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# Answer to Question #119250 in Electrical Engineering for Vineela

Question #119250
A delay difference of ‘x’ns between the slowest and fastest fiber with a core refractive index of 1.5 and refractive index difference of 2%. Estimate the following
The length of the optical fiber link
Bandwidth –length product for the maximum bit rate.
1
2020-06-05T05:36:49-0400

The delay difference is

"\\delta T_b\\approx\\frac{Ln_1\\Delta}{c}=\\frac{L\\cdot1.5\\cdot0.02}{2.998\\cdot10^6}=L\\cdot10^{-10}\\text{ s},"

where L is the length of the optical link, therefore, if "\\delta T_b=x\\cdot10^{-9},"

"L=10x\\text{ m}"

if x is measured in nanoseconds.

"\\sigma_s\\approx\\frac{Ln_1\\Delta}{2\\sqrt3 c}=\\frac{10x\\cdot1.5\\cdot0.02}{2\\sqrt3 \\cdot2.998\\cdot10^8}=2.889x\\cdot10^{-10}\\text{ s}."

Prior to find the bandwidth-length product, calculate the maximum bit rate:

"B_{T\\text{max}}=\\frac{0.2}{\\sigma_s}=\\frac{692.3}{x}\\cdot10^6\\text{ Hz}."

The bandwidth-length product is

"B_{T\\text{max}}\\cdot L=\\frac{692.3}{x}\\cdot10^6\\cdot10x=692.3\\cdot10^7\\text{ Hz}\\cdot\\text{km}."

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