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9 Interactions among Transmitters, Fibers, and Receivers

9 Interactions among Transmitters, Fibers, and Receivers

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4.9 Interactions among Transmitters, Fibers, and Receivers 115

4.9.1 Double Rayleigh Backscattering: Interferometric Intensity Noise
Some portion of light that is scattered backward through the fiber due to Rayleigh
scattering will be rescattered in the forward direction and will combine with the
normally transmitted light. Since the double-scattered light from various points
along the fiber will not be coherent with the principal optical signal, the effect
when both reach the optical detector is that they mix to produce products at
the differences in optical frequencies (and multiples thereof) and will show up
as an effective increase in link noise. This interferometric intensity noise (IIN) is
spread across a spectrum that is about twice the total effective linewidth of the
transmitter (including the effect of chirp if present). The effective link IIN is given
by
!
2
Á 3
1 À
À2 aL
À14
3:6 Â 10

1Àe
6
7
2a
7
IIN ¼ 10 log6
4
5
D fRMS

(4.18)

where
IIN ¼ the level of double-scattering-caused noise relative to the unmodulated
light level, in dB=Hz
L ¼ the length of the fiber in km
a ¼ 1 À 10Àa0 =10
a0 ¼ the loss of the fiber in dB=km
DfRMS ¼ the total rms effective linewidth (In the case of directly modulated
transmitters, this is the total wavelength spread (chirp) of the source as
a result of modulation; in the case of externally modulated transmitters,
this is the linewidth of the unmodulated source if not dithered or phasemodulated.)19
For affected frequencies, IIN can be related to in-channel C=N in the same way as
transmitter RIN:
 
mi
(4.19)
C=NIIN ¼ IIN À 10 logðBWÞ þ 20 log pffiffiffi
2
where
C=NIIN ¼ the contribution of the IIN effects to the C=N of a signal, expressed in dB
IIN ¼ the interferometric noise level (relative to the unmodulated light power),
as calculated in Equation 4.18 and expressed in dB=Hz
BW ¼ the receiver noise bandwidth, in Hz, for the communications channel
being evaluated
mi ¼ the peak modulation of the light source by the signal
Figure 4.18 shows an example of the effect of IIN on video C=N as a function
of fiber length for several optical linewidths at 1310 nm. The assumed OMI per
carrier was 3%.

116 CHAPTER 4 Linear Fiber-Optic Signal Transportation

80
Linewidth
30 GHz

75

10 GHz
3 GHz

70

1 GHz

C/N (dB)

65
60
55
50
45
40
5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95 100

Line length (km)

FIGURE 4.18
C=N degradation due to IIN.

For externally modulated sources, absent SBS suppression techniques that cause
considerable line spreading, the linewidth is so narrow that IIN noise density is very
high and is concentrated at very low frequencies. In order to avoid severe IIN degradation to television channel 2, which starts at 54 MHz, the linewidth must be either
less than a few megahertz or artificially spread to levels at least comparable with
those found with directly modulated lasers. Since a wider spectral line may be
required as part of SBS suppression techniques, the latter approach is generally
taken.
Finally, IIN may affect long upstream DFB links in a different way. The unmodulated linewidth of a typical DFB is approximately 10 MHz. Since an upstream link
may not be used continuously, when it is idle there may be a significant level of
IIN extending up to about 20 MHz much of the time. A possible answer is to apply
a “dithering” modulation to the laser continuously to ensure a wider chirped
linewidth.20

4.9.2 Phase Noise Contribution to Link Performance
Even though DFB diodes oscillate in only a single longitudinal mode, they still
exhibit some residual frequency instability. As in F-P diodes, this variance interacts
with dispersion to create link noise.

4.10 End-to-End Fiber-Optic Link Performance 117

The relationship between source phase noise and link C=N is given by the
formula21
 
À
Á
mi
2 4 2 2
(4.20)
C=NPMÀAM ¼ 398:55 À 10 log Dn BWRF D l fRF L þ 20 log pffiffiffi
2
where
C=NPMÀAM ¼ the contribution to channel C=N (in dB) due to the phase noise in
the optical source being converted to amplitude noise in the
detector
Dn ¼ the source linewidth in MHz
BWRF ¼ the noise susceptibility bandwidth of the channel in Hz
D ¼ the fiber dispersion constant in ps=nm-km
l ¼ the operating free-space optical wavelength in nm
fRF ¼ the modulating frequency in MHz
L ¼ the fiber length in km
mi ¼ the OMI per RF carrier at fRF
The 398.55 factor is the result of converting the various parameters to common
engineering units.
As can be seen, the noise affects the RF channels unequally, increasing as the square
of the RF channel frequency. It also increases as the square of the fiber length.
Phase-related amplitude noise is generally not of concern in 1310-nm links
using nonshifted fiber but may be significant in cases of long fiber links using
non–dispersion-shifted fiber at 1550 nm. As an example, assume a 750-MHz analog
video channel used to externally modulate (OMI=ch ¼ 3%) an amplified 1550-nm
DFB whose optical linewidth is 1 MHz. The signal is then transmitted through a
60-km fiber whose chromatic dispersion is 17 ps=nm-km. The detected signal will
exhibit a C=N due to PM–AM conversion of 53.8 dB.

4.10 END-TO-END FIBER-OPTIC LINK PERFORMANCE
The characteristics of the transmitter, interconnecting fiber, receiver, and, optionally,
any amplifiers work together to determine the link performance. In particular, the
interaction between the signals and the transmission media is much more complex
in optical than in coaxial links.

4.10.1 Noise Performance
The total link C=N will have contributions due to transmitter RIN, detector shot
noise, and postamplifier noise, as well as due to the IIN interaction among laser

118 CHAPTER 4 Linear Fiber-Optic Signal Transportation

linewidth, double scattering, and detector mixing. These noise effects are uncorrelated and so will add on a power basis:
ÀC=N Á
ÀC=N Á !
RIN
À
À 10IIN
10
þ 10
C=NLINK ¼ À 10 log 10
(4.21)
ÀC=N Á
ÀC=N
Á!
SHOT
POSTAMPLIFIER
À
À
10
10
þ 10
þ10
where
C=NLINK
C=NRIN
C=NIIN
C=NSHOT

C=NPOSTAMPLIFIER

¼ the net per-channel C=N
¼ the per-channel transmitter relative intensity noise (Eq. 4.11)
¼ the per-channel interferometric intensity noise (Eq. 4.19)
¼ the per-channel shot noise at the detector input (Eq. 4.15)
¼ the per-channel postamplifier noise contribution (Eq. 4.16 or
4.17)

If the end-to-end C=N of a simple DFB link is plotted as a function of optical loss, the
curve will typically have three asymptotes, as shown in Figure 4.19 (the effects of
IIN are not readily plotted on the same chart because they vary not with received
optical power but with line length).
For high received power levels, the transmitter RIN will dominate, and the C=N
will be independent of path loss; at lower received levels, the shot noise will begin
80
Xmtr RIN
Shot noise
Postamp
Link total

70

C/N (dB)

60

50

40

30

20
10

8

6

4

2

0

–2 –4 –6 –8 –1
0
Received optical power (dBm)

FIGURE 4.19
Typical fiber-optic link C=N contributions.

–12 –14 –16 –18 –20

4.10 End-to-End Fiber-Optic Link Performance 119

to dominate and the link C=N will change 1 dB for every decibel of reduction in
received power level. At some point, the postamplifier noise will begin to dominate,
and the link will begin to degrade 2 dB for every decibel of loss, due to the squarelaw receiver response. The range of receiver power over which each of these effects
dominates depends, of course, on the quality of the individual components. For
typical links, the slope of C=N versus level near 0-dBm received power is about 1:1.
In addition to the factors shown in Equation 4.21, other elements and interactions may affect the end-to-end C=N. For instance, if an EDFA is used, its C=N must
be included within the parentheses as an additional factor. In long 1550-nm links,
residual phase noise may be a factor.
The companion software applications available on the website dedicated to this
book (www.elsevierdirect.com/companions/9780123744012) include an Excel
spreadsheet, entitled Single-Wavelength Performance Calculator.xls, that allows
simple calculation of the C=N and CSO of most linear optical links in which only a
single optical signal is transmitted through each fiber. A separate calculator, discussed in the next chapter, predicts cross-modulation among multiple optical signals
sharing a fiber.

4.10.2 Small-Signal Distortions
Directly modulated DFB transmitters behave similarly to single-ended RF amplifiers,
generating both second- and third-order distortion whose amplitudes, as a function
of RF drive level, increase roughly 1 dB=dB (in the case of second-order products)
and 2 dB=dB (in the case of third-order products). As with their coaxial counterparts,
CSO products tend to be the limiting distortion. As discussed earlier, typical specifications for such transmitters are 60 to 62 dB for C=CSO and 65 dB for C=CTB under
normal operating conditions with a loading of 77 unmodulated carriers. These distortions arise from the combination of small transfer function nonlinearities and
large signal clipping.
Externally modulated transmitters exhibit symmetrical distortion and are thus
similar to conventional push–pull coaxial amplifiers in that regard. That, combined
with the predictability of the nonlinearities, allows C=CSO and C=CTB values of
65 or better with channel loadings of 77 unmodulated carriers.
Distortion occurring in the optical receiver must be added to that generated in
the transmitter. Like the transmitter, the detector–postamplifier combination
behaves like a single-ended amplifier, with dominant second-order distortion. Often
manufacturers specify link performance with a given received power, rather than
individually specifying transmitter and receiver.
When the link loss includes fiber, the CSO degradations due to both chirp-induced
dispersion and SPM must be included in the calculation of end-to-end performance.
Since the CSO distortion mechanisms are synchronized primarily with the modulating waveform (with the exception of the small-signal DFB nonlinearities), the various
CSO contributions could be expected to add on a voltage (20 log) basis rather than
a power basis. Although this is true, the chirp and SPM effects may, in fact, be of

120 CHAPTER 4 Linear Fiber-Optic Signal Transportation

opposite polarity and tend to cancel each other rather than add. Nevertheless, an
assumption of voltage addition is the most conservative approach to link design.
One technique for reducing the effects of chirp, SPM, and receiver-generated
CSO is to transmit both outputs of a Mach–Zehnder type modulator through parallel
networks to the receiver. If the two signals are separately detected and then combined out of phase at RF, these second-order effects will tend to cancel, just as they
do in push–pull RF amplifiers. C=CSO values of greater than 70 dB have been
reported using this technique, known commercially as a Harmonic Link Extender.
As an added benefit, when the signals are combined, the noise will be largely uncorrected (except for the contribution from transmitter RIN) and so will add on
a power basis, whereas the signals will add on a voltage basis, resulting in a net
3-dB increase in C=N in the link. Link performance of 55-dB C=N over 50-km links
at 1550 nm has been reported.22

4.10.3 Clipping Distortion
The ratio of peak-to-average absolute voltage in a simple unmodulated carrier is
about 1.6:1. When two equal-amplitude unrelated carriers are summed, however,
the relationship is not as simple. Figure 4.20 shows three possible waveforms resulting from the simple addition of two sine waves when one is exactly twice the
frequency of the other. Depending on their relative phases, the peak voltages can
vary by nearly a factor of 2.
The case when many signals are summed is much more complex. When many
summed signals are randomly distributed in both frequency and phase, the peakto-average level seldom exceeds 14 dB, as discussed in Chapter 7 (although with
occasional higher peaks). The downstream spectrum of cable systems is not random, however. The most extreme case occurs when a large number of carriers are
harmonics of a common root frequency (as in the CEA-542-B HRC channelization
2

Instantaneous voltage

1.5
1
0.5
0
–0.5
–1
–1.5
–2

FIGURE 4.20
Addition of two sine waves with various phase differences.

4.10 End-to-End Fiber-Optic Link Performance 121

plan) and all the carrier phases are aligned. In that case, the time domain waveform
can resemble a string of impulses spaced by a time interval equal to the period of the
common root frequency. This is not a surprising result since the Fourier transform of
an infinite string of zero-width pulses is an infinite string of carriers.23
In the more commonly used CEA-542-B Standard frequency plan, most of the
visual carriers are offset by approximately 1.25 MHz from harmonics of 6 MHz and
are neither frequency nor phase related. Despite this, the composite waveform has
characteristics that are close to harmonically related carriers if the carrier phases
do happen to align at some time. Figure 4.21 shows the resultant instantaneous voltage of the standard channels between 54 and 550 MHz, with each assigned a frequency at random within its tolerance range but with the signal phases aligned at
t ¼ 30 ns on the horizontal scale. The peak-to-average voltage is approximately
34:1. If we look at the same waveform later in time, however, the phases slowly
move out of coincidence and the peak voltage decreases. Figure 4.22 shows the condition at t ¼ 15 ms. By 20 to 30 ms, the pulses are no longer distinguishable. Figure 4.23 shows a typical situation with truly random phase relationships.
Observations of actual headends carrying NTSC-modulated carriers have confirmed that peak-to-average ratios generally vary from about 3.5:1 to greater than
7:1. When some subset of carriers happen to phase-align, the result is voltage peaks
spaced approximately 167 ns apart (the inverse of the 6-MHz channel spacing),
which build up to a peak over a few tens of microseconds and then decrease again
as the carriers move out of phase coincidence.
The importance of this occasionally occurring peak voltage condition is that,
depending on the OMI, the optical transmitter may be driven into hard limiting
(clipping) when a sufficient number of carriers are in phase alignment. This is

80

Relative voltage

60
40
20
0
–20
–40
–60
–80

0

100

200

300

400

Max=77 Ave=2.26 Max/ave=34.1

500
600
Time (ns)
Start=–30 ns

700

800

900

1000

FIGURE 4.21
Instantaneous voltage from the addition of 77 FDM carriers with standard frequency assignments
and tolerances with phases aligned at t ¼ 30 ns.

122 CHAPTER 4 Linear Fiber-Optic Signal Transportation

80

Relative voltage

60
40
20
0
–20
–40
–60
–80

0

100

200

300

400

Max=39.1 Ave=4.46 Max/ave=8.8

500
600
Time (ns)

700

800

900

1000

700

800

900

1000

Start=1.5ns

FIGURE 4.22
Spike degeneration after 15 ms.
30

Relative voltage

20
10
0
–10
–20
–30
0

100

200

300

400

Max=20.4 Ave=5.00 Max/ave=4.1

500
600
Time (ns)
Start=3ns

FIGURE 4.23
Typical headend output waveform.

particularly true in the case of directly modulated laser diodes, where a sharp knee
occurs in the transfer function below which the light output is extinguished. When
that occurs, intermodulation products are generated. As Figure 4.24 shows, both
even- and odd-order distortion products are generated when one polarity of a sine
wave is clipped off (although second-order products are always the largest). Thus,
both CTB and CSO will show an increase when clipping happens with sufficient frequency to be statistically significant. Since clipping produces a string of pulses with
the characteristic 167-ns spacing, the largest components produced will fall at
harmonics of 6 MHz (which is at the position of the lower CSO beat when the

4.10 End-to-End Fiber-Optic Link Performance 123

–10

Harmonic amplitude (dB)

–15
–20
–25
–30

0.5
0.4

–35
0.2

–40
2

3

4

5

6
Harmonic number

0.3
Proportion clipped

0.1
7

8

FIGURE 4.24
Harmonic content of a clipped sine wave.

CEA Standard or IRC channel allocation scheme is used, and at the video carrier frequency when the CEA HRC channel scheme is used). With highly linear diodes, clipping may, in fact, be the principal contributor to IM products.
In the case of Mach–Zehnder external modulators, the nonlinearities are symmetrical, and the limiting is “softer,” resulting in less clipping and primarily odd-order
resultant distortion.24 Regardless of the modulation method used, the visible effect
on analog video channels is that, as OMI is increased, “dashes” resembling electrical
interference begin to appear on the displayed picture. These visible effects are due
to the integrated effect of a group of pulses (the spacing of which is closer than the
television can resolve).
In the case of high-order digitally modulated carriers sharing a linear link with a
comb of analog television carriers, the result of clipping is an increase in bit error
rate (BER). Data taken by one of the authors found that the BER through a fiber link
loaded with 80 normally modulated video channels and one 64-QAM data channel
(whose signal level was 10 dB below the video channels) was approximately
1.3 Â 10À10. As the OMI was increased, the BER did not change until a critical
threshold was reached, whereupon the BER increased to 7.6 Â 10À8, a 600:1 degradation, with an OMI increase of less than 1 dB. This confirms findings of other researchers in this field. The observations of researchers using normal NTSC video signals
were that the BER increased to unacceptably high values before any degradation was
visible in displayed analog pictures.25

124 CHAPTER 4 Linear Fiber-Optic Signal Transportation

The crucial question is how often clipping occurs. This has been explored by a
number of authors.
pffiffiffiffiDavid Grubb and Yudhi Trisno suggested that if OMI per channel
is held to 0.348= N (where N is the number of channels), the voltage will exceed
the clipping threshold about 2.5 Â 10À5 of the time.26 That analysis, however, was
based on unmodulated, randomly phased carriers. They noted, however, that
optimal phasing of harmonically related carriers can reduce the theoretical peak
voltage. The ratio of theoretical maximum
voltage to the maximum achievable
pffiffiffiffi
with phases aligned optimally is ( N )=1.5. If the signals feeding an optical
pffiffiffiffi
transmitter were so related, the modulation index could be increased to 0.67= N ,
or about 5.7 dB higher. This would translate directly to an achievable C=N
increase in the link (whose exact amount is related to the relative contribution of
transmitter, shot, and postamplifier noise, as discussed earlier in this chapter).
Another factor is video modulation. Since NTSC signals are at maximum carrier
level only a small percentage of the time (during synchronizing peaks), the sum of the
instantaneous voltages of a number of randomly timed video channels is almost always
lower than that of unmodulated carriers. As with carrier phasing, however, the key
word is almost since the synchronizing pulses for multiple channels will occasionally
drift into alignment. Stuart Wagner and colleagues have measured clipping noise and
its effect on the BER of a digital signal carried along with 40 randomly timed analog
video channels in a fiber link. They found that the peak OMI per analog carrier could
be increased by approximately half the average difference in power level (in decibels)
between the unmodulated and modulated carriers with no increase in noise or BER.27
As discussed in Chapter 2, the usual assumption is that average power levels are about
6 dB below peak levels. In particular, the black level of a video signal is about 2.5 dB
below sync, so with random video timing it should be possible, on average, to raise
peak OMI per channel by about 3 dB compared with the unmodulated carrier case.
On the other hand, with optimum video timing it should be possible to keep the
total carrier power close to the average power by minimizing instances where carriers are simultaneously at peak levels. In that case, it should be possible to increase
OMI by the difference between peak and average power, 6 dB, without increasing
clipping distortion.28 That increase will lead to a similar increase in link C=N.

4.11 SUMMARY
Linear fiber-optic links are capable of transporting the full spectrum of cable television services over distances exceeding 20 miles without amplification. Amplification, readily available at 1550-nm wavelength, can extend the attainable distance
several-fold, with only a minor impact on end-to-end performance.
The basic C=N performance of optical links is limited by transmitter intensity
noise, optical shot noise, the interaction between transmitter linewidth and doubly
scattered light in the fiber, and receiver postamplifier noise. The interaction
between transmitter residual phase noise and the fiber can further reduce the noise
under some conditions.

4.11 Summary 125

Distortion is fundamentally limited by both small-signal nonlinearities in the
transmitter and clipping caused by large-signal peaks. Additionally, interaction
between incidental transmitter FM and fiber dispersion can cause second-order distortion, as can interaction between peak power levels and the glass material itself.
Increasing the optical modulation index per carrier in an optical link will
improve C=N at the expense of distortion; increasing operating levels in a coaxial
network will have the same effect. Similarly, decreasing the number of carriers will
allow higher C=N and lower distortion per channel, as in a coaxial network.
Chapter 5 will discuss multi-wavelength transmission through shared fibers.
Chapter 7 will discuss the total end-to-end performance of cascaded fiber-optic
and coaxial broadband distribution networks; Chapter 10, various HFC architectures; Chapter 11, fiber-deep architecture; and Chapter 12, the reliability of various
HFC architectures.

ENDNOTES
1. Ronald C. Cotten, Lightwave Transmission Applications. Louisville, CO: CableLabs,
September 1993, pp. 80–84.
2. Data provided by CommScope, Inc., Hickory, NC.
3. AT&T Generic Specification: Fiber-Optic Outside Plant Cable, Issue 11. Norcross, GA:
AT&T Network Cable Systems, December 1995.
4. CommScope Fiber Optic Cable Catalog. Hickory, NC: CommScope, Inc., September
1995.
5. AT&T Generic Specification.
6. Claude Romans and David Large, “Optical Bus Architecture for Co-Deployment of Telephone and CATV Services in the FRG,” in Conference Record, Globecom ‘89. IEEE Communications Society, November 1989, pp. 37.5.1–37.5.9.
7. AT&T Generic Specification.
8. David Grubb III and Yudhi Trisno, “AM Fiber Optic Trunks—A Noise and Distortion
Analysis,” in 1989 NCTA Technical Papers. Washington, DC: National Cable & Telecommunications Association, May 1989.
9. F.W. Willems, W. Muys, and J.S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and Interferometric Noise in Externally Modulated Lightwave AMSCM Systems,” IEEE Photonics Technology Letters, vol. 6, no. 12 (December 1994).
See also S.W. Merritt, G.J. McBrien, and E.R. Yates, “Integrated Optic Modulators for
1-GHz HFC Systems,” CED, February 1996.
10. Dogan A. Atlas, “Fiber-Induced Distortion and Phase Noise to Intensity Noise Conversion in Externally Modulated CATV Systems,” in 1996 NCTA Technical Papers, Washington, DC: National Cable & Telecommunications Association, 1996.
11. AT&T Corporation, LGX Broadband Fiber Management System Application Guide.
Norcross, GA: AT&T Network Systems, 1995.
12. Dan Harris, “Primer on Baseband Digital Transmission on Single-Mode.” Communications Technology, August 1996, pp. 92–98.