3.1 Fiber Attenuation
95
for example. Then at 1310 nm the optical power at 10 km P(10 km) as a fraction of
the input power P(0) is
P(10 km)
P(0)
= 10
−αz/10
= 10
−(0.35)(10)/10
= 0.447 = 44.7%
For operation at 1550 nm, the optical power at 10 km P(10 km) as a fraction of
the input power P(0) is
P(10 km)
P(0)
= 10
−αz/10
= 10
−(0.20)(10)/10
= 0.63 = 63%
This means that after a 10 km transmission distance, at 1310 nm the optical signal
power would decrease by 3.5 dB (that is, 10 log 0.447 = −3.5 dB) or be 44.7% of
the input power. Likewise, at 1550 nm the output optical power is 63% of the input
power (a decrease of 10 log 0.630 = −2.0 dB). Viewed alternatively, at 1310 nm the
loss over 10 km is (10 km) (0.35 dB/km) = 3.5 dB loss and at 1550 nm the loss over
10 km is (10 km) (0.20 dB/km) = 2.0 dB loss.
Figure 3.1 shows the relationship between decibels and power ratios ranging from
0.1 to 1.0. Thus, as shown in Example 3.1, the dashed lines illustrate that transmission
over a 10 km distance using a fiber with an attenuation of 0.5 dB/km results in a 5 dB
power attenuation yielding an output-to-input power ratio of 31.6%. Similarly, over
a 10 km distance a fiber with an attenuation of 0.3 dB/km results in a 3 dB power
attenuation yielding a power ratio of 50%.
Example 3.2 As Sect. 1.3 describes, optical powers are commonly expressed in units
of dBm, which is the decibel power level referred to 1 mW. Consider a 30 km long
Power ratio
1.0
0.5
0.2
0.1
Decibels (dB)
0
5
10
3
0.32
0.3 dB/km
0.5 dB/km
Examples for a 10-km
transmission distance
Fig. 3.1 The relationship between decibels and power ratios ranging from 0.1 to 1.0
95
for example. Then at 1310 nm the optical power at 10 km P(10 km) as a fraction of
the input power P(0) is
P(10 km)
P(0)
= 10
−αz/10
= 10
−(0.35)(10)/10
= 0.447 = 44.7%
For operation at 1550 nm, the optical power at 10 km P(10 km) as a fraction of
the input power P(0) is
P(10 km)
P(0)
= 10
−αz/10
= 10
−(0.20)(10)/10
= 0.63 = 63%
This means that after a 10 km transmission distance, at 1310 nm the optical signal
power would decrease by 3.5 dB (that is, 10 log 0.447 = −3.5 dB) or be 44.7% of
the input power. Likewise, at 1550 nm the output optical power is 63% of the input
power (a decrease of 10 log 0.630 = −2.0 dB). Viewed alternatively, at 1310 nm the
loss over 10 km is (10 km) (0.35 dB/km) = 3.5 dB loss and at 1550 nm the loss over
10 km is (10 km) (0.20 dB/km) = 2.0 dB loss.
Figure 3.1 shows the relationship between decibels and power ratios ranging from
0.1 to 1.0. Thus, as shown in Example 3.1, the dashed lines illustrate that transmission
over a 10 km distance using a fiber with an attenuation of 0.5 dB/km results in a 5 dB
power attenuation yielding an output-to-input power ratio of 31.6%. Similarly, over
a 10 km distance a fiber with an attenuation of 0.3 dB/km results in a 3 dB power
attenuation yielding a power ratio of 50%.
Example 3.2 As Sect. 1.3 describes, optical powers are commonly expressed in units
of dBm, which is the decibel power level referred to 1 mW. Consider a 30 km long
Power ratio
1.0
0.5
0.2
0.1
Decibels (dB)
0
5
10
3
0.32
0.3 dB/km
0.5 dB/km
Examples for a 10-km
transmission distance
Fig. 3.1 The relationship between decibels and power ratios ranging from 0.1 to 1.0