Timing jitter and phase noise in electronic oscillators

In the first part of this dissertation, low frequency l/f or flicker noise in the frequency range of Hz to kHz has been identified and demonstrated to be described by temperature fluctuations in heat conduction in bipolar transistors operated at higher power densities. This noise phenomenon is not described by current SPICE programs used in circuit simulations. This noise in the kHz range can modulate LC oscillators and can be the determining factor in causing phase noise in modern wireless communication systems. At lower frequencies or lower power densities flicker noise may still result from number fluctuations or mobility fluctuations but this is not as important in determining the phase noise at kHz offsets from the carrier frequencies. In the second part of this dissertation work, we have developed a large signal nonlinear transient simulation technique to simulate phase noise due to device noise in electronic oscillators. Simulation results are consistent with Leeson’s theory and the magnitude of the sidebands directly scales with the magnitude of injected noise. Simulation also shows phase noise at 4.7 MHz frequency offset is white noise dominated and in good agreement with the experimental data reported in the literature. In the third part of this dissertation work, we have developed a large signal nonlinear transient simulation technique to simulate timing jitter in electronic oscillators. Simulation results are consistent with the accepted theory, analytical formula and A.Hajimiri's analytical model for white noise. Two important parameters cycle jitter, and cycle to cycle jitter used to describe jitter performance can be obtained from simulation. Simulation results are also compared with measurement and close agreement was observed between them. We have employed this methodology and investigated the timing jitter in silicon BJT /or SiGe HBT ECL ring oscillators, and we have shown silicon BJT /or SiGe HBT ring oscillators have lower jitter compared to their CMOS counterparts. As such silicon BJT and/or SiGe HBT ring oscillators are a potential choice for low jitter applications

Oscillator phase noise: a tutorial

Linear time-invariant (LTI) phase noise theories provide important qualitative design insights but are limited in their quantitative predictive power. Part of the difficulty is that device noise undergoes multiple frequency translations to become oscillator phase noise. A quantitative understanding of this process requires abandoning the principle of time invariance assumed in most older theories of phase noise. Fortunately, the noise-to-phase transfer function of oscillators is still linear, despite the existence of the nonlinearities necessary for amplitude stabilization. In addition to providing a quantitative reconciliation between theory and measurement, the time-varying phase noise model presented in this tutorial identifies the importance of symmetry in suppressing the upconversion of 1/f noise into close-in phase noise, and provides an explicit appreciation of cyclostationary effects and AM-PM conversion. These insights allow a reinterpretation of why the Colpitts oscillator exhibits good performance, and suggest new oscillator topologies. Tuned LC and ring oscillator circuit examples are presented to reinforce the theoretical considerations developed. Simulation issues and the accommodation of amplitude noise are considered in appendixes

A general theory of phase noise in electrical oscillators

A general model is introduced which is capable of making accurate, quantitative predictions about the phase noise of different types of electrical oscillators by acknowledging the true periodically time-varying nature of all oscillators. This new approach also elucidates several previously unknown design criteria for reducing close-in phase noise by identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total phase noise. In particular, it explains the details of how 1/f noise in a device upconverts into close-in phase noise and identifies methods to suppress this upconversion. The theory also naturally accommodates cyclostationary noise sources, leading to additional important design insights. The model reduces to previously available phase noise models as special cases. Excellent agreement among theory, simulations, and measurements is observed

Colored noise in oscillators. Phase-amplitude analysis and a method to avoid the Ito-Stratonovich dilemma

We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into an equivalent system subject to white Gaussian noise. A description in terms of phase and amplitude deviation is given for the transformed system. Using stochastic averaging technique, the equations are reduced to a phase model that can be analyzed to characterize phase noise. We find that phase noise is a drift-diffusion process, with a noise-induced frequency shift related to the variance and to the correlation time of colored noise. The proposed approach improves the accuracy of previous phase reduced models

Power waves formulation of oscillation conditions: avoidance of bifurcation modes in cross-coupled VCO architectures

This paper discusses necessity of power-waves formulation to extend voltage-current oriented approaches based on linear concepts such as admittance/impedance operators and transfer-function representations. Importance of multi-physics methodologies, throughout power-waves formulation, for the analysis and design of crystal oscillators is discussed. Interpretation of bifurcation modes in differential cross-coupled VCO architectures in terms of gyrator-like behavior, is proposed. Impact of amplitude level control (ALC) on large-signal phase noise performances is underlined showing necessity of robust control analysis approach relative to power-energy considerations

Multi-Loop-Ring-Oscillator Design and Analysis for Sub-Micron CMOS

Ring oscillators provide a central role in timing circuits for today?s mobile devices and desktop computers. Increased integration in these devices exacerbates switching noise on the supply, necessitating improved supply resilience. Furthermore, reduced voltage headroom in submicron technologies limits the number of stacked transistors available in a delay cell. Hence, conventional single-loop oscillators offer relatively few design options to achieve desired specifications, such as supply rejection. Existing state-of-the-art supply-rejection- enhancement methods include actively regulating the supply with an LDO, employing a fully differential or current-starved delay cell, using a hi-Z voltage-to-current converter, or compensating/calibrating the delay cell. Multiloop ring oscillators (MROs) offer an additional solution because by employing a more complex ring-connection structure and associated delay cell, the designer obtains an additional degree of freedom to meet the desired specifications. Designing these more complex multiloop structures to start reliably and achieve the desired performance requires a systematic analysis procedure, which we attack on two fronts: (1) a generalized delay-cell viewpoint of the MRO structure to assist in both analysis and circuit layout, and (2) a survey of phase-noise analysis to provide a bank of methods to analyze MRO phase noise. We distill the salient phase-noise-analysis concepts/key equations previously developed to facilitate MRO and other non-conventional oscillator analysis. Furthermore, our proposed analysis framework demonstrates that all these methods boil down to obtaining three things: (1) noise modulation function (NMF), (2) noise transfer function (NTF), and (3) current-controlled-oscillator gain (KICO). As a case study, we detail the design, analysis, and measurement of a proposed multiloop ring oscillator structure that provides improved power-supply isolation (more than 20dB increase in supply rejection over a conventional-oscillator control case fabricated on the same test chip). Applying our general multi-loop-oscillator framework to this proposed MRO circuit leads both to design-oriented expressions for the oscillation frequency and supply rejection as well as to an efficient layout technique facilitating cross-coupling for improved quadrature accuracy and systematic, substantially simplified layout effort

Virtual damping and Einstein relation in oscillators

This paper presents a new physical theory of oscillator phase noise. Built around the concept of phase diffusion, this work bridges the fundamental physics of noise and existing oscillator phase-noise theories. The virtual damping of an ensemble of oscillators is introduced as a measure of phase noise. The explanation of linewidth compression through virtual damping provides a unified view of resonators and oscillators. The direct correspondence between phase noise and the Einstein relation is demonstrated, which reveals the underlying physics of phase noise. The validity of the new approach is confirmed by consistent experimental agreement

Attosecond Precision Multi-km Laser-Microwave Network

Synchronous laser-microwave networks delivering attosecond timing precision are highly desirable in many advanced applications, such as geodesy, very-long-baseline interferometry, high-precision navigation and multi-telescope arrays. In particular, rapidly expanding photon science facilities like X-ray free-electron lasers and intense laser beamlines require system-wide attosecond-level synchronization of dozens of optical and microwave signals up to kilometer distances. Once equipped with such precision, these facilities will initiate radically new science by shedding light on molecular and atomic processes happening on the attosecond timescale, such as intramolecular charge transfer, Auger processes and their impact on X-ray imaging. Here, we present for the first time a complete synchronous laser-microwave network with attosecond precision, which is achieved through new metrological devices and careful balancing of fiber nonlinearities and fundamental noise contributions. We demonstrate timing stabilization of a 4.7-km fiber network and remote optical-optical synchronization across a 3.5-km fiber link with an overall timing jitter of 580 and 680 attoseconds RMS, respectively, for over 40 hours. Ultimately we realize a complete laser-microwave network with 950-attosecond timing jitter for 18 hours. This work can enable next-generation attosecond photon-science facilities to revolutionize many research fields from structural biology to material science and chemistry to fundamental physics.Comment: 42 pages, 13 figure