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An LED operating at $850 \mathrm{~nm}$ has a spectral width of $45 \mathrm{~nm}$. What is the pulse spreading in $\mathrm{ns} / \mathrm{km}$ due to material dispersion?
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Solution:

λ = 850 nm

σ = 45 nm

pulse broadening due to material dispersion is given by,

$\sigma_m=\sigma L M$

$ \text { Material dispersion constant } D_{\text {mat }}=\frac{-\lambda}{c} \cdot \frac{d^2 n}{d \lambda^2} $

For LED sources operating at 850 nm,

$ \left|\lambda^2 \frac{d^2 n}{d \lambda^2}\right|=0.025 $

$ …

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