Leeson Phase Noise

Leeson's model predicts an oscillator's single-sideband phase noise L(f_m) from four things: the resonator's loaded Q, the active device's noise figure, the power delivered to the resonator, and the flicker (1/f) corner. It captures the classic shape — a 1/f³ close-in region rolling into 1/f² and then a flat noise floor. Enter the parameters to get L at a chosen offset and the whole profile.

Equations & Parameters ▸

\(\mathcal{L}(f_m)=10\log_{10}\!\left[\dfrac{2FkT}{P_{avs}}\left(1+\left(\dfrac{f_0}{2Q_L f_m}\right)^2\right)\left(1+\dfrac{f_c}{f_m}\right)\right]\)

f₀	Oscillation (carrier) frequency (MHz).
Q_L	Loaded quality factor of the resonator. Higher Q → lower close-in phase noise.
NF	Active-device noise figure (dB); F = 10^(NF/10).
P_avs	Signal power delivered to the resonator/device (dBm).
f_c	Flicker (1/f) corner frequency (kHz).
f_m	Offset frequency from the carrier (kHz).

Reference: D. B. Leeson, "A simple model of feedback oscillator noise spectrum," Proc. IEEE 54(2), 329 (1966). k = 1.380649×10⁻²³ J/K.

Inputs

Carrier, f₀

MHz

Carrier

Loaded Q, Q_L

Resonator

Noise figure, NF

Device

Power, P_avs

dBm

Drive level

Flicker corner, f_c

kHz

1/f corner

Offset, f_m

kHz

Read-out offset

Temperature, T

Default 290

Results

Phase noise

L(f_m) at offset—

Leeson corner f₀/2Q_L—

Noise floor (far offset)—

Diagram

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