Photonica
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Glossary entry

Noise figure (NF)

The factor by which an optical amplifier degrades the input signal-to-noise ratio, in dB. The figure of merit for amplifier quality.

Noise figure in decibels is

NF  =  10log⁡10 ⁣(SNRinSNRout)  =  10log⁡10F,\text{NF} \;=\; 10 \log_{10}\!\left( \frac{\text{SNR}_\text{in}}{\text{SNR}_\text{out}} \right) \;=\; 10 \log_{10} F,

where FF is the linear noise factor and SNR is the signal-to-noise ratio at the photodetected output.

For an optical amplifier with gain GG and spontaneous emission factor nspn_\text{sp}:

F  =  2 nsp(1−1G)+1G.F \;=\; 2 \, n_\text{sp} \left( 1 - \frac{1}{G} \right) + \frac{1}{G}.

In the high-gain limit (G≫1G \gg 1):

F  →  2 nsp,F \;\rightarrow\; 2 \, n_\text{sp},

with a fundamental quantum-mechanical lower bound of nsp=1n_\text{sp} = 1 (full population inversion), giving NF ≥3\geq 3 dB. Real amplifiers exceed this due to partial inversion and additional loss mechanisms.

Typical values:

AmplifierNF
EDFA (low-noise pre-amp)3.5 – 5 dB
EDFA (general telecom)4 – 6 dB
EDFA (booster, high gain)5 – 7 dB
Semiconductor optical amplifier (SOA)7 – 12 dB
Distributed Raman amplifier−2-2 to +3+3 dB (effective)
YDFA (ytterbium-doped)4 – 8 dB

Raman amplifiers achieve effective NF below 0 dB because gain is distributed along the transmission fiber — the signal is amplified before it is fully attenuated, effectively reducing the equivalent input loss compared to a discrete amplifier at the span end.

Cascade. For NN amplifiers in series with gains GiG_i and noise factors FiF_i (Friis formula):

Ftotal  =  F1+F2−1G1+F3−1G1G2+…F_\text{total} \;=\; F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \ldots

The first amplifier in a chain dominates the overall noise figure if its gain is high. This is why pre-amplifiers immediately following the receiver are specified for low NF, while later amplifiers can tolerate higher NF.

NF directly limits the achievable OSNR of an amplified link — each amplifier in a span adds noise proportional to Fi/GiF_i / G_i. Minimizing per-amplifier NF and selecting span lengths to maintain adequate per-stage gain is the central design problem for long-haul telecom.