Properties and modes of FLL with the frequency detector on RF FODL are
described by the symbolic equation ( p ¼ d/dt) for the current frequency of the
controlled OEO:
ω þ Ω Á K p
ð Þ Á F pτ
ð Þ ¼ ω 0 :
ð7:74Þ
Here the function F ¼ F
1À exp Àτp
ð
Þ
τp
τω k
h
i
and we take into consideration not only
inertness of the control circuit with the operator transfer function K( p)‚ but the total
signal delay in RF FODL in the form of the operator of the ideal delay exp(Àpt)‚
including in the argument of the 2π-periodic characteristic F(φ),where φ(ω)—is the
current phase incursion of the radio signal in RF FODL.
With the help Eq. (7.74), in Fig. 7.36b, the regulation characteristic of the FLL
system is shown, i.e., the function of the stabilized frequency versus the variation of
the natural frequency of autonomous OEO.
With the help of Eq. (6.126), we can obtain the expression describing the
stabilization action of FLL with the frequency detector on RF FODL in the vicinity
of any nominal frequency:ω À ω nom, n ¼ (ω 0 À ω nom, n )/[1 + Ω Á τ Á K(0) Á F
0
(φ 0 )] .
We see that the regulation coefficient of the system A ¼ ΩτK(0)F
0
(φ 0 ) containing
of the largest correcting offset Ω, the transfer function of the control circuit on DC K
(0) and the slope F
0 (φ 0 ) of the frequency detector characteristic, increases with the
growth of the signal delay τ in RF FODL.
With the help of FLL system (of the PLL system) with RF FODL, we can solve
not only the problem of frequency stabilization, but also the problem of tracking for
unknown frequency ω ext (t) of the external signal, if to add the mixer to the initial
structure, as shown in Fig. 7.37a. In such a system, the current frequency of the
external signal displaced on the value of any RF FODL plays the role of the nominal
frequency ω nom, n (t) ¼ ω ext (t) + 2πn/τ.
To exclude the ambiguity at the choice of necessary value of operation frequency,
it is enough to use the limiter in the output of the phase detector. The solid line in
regulation characteristics presented in Fig. 7.37b depicts the action of such a limiter.
The stability of nominal frequencies can be estimated with the help of obvious
relationship:
Δω nom,n
ω nom,n
¼
ω ext
ω nom,n
Δω ext
ω ext
þ
2πn
τω nom,n
Δτ
τ
:
ð7:75Þ
The value of the frequency instability of the external signal can be made small
using quartz oscillators or quantum generator:
Δω ext
ω ext
1 Â 10
À9 . The relative temperature instability of delay in RF FODL is about 10
À5 1/
С and less for thermalcompensated optical fibers.
The phase difference in the output of the phase detector in PLL system
(Fig. 7.37c) is: Δφ OEO (t) ¼ φ OEO (t À T FODL ) À φ OEO (t). The control signal from
the output of the control circuit g(t) is applied to OEO.
7.7 Systems of Frequency and Phase Automatic Control in OEO
451
described by the symbolic equation ( p ¼ d/dt) for the current frequency of the
controlled OEO:
ω þ Ω Á K p
ð Þ Á F pτ
ð Þ ¼ ω 0 :
ð7:74Þ
Here the function F ¼ F
1À exp Àτp
ð
Þ
τp
τω k
h
i
and we take into consideration not only
inertness of the control circuit with the operator transfer function K( p)‚ but the total
signal delay in RF FODL in the form of the operator of the ideal delay exp(Àpt)‚
including in the argument of the 2π-periodic characteristic F(φ),where φ(ω)—is the
current phase incursion of the radio signal in RF FODL.
With the help Eq. (7.74), in Fig. 7.36b, the regulation characteristic of the FLL
system is shown, i.e., the function of the stabilized frequency versus the variation of
the natural frequency of autonomous OEO.
With the help of Eq. (6.126), we can obtain the expression describing the
stabilization action of FLL with the frequency detector on RF FODL in the vicinity
of any nominal frequency:ω À ω nom, n ¼ (ω 0 À ω nom, n )/[1 + Ω Á τ Á K(0) Á F
0
(φ 0 )] .
We see that the regulation coefficient of the system A ¼ ΩτK(0)F
0
(φ 0 ) containing
of the largest correcting offset Ω, the transfer function of the control circuit on DC K
(0) and the slope F
0 (φ 0 ) of the frequency detector characteristic, increases with the
growth of the signal delay τ in RF FODL.
With the help of FLL system (of the PLL system) with RF FODL, we can solve
not only the problem of frequency stabilization, but also the problem of tracking for
unknown frequency ω ext (t) of the external signal, if to add the mixer to the initial
structure, as shown in Fig. 7.37a. In such a system, the current frequency of the
external signal displaced on the value of any RF FODL plays the role of the nominal
frequency ω nom, n (t) ¼ ω ext (t) + 2πn/τ.
To exclude the ambiguity at the choice of necessary value of operation frequency,
it is enough to use the limiter in the output of the phase detector. The solid line in
regulation characteristics presented in Fig. 7.37b depicts the action of such a limiter.
The stability of nominal frequencies can be estimated with the help of obvious
relationship:
Δω nom,n
ω nom,n
¼
ω ext
ω nom,n
Δω ext
ω ext
þ
2πn
τω nom,n
Δτ
τ
:
ð7:75Þ
The value of the frequency instability of the external signal can be made small
using quartz oscillators or quantum generator:
Δω ext
ω ext
1 Â 10
À9 . The relative temperature instability of delay in RF FODL is about 10
À5 1/
С and less for thermalcompensated optical fibers.
The phase difference in the output of the phase detector in PLL system
(Fig. 7.37c) is: Δφ OEO (t) ¼ φ OEO (t À T FODL ) À φ OEO (t). The control signal from
the output of the control circuit g(t) is applied to OEO.
7.7 Systems of Frequency and Phase Automatic Control in OEO
451