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9 Analog Optical Fiber Channels
As a result, when N signals are frequency multiplexed and used to modulate a
single optical source, the carrier-to-noise ratio of a single channel is degraded by 10
log N. If only a few channels are combined, the signals will add in voltage rather
than power, so that the degradation will have a 20 log N characteristic.
When multiple carrier frequencies pass through a nonlinear device such as a
laser diode, signal products other than the original frequencies can be produced.
These undesirable signals are called intermodulation products, and they can cause
serious interference in both in-band and out-of-band channels. The result is a degradation of the transmitted signal. Among the intermodulation products, generally only
the second-order terms and third-order terms are considered because higher-order
products tend to be significantly smaller.
Third-order intermodulation (IM) distortion products at frequencies f i + f j − f k
(which are known as triple-beat IM products) and 2f i − f j (which are known as
two-tone third-order IM products) are the most dominant, because many of these fall
within the bandwidth of a multichannel system. For example, a 50-channel CATV
network operating over a standard frequency range of 55.25–373.25 MHz has 39
second-order IM products at 54.0 MHz and 786 third-order IM tones at 229.25 MHz.
The amplitudes of the triple-beat products are 3-dB higher than the two-tone thirdorder IM products. In addition, because there are N(N − 1)(N − 2)/2 triple-beat
terms compared with N(N − 1) two-tone third-order terms, the triple- beat products
tend to be the major source of IM noise.
If a signal passband contains a large number of equally spaced carriers, several IM
terms will exist at or near the same frequency. This so-called beat stacking is additive
on a power basis. For example, for N equally spaced equal-amplitude carriers, the
number of third-order IM products that fall right on the rth carrier is given by [12]
D 1,2 =
1
2
N − 2 −
1
2
1 − (−1)
N
(−1)
r
(9.16)
for two-tone terms of the type 2f i − f j , and by
D 1,1,1 =
r
2
(N − r + 1) +
1
4
(N − 3)
2
− 5 −
1
2
1 − (−1)
N
(−1)
N +r
(9.17)
for triple-beat terms of the type f i + f j − f k .
Whereas the two-tone third-order terms are fairly evenly spread through the operating passband, the triple-beat products tend to be concentrated in the middle of the
channel passband, so that the center carriers receive the most intermodulation interference. Tables 9.1 and 9.2 show the distributions of the third-order triple-beat and
two-tone IM products for the number of channels N ranging from 1 to 8.
The results of beat stacking are referred to as composite second order (CSO) and
composite triple beat (CTB) and they describe the performance of multichannel AM
links. The word composite means that the overall distortion is due to a collection of
discrete distortions. CSO and CTB are defined as [1, 12, 13]
9 Analog Optical Fiber Channels
As a result, when N signals are frequency multiplexed and used to modulate a
single optical source, the carrier-to-noise ratio of a single channel is degraded by 10
log N. If only a few channels are combined, the signals will add in voltage rather
than power, so that the degradation will have a 20 log N characteristic.
When multiple carrier frequencies pass through a nonlinear device such as a
laser diode, signal products other than the original frequencies can be produced.
These undesirable signals are called intermodulation products, and they can cause
serious interference in both in-band and out-of-band channels. The result is a degradation of the transmitted signal. Among the intermodulation products, generally only
the second-order terms and third-order terms are considered because higher-order
products tend to be significantly smaller.
Third-order intermodulation (IM) distortion products at frequencies f i + f j − f k
(which are known as triple-beat IM products) and 2f i − f j (which are known as
two-tone third-order IM products) are the most dominant, because many of these fall
within the bandwidth of a multichannel system. For example, a 50-channel CATV
network operating over a standard frequency range of 55.25–373.25 MHz has 39
second-order IM products at 54.0 MHz and 786 third-order IM tones at 229.25 MHz.
The amplitudes of the triple-beat products are 3-dB higher than the two-tone thirdorder IM products. In addition, because there are N(N − 1)(N − 2)/2 triple-beat
terms compared with N(N − 1) two-tone third-order terms, the triple- beat products
tend to be the major source of IM noise.
If a signal passband contains a large number of equally spaced carriers, several IM
terms will exist at or near the same frequency. This so-called beat stacking is additive
on a power basis. For example, for N equally spaced equal-amplitude carriers, the
number of third-order IM products that fall right on the rth carrier is given by [12]
D 1,2 =
1
2
N − 2 −
1
2
1 − (−1)
N
(−1)
r
(9.16)
for two-tone terms of the type 2f i − f j , and by
D 1,1,1 =
r
2
(N − r + 1) +
1
4
(N − 3)
2
− 5 −
1
2
1 − (−1)
N
(−1)
N +r
(9.17)
for triple-beat terms of the type f i + f j − f k .
Whereas the two-tone third-order terms are fairly evenly spread through the operating passband, the triple-beat products tend to be concentrated in the middle of the
channel passband, so that the center carriers receive the most intermodulation interference. Tables 9.1 and 9.2 show the distributions of the third-order triple-beat and
two-tone IM products for the number of channels N ranging from 1 to 8.
The results of beat stacking are referred to as composite second order (CSO) and
composite triple beat (CTB) and they describe the performance of multichannel AM
links. The word composite means that the overall distortion is due to a collection of
discrete distortions. CSO and CTB are defined as [1, 12, 13]