Leeson Model
Understanding the Leeson Model
The Leeson model relates the fundamental oscillator parameters to the output phase noise spectrum. It shows that phase noise improves with higher resonator Q, higher signal power, lower device noise figure, and lower flicker noise corner frequency.
Leeson's Equation
L(fm) = 10 log10[(2FkT/P_s) x (1 + (f0/(2Q_L fm))^2) x (1 + fc/fm)]
Where: fm = offset frequency, f0 = oscillation frequency, Q_L = loaded Q, F = device noise figure, P_s = signal power, fc = flicker noise corner, k = Boltzmann's constant, T = temperature.
Phase Noise Regions
- 1/f^3 region: Close to carrier. Dominated by upconverted flicker noise. Extends to fc.
- 1/f^2 region: From fc to f0/(2Q). Dominated by white noise modulating the oscillation.
- Noise floor: Beyond f0/(2Q). Flat at 10log(2FkT/P_s). Thermal noise floor.
L(fm) = 10 log[(2FkT/Ps)(1+(f0/(2QLfm))^2)(1+fc/fm)]
Key parameters:
f0 = oscillation frequency
QL = loaded Q of resonator
F = active device noise figure (linear)
Ps = signal power in resonator (Watts)
fc = flicker corner frequency (Hz)
Frequently Asked Questions
What is the Leeson model?
The Leeson model predicts oscillator phase noise from resonator Q, device noise figure, signal power, and flicker noise corner. It shows three phase noise regions: 1/f^3 near the carrier, 1/f^2 at moderate offsets, and a flat noise floor far from the carrier.
How does Q affect phase noise?
Phase noise is inversely proportional to Q^2. Doubling the loaded Q improves phase noise by 6 dB. This is why high-Q resonators (sapphire, cavity, YIG) produce the lowest phase noise oscillators.
What are the limitations of the Leeson model?
The Leeson model is semi-empirical: it assumes a linear model for a fundamentally nonlinear process (oscillation). It does not predict the noise figure F from device physics; it must be measured or estimated. Actual oscillator noise figure can be 10-30 dB higher than the small-signal noise figure.