Abstract — 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. Index Terms—Jitter, oscillator noise, oscillators, oscillator stability, phase jitter, phase locked loops, phase noise, voltage controlled oscillators. I.

This paper presents a study of phase noise in two inductorless CMOS oscillators. First-order analysis of a linear oscillatory system leads to a noise shaping function and a new definition of Q. A linear model of CMOS ring oscillators is used to calculate their phase noise, and three phase noise phenomena, namely, additive noise, high-frequency multiplicative noise, and low-frequency multiplicative noise, are identified and formulated. Based on the same concepts, a CMOS relaxation oscillator is also analyzed. Issues and techniques related to simulation of noise in the time domain are described, and two prototypes fabricated in a 0.5-m CMOS technology are used to investigate the accuracy of the theoretical predictions. Compared with the measured results, the calculated phase noise values of a 2-GHz ring oscillator and a 900-MHz relaxation oscillator at 5 MHz offset have an error of approximately 4 dB. I. INTRODUCTION V OLTAGE-CONTROLLED oscillators (VCO's) are an integral part of phas...

work in this thesis would not have been possible without many people whose contributions are now acknowledged. At Analog Devices Semiconductor: Larry DeVito, Rosamaria Croughwell, and Alex Gusinov, engineers with whom it was a genuine pleasure to work; Bob Surette, for outstanding support in laboratory measurements; Tony Freitas, for considerable layout expertise; Dennis Buss, for all-important financial support; Maryanne Masterson and Frank Holden for fabrication and trim support; Bob Adams, Paul Brokaw, Barrie Gilbert, Janos Kovacs, and Chris Mangelsdorf for enlightening conversations. At Tektronix: Scott Casstevens, for providing the CSA803A for high accuracy jitter measurements; Laszlo Dobos, for his insights into jitter. At Boston University: Anton Mavretic, for his direction and support; David Perreault, Mark Horenstein, and Emile Gergin for their time and effort on the

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 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 exh...

Transceiver architectures are proposed that best harness the tiny size, zero dc power dissipation, and ultra-high-Q of vibrating micromechanical resonator circuits. Among the more aggressive architectures proposed are one based on a micromechanical RF channel-selector and one featuring an all-MEMS RF front-end. These architectures maximize performance gains by using highly selective, low-loss micromechanical circuits on a massive scale, taking full advantage of Q versus power trade-offs. Micromechanical filters, mixerfilters, and switchable synthesizers are identified as key blocks capable of substantial power savings when used in the aforementioned architectures. As a result of this architectural exercise, more focused directions for further research and development in RF MEMS are identified.

Abstract—An overview on the use of microelectromechanical systems (MEMS) technologies for timing and frequency control is presented. In particular, micromechanical RF filters and reference oscillators based on recently demonstrated vibrating on-chip micromechanical resonators with Q’s>10,000 at 1.5 GHz, are described as an attractive solution to the increasing count of RF components (e.g., filters) expected to be needed by future multi-band wireless devices. With Q’s this high in onchip abundance, such devices might also enable a paradigmshift in the design of timing and frequency control functions, where the advantages of high-Q are emphasized, rather than suppressed (e.g., due to size and cost reasons), resulting in enhanced robustness and power savings. With even more aggressive three-dimensional MEMS technologies, even higher onchip Q’s have been achieved via chip-scale atomic physics packages, which so far have achieved Q’s>10 7 using atomic cells measuring only 10 mm 3 in volume, consuming just 5 mW of power, all while still allowing Allan deviations down to 10-11 at one hour. Keywords—MEMS, micromechanical, quality factor, resonator, oscillator, filter, wireless communications, mechanical circuit, chip-scale atomic clock, physics package. I.

Micromechanical (or "mechanical) communication circuits fabricated via IC-compatible MEMS technologies and capable of low-loss filtering, mixing, switching, and frequency generation, are described with the intent to miniaturize wireless transceivers. Receiver architectures are then proposed that best harness the tiny size, zero dc power dissipation, and ultra-high-Q of vibrating mechanical resonator circuits. Among the more aggressive architectures proposed are one based on a mechanical RF channel-selector and one featuring an all-MEMS RF front-end. These architectures maximize performance gains by using highly selective, low-loss mechanical circuits on a massive scale, taking full advantage of Q versus power trade-offs. Micromechanical filters, mixer-filters, and switchable synthesizers are identified as key blocks capable of substantial power savings when used in the aforementioned architectures. As a result of this architectural exercise, more focused directions for further research and development in RF MEMS are identified.

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Doctor of Philosophy in Electrical Engineering and Computer Science A digital compensation method is described that allows fractional-N frequency synthesizers to be directly modulated at high data rates while simultaneously achieving good noise performance. The technique allows digital phase/frequency modulation to be achieved at high data rates (> 1 Mbit/s) without mixers or D/A converters in the modulation path. The resulting transmitter design is primarily digital in nature and reduced to its fundamental components — a frequency synthesizer that accurately sets the output frequency, and a digital transmit filter that provides good spectral efficiency. The synthesizer is implemented as a phase locked loop (PLL). To achieve good noise performance with a simple design, the PLL bandwidth is set to a low value relative to the data bandwidth. A digital compensation filter is then used to undo the attenuation of the PLL transfer function seen by the data. This filter adds little complexity to the transmitter architecture since it can be combined with the digital

Abstract — A completely monolithic high- oscillator, fabricated via a combined CMOS plus surface micromachining technology, is described, for which the oscillation frequency is controlled by a polysilicon micromechanical resonator with the intent of achieving high stability. The operation and performance of micromechanical resonators are modeled, with emphasis on circuit and noise modeling of multiport resonators. A series resonant oscillator design is discussed that utilizes a unique, gain-controllable transresistance sustaining amplifier. We show that in the absence of an automatic level control loop, the closed-loop, steady-state oscillation amplitude of this oscillator depends strongly upon the dc-bias voltage applied to the capacitively driven and sensed "resonator. Although the highof the micromechanical resonator does contribute to improved oscillator stability, its limited power-handling ability outweighs the benefits and prevents this oscillator from achieving the high short-term stability normally expected of high- oscillators. Index Terms — Fabrication, microelectromechanical devices, microelectromechanical systems (MEMS), micromachining, micromechanical, nonlinear oscillators, oscillators, oscillator stability, phase noise, resonators. I.