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

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 Robust 43-GHz VCO in CMOS for OC-768 SONET Applications

In this paper, we present a 43-GHz LC-VCO in 0.13-/spl mu/m CMOS for use in SONET OC-768 optical networks. A tuned output buffer is used to provide 1.3 V/sub p-p/ (single-ended) into a 90-fF capacitive load as is required when the VCO is used in typical clock and data recovery (CDR) circuits. Phase noise is -90 dBc/Hz at a 1-MHz offset from the carrier; this meets SONET jitter specifications. The design has a tune range of 4.2%. The VCO, including output buffers, consumes 14 mA from a 1-V supply and occupies 0.06 mm/sup 2/ of die area. Modern CMOS process characteristics and the high center frequency of this design mean that the tank loss is not dominated by the integrated inductor, but rather by the tank capacitance. An area-efficient inductor design that does not require any optimization is used

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