Question
Communication signals are transmitted over long distances through optic fibres.
A signal is transmitted along an optic fibre with attenuation per unit length of $0.40 \mathrm{~dB} \mathrm{~km}^{-1}$. The signal must be amplified when the power of the signal has fallen to $0.02 \%$ of the input power.
a. Describe why a higher data transfer rate is possible in optic fibres than in twisted pair cables.
b(i)State one cause of attenuation in the optic fibre.
$\mathrm{b}$ (iiDetermine the distance at which the signal must be amplified.
▶️Answer/Explanation
Ans:
a. fibres have broader bandwidth than cables
therefore can carry multiple signals simultaneously
b(i)absorption/scattering of light
OR
impurities in the “glass core of the» fibre
$
\mathrm{b} \text { (iigttenuation }=10 \log \left(2 \times 10^{-4}\right)=-37 \text { «dB» } \checkmark
$
amplification required after $\frac{37}{0.4}=92$ or 93 «km»
NOTE: Allow ECF from mp1 for wrong dB value.(eg: $42 \mathrm{~km}$ if \% symbol ignored).
Question
The refractive index $\mathrm{n}$ of a material is the ratio of the speed of light in a vacuum $\mathrm{c}$, to the speed of light in the material $\mathrm{V}$ or $\mathrm{n}=\frac{\mathrm{c}}{\mathrm{v}}$.
The speed of light in a vacuum $\mathrm{c}$ is $2.99792 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$. The following data are available for the refractive indices of the fibre core for two wavelengths of light:
a. Outline the differences between step-index and graded-index optic fibres.[2]
bi. Determine the difference between the speed of light corresponding to these two wavelengths in the core glass.[2]
bii. An input signal to the fibre consists of wavelengths that range from $1299 \mathrm{~nm}$ to $1301 \mathrm{~nm}$. The diagram shows the variation of intensity with time
of the input signal.$[2]$
Sketch, on the axes, the variation of signal intensity with time after the signal has travelled a long distance along the fibre.
biii.Explain the shape of the signal you sketched in (b)(ii).[2]
biv.A signal consists of a series of pulses. Outline how the length of the fibre optic cable limits the time between transmission of pulses in a practical
system.[2]
▶️Answer/Explanation
Ans:
a. refractive index of step index fibre is constant
refractive index of graded index fibre decreases with distance from axis/centre
graded index fibres have less dispersion
step index fibre: path of rays is in a zig-zag manner
graded index fibre: path of rays is in curved path
For MP2 do not accept vague statements such as “index increases/varies with distance from centre”.
bi. $\mathrm{v}=\frac{\mathrm{c}}{\mathrm{n}}=\mathrm{v}_{1299}=\frac{2.99792 \times 10^8}{1.45061}=2.06666 \times 10^8 \ll \mathrm{ms}^{-1} » \boldsymbol{A N D}$
$
\mathrm{V}_{1301}=\frac{2.99792 \times 10^8}{1.45059}=2.06669 \times 10^8 \ll \mathrm{ms}^{-1} »
$
OR
bii. pulse wider
pulse area smaller
For MP2 do not accept lower amplitude unless pulse area is also smaller.
biii.reference to dispersion
OR
reference to time/speed/path difference
reference to power loss/energy loss/scattering/attenuation
biv.longer cables give wider pulses
which overlap/interfere if $T$ too small/ $f$ too high OWTTE