APPENDIX A. SYSTEM OF UNITS 519
optical power during transmission and thus can be expressed as a power ratio. For
example, if a 1-mW signal reduces to 1μW after transmission over 100 km of fiber,
the 30-dB loss over the entire fiber span translates into a loss of 0.3 dB/km. The same
technique can be used to define the insertion loss of any component. For instance,
a 1-dB loss of a fiber connector implies that the optical power is reduced by 1 dB
(by about 20%) when the signal passes through the connector. The bandwidth of an
optical filter is defined at the 3-dB point, corresponding to 50% reduction in the signal
power. The modulation bandwidth of ight-emitting diodes (LEDs) in Section 3.2 and
of semiconductor lasers in Section 3.5 is also defined at the 3-dB point, at which the
modulated powers drops by 50%.
Since the losses of all components in a fiber-optic communication systems are ex-
pressed in dB, it is useful to express the transmitted and received powers also by using
a decibel scale. This is achieved by using a derived unit, denoted as dBm and defined
as
power(in dBm)=10 log 10
(power
1mW)
, (A.3)
where the reference level of 1 mW is chosen simply because typical values of the
transmitted power are in that range (the letter m in dBm is a reminder of the 1-mW
reference level). In this decibel scale for the absolute power, 1 mW corresponds to
0 dBm, whereas powers below 1 mW are expressed as negative numbers. For example,
a 10-μW power corresponds to−20 dBm. The advantage of decibel units becomes
clear when the power budget of lightwave systems is considered in Chapter 5. Because
of the logarithmic nature of the decibel scale, the power budget can be made simply by
subtracting various losses from the transmitter power expressed in dBm units.