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ڈسپرشن اور بینڈوڈتھ
ہماری ٹیم ترجمے پر کام کر رہی ہے۔ یہ مضمون عارضی طور پر اردو میں دستیاب نہیں ہے، اس لیے اسے انگریزی میں دکھایا جا رہا ہے۔
Attenuation makes a pulse weaker; dispersion makes it wider. Different parts of the light — different modes, different wavelengths, different polarizations — travel at slightly different speeds and arrive at slightly different times, so a sharp "1" smears into its neighbours. At low rates and short distances this is invisible; at 10 Gb/s over 80 km or at 25 Gb/s over 100 m of multi-mode it is the limit. This page explains the three kinds of dispersion, the bandwidth–distance product of multi-mode fibre, how to estimate a dispersion-limited reach, and how modules and systems compensate.
Three kinds of dispersion
| Kind | Cause | Where it dominates | Typical size |
|---|---|---|---|
| Modal (intermodal) | different modes take different paths | multi-mode fibre | ns/km in step-index; ~0.1–0.5 ns/km graded-index; described as bandwidth in MHz·km |
| Chromatic | the glass's index depends on wavelength (material) and the guide geometry adds its own (waveguide); a source has non-zero spectral width | single-mode at 1550 nm; long links at 10G+ | 17 ps/(nm·km) at 1550 on G.652; ≈ 0 at 1310 |
| Polarization-mode (PMD) | the two polarization states travel at slightly different speeds due to fibre asymmetry | 40G+ NRZ over long fibre; old fibre | 0.05–0.5 ps/√km |
Modal dispersion and multi-mode bandwidth
Multi-mode fibre is rated by effective modal bandwidth (EMB) in MHz·km: the frequency at which the fibre's response has fallen 3 dB, times the length. Bandwidth divides by length:
| Grade | EMB at 850 nm | Bandwidth over 100 m | Bandwidth over 300 m |
|---|---|---|---|
| OM1 | 200 MHz·km | 2 GHz | 0.67 GHz |
| OM2 | 500 | 5 GHz | 1.7 GHz |
| OM3 | 2 000 | 20 GHz | 6.7 GHz |
| OM4 | 4 700 | 47 GHz | 15.7 GHz |
A rule of thumb: a link needs bandwidth ≈ 0.7 × bit rate for NRZ. 10 Gb/s wants ~7 GHz → OM3 to ~285 m (standard says 300 m); 25 Gb/s wants ~17.5 GHz → OM4 to ~270 m in theory, but the receiver's dispersion tolerance and VCSEL spectral width bring the standard to 100 m. Hence the reach table:
| Rate per lane | OM3 | OM4 | Limit |
|---|---|---|---|
| 1 Gb/s | 550–1 000 m | 550–1 100 m | attenuation as much as bandwidth |
| 10 Gb/s | 300 m | 400 m | modal bandwidth |
| 25 Gb/s NRZ | 70 m | 100 m | modal + chromatic (VCSEL spectral width) |
| 50 Gb/s PAM4 | 70 m | 100 m | same, plus PAM4 SNR penalty |
| 100 Gb/s PAM4 (802.3db) | — | 50–100 m | with DSP equalisation |
Full table: Reach tables. The launch condition (encircled flux) is standardised so these figures hold with real VCSELs.
Chromatic dispersion on single-mode fibre
The dispersion coefficient D (ps per nm of source width per km) crosses zero near 1 310 nm in standard G.652 fibre and is ≈ +17 ps/(nm·km) at 1 550 nm. Pulse spreading:
Δt = D × Δλ × L
| Source | Spectral width Δλ | D at λ | L | Δt | Bit period (10G ≈ 100 ps) |
|---|---|---|---|---|---|
| DFB laser at 1310 nm | 0.1 nm (or 1 nm −20 dB) | ≈ 0–3 ps/(nm·km) | 10 km | < 10 ps | fine |
| DFB at 1550 nm, 10G, DML | 0.2 nm (chirp widens it) | 17 | 80 km | 270 ps | too much — needs EML (low chirp) or DCM |
| EML at 1550 nm, 10G | ~0.1 nm effective | 17 | 80 km | ~140 ps → tolerable with penalty | 10GBASE-ZR |
| Fabry-Pérot laser at 1310 | 3–5 nm | 3 | 2 km | 20–30 ps | fine at 1G, marginal at 10G |
| LED at 1300 (legacy) | 50–100 nm | 3 | 2 km | 300–600 ps | 100 Mb/s only |
| VCSEL 850 nm on OM4 | 0.5 nm RMS | ~ −100 ps/(nm·km) at 850 | 0.1 km | 5 ps | chromatic matters at 25G+ |
Dispersion tolerance appears in datasheets as ps/nm (e.g. 800 ps/nm for a 40 km ER module = 17 × 40 × ~1.2 nm): the link's D × L must stay below it (Reading a datasheet).
Dispersion-limited reach (NRZ, uncompensated)
| Rate | 1310 nm on G.652 | 1550 nm on G.652 | Note |
|---|---|---|---|
| 2.5 Gb/s | > 100 km | ~600–1 000 km | attenuation limits first |
| 10 Gb/s | ~40–60 km (source-limited) | ~60–80 km (EML), ~10–20 km (DML) | why 10G ER/ZR use EML |
| 25 Gb/s | 10 km (25GBASE-LR) | ~10–15 km | 25GBASE-ER at 1550 needs careful design |
| 40 Gb/s serial | ~4 km | ~4 km | reason 40G/100G went to 4 × 10G/25G WDM |
| 100 Gb/s single λ PAM4 (DR/FR/LR1) | 2–10 km at 1310 | — | 1310 nm chosen for ≈ 0 dispersion; DSP handles the rest |
Rule of thumb: reach scales with 1/(bit rate)² for a fixed source width — doubling the rate cuts dispersion-limited distance by four.
Compensation and mitigation
| Method | Where | How |
|---|---|---|
| Choose 1310 nm | DR/FR/LR at 100G+ | zero-dispersion window; pays 0.35 dB/km instead of 0.2 |
| Low-chirp source (EML, external modulator) | 10G ER/ZR, DWDM 10G | narrower effective spectrum (Lasers) |
| Dispersion compensation module (DCM) | 10G DWDM spans | spool of negative-dispersion fibre or fibre Bragg grating cancels D × L |
| Dispersion-shifted / NZ-DSF fibre (G.653/G.655) | legacy long-haul plant | zero or small D at 1550 |
| Electronic dispersion compensation | 10GBASE-LRM (EDC in host), PAM4 DSP (FFE/DFE/MLSE) | equaliser undoes the smear digitally (DSP) |
| Coherent detection + DSP | 100G–800G ZR/ZR+ | dispersion compensated entirely in the digital domain, thousands of ps/nm (Coherent) |
| FEC | 25G+ | corrects the errors dispersion causes rather than preventing them (FEC & AN) |
Polarization-mode dispersion
Fibre is never perfectly round; the two polarization axes see slightly different indices and the pulse splits by a differential group delay that grows with the square root of length (random mode coupling). Modern fibre: ≤ 0.1 ps/√km → 1 ps over 100 km, harmless up to 40 Gb/s NRZ. Old (pre-1995) fibre: 0.5–2 ps/√km, a problem at 10G over 100 km+ and a reason coherent DSP tracks polarization continuously.
How dispersion shows up
| Observation | Meaning |
|---|---|
| Rx power well above sensitivity, yet errors or no link | dispersion (or reflections) — power is not the problem (Rx power & budget) |
| Link works at 1G, fails at 10G on the same fibre | modal bandwidth (MMF) or DML chirp at 1550 (SMF) |
| 10 km LR module fine, 40 km ER fine, ZR marginal | chromatic dispersion accumulating |
| FEC corrected errors high, uncorrectable rare | eye closure from dispersion partially corrected (VDM & FEC metrics) |
| Reach shortfall on OM3 with a "300 m" module | encircled-flux non-compliance or OM3 mislabelled OM2 |
In CodingBox
Dispersion tolerance is not stored in the EEPROM, but the fields that predict it are: wavelength (1310 vs 1550), laser type from the compliance codes (SR VCSEL, LR DFB, ER EML), and the OM3/OM4/SMF length fields the vendor rated the module for. CodingBox shows them so a "why does this 1550 nm module not do 80 km" question has data behind it (Check transceiver).
The other limit at high launch power — self- and cross-phase modulation, four-wave mixing, Brillouin and Raman scattering, and why dispersion actually helps against some of them: Non-linear effects.