Page 249 - Optical Communications Essentials

Performance Measures

Performance Measures 239

L have a loss αL (where α is the fiber attenuation) and an in-line amplifier with
a gain equal to the span loss. The OSNR then is

P signal
OSNR (14.8)
N αL F hν∆ν
Here, hν is the photon energy, and ∆ν is the optical frequency range in which the
OSNR is measured, which typically is 12.5GHz (a 0.1-nm width at 1550nm). At
1550 nm, we have (hν)(∆ν) 1.58 10 6 mW, so that 10 log [(hν)(∆ν)]
58dBm. Then Eq. (14.8) may be expressed in decibels as

OSNR(dB) P signal (dBm) 10logN αL(dB) F(dB) 10log[(hν)(∆ν)]
P signal (dBm) 10logN αL(dB) F(dB) 58 dBm (14.9)

For a 50-km spacing between amplifiers, the span loss αL 12.5dB, and for a
100-km spacing we have αL 25dB. Then with OSNR 20dB, it is seen that
for a 100-km spacing the limit on N is 6 (or a link length of 700km), whereas
for a 50-km spacing the limit on N is 112 in-line amplifiers (or a link length of
5650km).
This illustrates the strong effect of in-line amplifier spacing on the OSNR.
For short-haul systems the OSNR can be improved by merely launching more
power into the fiber. On the other hand, in long-haul systems, nonlinear effects
in the fiber will limit the maximum allowable launch power. Chapter 15 discusses
these nonlinear effects and the limits they place on system performance. Note that
in either the long-haul or the short-haul case, usually there are maximum power
limitations that are allowed based on laser power-level safety considerations.

14.3. Analog Link Performance
Although most fiber optic systems are implemented digitally, there are certain
applications where it is desirable to transmit analog signals directly over the
fiber without first converting them to a digital form. These applications include
cable television (CATV) distribution and microwave links such as connections
between remotely located antennas and base stations.

14.3.1. Carrier-to-noise ratio (CNR)
Traditionally, in an analog system a carrier-to-noise ratio analysis is used
instead of a signal-to-noise ratio analysis, since the information signal normally
is superimposed on a radio-frequency (RF) carrier through an optical intensity
modulation scheme. To find the carrier power, consider first the generated ana-
log signal. As shown in Fig. 14.5, the drive current through the optical source is
the sum of a fixed bias current and a time-varying sinusoid. If the time-varying
analog drive signal is s(t), then the output optical power P(t) is

P(t) P t [1 ms(t)] (14.10)

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