Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated

Influence of jitter on limit cycles in bang-bang clock and data recovery circuits

In bang-bang (BB) clock and data recovery circuits (CDR) limit cycles can occur, but these limit cycles are undesired for a good operation of the BB-CDR. Surprisingly, however, a little bit of noise in the system is beneficial, because it will quench the limit cycles. Until now, authors have always assumed that there is enough noise in a BB-CDR such that no limit cycle occurs. In this work, a pseudo-linear analysis based on describing functions is used to investigate this. In particular, the relationship between the input noise and the amplitude of eventual limit cycles is investigated. An important result of the theory is that it allows to quantify the influence of the different loop parameters on the minimal amount of input jitter needed to destroy the limit cycle. Additionally, for the case that there is not enough noise, the worst case amplitude of the limit cycle (which is unavoidable in this case) is quantified as well. The presented analysis exhibits excellent matching with time domain simulations and leads to very simple analytical expressions

Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated

올 디지털 클럭 및 데이터 복원 회로를 적용한 고속 광 수신기 설계

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 8. 정덕균.This thesis presents a 22- to 26.5-Gb/s optical receiver with an all-digital clock and data recovery (ADCDR) fabricated in a 65-nm CMOS process. The receiver consists of an optical front-end and a half-rate bang-bang clock and data recovery circuit. The optical front-end achieves low power consumption by using inverter-based amplifiers and realizes sufficient bandwidth by applying several bandwidth extension techniques. In addition, in order to minimize additional jitter at the front-end, not only magnitude and bandwidth but also phase delay responses are considered. The ADCDR employs an LC quadrature digitally-controlled oscillator (LC-QDCO) to achieve a high phase noise figure-of-merit at tens of gigahertz. The recovered clock jitter is 1.28 psrms and the measured jitter tolerance exceeds the tolerance mask specified in IEEE 802.3ba. The receiver sensitivity is 106 and 184 μApk-pk for a bit error rate of 10−12 at data rates of 25 and 26.5 Gb/s, respectively. The entire receiver chip occupies an active die area of 0.75 mm2 and consumes 254 mW at a data rate of 26.5 Gb/s. The energy efficiencies of the front-end and entire receiver at 26.5 Gb/s are 1.35 and 9.58 pJ/bit, respectively.CHAPTER 1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 THESIS ORGANIZATION 5 CHAPTER 2 DESIGN OF OPTICAL FRONT-END 7 2.1 OVERVIEW 7 2.2 BACKGROUND ON OPTICAL FRONT-END 9 2.2.1 PHOTODIODE 9 2.2.2 TRANSIMPEDANCE AMPLIFIER 11 2.2.3 POST AMPLIFIER 17 2.2.4 SHUNT INDUCTIVE PEAKING 25 2.3 CIRCUIT IMPLEMENTATION 29 2.3.1 OVERALL ARCHITECTURE 29 2.3.2 TRANSIMPEDANCE AMPLIFIER 31 2.3.3 POST AMPLIFIER 34 2.4 NOISE ANALYSIS 43 2.4.1 PHOTODIODE 43 2.4.2 OPTICAL FRONT-END 44 2.4.3 SENSITIVITY 46 CHAPTER 3 DESIGN OF ADCDR FOR OPTICAL RECEIVER 48 3.1 OVERVIEW 48 3.2 BACKGROUND ON PLL-BASED ADCDR 51 3.2.1 PHASE DETECTOR 51 3.2.2 DIGITAL LOOP FILTER 54 3.2.3 DIGITALLY-CONTROLLED OSCILLATOR 56 3.2.4 ANALYSIS OF BANG-BANG ADCDR 67 3.3 CIRCUIT IMPLEMENTATION 70 3.3.1 OVERALL ARCHITECTURE 70 3.3.2 PHASE DETECTION LOGIC 75 3.3.3 DIGITAL LOOP FILTER 77 3.3.4 LC QUADRATURE DCO 78 CHAPTER 4 EXPERIMENTAL RESULTS 82 CHAPTER 5 CONCLUSION 90 BIBLIOGRAPHY 92 초록 101Docto

최적 위상 검출 회로를 이용한 클럭 및 데이터 복원 회로에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2014. 8. 김재하.Bang-bang phase detectors are widely used for today's high-speed communication circuits such as phase-locked loops (PLLs), delay-locked loops (DLLs) and clock-and-data recovery loops (CDRs) because it is simple, fast, accurate and amenable to digital implementations. However, its hard nonlinearity poses difficulties in design and analyses of the bang-bang controlled timing loops. Especially, dithering in bang-bang controlled CDRs sets conflicting requirements on the phase adjustment resolution as one tries to maximize the tracking bandwidth and minimize jitter. A fine phase step is helpful to minimize the dithering, but it requires circuits with finer resolution that consumes large power and area. In this background, this dissertation introduces an optimal phase detection technique that can minimize the effect of dithering without requiring fine phase resolution. A novel phase interval detector that looks for a phase interval enclosing the desired lock point is shown to find the optimal phase that minimizes the timing error without dithering. A digitally-controlled, phase-interpolating DLL-based CDR fabricated in 65nm CMOS demonstrates that it can achieve small area of 0.026mm^2 and low jitter of 41mUIp-p with a coarse phase adjustment step of 0.11UI, while dissipating only 8.4mW at 5Gbps. For the theoretic basis, various analysis techniques to understand bang-bang controlled timing loops are also presented. The proposed techniques are explained for both linearized loop and non-linear one, and applied to the evaluation of the proposed phase detection technique.1 Introduction 1 1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesis Contribution and Organization . . . . . . . . . . . . . . . . . 6 2 Pseudo-Linear Analysis of Bang-Bang Controlled Loops 9 2.1 Model of a Second-Order, Bang-Bang Controlled Timing Loop . . . 9 2.2 Necessary Condition for the Pseudo-Linear Analysis . . . . . . . . . 12 2.3 Derivation of Necessity Condition for the Pseudo-Linear Analysis . . 17 2.4 A Linearized Model of the Bang-Bang Phase Detector . . . . . . . . 18 2.5 Linearized Gain of a Bang-Bang Phase Detector for Jitter Transfer and Jitter Generation Analyses . . . . . . . . . . . . . . . . . . . . . 21 2.6 Jitter Transfer and Jitter Generation Analyses . . . . . . . . . . . . 29 2.7 Linearized Gains of a Bang-bang Phase Detector for Jitter Tolerance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.8 Jitter Tolerance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 41 3 Nonlinear Analysis of Bang-Bang Controlled Loops 48 3.1 Transient Analysis of Bang-Bang Controlled Timing Loops . . . . . 48 3.2 Phase-portrait Analysis of Bang-Bang Controlled Timing Loops . . . 51 3.3 Markov-chain Analysis of Bang-Bang Controlled Timing Loops . . . 53 3.4 Analysis of Clock-and-Data Recovery Circuits . . . . . . . . . . . . . 57 3.4.1 Prediction of Bit-Error Rate . . . . . . . . . . . . . . . . . . 57 3.4.2 Eect of Transition Density . . . . . . . . . . . . . . . . . . . 58 3.4.3 Eect of Decimation . . . . . . . . . . . . . . . . . . . . . . . 61 3.4.4 Analysis of Oversampling Phase Detectors . . . . . . . . . . . 66 4 Design of Ditherless Clock and Data Recovery Circuit 75 4.1 Optimal Phase Detection . . . . . . . . . . . . . . . . . . . . . . . . 75 4.2 Proposed Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.3 Analysis of the CDR with Phase Interval Detection . . . . . . . . . . 84 4.4 Circuit Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4.1 Sampling Receiver . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4.2 Phase Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.4.3 Digital Loop Filter . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4.4 Phase Locked-Loop . . . . . . . . . . . . . . . . . . . . . . . . 98 4.4.5 Phase Interpolator . . . . . . . . . . . . . . . . . . . . . . . . 99 4.5 Built-In Self-Test Circuit for Jitter Tolerance Measurement . . . . . 102 4.6 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5 Conclusion 114 References 116Docto