Fiber Bandwidth Calculation

Calculate bandwidth limitations from chromatic dispersion, modal dispersion (MMF), and PMD for various fiber types and link configurations.

Model: Textbook approximation

Fiber TypeLength (km)Wavelength (nm)Source rms Spectral Width σ_λ (nm)Bit Rate (Gb/s)PMD Coefficient (ps/√km)

Bit-Rate Limit

14.5 Gb/s

over 10 km, all mechanisms

Max Reach at 10 Gb/s

17.5 km

D(λ)

17.46 ps/(nm·km)

Chromatic

σ = 17.29 ps

optimum input pulse · B ≤ 14.5 Gb/s

PMD

⟨Δτ⟩ = 0.316 ps

B ≤ 0.1/⟨Δτ⟩ = 316 Gb/s

Combined rms Width

σ = 17.29 ps

chromatic ⊕ modal · B ≤ 14.5 Gb/s

Bit-Rate Limit vs Distance

Maximum Reach by Data Rate

Green: reaches the 10 km link length.

Key Formulas

D(λ) = (S₀/4)(λ − λ₀⁴/λ³)

σ_CD² ≈ (|D|Lσ_λ)² + |β₂|L [input pulse width chosen to minimise σ; β₃ also included]

σ_modal = 0.187 · L / (BW·L) [Gaussian with the rated 3-dB bandwidth]

σ = √(σ_CD² + σ_modal²), B ≤ 1/(4σ)

PMD: ⟨Δτ⟩ = PMD·√L ≤ 0.1/B

Modal bandwidth at 850 nm: OM1 200, OM2 500, OM3 2000 (EMB), OM4 4700 (EMB) MHz·km

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Gaussian rms budget, 4Bσ ≤ 1: chromatic (spec-limit λ₀, S₀, optimum input pulse) and modal (rated 850 nm bandwidth) add in quadrature; PMD by ⟨Δτ⟩ ≤ 0.1 T. SMF only above its 1260 nm cable cutoff. Ignores DMD, launch and transceiver limits.

Agrawal G. P. (2010). Fiber-Optic Communication Systems, 4th ed., §2.4.3 (4Bσ ≤ 1). Wiley. doi:10.1002/9780470918524
ITU-T G.652 (11/2016). Characteristics of a single-mode optical fibre and cable. D(λ) = (S₀/4)(λ − λ₀⁴/λ³) with 1300 ≤ λ₀ ≤ 1324 nm and S₀ ≤ 0.092 ps/(nm²·km). itu.int
Prysmian BendBright OM3 datasheet (IEC 60793-2-10 A1a.2): 1295 ≤ λ₀ ≤ 1340 nm, S₀ ≤ 0.105 ps/(nm²·km). prysmian.com
ISO/IEC 11801-1:2017. Information technology — Generic cabling for customer premises. Minimum modal bandwidth at 850 nm: OM1 200, OM2 500, OM3 2000 (EMB), OM4 4700 (EMB) MHz·km.
Poole C. D. (1988). Statistical treatment of polarization dispersion in single-mode fiber. Opt. Lett. 13, 687. Maxwellian statistics of the DGD. doi:10.1364/ol.13.000687

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Fiber Bandwidth Calculation

Calculate bandwidth limitations from chromatic dispersion, modal dispersion (MMF), and PMD for various fiber types and link configurations.

Fiber TypeLength (km)Wavelength (nm)Source rms Spectral Width σ_λ (nm)Bit Rate (Gb/s)PMD Coefficient (ps/√km)

Bit-Rate Limit

14.5 Gb/s

over 10 km, all mechanisms

Max Reach at 10 Gb/s

17.5 km

D(λ)

17.46 ps/(nm·km)

Chromatic

σ = 17.29 ps

optimum input pulse · B ≤ 14.5 Gb/s

PMD

⟨Δτ⟩ = 0.316 ps

B ≤ 0.1/⟨Δτ⟩ = 316 Gb/s

Combined rms Width

σ = 17.29 ps

chromatic ⊕ modal · B ≤ 14.5 Gb/s

Bit-Rate Limit vs Distance

Maximum Reach by Data Rate

Green: reaches the 10 km link length.

Key Formulas

D(λ) = (S₀/4)(λ − λ₀⁴/λ³)

σ_CD² ≈ (|D|Lσ_λ)² + |β₂|L [input pulse width chosen to minimise σ; β₃ also included]

σ_modal = 0.187 · L / (BW·L) [Gaussian with the rated 3-dB bandwidth]

σ = √(σ_CD² + σ_modal²), B ≤ 1/(4σ)

PMD: ⟨Δτ⟩ = PMD·√L ≤ 0.1/B

Modal bandwidth at 850 nm: OM1 200, OM2 500, OM3 2000 (EMB), OM4 4700 (EMB) MHz·km

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Agrawal G. P. (2010). Fiber-Optic Communication Systems, 4th ed., §2.4.3 (4Bσ ≤ 1). Wiley. doi:10.1002/9780470918524
ITU-T G.652 (11/2016). Characteristics of a single-mode optical fibre and cable. D(λ) = (S₀/4)(λ − λ₀⁴/λ³) with 1300 ≤ λ₀ ≤ 1324 nm and S₀ ≤ 0.092 ps/(nm²·km). itu.int
Prysmian BendBright OM3 datasheet (IEC 60793-2-10 A1a.2): 1295 ≤ λ₀ ≤ 1340 nm, S₀ ≤ 0.105 ps/(nm²·km). prysmian.com
ISO/IEC 11801-1:2017. Information technology — Generic cabling for customer premises. Minimum modal bandwidth at 850 nm: OM1 200, OM2 500, OM3 2000 (EMB), OM4 4700 (EMB) MHz·km.
Poole C. D. (1988). Statistical treatment of polarization dispersion in single-mode fiber. Opt. Lett. 13, 687. Maxwellian statistics of the DGD. doi:10.1364/ol.13.000687

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