input and output of RF amplifier (3, 4). Figure 6.23b shows the OEO MZ with the
single equivalent noise source ξ n .
In the general case, for OEO MZ, the PSD curve of phase fluctuations S ΨAG has
the complicate analytical shape, which is determined by the in-phase S μRe (ω) and the
quadrature S μIm (ω) components:
S ΨАГ
P G
¼
Y a Re À σ U
ð
Þ
2 Á S ImPDNA þ Y aIm
2
Á S Re PDNA À 2 Y a Re À σ U
ð
ÞÁY aIm
2 S ImRePDNA
P G Y a Re À σ U
½
ÁY a Re À 1
½
þY aIm
½
2
n
o 2
,
ð6:64Þ
where P G is the microwave power of the fundamental harmonic of OEO MZ,
S ImPDNA ¼ G 12 K
2
PD P G Á S ImL þ S ImPD þ S ImNA , S Re FDNY ¼ G 12 P G K
2
PD S Re L þ
S Re FD þ S Re NA are the quadrature and in-phase components of laser total noises.
We can assume that PD and NA have, for example:
S L % S ImL % S Re L ¼
S βPN
P 0L F
2 T
2
0L
,
ð6:65Þ
where G 12 ¼ 1 À (A 1 /A 2 ) Á exp (ÀT FOS /T c ) ¼ 1 À K Ψ12 , K Ψ12 ¼ (A 1 /
A 2 )Á exp (ÀT FOS /T c ) is the correlation coefficient defining by MZ and approximately
equal to 1 with accuracy 0.9–0.999 depending on the geometrical length of the
optical fiber, K
2
PD is the coefficient, which takes into account the spectrum transformations at passing through MZ and at photodetection of PSD of the laser
emission in the MZ input and the RF oscillation PSD in the PD load.
With purpose of the simple expressions, we assume that in-phase and quadrature
components of the own noises of PD is approximately the same:
S RePD % S ImPD ¼ 2eI 0PD R PD ¼ 2eS 0PD Á P 0L R PD , where the electron charge
e ¼ 1.6 Á 10
À19 Q, I 0PD is DC component of the PD photo-current, which is
I 0PD ¼ S 0PD Á P 0L , where S 0PD is the static slope of the watt–ampere PD characteristic, R PD is the load resistance of PD in DC.
We suppose that own noises of the ultra-wideband low-noise noninertial RF NA
are determined only by “thermal” noises (i.e., we do not take into consideration
flicker-noises etc.). For calculation simplicity, we assume that in-phase and quadrature components of PSD of “thermal” noises in the NA input are equal [3]:
S ReNY ¼ S ImNY ¼ D Y kT, where D Y is the noise-factor of NA, k ¼ 1.38 Á 10
À23 J/
K is the Boltzmann constant, T is the absolute temperature in Kelvin degrees.
Then, at substitution S RePD % S ImPD and S ReNY ¼ S ImNY , the expression (6.64) is
written as:
332
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .
single equivalent noise source ξ n .
In the general case, for OEO MZ, the PSD curve of phase fluctuations S ΨAG has
the complicate analytical shape, which is determined by the in-phase S μRe (ω) and the
quadrature S μIm (ω) components:
S ΨАГ
P G
¼
Y a Re À σ U
ð
Þ
2 Á S ImPDNA þ Y aIm
2
Á S Re PDNA À 2 Y a Re À σ U
ð
ÞÁY aIm
2 S ImRePDNA
P G Y a Re À σ U
½
ÁY a Re À 1
½
þY aIm
½
2
n
o 2
,
ð6:64Þ
where P G is the microwave power of the fundamental harmonic of OEO MZ,
S ImPDNA ¼ G 12 K
2
PD P G Á S ImL þ S ImPD þ S ImNA , S Re FDNY ¼ G 12 P G K
2
PD S Re L þ
S Re FD þ S Re NA are the quadrature and in-phase components of laser total noises.
We can assume that PD and NA have, for example:
S L % S ImL % S Re L ¼
S βPN
P 0L F
2 T
2
0L
,
ð6:65Þ
where G 12 ¼ 1 À (A 1 /A 2 ) Á exp (ÀT FOS /T c ) ¼ 1 À K Ψ12 , K Ψ12 ¼ (A 1 /
A 2 )Á exp (ÀT FOS /T c ) is the correlation coefficient defining by MZ and approximately
equal to 1 with accuracy 0.9–0.999 depending on the geometrical length of the
optical fiber, K
2
PD is the coefficient, which takes into account the spectrum transformations at passing through MZ and at photodetection of PSD of the laser
emission in the MZ input and the RF oscillation PSD in the PD load.
With purpose of the simple expressions, we assume that in-phase and quadrature
components of the own noises of PD is approximately the same:
S RePD % S ImPD ¼ 2eI 0PD R PD ¼ 2eS 0PD Á P 0L R PD , where the electron charge
e ¼ 1.6 Á 10
À19 Q, I 0PD is DC component of the PD photo-current, which is
I 0PD ¼ S 0PD Á P 0L , where S 0PD is the static slope of the watt–ampere PD characteristic, R PD is the load resistance of PD in DC.
We suppose that own noises of the ultra-wideband low-noise noninertial RF NA
are determined only by “thermal” noises (i.e., we do not take into consideration
flicker-noises etc.). For calculation simplicity, we assume that in-phase and quadrature components of PSD of “thermal” noises in the NA input are equal [3]:
S ReNY ¼ S ImNY ¼ D Y kT, where D Y is the noise-factor of NA, k ¼ 1.38 Á 10
À23 J/
K is the Boltzmann constant, T is the absolute temperature in Kelvin degrees.
Then, at substitution S RePD % S ImPD and S ReNY ¼ S ImNY , the expression (6.64) is
written as:
332
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .