# Phase noise in oscillators: DAEs and colored noise sources

@article{Demir1998PhaseNI, title={Phase noise in oscillators: DAEs and colored noise sources}, author={Alper Demir}, journal={1998 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (IEEE Cat. No.98CB36287)}, year={1998}, pages={170-177} }

Oscillators are key components of electronic systems. Undesired perturbations, i.e. noise, in practical electronic systems adversely affect the spectral and timing properties of oscillators resulting in phase noise, which is a key performance limiting factor, being a major contributor to bit-error-rate (BER) of RF communication systems, and creating synchronization problems in clocked and sampled data systems. We first present a theory and numerical methods for nonlinear perturbation and noise…

## 57 Citations

Phase noise in oscillators as differential-algebraic systems with colored noise sources

- Computer ScienceSPIE International Symposium on Fluctuations and Noise
- 2004

This paper reviews the work on the theory and numerical methods for nonlinear perturbation and noise analysis of oscillators described by a system of differential-algebraic equations (DAEs) with white and colored noise sources and discusses some open problems and issues in the modeling and analysis of phase noise both in free running oscillators and in phase/injection-locked ones.

Oscillator Noise Analysis

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A discussion explaining the origins and the proper definition of this transfer or sensitivity function, followed by a critical review of its origins and proper definition are provided.

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A unified analysis of the relationships between time-domain jitter and various spectral characterizations of phase noise is presented and practical results on computing jitter from spectral phase noise characteristics for oscillators and PLLs with both white (thermal, shot) and 1/f noise are presented.

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Spectral purity of an oscillator, quantified in terms of phase noise is the most critical and important parameter for RF/ wireless communication systems and digital electronic systems. Over years…

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Voltage controlled oscillators (VCOs) have gain paramount importance in frequency modulation (FM) and pulse modulation (PM) circuits, phase locked loops (PLLs), function generators, frequency…

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

- PhysicsProceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175)
- 1998

This paper develops a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism, and obtains an exact, nonlinear equation for phase error, which leads to a precise characterisation of timing jitter and spectral dispersion.

Phase and Amplitude Noise Analysis in Microwave Oscillators Using Nodal Harmonic Balance

- PhysicsIEEE Transactions on Microwave Theory and Techniques
- 2007

In this paper, a nodal harmonic balance (HB) formulation is presented for the phase and amplitude noise analysis of free-running oscillators. The implications of using different constraints in the…

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- Computer ScienceProceedings of the IEEE 1999 Custom Integrated Circuits Conference (Cat. No.99CH36327)
- 1999

This tutorial presents the basic concepts and fundamental techniques used in noise analysis and modeling both for linear and nonlinear circuits, and concentrates on some specific noise modeling and analysis problems in mixed-signal communication system design.

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.

Noise in a phase-quadrature pulsed energy restore oscillator

- Physics2011 20th European Conference on Circuit Theory and Design (ECCTD)
- 2011

An extended steady state method with this capability has been implemented in the simulator and it has been used to asses the design choices in a test case oscillator, as described in this paper.

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