigated because of their simple structure. These transmitters can achieve low-power and stable operation either with the help of recalibration or by sacrificing tuning capability. In contrast, phase-locked-loop-based (PLL) transmitters are less researched. The PLL uses a feedback loop to lock the carrier to a reference frequency with a programmable ratio and thus achieves good frequency stability and convenient tunability. This work focuses on PLL-based transmitters. The initial goal of this work is to reduce the power consumption of the oscillator and frequency divider, the two most power-consuming blocks in a PLL. Novel topologies for these two blocks are proposed which achieve ultra-low-power operation. Along with measured performance, mathematical analysis to derive rule-of-thumb design approaches are presented. Finally, the full transmitter is implemented using these blocks in a 130 nanometer CMOS process and is successfully tested for low-power operation

Ku band rotary traveling-wave voltage controlled oscillator

Voltage-controlled oscillator (VCO) plays a key role in determination of the link budget of wireless communication, and consequently the performance of the transceiver. Lowering the noise contribution from the VCO to the entire system is always challenging and remains the active research area. Motivated by high demands for the low-phase noise, low-power consumption VCO in the application of 5G, radar-sensing system, implantable device, to name a few, this research focused on the design of a rotary travelling-wave oscillator (RTWO). A power conscious RTWO with reliable direction control of the wave propagation was investigated. The phase noise was analyzed based on the proposed RTWO. The phase noise reduction technique was introduced by using tail current source filtering technique in which a figure-8 inductors were employed. Three RTWO were implemented based on GF 130 nm standard CMOS process and TSMC 130 nm standard CMOS process. The first design was achieving 16-GHz frequency with power consumption of 5.8-mW with 190.3 dBc/Hz FoM at 1 MHz offset. The second and third design were operating at 14-GHz with a power consumption range of 13-18.4mW and 14.6-20.5mW, respectively. The one with filtering technique achieved FoM of 184.8 dBc/Hz at 1 MHz whereas the one without inudctor filtering obtained FoM of 180.8 dBc/Hz at 1 MHz offset based on simulation

Computationally Efficient Innovative Techniques for the Design-Oriented Simulation of Free-Running and Driven Microwave Oscillators

Analysis techniques for injection-locked oscillators/amplifiers (ILO) can be broadly divided into two classes. To the first class belong methods with a strong and rigorous theoretical basis, that can be applied to rather general circuits/systems but which are very cumbersome and/or time-consuming to apply. To the second class belong methods which are very simple and fast to apply, but either lack of validity/accuracy or are applicable only to very simple or particular cases. In this thesis, a novel method is proposed which aims at combining the rigorousness and broad applicability characterizing the first class of analysis techniques above cited with the simplicity and computational efficiency of the second class. The method relies in the combination of perturbation-refined techniques with a fundamental frequency system approach in the dynamical complex envelope domain. This permits to derive an approximate, but first-order exact, differential model of the phase-locked system useable for the steady-state, transient and stability analysis of ILOs belonging to the rather broad (and rigorously identified) class of nonlinear oscillators considered. The hybrid (analytical-numerical) nature of the formulation developed is suited for coping with all ILO design steps, from initial dimensioning (exploiting, e.g., the simplified semi-analytical expressions stemming from a low-level injection operation assumption) to accurate prediction (and fine-tuning, if required) of critical performances under high-injection signal operation. The proposed application examples, covering realistically modeled low- and high-order ILOs of both reflection and transmission type, illustrate the importance of having at one's disposal a simulation/design tool fully accounting for the deviation observed, appreciable for instance in the locking bandwidth of high-frequency circuits with respect to the simplified treatments usually applied, for a quick arrangement, in ILO design optimization procedures.Analysis techniques for injection-locked oscillators/amplifiers (ILO) can be broadly divided into two classes. To the first class belong methods with a strong and rigorous theoretical basis, that can be applied to rather general circuits/systems but which are very cumbersome and/or time-consuming to apply. To the second class belong methods which are very simple and fast to apply, but either lack of validity/accuracy or are applicable only to very simple or particular cases. In this thesis, a novel method is proposed which aims at combining the rigorousness and broad applicability characterizing the first class of analysis techniques above cited with the simplicity and computational efficiency of the second class. The method relies in the combination of perturbation-refined techniques with a fundamental frequency system approach in the dynamical complex envelope domain. This permits to derive an approximate, but first-order exact, differential model of the phase-locked system useable for the steady-state, transient and stability analysis of ILOs belonging to the rather broad (and rigorously identified) class of nonlinear oscillators considered. The hybrid (analytical-numerical) nature of the formulation developed is suited for coping with all ILO design steps, from initial dimensioning (exploiting, e.g., the simplified semi-analytical expressions stemming from a low-level injection operation assumption) to accurate prediction (and fine-tuning, if required) of critical performances under high-injection signal operation. The proposed application examples, covering realistically modeled low- and high-order ILOs of both reflection and transmission type, illustrate the importance of having at one's disposal a simulation/design tool fully accounting for the deviation observed, appreciable for instance in the locking bandwidth of high-frequency circuits with respect to the simplified treatments usually applied, for a quick arrangement, in ILO design optimization procedures

The Effects of Instrumental Noise on Searches for Generic Transient Gravitational Waves in Advanced LIGO

One hundred years after Albert Einstein predicted the existence of gravitational waves as a result of his theory of general relativity, the Laser Interferometer Gravitational-Wave Observatory (LIGO), made the first direct detection of a gravitational-wave signal from a binary black hole merger, GW150914. GW150914 was found not only by search methods specifically developed to find the distinctive waveform produced by coalescing binaries, but also by generic searches designed to find any arbitrary short-duration signal in the LIGO data. The impact of noise on the searches must be carefully investigated in order to reduce the search background and enable confident gravitational-wave detections. In this dissertation, I will present my work on characterizing transient noise sources in the detectors and implementing data quality vetoes to reduce their effects on the generic transient gravitational-wave searches. Chapters 3 and 4 describe my work on the data quality of the searches for generic transient gravitational waves. I worked on the development of data quality vetoes during the first observing run and the decisions about which vetoes to implement in the transient searches. I also analyzed the transient noise sources that the vetoes were unable to eliminate, using statistical methods to search for potential instrumental causes. Since the development of data quality vetoes requires a thorough understanding of every component of the detectors, I have also conducted a detailed investigation into the transients in the suspension systems used to isolate the LIGO optics from seismic motion. Chapter 5 presents the details of this work. The first gravitational wave detection was only the beginning an exciting era of gravitational-wave astronomy that will give us a new way of understanding the universe. Even in the first observing run, a second binary black hole merger was observed. The methods used in this dissertation to investigate and reduce background noise will continue to play an important role in making these detections possible. As the detectors improve in the future and continue to take data, more signals will be detected, bringing us a wealth of new information about black holes and other types of sources