230566 - FIBERS AND TELECOMMUNICATIONS

SOLUTIONS TO EXERCISES

1. Consider a single mode optical fiber with an attenuation of 0.2 dB/km and a dispersion limit of 200 Gbps·km. The transmitter power is 1 mW and the receiver sensitivity is 1E-5 mW.  The link operates at a rate of 2.4 Gbps.   Assume a 10 dB power margin for losses in connectors. Calculate the maximum length of the  optical link.

Solution

2. Suppose a 1 mW, 1550 nm signal is transmitted across a 5 km fiber, through an 8 x 8 passive star coupler, and through another 15 km of fiber before reaching its destination. No amplifiers are used. What is the power of the signal at the destination? (Consider a single mode optical fiber with an attenuation of 0.2 dB/km)

3. Consider a broadcast star network with N = 2^k nodes where k is an integer. The network is built out of 2 x 2 couplers with excess loss b and coupling coefficient (or splitting ratio in dB) a. Each transmitter has a laser with power Pt.

(a) Find the power levels received by the receivers when a single transmitter (say transmitter T1) transmits. That is, determine how many different power levels are received by the N receivers, and how many receivers receive each of these levels. Hint: Construct a tree with the transmitter at the root.

4. A 16 x 16 passive-star hub has been constructed from 1x2 splitters. Each 1x2 splitter results in a 3 dB power loss. Each host is up to 10 km away from the star, with a signal attenuation of 0.2 dB/km. If each host must receive signal power of at least 0.01 mW to clearly recognize signals, how strong must each host's transmission signal be? (Depends on your design of the passive-star as discussed in class.)

5. Let us consider the costs of deploying a point-to-point network, an active star (curb-switched network), and a passive optical network (PON) shown in next Fig. 

 Ten homes in a residential network wish to be connected to a central office (CO) via fiber, so as to receive a shared bandwidth connection of 1 Gbps.
Assume the following estimated costs (numbers are for example only):
(a) Cost of fiber installation: €200/meter
(b) Cost of curb switch: €15000 + €500 x number of ports
(c) Cost of passive optical splitter: €750 + €100 x number of ports
(d) Cost of a transceiver (either at CO/OLT or at ONU): €750
(e) Distance of homes from CO: 5 km
(f) Possible location of curb switch/splitter: 50 meters away from each home.

Compare the costs of network deployments using each of the three approaches. Please try to justify the importance of a PON.

6. Consider a PON which has 32 ONUs. Let the transmission power of the OLT transceiver be 0.01 mW, and the receiver be able to detect signals of at least 0.0001 mW for a reasonable bit-error rate. Assume that the splitter is 10% lossy (excess loss). The optical fiber has an attenuation of 0.2 dB/km. What is the maximum possible distance of an ONU from the OLT. What is the RTT corresponding to this distance.

7. Dry fibers have acceptable losses over a spectral region extending from 1.3 to 1.6 mm. Estimate the capacity of a WDM system covering this entire region using 40-Gb/s channels spaced apart by 50 GHz.

8. The C and L spectral bands cover a wavelength range from 1.53 to 1.61 mm. How many channels can be transmitted through WDM when the channel spacing is 25 GHz? What is the effective bit rate-distance product when a WDM signal covering the two bands using 10-Gb/s channels is transmitted over 2000 km?

Solution

9. 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.

Solution

10. 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 satisfactorily. 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?

Solution

11. A 1.3-mm 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 InGaAs p-i-n receiver has a sensitivity of 250 nW. Make the power budget and estimate the repeater spacing.

Solution