Chromatic Dispersion Limits Explained: Why 400G-DR4 Fails at 2.5 km
O-band chromatic dispersion math for 400G-DR4 at 2.5 km, and why the failure is really the 802.3bs 3 dB insertion loss plus 3 dB penalty allocation, not dispersion.
The short answer
A 400G-DR4 link that is clean at 500 m and falls apart at 2.5 km is almost never losing to chromatic dispersion. In the 1304.5–1317.5 nm window that 400GBASE-DR4 occupies, standard G.652 fiber contributes about 0.6 to 1.6 ps/(nm·km), so 2.5 km accumulates 1.5 to 4 ps/nm. At 53.125 GBd the symbol period is 18.8 ps; 4 ps/nm of dispersion against a 0.1 nm source width moves the pulse by 0.4 ps. That is not a mechanism that closes an eye.
What runs out at 2.5 km is the budget. IEEE 802.3bs gives 400GBASE-DR4 a 6 dB power budget, but three of those decibels are a penalty allocation, only 3 dB is channel insertion loss, and the standard explicitly allows zero additional insertion loss. Push the distance to 2.5 km and the fiber term grows from 0.25 dB to roughly 1.25 dB — taken directly out of the connector allowance — while multipath interference (MPI) and reflectance from the extra mated pairs spend the penalty allocation that was never meant to cover them.
Dispersion is therefore the wrong suspect for a 2.5 km DR4 failure. Loss, endface quality, reflectance and FEC margin are the right ones; the arithmetic below shows how to tell them apart.
What dispersion looks like in the O-band
ITU-T G.652 does not pin the zero-dispersion wavelength; it allows λ₀ anywhere between 1300 and 1324 nm, with a zero-dispersion slope S₀ of at most 0.092 ps/(nm²·km). Dispersion follows from those two numbers:
D(λ) = (S₀ / 4) · (λ − λ₀⁴ / λ³)
Close to λ₀ the linear form D ≈ S₀·(λ − λ₀) is within about 5%, which is enough for planning. The 24 nm window for λ₀ is the reason two fibers that both carry a G.652 compliance certificate can differ by several ps/(nm·km) on the same wavelength — and why a reach calculation has to use the worst case, not the typical fiber.
| Wavelength | D at λ₀ = 1300 nm | D at λ₀ = 1310 nm | D at λ₀ = 1324 nm |
|---|---|---|---|
| 1271 nm (FR4 lane 0) | −2.76 ps/(nm·km) | −3.76 | −5.19 (worst case) |
| 1291 nm (FR4 lane 1) | −0.84 | −1.79 | −3.15 |
| 1304.5 nm (DR4 lower edge) | +0.41 | −0.51 | −1.83 |
| 1311 nm (FR4 lane 2) | +1.00 | +0.09 | −1.21 |
| 1317.5 nm (DR4 upper edge) | +1.58 (worst case) | +0.68 | −0.60 |
| 1331 nm (FR4 lane 3) | +2.75 | +1.89 | +0.64 |
| 1550 nm (C-band reference) | +18.0 | +17.5 | +16.7 |
The DR4 band sits in the flat part of the curve: worst case 1.58 ps/(nm·km) against 17 ps/(nm·km) in the C-band. And 1311 nm is dispersion-free for any compliant fiber, which is why both the first single-mode systems and today's datacenter optics chose this neighbourhood.
From ps/nm to an actual penalty
The first-order pulse spread is the product of dispersion, length and source width:
Δτ = D · L · Δλ
For an intensity-modulated signal the more useful quantity is the frequency at which the two modulation sidebands arrive in antiphase and the fiber response nulls:
f_notch = √( c / (2 · D·L · λ²) )
Both forms ignore chirp, but they are conservative and answer the only question that matters first: can dispersion bite at all? Compare f_notch with the lane's Nyquist frequency — 26.6 GHz for 53.125 GBd PAM4, 12.9 GHz for 25.78 GBd NRZ.
| Scenario | D | D·L | Δτ at 0.1 nm source | f_notch |
|---|---|---|---|---|
| DR4, 500 m at 1317.5 nm (worst case) | 1.58 ps/(nm·km) | 0.8 ps/nm | 0.08 ps | 333 GHz |
| DR4, 2.5 km at 1317.5 nm (worst case) | 1.58 | 4.0 ps/nm | 0.40 ps | 149 GHz |
| FR4, 2 km at 1331 nm (worst case) | 2.75 | 5.5 ps/nm | 0.55 ps | 126 GHz |
| FR4, 2 km at 1271 nm (λ₀ = 1324 nm) | 5.19 | 10.4 ps/nm | 1.04 ps | 95 GHz |
| ER4-class, 40 km at 1309 nm | 1.40 | 56 ps/nm | 5.6 ps | 40 GHz |
| 100GBASE-LR4, 10 km at 1311 nm | 1.21 | 12 ps/nm | 1.2 ps | 85 GHz |
| C-band, 80 km at 1550 nm | 17.0 | 1360 ps/nm | 136 ps | 6.8 GHz |
Every O-band case has its notch at least 95 GHz — 3.5× the 26.6 GHz Nyquist frequency of a 400G lane. The C-band case at 80 km notches at 6.8 GHz, below what a 10G NRZ signal needs: that is the textbook dispersion-limited link, and a different regime entirely.
The 40 km ER4-class row is the middle ground: a 40 GHz notch does not kill a 25.78 GBd signal outright, but the phase curvature inside the band consumes a real share of the 2.5 dB TDP the standards allocate.
The budget that actually runs out
Here is the DR4 link model from 802.3bs, and it deserves to be read carefully:
| Parameter | 400GBASE-DR4 value |
|---|---|
| Power budget (for maximum TDP) | 6 dB |
| Operating distance | 500 m |
| Channel insertion loss | 3 dB |
| Allocation for penalties (at max TDP) | 3 dB |
| Additional insertion loss allowed | 0 dB |
The 6 dB is not six decibels of fiber. Half of it is penalties, and the "additional insertion loss allowed = 0 dB" line forbids trading penalty headroom for extra cable. Now look at what the 3 dB channel insertion loss is made of. The standard computes it as the rated distance times 0.5 dB/km at 1304.5 nm, plus an allocation for connection and splice loss:
| Item | 500 m design | 2.5 km design |
|---|---|---|
| Fiber at the 0.5 dB/km allocation | 0.25 dB | 1.25 dB |
| Remaining connector/splice allowance | about 2.75 dB | about 1.75 dB |
| Installed fiber at 0.35 dB/km (typical) | 0.18 dB | 0.88 dB |
| MPO-12 APC mated pair, both ends (typical) | 0.70 dB | 0.70 dB |
| One patch-panel adapter pair | 0.50 dB | 0.50 dB |
| Splice case (two splices) | 0.20 dB | 0.20 dB |
| Realistic total | 1.58 dB | 2.28 dB |
Read the bottom two rows against the third. A 2.5 km trunk with two MPO ends and one patch panel lands at about 2.3 dB — inside the 3 dB channel loss, but leaving only 0.7 dB where the 500 m reference design left 1.4 dB. That 0.7 dB is the whole allowance for a re-polished connector, a max-loss MPO pair (commonly specified at 0.75 dB, not 0.35 dB), a dirty endface, or a badly measured splice — and none of it can be borrowed from the penalty allocation.
This is why field reports disagree. Links at 2.3 dB work. Links at 2.5 dB with a max-loss MPO pair, a UPC plug in an APC adapter, and a module near its 3.4 dB TDECQ limit do not. The distance did not fail; the stack did.
Why the standard stops at 500 m
Four mechanisms are pinned to the reference channel rather than to distance in general:
- TDP/TDECQ is measured, not derived. The transmitter is characterised against a defined channel including that channel's dispersion and MPI. Beyond it nothing is promised; with 0.7 dB of margin, "nearly flat" is not zero.
- MPI is a noise floor, not a loss. Each extra mated pair adds a double-reflection path whose interference is signal-dependent, degrading BER at unchanged receive power. It is the most common cause of "Rx power is fine, link is bad."
- Reflectance grows with interfaces. 802.3bs caps maximum discrete reflectance at −35 dB and receiver reflectance at −26 dB. One UPC plug in an APC adapter can violate both locally.
- There is no in-module FEC to buy margin back. DR4 relies on the host's KP4 RS(544,514) code, whose pre-FEC threshold is around 2.4×10⁻⁴ BER. Near that threshold, an extra decibel of penalty converts into post-FEC errors almost one for one.
The general accounting method — span loss, penalties, margin, and where each decibel comes from — is laid out in the 400G/800G link budget walkthrough; the standard-by-standard mapping of which document defines which PMD is in the IEEE 802.3 400G/800G standards map.
Where dispersion really does bind
| Interface | Band / lanes | Rated reach | Accumulated D·L | What actually limits it |
|---|---|---|---|---|
| 400GBASE-DR4 | 1304.5–1317.5 nm, 8 parallel fibers | 500 m | ≤ 0.8 ps/nm | insertion loss, MPI, reflectance |
| 400GBASE-FR4 | 4 CWDM lanes, 1271–1331 nm, duplex | 2 km | ≤ 10.4 ps/nm | loss and penalty allocation |
| 400GBASE-ER8 | 8 LAN-WDM lanes, O-band | 40 km | tens of ps/nm | TDP allocation, receiver sensitivity |
| 100GBASE-LR4 | 4 LAN-WDM lanes near 1310 nm | 10 km | ≈ 12 ps/nm | loss, not dispersion |
| 10G/25G in C-band | 1550 nm, single λ | 40–80 km | 680–1360 ps/nm | genuine dispersion limit |
| 400ZR coherent | C-band, DSP-equalised | 80–120 km | 1360–2040 ps/nm | OSNR, not residual CD |
Dispersion becomes a design constraint when you leave the O-band, not when you lengthen the cable. Coherent 400ZR carries the same 1360 ps/nm that would destroy a 10G direct-detect link, paying for it in OSNR instead; see the 400ZR OSNR calculation.
Diagnosing a 2.5 km DR4 link
flowchart TD
A[Link down or high BER] --> B{DDM Rx power within<br/>rated range?}
B -- No --> C[Loss problem: measure IL<br/>against 3 dB budget]
B -- Yes --> D{Endface polish matches?<br/>APC vs UPC, MPO clean?}
D -- No --> E[Clean or replace cord<br/>re-test pre-FEC BER]
D -- Yes --> F{Pre-FEC BER near<br/>2.4E-4 KP4 threshold?}
F -- Yes --> G[Reflectance or MPI:<br/>count mated pairs,<br/>check ORL, swap worst cord]
F -- No --> H{All lanes degraded<br/>or only some?}
H -- Some --> I[Swap module and cord,<br/>compare TDECQ/DDP]
H -- All --> J[Distance exceeds spec:<br/>move to FR4 duplex<br/>or ER8/ZR]Power first: cheap and quantitative. Then polish and cleanliness, the highest-yield fix on marginal links. Then BER structure — all eight lanes failing at once points at the plant or the distance, while one or two degraded lanes point at a module, a cord, or a single bad fiber in the trunk. The full isolation procedure, including the cases where the port never leaves down state, is in the not-linking troubleshooting guide.
Practical rules for the 2.5 km case
- Treat 500 m as a contract, not a cliff. A 2.5 km DR4 link at 2.2 dB may run for years, but it is outside the specification: no guaranteed TDECQ, no guaranteed MPI tolerance, no recourse if a new batch of modules behaves differently.
- Count mated interfaces, not just kilometres. At 0.35 dB per APC pair, one extra patch panel costs the same as 1 km of fiber. A duplex FR4 link removes six fibers and two MPO interfaces — often the real reason it survives where a DR4 trunk does not.
- Budget reflectance explicitly. APC everywhere, clean endfaces before first light-up, and verify ORL on marginal links. Loss you can measure on DDM; a reflection you cannot see.
- Watch pre-FEC BER over temperature, not Rx power. Thermal drift moves both the transmitter's TDECQ and connector loss; BER responds first.
- If the link must be compliant, change the interface. ER8 or a coherent 400ZR option removes the argument entirely, and the QSFP-DD vs OSFP comparison covers the packaging side of that decision.
Bottom line
- At 1310 nm over 2.5 km, accumulated dispersion is 1.5–4 ps/nm and the dispersion notch sits above 140 GHz — three orders of magnitude away from being the limiting mechanism.
- The DR4 failure mode at 2.5 km is budget arithmetic: 1.25 dB of fiber replaces 0.25 dB, the connector allowance drops from 2.75 dB to 1.75 dB, and the 3 dB penalty allocation cannot legally be spent on loss.
- Dispersion becomes the binding constraint in the C-band, where 80 km of G.652 accumulates 1360 ps/nm and the notch falls to 6.8 GHz.
- Diagnose in the order power → polish → BER structure → distance. Blaming dispersion sends you looking for a compensator that does not exist at this wavelength.
Compiled from IEEE 802.3bs and 802.3cu PMD parameters, ITU-T G.652 dispersion specifications, and published transceiver datasheets; all calculations recomputed for this note, original synthesis, no reproduction.
FAQ
- Does 400G-DR4 work at 2 km?
- Not to specification. IEEE 802.3bs rates 400GBASE-DR4 at 500 m with 3 dB channel insertion loss, and it allocates zero additional insertion loss. A 2 km run usually has 1.5–2.2 dB of loss and will often light up, but every dB above the connector allowance at 500 m is outside the contract, so treat it as an engineering risk rather than a design point.
- How much chromatic dispersion can a 50G PAM4 lane tolerate?
- At 53.125 GBd the symbol period is 18.8 ps, and the O-band 400G lanes are specified with a transmitter and dispersion penalty of 2.5 dB (DR4) or a TDECQ of 3.4 dB (FR4). In practice tens of ps/nm are harmless; the penalty only becomes visible when the accumulated D·L product reaches the hundreds of ps/nm, which at 1310 nm needs tens of kilometres, not 2.5.
- Why does DR4 stop at 500 m if 2.5 km only adds about 1 dB?
- Because the standard's 3 dB channel loss already contains an allowance for connectors and splices — roughly 2.75 dB once the 500 m of fiber is accounted for. Extending to 2.5 km raises the fiber term to about 1.25 dB and silently takes that dB out of the connector allowance, while multipath interference and reflectance from the extra mated pairs add penalty on top.
- What should I check first when a 2.5 km DR4 link will not come up?
- Check the endface polish and cleanliness before anything else. A UPC plug into an APC MPO adapter, or a contaminated 12-fiber endface, produces exactly the symptom people attribute to dispersion: normal receive power, rising pre-FEC BER, and a link that never reaches post-FEC error-free.
- Is dispersion compensation ever needed at 1310 nm?
- No. With D between roughly −5 and +3 ps/(nm·km) across the O-band, a 2.5 km span accumulates a few ps/nm, and the resulting notch frequency sits well above 100 GHz — more than three times the Nyquist frequency of a 53.125 GBd signal. Dispersion compensation belongs in the C-band at 1550 nm, where 80 km of G.652 accumulates about 1360 ps/nm.