Optical Fiber Transport & Coherent DWDM Telecom
Optical DWDM EDFA Noise Figure & Cascaded OSNR Formula
Calculate 1550 nm C-Band Single-Span Optical Signal-to-Noise Ratio (0.1 nm reference bandwidth), Multi-Span ASE Accumulation Penalty 10*LOG10(N), Cascaded End-to-End OSNR_dB = 58 + P_in_dBm - NF_dB - 10*LOG10(N), and Coherent FEC Margin.
Track Amplified Spontaneous Emission (ASE) across N identical EDFA fiber spans!
Long-haul Dense Wavelength-Division Multiplexing (DWDM) transport links periodically boost attenuated 1550 nm C-band channels using Erbium-Doped Fiber Amplifiers (EDFAs) whose gain exactly offsets each fiber span’s attenuation. However, every EDFA injects incoherent Amplified Spontaneous Emission (ASE) quantum noise bounded by the 3.0 dB high-gain inversion quantum limit! Under ITU-T G.697 in the standard 0.1 nm (12.5 GHz) optical reference bandwidth—where quantum noise floor h*nu*B_ref is -58.0 dBm—end-to-end Optical Signal-to-Noise Ratio across N identical spans is OSNR_dB = 58 + P_in_dBm - NF_dB - 10 * LOG10(N), where P_in_dBm is per-channel optical power entering each EDFA (launch power minus span loss)!
Verify in a shared DWDM link-engineering workbook—EDFA_Input_Power P_in = -20.0 dBm (e.g., +2 dBm launch minus 22 dB fiber span loss, B2), EDFA_Noise_Figure NF = 5.0 dB (B3), Identical_Fiber_Spans N = 10 (B4), and Coherent_FEC_OSNR_Limit = 18.0 dB (B5): Single-Span OSNR is 58 + (-20) - 5 = 33.00 dB (E2); 10-Span ASE Accumulation Penalty is 10 * LOG10(10) = 10.00 dB (E3); End-to-End Cascaded OSNR equals 33.00 - 10.00 = 23.00 dB (E4); leaving a +5.00 dB Coherent Pre-FEC System Margin (E5)! If a transport peer proposes extending the unregenerated optical path to N = 100 submarine spans via a cell suggestion, inspect E4 dropping to 13.00 dB (-5.00 dB FEC margin deficit) before accepting!
| DWDM 1550nm Link Metric (Pin=-20 dBm, NF=5.0 dB, N=10 Spans, FEC=18.0 dB) | Formula | Verified Output |
|---|---|---|
| Single-Span OSNR (0.1 nm BW) | 58 + P_in_dBm - NF_dB | 33.00 dB |
| Multi-Span ASE Penalty (dB) | 10 * LOG10(N_spans) | 10.00 dB (20.00 dB @ N=100) |
| End-to-End Cascaded OSNR (dB) | 58 + P_in_dBm - NF_dB - 10*LOG10(N) | 23.00 dB (13.00 dB @ N=100) |
| Coherent Pre-FEC Margin (dB) | Cascaded_OSNR_dB - FEC_Limit_dB | +5.00 dB (-5.00 dB @ N=100) |
ITU-T C-Band Cascaded EDFA OSNR Formula
Enforce the physical 3.0 dB phase-insensitive EDFA quantum noise-figure floor (NF_dB >= 3), span count N >= 1, and positive FEC threshold!
=LET(p_in, B2, nf_d, B3, n_sp, B4, fc_t, B5, IF(OR(nf_d < 3, n_sp < 1, fc_t <= 0), "Invalid EDFA Link Budget", ROUND(58 + p_in - nf_d - 10 * LOG10(n_sp), 2)))100-Span Transoceanic Cascade Check & 3 dB Quantum Floor Guard
Set Fiber_Spans_N B4 = 100: ASE penalty doubles to 20.00 dB, pulling OSNR down to 13.00 dB (-5.00 dB below FEC threshold). Entering NF = 2.5 dB (< 3.0 dB quantum limit) triggers "Invalid EDFA Link Budget"!
=IF(ISTEXT(E4), E4, ROUND(E4 - B5, 2))Try the example
Use the original values or change them to test your understanding.