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Application of the optical fiber to generation and measurement of low-phase-noise microwaves
• Basics
• Single-channel phase noise measurements
• Cross-spectrum phase noise measurements
• Opto-electronic oscillator
K. VolyanskiyΩß, J. CusseyΩ†, H. TavernierΩ, P. SalzensteinΩ,G. Sauvage¥, L. LargerΩ, E. RubiolaΩ
Ω FEMTO-ST Institute, CNRS and Université de Franche Comtéß St.Petersburg State University of Aerospace Instrumentation, Russia
† Now with Smart Quantum, Lannion & Besançon, France¥ Aeroflex, Paris, France
Outline
The delay-line as a discriminator2
• Coax cable: 50 dB attenuation limits to
• 950 ns @ 1 GHz (Q=3000) - RG213
• 300 ns @ 10 GHz (Q=11500) - RG402
• Optical fiber:
• max delay is not limited by the attenuation
• 1-100 μs delay is possible(Q=105–107 @ 31 GHz)
• Works at any frequency ν = n/τ, integer τ (the resonator does not)
• Sφ measurement of an oscillator
• Dual-channel Sφ measurement of an oscillator
• Stabilization of an oscillator
• Opto-electronic oscillator
arg
H(f
)
f!0
slope 2"!0#
arg
H(f
)
!0
delay line resonatorslope 2Q
f
Qeq = !"0#comparing the slope:
Virtues Problems & solution
The delay line turns a frequency into a phase
total white noise
Opto-electronic delay line3162 E. Rubiola Phase Noise . . . in Oscillators March 5, 2008
le-oeo
power
!ddelayiso iso isolaser EOM output
microwavesoptics
selectorampli
Figure 5.17: Photonic delay-line oscillator.
Introducing the amplifier power-law model S!(f) = b0 + b!1f , limited to white
and flicker noise, we get
S"(f) = b0!2
m
4"2m2
1f2
+ b!1!2
mb!1
4"2m2
1f3
. (5.76)
The fractional-frequency fluctuation spectrum Sy(f) is found by using Sy(f) =f2
#2m
S"(f). Thus,
Sy(f) = b01
4"2m2
1f2
+ b!11
4"2m2
1f3
. (5.77)
After matching the above to the power-law Sy(f) =!
i hif i, we find
h0 =b0
4"2m2(5.78)
and
h!1 =b!1
4"2m2. (5.79)
Using Table 1.4, the Allan variance is
#2y($) =
"1/$2
terms
#+
b0
4"2m2
12$
+b!1
4"2m22 ln(2) . (5.80)
5.8 Examples
Example 5.1 Photonic delay-line oscillator.We analyze the photonic delay-line oscillator of Fig. 5.17, based on the
following parameters, and inspired to the references [29] and [109]
shot noise
P (t) = P (1 + m cos !µt)
i(t) =q!
h"P (1 + m cos #µt)
Pµ =12
m2R0
! q!
h"
"2P 2
intensity modulation
photocurrent
microwave power
Ns = 2q2!
h"PR0
thermal noise Nt = FkT0
S!0 =2
m2
!2h!"
"
1P
+FkT0
R0
"h!"
q"
#2 "1P
#2$shot thermal
• amplifier GaAs: b–1 ≈ –100 to –110 dBrad2/Hz, SiGe: b–1 ≈ –120 dBrad2/Hz• photodetector b–1 ≈ –120 dBrad2/Hz [Rubiola & al. MTT/JLT 54(2), feb. 2006• (mixer b–1 ≈ –120 dBrad2/Hz)• the phase flicker coefficient b–1 is about independent of power• in a cascade, (b–1)tot adds up, regardless of the device order
flicker phase noise
optical-fiber phase noise? still an experimental parameter
Opto-electronic frequency discriminator4
10 GHz, 10 μs• delay –> frequency-to-phase conversion
• works at any frequency
• long delay (microseconds) is necessary for high sensitivity
• the delay line must be an optical fiberfiber: attenuation 0.2 dB/km, thermal coeff. 6.8 10-6/Kcable: attenuation 0.8 dB/m, thermal coeff. ~ 10-3/K
Rubiola-Salik-Huang-Yu-Maleki, JOSA-B 22(5) p.987–997 (2005)
!(s) = H!(s)!i(s)
Laplace transforms
Sy(f) = |Hy(f)|2 S! i(s)
|H!(f)|2 = 4 sin2(!f")
|Hy(f)|2 =4!2
0
f2sin2("f#)
ment and its equivalent in the Laplace transform domain.by inspection of Fig. 3,
!o!s" = H"!s"!i!s", !4"
where H"!s"=1!exp!!s#". Turning the Laplace trans-forms into power spectra Eq. (4) becomes
S"o!f" = #H"!jf"#2S"i!f", !5"
where
#H"!jf"#2 = 4 sin2!$f#". !6"
The spectrum of frequency fluctuation Sy!f" is related toS"!f" through
Sy!f" =f2
%02S"i!f". !7"
Combining Eqs. (5) and (7), we get
Sy!f" = #Hy!jf"#2S"i!f", !8"
where
#Hy!jf"#2 =4%0
2
f2 sin2!$f#". !9"
Equation (5) is used to derive the phase noise S"i!f" of theoscillator under test. Alternatively, Eq. (7) is used to de-rive the frequency noise Sy!f". We prefer S"!f", indepen-dent of how the final results will be expressed, becausethe background noise of the instrument appears as S"!f".
Figure 4 shows the transfer functions #H"!jf"#2 and#Hy!jf"#2 for %0=10 GHz and #d=10 &s (2-km delay line),which is typical of our experiments. For f!0, it holds#H"!jf"#2$ f2. Fortunately, high slope processes such asflicker of frequency dominate in this region (see Fig. 1),which compensates #H"!jf"#2. The phase-noise measure-ment is therefore possible, providing that the delay #d canbe appropriately chosen. #H"!jf"#2, as well as #Hy!jf"#2, hasa series of zeros at f=n /#d, with integer n'1. The experi-mental results are not useful in the vicinity of these zeros.At the beginning of our experiments we hoped to recon-struct the spectrum beyond the first zero at f=1/#d by ex-ploiting the maxima at f= !2i+1" / !2#d" (integer i'1). This
turned out to be difficult. One problem is the resolution ofthe FFT analyzer, as the density of zeros increases on alogarithmic scale. Another problem is the presence ofstray signals in the measured spectrum, which make un-reliable the few data around the maxima. The practicallimit is about f=0.95/#d, where #H"!jf"#2=!16 dB, and atmost some points around f=3/ !2#d" between the first andsecond zeros.
4. SOURCES OF NOISEThe basic block for photonic phase-noise measurements isshown in Fig. 3(a). In normal operation the random phase"!t" results from the fluctuations of the input frequency.In this section we analyze the sources of noise of theblock, since "o!t" is acquired form the noise of electricaland optical components.
The power P(!t" of the optical signal is sinusoidallymodulated at the microwave angular frequency )& with amodulation index m
P(!t" = P(!1 + m cos )&t". !10"
Here, we use the subscripts ( and & for “light” and “mi-crowave,” and the overbar to denote the average. Equa-tion (10) is similar to the traditional amplitude modula-tion of radio broadcasting, but optical power is modulatedinstead of rf voltage. In the presence of a distorted (non-linear) modulation, we take the fundamental of the modu-lating signal, at )&.
The detector photocurrent is
i!t" =q*
h%(
P(!1 + m cos )&t", !11"
where q=1.602+10!19 C is the electron charge, * is thequantum efficiency of the photodetector, and h=6.626+10!34 J/Hz the Planck constant. Only the ac termm cos )&t of Eq. (11) contributes to the microwave signal.The microwave power fed into the load resistance R0 isP&=R0iac
2 , hence
P& =1
2m2R0% q*
h%(&2
P(2. !12"
A. White NoiseThe discrete nature of photons leads to the shot noise ofpower spectral density Ns=2qiR0 [W/Hz] at the detectoroutput. By virtue of Eq. (11),
Ns = 2q2*
h%(
P(R0. !13"
In addition, there is the equivalent input noise of the am-plifier loaded by R0, whose power spectrum is
Nt = FkBT0, !14"
where F is the noise figure of the amplifier, kB=1.38+10!23 J/K is the Boltzmann constant, and T0 is the tem-perature. The white noise Ns+Nt turns into a noise floorS"0= !Ns+Nt" /P& of S"!f". By use of Eqs. (12)–(14), thefloor is
Fig. 4. Transfer functions #H"!jf"#2 and #Hy!jf"#2 plotted for %0=10 GHz and #d=10 &s.
990 J. Opt. Soc. Am. B/Vol. 22, No. 5 /May 2005 Rubiola et al.
10 GHz, 10 μs
−
Σ kϕ
−se τ
Φo(s)Φi(s) Vo(s) kϕΦo(s)=
Φo(s) τ!s(1!e )Φ i(s)=
mixer
+
detector
mW10
Pλτd = 1.. 100 µ s
EOM
90° adjust
τ∼_0
laser
µm1.55
mW100
_∼τd 0 20!40dB
R0
52 dB
FF
Tan
aly
z.
(t)vo
out
(0.2!20 km)
power ampli
inputmicrowave
(calib.)
phase
Note that here one arm is a microwave cable
Laplace transforms
Att FFTDC
ModulateurMach-ZehnderJDS Uniphase
Diode LaserJDS Uniphase
1,5 µm=
Contrôleurde polarisation
PhotodiodeDSC40S
Déphaseur
Ampli DC
Analyseur FFT(HP 3561A)
Coupleur10 dB
Ampli RF
3dB
AmpliAML
8-12GHz
Oscillateur Saphir
LO
RF
5 dBm
10 dBm
ISOISO
Fibre 2 Km
laser EOM SiGe ampli
phase
2 km
sapphire oscillator
Att FFTDC
ModulateurMach-ZehnderJDS Uniphase
Diode LaserJDS Uniphase
1,5 µm=
Contrôleurde polarisation
PhotodiodeDSC40S
Déphaseur
Ampli DC
Analyseur FFT(HP 3561A)
Coupleur10 dB
Ampli RF
3dB
AmpliAML
8-12GHz
Oscillateur Saphir
LO
RF
5 dBm
10 dBm
ISOISO
Fibre 2 Km
laser EOM SiGe ampli
phase
2 km
sapphire oscillator
The effect of AM noise and RIN5
!
!" #$%&'(')*$+, -., /, %.*0(.*, -., 1(0)2, &3'*., (.4($0&'+2, 5.*, &()+6)&'07, .**')*, 80., +$0*,'9$+*,.::.620;*,*0(,5.,1'+6,-.,%.*0(.,-.,1(0)2,-.,&3'*.,*'+*,5)4+.,<,(.2'(-=,
,
,!
!
!
,,,,,,>",,?()7,'&&($7)%'2):,-.*,&()+6)&'07,6$%&$*'+2*,02)5)*;*,@,
"#$%&!'()&*!+",-!./00!12,@,!,ABCC,D,
"#$%&!'()&*!3456!7#8#9):!./;.!12,@,!,A/CC,D,
<$%:'(9&:*!+",-!<(=>?@&>A%&*!B#$C(9&!%&!'#9>#:2!=$:D&!@!@,!,A/EC,D,
E>$9$%#$%&!"#)=$F&*G!",3HI,,@,AECC,D,
42D'#J#=(9&:*!4<K,@,BFCC,D,
"LD>()&:*!M7!4MM4!NHOP,@,!GC,D,
42D'#J#=(9&:*!QE,@,!,!CCC,D,
,
,
,
,
,
! .;
Background noise measured with !=0 1 • sapphire oscillator & laser #1 2 • sapphire oscillator & laser #2 3 • synthesizer (Anritsu) & laser #1
S!!f",
dBrad2/Hz
frequency, Hz
Pλ(t) → VOS(t–τ)
Pμ(t) → VOS(t–τ)
Pμ(t) → VOS(t)
The AM noise turns into Vos fluctuation, which may limit the sensitivity
The delay de-correlates the AM noise. Thus there is no null of sensitivity
The laser RIN turns into Vos fluctuation, which may limit the sensitivity
AM noise
Laser RIN
Instrument background measured at zero-length fiber
Lowest AM noise and Lowest RIN give the lowest background noise
Measurement of a sapphire oscillator6
• The instrument noise scales as 1/τ, yet the blue and black plots overlapmagenta, red, green => instrument noise blue, black => noise of the sapphire oscillator under test
• We can measure the 1/f3 phase noise (frequency flicker) of a 10 GHz sapphire oscillator (the lowest-noise microwave oscillator)
• Low AM noise of the oscillator under test is necessary
Att FFTDC
ModulateurMach-ZehnderJDS Uniphase
Diode LaserJDS Uniphase
1,5 µm=
Contrôleurde polarisation
PhotodiodeDSC40S
Déphaseur
Ampli DC
Analyseur FFT(HP 3561A)
Coupleur10 dB
Ampli RF
3dB
AmpliAML
8-12GHz
Oscillateur Saphir
LO
RF
5 dBm
10 dBm
ISOISO
Fibre 2 Km
laser EOM SiGe ampli
phase
2 km
sapphire oscillator
Phase noise measurement7
A.L. Lance, W.D. Seal, F. Labaar ISA Transact.21 (4) p.37-84, Apr 1982
Original idea:D. Halford’s NBS notebook F10 p.19-38, apr 1975
First published: A. L. Lance & al, CPEM Digest, 1978
The delay line converts the frequency noise into phase noise
The high loss of the coaxial cable limits the maximum delay
Updated version:The optical fiber provides long delay with low attenuation (0.2 dB/km or 0.04 dB/μs)
Dual-channel (correlation) measurement8
Improvements
derives from: E. Salik, N. Yu, L. Maleki, E. Rubiola, Proc. Ultrasonics-FCS Joint Conf., Montreal, Aug 2004 p.303-306
• Understanding flicker (photodetectors and amplifiers)
• SiGe technology provides lower 1/f phase noise
• CATV laser diodes exhibit lower AM/FM noise
• Low Vπ EOMs show higher stability because of the lower RF power
• Optical fiber sub-mK temperature controlled
!"!
!"#
!"$
!"%
!"&
!!'"
!!("
!!%"
!!#"
!!""
!'"
!("
!%"
!#"
)*+,-./0.12345
6!12781*97#:345
;<9/0=.*17.1>*[email protected]=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG56A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
J.Cussey 20/02/07 Mesure200avg.txt –20
–180
–40
–60
–80
–160
–140
–120
–100
101 102 103 104 105
Fourier frequency, Hz
!"!
!"#
!"$
!"%
!"&
!!'"
!!("
!!%"
!!#"
!!""
!'"
!("
!%"
!#"
)*+,-./0.12345
6!12781*97#:345
;<9/0=.*17.1>*[email protected]=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG56A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
J.Cussey 20/02/07 Mesure200avg.txt
!"!
!"#
!"$
!"%
!"&
!!'"
!!("
!!%"
!!#"
!!""
!'"
!("
!%"
!#"
)*+,-./0.12345
6!12781*97#:345
;<9/0=.*17.1>*[email protected]=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG56A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
J.Cussey 20/02/07 Mesure200avg.txt
S!
(f),
dBra
d2/H
z
residual phase noise (cross-spectrum),short delay ("!0), m=200 averaged spectra,unapplying the delay eq. with "=10 "s (2 km)
J.Cussey, feb 2007
!"!
!"#
!"$
!"%
!"&
!!'"
!!("
!!%"
!!#"
!!""
!'"
!("
!%"
!#"
)*+,-./0.12345
6!12781*97#:345
;<9/0=.*17.1>*[email protected]=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG56A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
J.Cussey 20/02/07 Mesure200avg.txt
!"!
!"#
!"$
!"%
!"&
!!'"
!!("
!!%"
!!#"
!!""
!'"
!("
!%"
!#"
)*+,-./0.12345
6!12781*97#:345
;<9/0=.*17.1>*[email protected]=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG56A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
J.Cussey 20/02/07 Mesure200avg.txt
!y = 10 –12
baseline
Dual-channel (correlation) measurement9
FFT
average
effect
the residual noise is clearly limited by the number of averaged spectra, m=200
FFT
average
effect
FFT
average
effect
Measurement of the delay-line noise (1)10
• matching the delays, the oscillator phase noise cancels
• this scheme gives the total noise 2 × (ampli + fiber + photodiode + ampli) + mixer thus it enables only to assess an upper bound of the delay-line noise
11
• The method enables only to assess an upper bound of the delay-line noise b–1 ≤ 5×10–12 rad2/Hz for L = 2 km (–113 dBrad2/Hz)
• We believe that this residual noise is the signature of the two GaAs power amplifier that drives the MZ modulator
b–1 = 10–11 (–110 dB)
Measurement of the delay-line noise (2)
Delay-line oscillator – operation12
!+
+A
freenoise
oV’(s)
Vo(s)
Vi(s)
initial conditions,noise, or lockingsignal
"f(s)selector
"d#de!s=(s)
delay
#de!s
model output
outputoscillator
true
in practice, delay + selector
delay=(s)" 0
+2π/τd
. . . .
H(s)
. . . .
σ
l=+3
l=+2
l=+1
l=0
l=!1
l=!2
l=!3
. . . .
. . . .
j ω
τdln(A)
1
+6π/τd
−6π/τd
+4π/τd
−2π/τd
−4π/τd
0 1 2 30123456789
1011121314151617181920
f * tau
trans
fer f
unct
ion
|H
(jf)|^
2
A=1
A=0.75
A=0.71
A=0.65
A=0.50A=0.30
file le−calc−hdly−fltsrc allplots−leeson
delay−line loop, no selection filter
General feedback theory
H(s) =Vo(s)Vi(s)
=1
1!A!(s)
Delay-line oscillator
H(s) =1
1!Ae!s!d
Location of the roots
sl =1"d
ln(A) + j2#
"dl integer l " (!#,#)
E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge 2008, ISBN13 9780521886772
Barkhausen conditionfor oscillation: Aß = 1
Delay-line oscillator – phase noise13
1000 10000 1e+05 1e+060.01
0.1
1
10
100
1000
10000
1e+05
1e+06
1e+07
1e+08phase noise |H(jf)|^2delay−line oscillator with selector
frequency, Hz
parameters: tau = 2E−5 s m = 2E5 nu_m = 10 GHz Q = 2000
file le−calc−dly−hphasesrc allplots−leeson
1Σ+
+
(s)Ψ (s)Φfreenoise
(s)B fτ1 / (1+s )=(s)B τde!s=delay
(s)B τde!s=delay
phase noiseinput
phase noiseoutput
selector
in practice, delay + selector
ωm
σµ=0
µ=−1
µ=−2
. . . .
. . . .
µ=+2
µ=+1
= j
ωm
2Q
µmτd
Δω = − 2Q
µmτd
Δω = − 2Q
ωm (2π/τd )
2Q2 µm
2
τd
σ = −
(2π/τd ) µ
(2π/τd ) µ
E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge 2008, ISBN13 9780521886772
General feedback theory
H(s) =!(s)"(s)
=1
1! B(s)
Delay-line oscillator
H(s) =1 + s!f
1 + s!f ! e!s!d
Location of the roots
sµ = !2Q2
!d
! µ
m
"2+ j
2"
!dµ! 2Q
!d
µ
m
Delay-line oscillator – expected flicker14
fL =1
4!2"2
fL =!0
2Q
Qeq = !"0# Qeq=3×105 ← L=4km
S!(f) ! f2L
f2S"(f) for f " fL
fL=8kHz
Leesonformula
!y ! 2.9"10!12
10–11
Allan deviation
h!1 = b!3/!20 6.3×10–24
8.8×10–24!2y = 2 ln(2) h!1
b–3 = 6.3×10–4 (–32 dB)
Delay-line oscillator – measured noise15
expected phase noise b–3 ≈ 6.3×10–4 (–32 dB)
• 1.310 nm DFB CATV laser
• Photodetector DSC 402 (R = 371 V/W) • RF filter ν0 = 10 GHz, Q = 125
• RF amplifier AML812PNB1901 (gain +22dB)
our OEO
b–3=10–3 (–30dB)
Agilent E8257c, 10 GHz, low-noise opt.
Wenzel 501-04623 OCXO 100 MHz mult. to 10 GHz
101
102
103
104
105
–20
–40
–60
–80
–160
–140
–120
–100
0
S!
(f),
dBra
d2/H
z
Phase noise of the opto-electronic oscillator (4 km)
frequency, Hz
E. Rubiola, apr 2008OEO: Kirill Volyanskiy, may 2007
Conclusions
• The optical fiber is suitable to a wide range of microwave frequency with fine pitch
• At room temperature, short-term stability is similar/better to a sapphire oscillator
• Single- and dual-channel phase noise measurements• Opto-electronic oscillator, theory and experiments
16
Thanks to L. Maleki, N. Yu, E. Salik (JPL/OEwaves) for numerous discussionsGrants from ANR, CNES, and Aeroflex
home page http://rubiola.org