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4 Light Sources for Fiber Links
Here, m is the modulation index (or modulation depth) defined as
m =
I
I
B
(4.56)
where I
B = I B for LEDs and I
B = I B − I th for laser diodes. The parameter I is the
variation in current about the bias point. To prevent distortions in the output signal,
the modulation must be confined to the linear region of the curve for optical output
versus drive current. Furthermore, if I is greater than I
B (i.e., m is greater than 100
percent), the lower portion of the signal gets cut off and severe distortion will result.
Typical m values for analog applications range from 0.25 to 0.50.
In analog applications, any device nonlinearities will create frequency components
in the output signal that were not present in the input signal. Two important nonlinear
effects are harmonic and intermodulation distortions. If the signal input to a nonlinear
device is a simple cosine wave x(t) = A cos ωt with frequency ω and amplitude A,
the output will be
y(t) = A 0 + A 1 cos ωt + A 2 cos 2ωt + A 3 cos 3ωt + · · ·
(4.57)
where the factors A j are the amplitudes of the jth harmonic. That is, the output signal
will consist of a component at the input frequency ω plus spurious components at zero
frequency, at the second harmonic frequency 2ω, at the third harmonic frequency
3ω, and so on. This effect is known as harmonic distortion. The amount of nth-order
distortion in decibels is given by
nth-order harmonic distortion = 20 log
A n
A 1
(4.58)
To determine intermodulation distortion, the modulating signal of a nonlinear
device is taken to be the sum of two cosine waves x(t) = A 1 cos ω 1 t + A 2 cos ω 2 t.
The output signal will then be of the form
y(t) =
m,n
B mn cos(mω 1 + nω 2 )
(4.59)
where m and n = 0, ±1, ±2, ±3,…. This signal includes all the harmonics of ω 1 and
ω 2 plus cross-product terms such as ω 2 − ω 1 , ω 2 + ω 1 , ω 2 − 2ω 1 , ω 2 + 2ω 1 , and so
on. The sum and difference frequencies give rise to the intermodulation distortion.
The sum of the absolute values of the coefficients m and n determines the order of the
intermodulation distortion. For example, the second-order intermodulation products
are at ω 1 ± ω 2 with amplitude B 11 , the third-order intermodulation products are at ω 1
± 2ω 2 and 2ω 1 ± ω 2 with amplitudes B 12 and B 21 , and so on. (Harmonic distortions
are also present wherever either m = 0 and n = 0 or when m = 0 and n = 0. The
corresponding amplitudes are B m0 and B 0n , respectively.) In general, the odd-order
intermodulation products with m = n ± 1 (such as 2ω 1 − ω 2 , 2ω 2 − ω 1 , 3ω 1 −
4 Light Sources for Fiber Links
Here, m is the modulation index (or modulation depth) defined as
m =
I
I
B
(4.56)
where I
B = I B for LEDs and I
B = I B − I th for laser diodes. The parameter I is the
variation in current about the bias point. To prevent distortions in the output signal,
the modulation must be confined to the linear region of the curve for optical output
versus drive current. Furthermore, if I is greater than I
B (i.e., m is greater than 100
percent), the lower portion of the signal gets cut off and severe distortion will result.
Typical m values for analog applications range from 0.25 to 0.50.
In analog applications, any device nonlinearities will create frequency components
in the output signal that were not present in the input signal. Two important nonlinear
effects are harmonic and intermodulation distortions. If the signal input to a nonlinear
device is a simple cosine wave x(t) = A cos ωt with frequency ω and amplitude A,
the output will be
y(t) = A 0 + A 1 cos ωt + A 2 cos 2ωt + A 3 cos 3ωt + · · ·
(4.57)
where the factors A j are the amplitudes of the jth harmonic. That is, the output signal
will consist of a component at the input frequency ω plus spurious components at zero
frequency, at the second harmonic frequency 2ω, at the third harmonic frequency
3ω, and so on. This effect is known as harmonic distortion. The amount of nth-order
distortion in decibels is given by
nth-order harmonic distortion = 20 log
A n
A 1
(4.58)
To determine intermodulation distortion, the modulating signal of a nonlinear
device is taken to be the sum of two cosine waves x(t) = A 1 cos ω 1 t + A 2 cos ω 2 t.
The output signal will then be of the form
y(t) =
m,n
B mn cos(mω 1 + nω 2 )
(4.59)
where m and n = 0, ±1, ±2, ±3,…. This signal includes all the harmonics of ω 1 and
ω 2 plus cross-product terms such as ω 2 − ω 1 , ω 2 + ω 1 , ω 2 − 2ω 1 , ω 2 + 2ω 1 , and so
on. The sum and difference frequencies give rise to the intermodulation distortion.
The sum of the absolute values of the coefficients m and n determines the order of the
intermodulation distortion. For example, the second-order intermodulation products
are at ω 1 ± ω 2 with amplitude B 11 , the third-order intermodulation products are at ω 1
± 2ω 2 and 2ω 1 ± ω 2 with amplitudes B 12 and B 21 , and so on. (Harmonic distortions
are also present wherever either m = 0 and n = 0 or when m = 0 and n = 0. The
corresponding amplitudes are B m0 and B 0n , respectively.) In general, the odd-order
intermodulation products with m = n ± 1 (such as 2ω 1 − ω 2 , 2ω 2 − ω 1 , 3ω 1 −