This equation system reflects the connection of OEO MZ circuit parameters,
which is shown in Fig. 6.12a. The first equation of the system determines the
connection of the oscillating characteristics Q 0 ( p), the laser parameters with fluctuations ξ SN . The second equation defines the instantaneous value of the AC current in
the PD load.
Here T FODL ¼ T FOS is the delay in FOS, u MZ is the instantaneous voltage (AC) in
the MZ electrical input, φ 0MZ is the constant phase incursion in MZ, U 0MZπ is the
constant bias voltage in MZ, E L E
Ã
Lτ
is the average from the product of delayed and
non-delayed field oscillations for account of the noise after the optical emission
passage through MZ, γ is the coefficient of the excitation irregularity of optical
channels in MZ. If to recalculate of the laser noises ξ SN in the input of the RF
amplifier and to take into consideration that ξ n is the noise taking into account the
detected noises of the laser ξ SN and noises of the RF parts ξ U , then the symbolic
differential equation (6.46) will take the form:
p
2
þ
1
T F
p þ 2π f eF0
ð
Þ
2
!
u MZ ¼ K FODL
j
j=S PD
ð
Þ pS A E 0L
j j
2 , i PD
exp ÀpT FOS
½
þξ n :
ð6:30Þ
Below, we shall give the deduction of these formulas for PSD of the amplitude
noise and the phase noise according to the Evtianov–Kuleshov approach.
6.5.2 Abbreviated Differential Equations of OEO MZ
with Fluctuations
Let us consider the circuit in Fig. 6.12a–c with complex slowly changing oscillation
amplitude U а .
In order to obtain the abbreviated equations of OEO MZ with the single optical
fiber, we write differential equations for OEO in operator form (3.63):
p
2
þ 1=T EF
ð
Þp þ 2π f 0e
ð
Þ
2
h
i
u MZ ¼ 1=T EF
ð
ÞK 0FODL pi A u PD
ð Þ
exp Àj2π f 0e T FOS
ð
Þ þ ξ n
ð6:31Þ
in which the instantaneous voltage on the load resistance R PD of PD is u PD ¼ R PD Á i PD ,
and the instantaneous PD current i PD is i PD ¼ 0.5(E 0L )
2 K 0FOS.
MZ cos [π(U 0MZ À u MZ )/2U 0MZπ )], where (E 0L )
2
¼ P 0L is the power of laser
emission, U 0MZ is the DC bias voltage of the MZ modulator, K 0FOS. MZ is the RF
FODL transfer function on the frequency f 0e .
6.5 Differential Fluctuation Equations of OEO MZ
313
which is shown in Fig. 6.12a. The first equation of the system determines the
connection of the oscillating characteristics Q 0 ( p), the laser parameters with fluctuations ξ SN . The second equation defines the instantaneous value of the AC current in
the PD load.
Here T FODL ¼ T FOS is the delay in FOS, u MZ is the instantaneous voltage (AC) in
the MZ electrical input, φ 0MZ is the constant phase incursion in MZ, U 0MZπ is the
constant bias voltage in MZ, E L E
Ã
Lτ
is the average from the product of delayed and
non-delayed field oscillations for account of the noise after the optical emission
passage through MZ, γ is the coefficient of the excitation irregularity of optical
channels in MZ. If to recalculate of the laser noises ξ SN in the input of the RF
amplifier and to take into consideration that ξ n is the noise taking into account the
detected noises of the laser ξ SN and noises of the RF parts ξ U , then the symbolic
differential equation (6.46) will take the form:
p
2
þ
1
T F
p þ 2π f eF0
ð
Þ
2
!
u MZ ¼ K FODL
j
j=S PD
ð
Þ pS A E 0L
j j
2 , i PD
exp ÀpT FOS
½
þξ n :
ð6:30Þ
Below, we shall give the deduction of these formulas for PSD of the amplitude
noise and the phase noise according to the Evtianov–Kuleshov approach.
6.5.2 Abbreviated Differential Equations of OEO MZ
with Fluctuations
Let us consider the circuit in Fig. 6.12a–c with complex slowly changing oscillation
amplitude U а .
In order to obtain the abbreviated equations of OEO MZ with the single optical
fiber, we write differential equations for OEO in operator form (3.63):
p
2
þ 1=T EF
ð
Þp þ 2π f 0e
ð
Þ
2
h
i
u MZ ¼ 1=T EF
ð
ÞK 0FODL pi A u PD
ð Þ
exp Àj2π f 0e T FOS
ð
Þ þ ξ n
ð6:31Þ
in which the instantaneous voltage on the load resistance R PD of PD is u PD ¼ R PD Á i PD ,
and the instantaneous PD current i PD is i PD ¼ 0.5(E 0L )
2 K 0FOS.
MZ cos [π(U 0MZ À u MZ )/2U 0MZπ )], where (E 0L )
2
¼ P 0L is the power of laser
emission, U 0MZ is the DC bias voltage of the MZ modulator, K 0FOS. MZ is the RF
FODL transfer function on the frequency f 0e .
6.5 Differential Fluctuation Equations of OEO MZ
313