1.3 Decibel Notation
11
Transmission line
Point 1
Point 2
Signal amplitude
Point 3
Original
signal
Attenuated
signal
Amplified
signal
Amplifier
Fig. 1.5 Periodically placed amplifiers compensate for energy losses along a link
P 1
P 2
Transmission line
Point 1
Point 2
Signal amplitude
Fig. 1.6 Example of pulse attenuation in a link. P 1 and P 2 are the power levels of a signal at points
1 and 2
by many orders of magnitude can be compared easily when they are in decibel form.
For example, a power reduction by a factor of 1000 is a −30 dB loss, an attenuation
of 50% is a −3 dB loss, and a 10-fold amplification of the power is a +10 dB gain.
Another attractive feature of the decibel is that to measure the changes in the strength
of a signal, one merely adds or subtracts the decibel loss or gain numbers in a series
of connected optical link elements (e.g., optical fibers, couplers, power splitters, or
amplifiers) between two different points.
Example 1.3 Assume that after traveling a certain distance in some transmission
medium, the power of a signal is reduced to half, that is, P 2 = 0.5 P 1 in Fig. 1.6. At
this point, using Eq. (1.4) the attenuation or loss of power is
10 log
P 2
P 1
= 10 log
0.5P 1
P 1
= 10 log 0.5 = 10(−0.3) = −3 dB
11
Transmission line
Point 1
Point 2
Signal amplitude
Point 3
Original
signal
Attenuated
signal
Amplified
signal
Amplifier
Fig. 1.5 Periodically placed amplifiers compensate for energy losses along a link
P 1
P 2
Transmission line
Point 1
Point 2
Signal amplitude
Fig. 1.6 Example of pulse attenuation in a link. P 1 and P 2 are the power levels of a signal at points
1 and 2
by many orders of magnitude can be compared easily when they are in decibel form.
For example, a power reduction by a factor of 1000 is a −30 dB loss, an attenuation
of 50% is a −3 dB loss, and a 10-fold amplification of the power is a +10 dB gain.
Another attractive feature of the decibel is that to measure the changes in the strength
of a signal, one merely adds or subtracts the decibel loss or gain numbers in a series
of connected optical link elements (e.g., optical fibers, couplers, power splitters, or
amplifiers) between two different points.
Example 1.3 Assume that after traveling a certain distance in some transmission
medium, the power of a signal is reduced to half, that is, P 2 = 0.5 P 1 in Fig. 1.6. At
this point, using Eq. (1.4) the attenuation or loss of power is
10 log
P 2
P 1
= 10 log
0.5P 1
P 1
= 10 log 0.5 = 10(−0.3) = −3 dB