amplitude on the FOS optical input E 0Lin . For this transfer function K FOS ( j2πν) the
following expression is true: K FOS j2πν
ð
Þ¼
E 0Lout
E 0Lin
¼
K FOS
1þj 2πνT FOS
ð
Þ , where T FOS is the
time constant of FOS. Let us extract the module K FOS j2πν
ð
Þ
j
j¼
K FOS
1þ 2πfT FOS
ð
Þ
2
½
1=2 , and
the argument Arg[K FOS ( j2πν)] ¼ arctan(2πfT FOS ).
We note that at examination of OEO, we consider FOS as nondispersion linear
passive element, in which oscillations are delayed by the delay time T FOS .
3.3.5 The Radio-Frequency Filter
In the OEO system, the narrowband high-Q RF filter is intended for filtering the one
type of oscillation from the variety of possible oscillations. The transfer function of
the radio-frequency filter on current can be defined as
K FE ¼
I FEout
I FEin
¼
j2πf
ð
Þ 1=T eF
ð
Þ
j2πf
ð
Þ
2 þ 1=T eF
ð
Þ j2πf
ð
Þþ 2π f 0e
ð
Þ
2
,
ð3:39Þ
where I FEout , I FEin are amplitudes of AC components of electric currents (the first
harmonic) in output and input of electrical filter, relatively, δ e is the damping
factor of the RF filter: δ e ¼ 1/T eF ¼ f 0e /f 0e T eF ¼ f 0e /Q eF , T eF ¼ T F is the filter time
constant, Q eF is the filter Q-factor, f F0 ¼ f 0e is the filter natural frequency,
relatively.
3.3.6 The Nonlinear RF Amplifier in OEO
Let us consider the bipolar transistor amplifying stage on the common emitter
(CE) scheme as the nonlinear amplifier. The static characteristics of the CE transistor
are the input characteristics (the base electrode) i B ¼ f B (e B ) and the output characteristics (the collector electrode) i C ¼ f C (e C ). Here i B , e B are instantaneous values of
the base current and voltage; i C , e C are instantaneous values of the collector current
and voltage; I C0 , e C0 are DC components of the collector current and voltage; and
I B0 , e B0 , are DC components of the base current and voltage.
Now we examine the mode, in which the harmonic signal acts at the transistor input
(between base and emitter electrodes) at constant bias on the base and the collector.
The static transfer characteristics in the CE stage have a form: i C ¼ f CB (u B ) and can be
approximated by the polynomial of third order (for simplicity): i C ¼ αu B À βu
3
B . The
amplifier consisting of the series-connected transistor stages will have the total
characteristic in the form of combination of nonlinearities. The difficulty of obtaining
112 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
following expression is true: K FOS j2πν
ð
Þ¼
E 0Lout
E 0Lin
¼
K FOS
1þj 2πνT FOS
ð
Þ , where T FOS is the
time constant of FOS. Let us extract the module K FOS j2πν
ð
Þ
j
j¼
K FOS
1þ 2πfT FOS
ð
Þ
2
½
1=2 , and
the argument Arg[K FOS ( j2πν)] ¼ arctan(2πfT FOS ).
We note that at examination of OEO, we consider FOS as nondispersion linear
passive element, in which oscillations are delayed by the delay time T FOS .
3.3.5 The Radio-Frequency Filter
In the OEO system, the narrowband high-Q RF filter is intended for filtering the one
type of oscillation from the variety of possible oscillations. The transfer function of
the radio-frequency filter on current can be defined as
K FE ¼
I FEout
I FEin
¼
j2πf
ð
Þ 1=T eF
ð
Þ
j2πf
ð
Þ
2 þ 1=T eF
ð
Þ j2πf
ð
Þþ 2π f 0e
ð
Þ
2
,
ð3:39Þ
where I FEout , I FEin are amplitudes of AC components of electric currents (the first
harmonic) in output and input of electrical filter, relatively, δ e is the damping
factor of the RF filter: δ e ¼ 1/T eF ¼ f 0e /f 0e T eF ¼ f 0e /Q eF , T eF ¼ T F is the filter time
constant, Q eF is the filter Q-factor, f F0 ¼ f 0e is the filter natural frequency,
relatively.
3.3.6 The Nonlinear RF Amplifier in OEO
Let us consider the bipolar transistor amplifying stage on the common emitter
(CE) scheme as the nonlinear amplifier. The static characteristics of the CE transistor
are the input characteristics (the base electrode) i B ¼ f B (e B ) and the output characteristics (the collector electrode) i C ¼ f C (e C ). Here i B , e B are instantaneous values of
the base current and voltage; i C , e C are instantaneous values of the collector current
and voltage; I C0 , e C0 are DC components of the collector current and voltage; and
I B0 , e B0 , are DC components of the base current and voltage.
Now we examine the mode, in which the harmonic signal acts at the transistor input
(between base and emitter electrodes) at constant bias on the base and the collector.
The static transfer characteristics in the CE stage have a form: i C ¼ f CB (u B ) and can be
approximated by the polynomial of third order (for simplicity): i C ¼ αu B À βu
3
B . The
amplifier consisting of the series-connected transistor stages will have the total
characteristic in the form of combination of nonlinearities. The difficulty of obtaining
112 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .