Leeson's equation
Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum.
Leeson's expression[1] for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per Hertz) and augmented for flicker noise:[2]
![L(f_{m})=10\log {\bigg [}{\frac {1}{2}}{\bigg (}{\bigg (}{\frac {f_{0}}{2Q_{l}f_{m}}}{\bigg )}^{2}+1{\bigg )}{\bigg (}{\frac {f_{c}}{f_{m}}}+1{\bigg )}{\bigg (}{\frac {FkT}{P_{s}}}{\bigg )}{\bigg ]}](../I/m/0ecb8c57d69d9a5cee5808ec6d7f6c0acbcb532a.svg)
where f0 is the output frequency, Ql is the loaded Q, fm is the offset from the output frequency (Hz), fc is the 1/f corner frequency, F is the noise factor of the amplifier, k is Boltzmann's constant in Joules/Kevin, T is absolute temperature in Kelvins, and Ps is the output power.[3]
References
- ↑ Leeson, D. B. (February 1966), "A Simple Model of Feedback Oscillator Noise Spectrum", Proceedings of the IEEE, 54 (2): 329–330, doi:10.1109/PROC.1966.4682
- ↑ Rhea, Randall W. (1997), Oscillator Design & Computer Simulation (Second ed.), McGraw-Hill, ISBN 0-07-052415-7, p. 115.
- ↑ Zumbahlen, Hank; Analog Devices, Inc. (2011-08-30). Zumbahlen, Hank, ed. Linear Circuit Design Handbook. Newnes. ISBN 9780080559155.
Further reading
- Rubiola, Enrico (2008), Phase noise and frequency stability in oscillators, Cambridge, ISBN 978-0-521-15328-7
- Rohde, Ulrich L. (20 October 2011), Noise in Oscillators with Active Inductors (PDF), p. 9
External links
- Ali M. Niknejad, Oscillator Phase Noise, University of California, Berkeley, 2009 http://rfic.eecs.berkeley.edu/~niknejad/ee242/pdf/eecs242_lect22_phasenoise.pdf, stating "Leeson modified the above noise model to account for several experimentally observed phenomena". Also, "In Leeson’s model, the factor F is a fitting parameter rather than arising from any physical concepts. It’s tempting to call this the oscillator "noise figure", but this is misleading."
- John van der Merwe, An Experimental Investigation into the Validity of Leeson's Equation for Low Phase Noise Oscillator Design, December 2010, https://scholar.sun.ac.za/bitstream/handle/10019.1/5424/vandermerwe_experimental_2010.pdf
- Enrico Rubiola, The Leeson effect, http://arxiv.org/pdf/physics/0502143.pdf. Superseded by Rubiola 2008.
- http://www.ieee.li/pdf/essay/phase_noise_basics.pdf
- http://www.researchgate.net/publication/48339964_An_experimental_investigation_into_the_validity_of_Leeson's_equation_for_low_phase_noise_oscillator_design
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