# Phase noise in oscillators: a unifying theory and numerical methods for characterization

@article{Demir2000PhaseNI, title={Phase noise in oscillators: a unifying theory and numerical methods for characterization}, author={Alper Demir and Amit Mehrotra and Jaijeet S. Roychowdhury}, journal={IEEE Transactions on Circuits and Systems I-regular Papers}, year={2000}, volume={47}, pages={655-674} }

Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields, such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterization. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of…

## 1,154 Citations

Unified Theory of Oscillator Phase Noise I: White Noise

- PhysicsIEEE Transactions on Microwave Theory and Techniques
- 2013

The spectral purity of every oscillator system is limited by phase noise. In this work, we extend the techniques previously used to analyze phase noise in lasers to develop an intuitive, yet powerful…

A General Theory of Phase Noise in Transconductor-Based Harmonic Oscillators

- Physics, EngineeringIEEE Transactions on Circuits and Systems I: Regular Papers
- 2017

A rigorous phase noise analysis of a generic harmonic oscillator where the active core can be modeled as a transconductor is presented, and it is shown that the phase noise caused by transConductor white noise is always proportional to the phase Noise caused by resonator losses.

Phase diffusion and noise temperature of a microwave amplifier based on single unshunted Josephson junction

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Analytical Equations for Nonlinear Phase Errors and Jitter in Ring Oscillators

- PhysicsIEEE Transactions on Circuits and Systems I: Regular Papers
- 2007

A simple analytical equation for capturing phase errors in 3-stage ring oscillators is presented, based on a simple but useful idealization of the ring oscillator, which correctly captures the time- dependent sensitivity of oscillator phase to external perturbations.

Exact analytical equations for predicting nonlinear phase errors and jitter in ring oscillators

- Physics18th International Conference on VLSI Design held jointly with 4th International Conference on Embedded Systems Design
- 2005

A simple analytical equation for capturing phase errors in 3-stage ring oscillators is presented, based on a simple but useful idealization of the ring oscillator, and correctly captures the time-dependent sensitivity of oscillator phase to external perturbations.

The Complex World of Oscillator Noise: Modern Approaches to Oscillator (Phase and Amplitude) Noise Analysis

- PhysicsIEEE Microwave Magazine
- 2021

The study of fluctuations in oscillators has been a classical research topic in mathematics, physics, and engineering since the first half of the 20th century [1]-[4]. Besides the intellectual…

Analytical expressions for phase noise eigenfunctions of LC oscillators

- PhysicsASP-DAC 2004: Asia and South Pacific Design Automation Conference 2004 (IEEE Cat. No.04EX753)
- 2004

Analytical expressions for eigenfunctions that characterize the phase noise performance of generic LC oscillator structures and analytical expressions for the timing jitter and spectrum of such oscillators are obtained.

Frequency Precision of Oscillators Based on High-Q Resonators

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- 2015

We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the…

Measurements to reveal phase-noise producing mechanisms in resonator-oscillators

- PhysicsSPIE International Symposium on Fluctuations and Noise
- 2007

During the last decades, several theoretical models describing phase noise of oscillator signals have been established. Verification of these models has mainly been done by computer simulations.…

Phase Noise in Autonomous Oscillators

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- 2019

Due to its importance in circuit design, the problem of modeling phase noise in autonomous oscillators has attracted considerable attention over the last 50 years. Noteworthy phase noise studies…

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