Tool · Fiber and telecom

OSNR and Noise Figure Calculator

How much optical signal-to-noise ratio is left at the end of a chain of amplified spans, and how many spans can a link have before it falls below what the receiver needs? The calculator adds up the amplified spontaneous emission of every amplifier from the launch power, span loss, noise figure and reference bandwidth, and works out the gain and noise figure of a cascade of amplifiers and losses with the Friis formula. Background: OSNR, noise figure, and SOA vs EDFA vs Raman.

Amplified link

Wavelength λ (nm)

Launch power per channel (dBm)

Span loss (dB)

For example 80 km at 0.2 dB/km plus 4 dB of connectors and splices. Each amplifier makes up the loss of the span before it.

Amplifier noise figure (dB)

Number of spans N

Reference bandwidth

Required OSNR (dB)

Cascade noise figure

Up to five stages in the order the light meets them. A loss stage has a noise figure equal to its loss.

#	stage	gain or loss (dB)	NF (dB)
1
2
3
4
5

Presets

Linear noise only: amplified spontaneous emission from lumped amplifiers, with each amplifier’s gain equal to the span loss. Fiber nonlinearity, which sets the useful upper limit on launch power, and gain ripple, filtering and transponder noise are not modelled.

Readouts

OSNR versus number of spans

OSNR at the end of the linkrequired OSNR

Where the cascade noise comes from

Learn with it

Three short experiments. Each one sets the inputs, says where to look, and asks for a prediction before it shows the result.

Checked against

These checks run in your browser on every load. The closed forms are compared with values worked out by hand from the exact SI constants, and the span-by-span sum of amplifier noise is compared with the Friis cascade of the same link treated as one chain of losses and gains.

Check	Expected	Computed	Tolerance

The expected values follow the optical noise-figure definition and amplifier noise relations in Desurvire, Erbium-Doped Fiber Amplifiers, and Agrawal, Fiber-Optic Communication Systems, evaluated by hand for the stated links. The tolerance is the largest relative difference from Expected that still passes.

The model

An optical amplifier of gain $G$ and noise factor $F$ (the noise figure in linear units) adds amplified spontaneous emission. In a reference bandwidth $B$ , counting both polarizations, its power is

P_{\mathrm{ASE}} = (FG - 1)\,h\nu B = 2n_{\mathrm{sp}}(G-1)\,h\nu B

where $n_{\mathrm{sp}}$ is the spontaneous emission factor and $F = 1/G + 2n_{\mathrm{sp}}(G-1)/G$ in the usual optical definition. The limit $n_{\mathrm{sp}} = 1$ gives the 3 dB quantum limit of a high-gain amplifier. In a link of $N$ identical spans, each a loss $L$ followed by an amplifier with $G = L$ , the signal returns to the launch power $P_{\mathrm{launch}}$ after every amplifier and the noise of all of them adds:

\mathrm{OSNR} = \frac{P_{\mathrm{launch}}}{N\,(FL - 1)\,h\nu B} \;\approx\; 58\ \mathrm{dB} + P_{\mathrm{launch}}[\mathrm{dBm}] - L[\mathrm{dB}] - \mathrm{NF}[\mathrm{dB}] - 10\log_{10}N

The 58 dB is $-10\log_{10}(h\nu B / 1\ \mathrm{mW})$ for 0.1 nm at 1550 nm, and the approximation drops the 1 beside $FL$ . For stages in series (amplifiers, and passive losses whose noise factor equals their loss) the Friis formula gives the noise factor of the chain,

F_{\mathrm{tot}} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1G_2} + \cdots

so the first stage dominates when its gain is high, and a loss in front of it adds its full value in dB. The model counts only linear noise from lumped amplifiers with the gain of each set to the loss of the span before it. It leaves out fiber nonlinearity, which sets the upper limit on useful launch power, and gain ripple, filter narrowing, distributed Raman gain and transceiver noise, all of which lower the OSNR a real link delivers. The required OSNR depends on the modulation format, symbol rate and forward error correction, and is an input.

Worked example

Launch 0 dBm per channel into 20 dB spans with 5 dB amplifiers. Each amplifier sees −20 dBm and adds −32.97 dBm of ASE in 0.1 nm (12.48 GHz, where $h\nu B$ is −57.96 dBm), so one span leaves an OSNR of 32.97 dB and ten spans 22.97 dB. The rule of thumb gives 22.96 dB. A receiver that needs 15 dB is met with 7.97 dB to spare, and the link could run to 62 spans before falling short. In a cascade, a 20 dB preamplifier with a 4.5 dB noise figure ahead of a 17 dB, 6 dB booster gives 4.55 dB for the pair; 3 dB of loss in front of the preamplifier raises that to 7.55 dB.

References: E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications, Wiley (1994). G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed., Wiley (2010). H. T. Friis, “Noise figures of radio receivers,” Proceedings of the IRE 32, 419–422 (1944).