# First-Hand:Phase Noise

## Phase Noise

Submitted by David B. Leeson

The performance of electronic systems that process signals is limited by competing background random signals referred to as noise. In communications, navigation, radar and computing systems, the reception, detection or processing of signals is limited by their strength compared to the noise background that is present in electronic components and propagation paths.

In certain important systems, even very strong signals carry with them noise that itself limits performance. Examples I have worked with include (a) systems in which signal frequency, phase or time transmits the intended information (e.g., channelized radio systems, digital and FM radio links, time standards, radio-navigation systems, computers) and (b) systems in which sensitivity to weak signals is required in the presence of other, stronger, signals that may themselves carry noise (e.g., pulse Doppler radar, cellular telephony, amateur radio).

In these system types, the noise accompanying the signal can be the limiting factor in performance. Noise on a signal can be resolved through modulation theory into separate amplitude and phase components. The impact of the amplitude noise component is generally found to be much less significant, so the phase noise component is dominant. Extensive efforts continue to reduce phase noise in circuits and systems.

Phase noise originates primarily from random internal or environmentally caused frequency instability in the oscillators that generate the system signals (frequency, phase and time are directly related aspects of a signal). Environmentally caused instability (e.g., due to vibration or acoustic pressure) can be either random or coherent in response to the nature of its source, and if present typically predominates over quiescent noise effects.

Random signals are treated with the mathematics of statistics, including power spectra. Time-domain concepts such as variance, deviation or jitter were seen as natural for navigation or time-keeping systems, and for digital computers. Frequency-domain concepts such as power spectral density of signal, phase or frequency were developed for FM multiplex telephony, pulse Doppler radar and channelized systems.

By the 1960s, designers had established convenient but separate definitions and measurements of frequency stability, based on the mathematics and instrumentation most appropriate to their specialty. It would come to be appreciated that the time and frequency formats were related, and that translation was possible.

The requirement then arose for deep-space communications links, the design of which would require an appreciation of both domains. A sponsored series of dedicated meetings and publications identified mutually acceptable concepts for a common definition of phase noise, and hence frequency instability. As a young Doppler radar engineer then, I was fortunate to take part in this process.

Frequency and time definitions were rendered interchangeable through the recognition that, for the principal noise types observed in signal sources, the time- and frequency-domain definitions form a known mathematical Fourier-transform pair. Additionally, oscillator power spectral density of phase was shown to be predictable from knowledge of the signal level and the characteristics of the device and resonator.

In 1971, an IEEE standards committee created a paper that proposed definitions of frequency stability in terms that satisfied a wide range of applications. Subsequently, IEEE standards committees have created three generations of standards. Frequency instabilities are defined and measured in terms of the statistics of time series of frequency measurements or in terms of the related spectral density of phase.

The emergence of modern digital integrated circuits resulted in the need for more rigorous circuit analyses for strongly nonlinear circuits. Also, new oscillator types employed a wider range of frequency determining elements. At the same time, the abilities of modern computers and software made practical new methods of signal compression, processing, analysis and measurement. The literature of phase noise currently has some 16,000 citations.

## Further Reading

Oscillator Phase Noise: A 50-year Retrospective, D. B. Leeson, Frequency Control Symposium & the European Frequency and Time Forum (FCS), 2015 Joint Conference of the IEEE International, 2015, Pages: 332 - 337, DOI: 10.1109/FCS.2015.7138853

Oscillator Phase Noise: A 50-year Retrospective slides, presented May 21st, 2015

D.B. Leeson, "A simple model of feedback oscillator noise spectrum," Proceedings of the IEEE, Year: 1966, Volume: 54, Issue: 2, Pages: 329 - 330, DOI: 10.1109/PROC.1966.4682

D. B. Leeson, Oscillator Phase Noise: A 50-Year Review, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 63, No. 8, Pages: 1208-1225, August 2016, DOI: 10.1109/TUFFC.2016.2562663