Review of Injected Oscillators

Oscillators are critical components in electrical and electronic engineering and other engineering and sciences. Oscillators are classified as free-running oscillators and injected oscillators. This chapter describes the background necessary for the analysis and design of injected oscillators. When an oscillator is injected by an external periodic signal mentioned as an injection signal, it is called an injected oscillator. Consequently, two phenomena occur in the injected oscillators: (I) pulling phenomena and (II) locking phenomena. For locking phenomena, the oscillation frequency of the injection signal must be near free-running oscillation frequency or its sub-/super-harmonics. Due to these phenomena are nonlinear phenomena, it is tough to achieve the exact equation or closed-form equation of them. Therefore, researchers are scrutinizing them by different analytical and numerical methods for accomplishing an exact inside view of their performances. In this chapter, injected oscillators are investigated in two main subjects: first, analytical methods on locking and pulling phenomena are reviewed, and second, applications of injected oscillators are reviewed such as injection-locked frequency dividers at the latter. Furthermore, methods of enhancing the locking range are introduced

Architectures and Circuits Leveraging Injection-Locked Oscillators for Ultra-Low Voltage Clock Synthesis and Reference-less Receivers for Dense Chip-to-Chip Communications

High performance computing is critical for the needs of scientific discovery and economic competitiveness. An extreme-scale computing system at 1000x the performance of today’s petaflop machines will exhibit massive parallelism on multiple vertical fronts, from thousands of computational units on a single processor to thousands of processors in a single data center. To facilitate such a massively-parallel extreme-scale computing, a key challenge is power. The challenge is not power associated with base computation but rather the problem of transporting data from one chip to another at high enough rates. This thesis presents architectures and techniques to achieve low power and area footprint while achieving high data rates in a dense very-short reach (VSR) chip-to-chip (C2C) communication network. High-speed serial communication operating at ultra-low supplies improves the energy-efficiency and lowers the power envelop of a system doing an exaflop of loops. One focus area of this thesis is clock synthesis for such energy-efficient interconnect applications operating at high speeds and ultra-low supplies. A sub-integer clockfrequency synthesizer is presented that incorporates a multi-phase injection-locked ring-oscillator-based prescaler for operation at an ultra-low supply voltage of 0.5V, phase-switching based programmable division for sub-integer clock-frequency synthesis, and automatic calibration to ensure injection lock. A record speed of 9GHz has been demonstrated at 0.5V in 45nm SOI CMOS. It consumes 3.5mW of power at 9.12GHz and 0.052 of area, while showing an output phase noise of -100dBc/Hz at 1MHz offset and RMS jitter of 325fs; it achieves a net of -186.5 in a 45-nm SOI CMOS process. This thesis also describes a receiver with a reference-less clocking architecture for high-density VSR-C2C links. This architecture simplifies clock-tree planning in dense extreme-scaling computing environments and has high-bandwidth CDR to enable SSC for suppressing EMI and to mitigate TX jitter requirements. It features clock-less DFE and a high-bandwidth CDR based on master-slave ILOs for phase generation/rotation. The RX is implemented in 14nm CMOS and characterized at 19Gb/s. It is 1.5x faster that previous reference-less embedded-oscillator based designs with greater than 100MHz jitter tolerance bandwidth and recovers error-free data over VSR-C2C channels. It achieves a power-efficiency of 2.9pJ/b while recovering error-free data (BER 200MHz and the INL of the ILO-based phase-rotator (32- Steps/UI) is <1-LSB. Lastly, this thesis develops a time-domain delay-based modeling of injection locking to describe injection-locking phenomena in nonharmonic oscillators. The model is used to predict the locking bandwidth, and the locking dynamics of the locked oscillator. The model predictions are verified against simulations and measurements of a four-stage differential ring oscillator. The model is further used to predict the injection-locking behavior of a single-ended CMOS inverter based ring oscillator, the lock range of a multi-phase injection-locked ring-oscillator-based prescaler, as well as the dynamics of tracking injection phase perturbations in injection-locked masterslave oscillators; demonstrating its versatility in application to any nonharmonic oscillator

Analysis and design on low-power multi-Gb/s serial links

High speed serial links are critical components for addressing the growing demand for I/O bandwidth in next-generation computing applications, such as many-core systems, backplane and optical data communications. Due to continued process scaling and circuit innovations, today's CMOS serial link transceivers can achieve tens of Gb/s per pin. However, most of their reported power efficiency improves much slower than the rise of data rate. Therefore, aggregate I/O power is increasing and will exceed the power budget if the trend for more off-chip bandwidth is sustained. In this work, a system level statistical analysis of serial links is first described, and compares the link performance of Non-Return-to-Zero (2-PAM) with higher-order modulation (duobinary) signaling schemes. This method enables fast and accurate BER distribution simulation of serial link transceivers that include channel and circuit imperfections, such as finite pulse rise/fall time, duty cycle variation, and both receiver and transmitter forwarded-clock jitter. Second, in order to address link power efficiency, two test chips have been implemented. The first one describes a quad-lane, 6.4-7.2 Gb/s serial link receiver prototype using a forwarded clock architecture. A novel phase deskew scheme using injection-locked ring oscillators (ILRO) is proposed that achieves greater than one UI of phase shift for multiple clock phases, eliminating phase rotation and interpolation required in conventional architectures. Each receiver, optimized for power efficiency, consists of a low-power linear equalizer, four offset-cancelled quantizers for 1:4 demultiplexing, and an injection-locked ring oscillator coupled to a low-voltage swing, global clock distribution. Measurement results show a 6.4-7.2Gb/s data rate with BER < 10⁻¹² across 14 cm of PCB, and an 8Gb/s data rate through 4cm of PCB. Designed in a 1.2V, 90nm CMOS process, the ILRO achieves a wide tuning range from 1.6-2.6GHz. The total area of each receiver is 0.0174mm², resulting in a measured power efficiency of 0.6mW/Gb/s. Improving upon the first test chip, a second test chip for 8Gb/s forwarded clock serial link receivers exploits a low-power super-harmonic injection-locked ring oscillator for symmetric multi-phase local clock generation and deskewing. Further power reduction is achieved by designing most of the receiver circuits in the near-threshold region (0.6V supply), with the exception of only the global clock buffer, test buffers and synthesized digital test circuits at nominal 1V supply. At the architectural level, a 1:10 direct demultiplexing rate is chosen to achieve low supply operation by exploiting high-parallelism. Fabricated in 65nm CMOS technology, two receiver prototypes are integrated in this test chip, one without and the other with front-end boot-strapped S/Hs. Including the amortized power of global clock distribution, the proposed serial link receivers consume 1.3mW and 2mW respectively at 8Gb/s input data rate, achieving a power efficiency of 0.163mW/Gb/s and 0.25mW/Gb/s. Measurement results show both receivers achieve BER < 10⁻¹² across a 20-cm FR4 PCB channel

LOW-POWER FREQUENCY SYNTHESIS BASED ON INJECTION LOCKING

Ph.DDOCTOR OF PHILOSOPH

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

A 3.2 GHz Injection-Locked Ring Oscillator-Based Phase-Locked-Loop for Clock Recovery

An injection-locked ring oscillator-based phase-locked-loop targeting clock recovery for space application at 3.2 GHz is presented here. Most clock recovery circuits need a very low phase noise and jitter performance and are thus based on LC-type oscillators. These excellent performances come at the expense of a very poor integration density. To alleviate this issue, this work introduces an injection-locked ring oscillator-based PLL circuit. The combination of the injection-locking process with the use of ring oscillators allows for the benefit of excellent jitter performance while presenting an extremely low surface area due to an architecture without any inductor. The injection locking principle is addressed, and evidence of its phase noise and jitter improvements are confirmed through measurement results. Indeed, phase noise and jitter enhancements up to 43 dB and 23.3 mUI, respectively, were measured. As intended, this work shows the best integration density compared to recent similar state-of-the-art studies. The whole architecture measures 0.1 mm2 while consuming 34.6 mW in a low-cost 180 nm CMOS technology

Energy-efficient clock generation for communication and computing systems using injection locking

The design of high-performance, high-speed clock generation and distribution becomes challenging in terms of phase noise, jitter and power consumption, due to the fast development of communication and computing systems. Injection locking is a promising clocking technique since it can significantly improve the energy efficiency, suppress the phase noise of the ring oscillator, enable a fast startup and conveniently generate multiple time-interleaved phases. A quasi-linear model of injection-locked ring oscillator (ILRO) is utilized to mathematically formulate the frequency and time domain characteristics of the system, as well as the phase noise shaping and jitter tracking behavior. The settling behavior of ILRO is also exploited and shows a strong dependence on the locking range and the initial phase difference of the injected and the resultant oscillation signals. A forwarded-clock synchronization based on injection locking is designed for a 10 Gb/s photonic interconnect according to the specific features of optical links. A single clock recovery can be used for all the four channels, resulting in a large amount of power and area saving. The applications of sub-harmonic and super-harmonic injection locking in wireless communications for frequency multiplying and division are also discussed

Design of CMOS integrated frequency synthesizers for ultra-wideband wireless communications systems

Ultra¬wide band (UWB) system is a breakthrough in wireless communication, as it provides data rate one order higher than existing ones. This dissertation focuses on the design of CMOS integrated frequency synthesizer and its building blocks used in UWB system. A mixer¬based frequency synthesizer architecture is proposed to satisfy the agile frequency hopping requirement, which is no more than 9.5 ns, three orders faster than conventional phase¬locked loop (PLL)¬based synthesizers. Harmonic cancela¬tion technique is extended and applied to suppress the undesired harmonic mixing components. Simulation shows that sidebands at 2.4 GHz and 5 GHz are below 36 dBc from carrier. The frequency synthesizer contains a novel quadrature VCO based on the capacitive source degeneration structure. The QVCO tackles the jeopardous ambiguity of the oscillation frequency in conventional QVCOs. Measurement shows that the 5¬GHz CSD¬QVCO in 0.18 µm CMOS technology draws 5.2 mA current from a 1.2 V power supply. Its phase noise is ¬120 dBc at 3 MHz offset. Compared with existing phase shift LC QVCOs, the proposed CSD¬QVCO presents better phase noise and power efficiency. Finally, a novel injection locking frequency divider (ILFD) is presented. Im¬plemented with three stages in 0.18 µm CMOS technology, the ILFD draws 3¬mA current from a 1.8¬V power supply. It achieves multiple large division ratios as 6, 12, and 18 with all locking ranges greater than 1.7 GHz and injection frequency up to 11 GHz. Compared with other published ILFDs, the proposed ILFD achieves the largest division ratio with satisfactory locking range

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

A Sub-Centimeter Ranging Precision LIDAR Sensor Prototype Based on ILO-TDC

This thesis introduces a high-resolution light detection and ranging (LIDAR) sensor system-on-a-chip (SoC) that performs sub-centimeter ranging precision and maximally 124-meter ranging distance. With off-chip connected avalanche photodiodes (APDs), the time-of-flight (ToF) are resolved through 31×1 time-correlated single photon counting (TCSPC) channels. Embedded time-to-digital converters (TDCs) support 52-ps time resolution and 14-bit dynamic range. A novel injection-locked oscillator (ILO) based TDC are proposed to minimize the power of fine TDC clock distribution, and improve time precision. The global PVT variation among ILO clock distribution is calibrated by an on-chip phase-looked-loop (PLL) that assures a reliable counting performance over wide operating range. The proposed LIDAR sensor is designed, fabricated, and tested in the 65nm CMOS technology. Whole SoC consumes 37mW and each TDC channel consumes 788μW at nominal operation. The proposed TDC design achieved single-shot precision of 38.5 ps, channel uniformity of 14 ps, and DNL/INL of 0.56/1.56 LSB, respectively. The performance of proposed ILO-TDC makes it an excellent candidate for global counting TCSPC in automotive LIDAR