PROBLEMS 219
Problems
5.1 A distribution network uses an optical bus to distribute the signal to 10 users.
Each optical tap couples 10% of the power to the user and has 1-dB insertion
loss. Assuming that the station 1 transmits 1 mW of power over the optical bus,
calculate the power received by the stations 8, 9, and 10.
5.2 A cable-television operator uses an optical bus to distribute the video signal to
its subscribers. Each receiver needs a minimum of 100 nW to operate satisfacto-
rily. Optical taps couple 5% of the power to each subscriber. Assuming 0.5 dB
insertion loss for each tap and 1 mW transmitter power, estimate the number of
subscribers that can be added to the optical bus?
5.3 A star network uses directional couplers with 0.5-dB insertion loss to distribute
data to its subscribers. If each receiver requires a minimum of 100 nW and each
transmitter is capable of emitting 0.5 mW, calculate the maximum number of
subscribers served by the network.
5.4 Make the power budget and calculate the maximum transmission distance for a
1.3-μm lightwave system operating at 100 Mb/s and using an LED for launching
0.1 mW of average power into the fiber. Assume 1-dB/km fiber loss, 0.2-dB
splice loss every 2 km, 1-dB connector loss at each end of fiber link, and 100-
nW receiver sensitivity. Allow 6-dB system margin.
5.5 A 1.3-μm long-haul lightwave system is designed to operate at 1.5 Gb/s. It is
capable of coupling 1 mW of average power into the fiber. The 0.5-dB/km fiber-
cable loss includes splice losses. The connectors at each end have 1-dB losses.
The InGaAsp–i–nreceiver has a sensitivity of 250 nW. Make the power budget
and estimate the repeater spacing.
5.6 Prove that the rise timeTrand the 3-dB bandwidth∆fof aRCcircuit are related
byTr∆f= 0 .35.
5.7 Consider a super-Gaussian optical pulse with the power distribution
P(t)=P 0 exp[−(t/T 0 )^2 m],
where the parametermcontrols the pulse shape. Derive an expression for the
rise timeTrof such a pulse. Calculate the ratioTr/TFWHM, whereTFWHMis the
full width at half maximum, and show that for a Gaussian pulse (m=1) this ratio
equals 0.716.
5.8 Prove that for a Gaussian optical pulse, the rise timeTrand the 3-dB optical
bandwidth∆fare related byTr∆f= 0 .316.
5.9 Make the rise-time budget for a 0.85-μm, 10-km fiber link designed to operate at
50 Mb/s. The LED transmitter and the Sip–i–nreceiver have rise times of 10 and
15 ns, respectively. The graded-index fiber has a core index of 1.46,∆= 0 .01,
andD=80 ps/(km-nm). The LED spectral width is 50 nm. Can the system be
designed to operate with the NRZ format?
