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 ]}

where $f 0$ is the output frequency, $Q l$ is the loaded $Q$ , $f m$ is the offset from the output frequency (Hz), $f c$ is the $1/ f$ corner frequency, $F$ is the noise factor of the amplifier, $k$ is Boltzmann's constant in Joules/Kelvin, $T$ is absolute temperature in Kelvins, and $P s$ 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&ndash, 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.

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, https://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 Superseded by Rubiola 2008.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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[1] Leeson, D. B. (February 1966), "A Simple Model of Feedback Oscillator Noise Spectrum", Proceedings of the IEEE, 54 (2): 329&ndash, 330, doi:10.1109/PROC.1966.4682

[2] Rhea, Randall W. (1997), Oscillator Design & Computer Simulation (Second ed.), McGraw-Hill, ISBN 0-07-052415-7 , p. 115.

[3] Zumbahlen, Hank; Analog Devices, Inc. (2011-08-30). Zumbahlen, Hank, ed. Linear Circuit Design Handbook. Newnes. ISBN 9780080559155.

Electronic oscillators
Theory	Barkhausen stability criterion Harmonic oscillator Leeson's equation Nyquist stability criterion Oscillator phase noise Phase noise
LC oscillators	Armstrong or Meissner oscillator Clapp oscillator Colpitts oscillator Hartley oscillator Lampkin oscillator Meacham bridge oscillator Seiler oscillator Vackář oscillator resonant Royer
RC oscillators	Phase-shift oscillator Twin-T oscillator Wien bridge oscillator
Quartz oscillators	Butler oscillator Pierce oscillator Tri-tet oscillator
Relaxation oscillators	Blocking oscillator Multivibrator ring oscillator Pearson–Anson oscillator basic Royer
Other	Cavity oscillator Delay-line oscillator Opto-electronic oscillator Robinson oscillator Transmission-line oscillator Klystron oscillator Cavity magnetron Gunn oscillator

Leeson's equation

References

Further reading

External links