# Phase noise

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Phase noise

Phase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a wave, caused by time domain instabilities ("jitter"). Generally speaking radio frequency engineers speak of the phase noise of an oscillator, whereas digital system engineers work with the jitter of a clock.

An ideal oscillator would generate a pure sine wave. In the frequency domain, this would be represented as a single pair of delta functions (positive and negative conjugates) at the oscillator's frequency, i.e., all the signal's power is at a single frequency. All real oscillators have phase modulated noise components. The phase noise components spread the power of a signal to adjacent frequencies, resulting in sidebands.

Phase noise is typically expressed in units of dBc/Hz at various offsets from the carrier frequency. For example, a certain signal may have a phase noise of -80 dBc/Hz at an offset of 10 kHz and -95 dBc/Hz at an offset of 100 kHz. These are really phase noise density values. Phase noise can be measured and expressed as single sideband or double sideband values. Phase noise is sometimes also measured and expressed as a value integrated over a certain range of offset frequencies. For example, the phase noise may be -40 dBc integrated over the range of 1 kHz to 100 kHz. This Integrated phase noise (expressed in degrees) can be converted to jitter (expressed in seconds) using the following formula.

$Jitter\left(seconds\right) = Phase Error\left(degrees\right)/\left(360 x Frequency\left(hertz\right)\right)$

pectral purity

"Spectral purity" is how close an oscillator's output frequency comes to an ideal line of zero width. Wolaver, 1991, p.105 ]

References

* [http://www.designers-guide.org/Theory/ Noise in mixers, oscillators, samplers, and logic: an introduction to cyclostationary noise]
* [http://www.tf.nist.gov/phase/index.html National Institute of Standards and Technology Time and Frequency Metrology Group]

* Wolaver, Dan H. 1991. "Phase-Locked Loop Circuit Design", Prentice Hall, ISBN 0-13-662743-9
* A. Hajimiri and T.H. Lee, "A general theory of phase noise in electrical oscillators", IEEE Journal of Solid-State Circuits, Vol. 33, No 2, Feb. 1998 Pages:179 - 194, DOI 10.1109/4.658619
* A. Demir, A. Mehrotra and J. Roychowdhury, "Phase noise in oscillators: a unifying theory and numerical methods for characterization", IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications, Vol. 47, No 5, May 2000, Pages:655 - 674, DOI 10.1109/81.847872
* A. Chorti and M. Brookes, "A spectral model for RF oscillators with power-law phase noise", IEEE Trans. on Circuits and Systems I: Regular Papers, Vol. 53, No 9, Sept. 2006 Pages:1989 - 1999, DOI 10.1109/TCSI.2006.881182

ee also

*Jitter
*Spectral density
*Noise spectral density
*Flicker noise
*Spectral leakage

• A technical article about [http://www.telestrian.co.uk/phasenoise.html phase noise] in signal sources.
• [http://www.ke5fx.com/gpib/pn.htm Phase-noise measurement software] for various GPIB-equipped spectrum analyzers (freeware, includes Win32 C++ source)

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