The Optical Communications Reference

segment. It can be shown [40–42] that the OSNR for

each link segment is given by

OSNR ¼

P

in

ðNFÞ h

n

ð

D

fÞ

G

N

; (6.3.55)

where (NF ) is the noise figure of the amplifier (i.e., the

amplifier output when there is no input), h is Planck’s

constant, n is the optical frequency, N is the number of

amplifiers, G is the loss of one link segment, or span loss,

and D f is the bandwidth used to measure the noise factor

(typically, 0.1 nm or 12.5 GHz). Since each span is of

equal length, we assume that all spans have the same loss;

furthermore, we assume that all amplifiers have the same

noise factor. These are reasonably good assumptions

based on the uniformity of fiber and components avail-

able; either assumption can be changed in order to im-

prove the design accuracy. The total OSNR for the

system is given by a reciprocal sum of the OSNR for each

link segment:

1

OSNR

final

¼

X

N

i ¼1

1

OSNR

i

: (6.3.56)

Taking the common log (base 10) of both sides of Eq.

(6.3.58) to convert into dB, and assuming the typical

value for Df, yields

OSNR

dB

¼ 58 þ P

in



G

dB

 NF

dB

 10 log N:

(6.3.57)

The expression is typically written in this form because

both the span loss and noise factor are specified in dB,

rather than in linear form, so they do not need to be

converted. Equation (6.3.57) provides a useful approxi-

mation to the system OSNR. Additional loss can be

subtracted from the right-hand side of this expression to

account for other factors, such as gain flatness and gain

tilt of the amplifiers, and polarization dependent noise. In

a multiwavelength system, the design should be based on

the OSNR for the worst wavelength in the system (this is

sometimes assumed to be the first or last wavelength).

Alternatively, some designs assume that optical power

and noise are uniformly divided across all wavelengths of

the system, and either divide the total power by the

number of wavelengths or multiply the total noise by the

number of wavelengths. Various forms of this expression

are used in the literature, depending on the assumptions

made in the link design [40–42].

Case study WDM link budget design

There has always been a need for long-distance, disaster

recovery networks in the data communications indu stry.

These may be used for extending storage area networks,

enabling grid computing applications, or as part of the

ongoing convergence between data communication and

telecommunications. A common design problem involves

determining wh ether a wavelength-division multiplexing

(WDM) system, used as a protocol independent channel

extension, can operate with sufficient fidelity (low

enough bit error rate). Since these links are commonly

loss limited rather than dispersion limited, we can

estimate the requirements from an OSNR.

Consider as an example a WDM link 80 km long ,

originally designed for use with telecommunication

systems, which is being repurposed for an extended

distance datacom link. Since the link loss is too great

for a point-to-point WDM system, it has been divided

into four equal segments, each having 25 dB loss, using

optical amplifiers between each span. Each amplifier

has a fixed gain of 22 dB and a noise factor of 5 dB. We

further assume that the wavelengths are closely

enough spaced that their behavior can be approxi-

mated by a n average wavelength of around 1550 nm

with a small spectral width (25 kHz). Using this in-

formation, we can determine that the output OSNR

for this link is 27 dB. If we attempt to connect a piece

of datacom equipment with a lower receiver sensitivity

(say, 2 5 dB), then the span will not function despite

the use of several optical am plifiers in t he path . This

illustrates the importance of not only computing the

OSNR, but determining if it is adequate for the system

to be used.

REFERENCES

1. S. E. Miller, and A. G. Chynoweth, eds.

Optical fiber telecommunications. New

York: Academic Press (1979).

2. J. Gowar, Optical communication

systems. Englewood Cliffs, N.J.:

Prentice Hall (1984).

3. C. DeCusatis, ed. 1998, December.

Handbook of fiber optic data

communication. New York: Elsevier/

Academic Press, (second edition 2002);

see also Optical Engineering special

issue on Optical Data Communication.

4. R. Lasky, U. Osterberg, and D.

Stigliani, eds. Optoelectronics for data

communication. New York: Academic

Press (1995).

5. Digital video broadcasting (DVB)

Measurement Guidelines for DVB

systems, European

Tele-communications Standards

Institute ETSI Technical Report ETR

290, May 1997; Digital Multi-

Programme Systems for Television

Sound and Data Services fo rCable

Distribution, International

Telecommunications Union ITU-T

Recommendation J.83,1995; Digital

Broadcasting System for Television,

Sound and Data Services; Framing

Structure, Channel Coding and

379

Optical link budgets and design rules CHAPTER 6.3