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8 Digital Optical Fiber Links
(a) InGaAsP LED: −13-dBm fiber-coupled power
(b) InGaAspinphotodiode: −38-dBm sensitivity
(c) Graded-index fiber: 1.5-dB/km attenuation at 1300 nm
(d) Connector loss: 1 dB/connector
Allow a 6-dB system operating margin in each case.
8.4 An engineer has the following components available:
(a) GaAlAs laser diode operating at 850 nm and capable of coupling 1 mW
(0 dBm) into a fiber
(b) Ten sections of cable each of which is 500 m long, has a 4-dB/km
attenuation, and has connectors on both ends
(c) Connector loss of 2 dB/connector
(d) A pin photodiode receiver
(e) An avalanche photodiode receiver
Using these components, the engineer wishes to construct a 5-km link operating at 20 Mb/s. If the sensitivities of the pin and APD receivers are −45
and −56 dBm, respectively, show that the APD receiver should be used if a
6-dB operating margin is required for the system.
8.5 Using the step response g(t) = [1 − exp (−2πB e t)]u(t) from Eq. (8.4), show
that the 10-to-90% receiver rise time is given by Eq. (8.5). [Hint: First find
the values of t 10% and t 90% from g(t 10% ) = 0.1 and g(t 90% ) = 0.9. Then take
the natural log (ln) of each expression to find t rx = t 90% − t 10% which yields
Eq. (8.5).]
8.6 (a) Use Eq. (8.9) to verify the steps leading from Eqs. (8.11) to (8.12).
(b) As described in the text, show that Eq. (8.14) follows from Eqs. (8.10)
and (8.13).
8.7 A 90-Mb/s NRZ data transmission system that sends two DS3 (45-Mb/s)
channels uses a GaAlAs laser diode that has a 1-nm spectral width. The
rise time of the laser transmitter output is 2 ns. The transmission distance is
7 km over a graded-index fiber that has an 800-MHz·km bandwidth-distance
product.
(a) If the receiver bandwidth is 90 MHz and the mode-mixing factor q =
0.7, what is the system rise time? Does this rise time meet the NRZ
data requirement of being less than 70% of a pulse width?
(b) What is the system rise time if there is no mode mixing in the 7-km
link; that is, q = 1.0?
8.8 Verify the plot in Fig. 8.6 of the transmission distance versus data rate of
the following system. The transmitter is a GaAlAs laser diode operating at
850 nm. The laser power coupled into a fiber flylead is 0 dBm (1 mW), and
the source spectral width is 1 nm. The fiber has a 3.5-dB/km attenuation at
850 nm and a bandwidth of 800 MHz km. The receiver uses a silicon avalanche
photodiode that has the sensitivity versus data rate shown in Fig. 8.3. For
simplicity, the receiver sensitivity (in dBm) can be approximated from curve
8 Digital Optical Fiber Links
(a) InGaAsP LED: −13-dBm fiber-coupled power
(b) InGaAspinphotodiode: −38-dBm sensitivity
(c) Graded-index fiber: 1.5-dB/km attenuation at 1300 nm
(d) Connector loss: 1 dB/connector
Allow a 6-dB system operating margin in each case.
8.4 An engineer has the following components available:
(a) GaAlAs laser diode operating at 850 nm and capable of coupling 1 mW
(0 dBm) into a fiber
(b) Ten sections of cable each of which is 500 m long, has a 4-dB/km
attenuation, and has connectors on both ends
(c) Connector loss of 2 dB/connector
(d) A pin photodiode receiver
(e) An avalanche photodiode receiver
Using these components, the engineer wishes to construct a 5-km link operating at 20 Mb/s. If the sensitivities of the pin and APD receivers are −45
and −56 dBm, respectively, show that the APD receiver should be used if a
6-dB operating margin is required for the system.
8.5 Using the step response g(t) = [1 − exp (−2πB e t)]u(t) from Eq. (8.4), show
that the 10-to-90% receiver rise time is given by Eq. (8.5). [Hint: First find
the values of t 10% and t 90% from g(t 10% ) = 0.1 and g(t 90% ) = 0.9. Then take
the natural log (ln) of each expression to find t rx = t 90% − t 10% which yields
Eq. (8.5).]
8.6 (a) Use Eq. (8.9) to verify the steps leading from Eqs. (8.11) to (8.12).
(b) As described in the text, show that Eq. (8.14) follows from Eqs. (8.10)
and (8.13).
8.7 A 90-Mb/s NRZ data transmission system that sends two DS3 (45-Mb/s)
channels uses a GaAlAs laser diode that has a 1-nm spectral width. The
rise time of the laser transmitter output is 2 ns. The transmission distance is
7 km over a graded-index fiber that has an 800-MHz·km bandwidth-distance
product.
(a) If the receiver bandwidth is 90 MHz and the mode-mixing factor q =
0.7, what is the system rise time? Does this rise time meet the NRZ
data requirement of being less than 70% of a pulse width?
(b) What is the system rise time if there is no mode mixing in the 7-km
link; that is, q = 1.0?
8.8 Verify the plot in Fig. 8.6 of the transmission distance versus data rate of
the following system. The transmitter is a GaAlAs laser diode operating at
850 nm. The laser power coupled into a fiber flylead is 0 dBm (1 mW), and
the source spectral width is 1 nm. The fiber has a 3.5-dB/km attenuation at
850 nm and a bandwidth of 800 MHz km. The receiver uses a silicon avalanche
photodiode that has the sensitivity versus data rate shown in Fig. 8.3. For
simplicity, the receiver sensitivity (in dBm) can be approximated from curve