home page http://rubiola.org

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>*-?@17.1A=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>*-?@17.1A=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>*-?@17.1A=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>*-?@17.1A=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>*-?@17.1A=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