The delay-line as a discriminator The delay line turns a frequency - - PowerPoint PPT Presentation

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 Comté ß St.Petersburg State University of Aerospace Instrumentation, Russia † Now with Smart Quantum, Lannion & Besançon, France ¥ Aeroflex, Paris, France

Outline

The delay-line as a discriminator

2

• 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
• f an oscillator
• Stabilization of an oscillator
• Opto-electronic oscillator

arg H(f)

f

slope 20 arg H(f) delay line resonator slope 2Q

f

Qeq = πν0τ

comparing the slope:

Virtues Problems & solution

✔ ✔ ✔

The delay line turns a frequency into a phase

total white noise

Opto-electronic delay line

3

τd

delay iso iso laser

EOM microwaves

• ptics

shot noise P(t) = P(1 + m cos ωµt) i(t) = qη hν P(1 + m cos ωµt) P µ = 1 2 m2R0 qη hν 2 P 2 intensity modulation photocurrent microwave power Ns = 2q2η hν PR0 thermal noise Nt = FkT0 Sϕ0 = 2 m2

• 2hνλ

η 1 P + FkT0 R0 hνλ qη 2 1 P 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

• ptical-fiber phase noise? still an experimental parameter

Opto-electronic frequency discriminator

4 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 fiber

fiber: attenuation 0.2 dB/km, thermal coeff. 6.8 10-6/K cable: attenuation 0.8 dB/m, thermal coeff. ~ 10-3/K

Rubiola-Salik-Huang-Yu-Maleki, JOSA-B 22(5) p.987–997 (2005)

Φ(s) = Hϕ(s)Φi(s)

Laplace transforms

Sy(f) = |Hy(f)|2 Sϕ i(s)

|Hϕ(f)|2 = 4 sin2(πfτ) |Hy(f)|2 = 4ν2 f 2 sin2(πfτ) 10 GHz, 10 μs

−

Σ

kϕ −s

e

τ Φo(s) Φi(s) V

• (s) kϕΦo(s)

= Φo(s)

τ −s

(1−e )Φi(s) = mixer

+

detector

mW 10

Pλ τd = 1.. 100 µ s

EOM

90° adjust τ∼ _0 laser µm 1.55

mW 100

_ ∼ τd 0 20−40 dB R0 52 dB FFT analyz. (t) vo

• ut

(0.2−20 km) power ampli input microwave (calib.) phase

Note that here one arm is a microwave cable Laplace transforms

Att FFT

DC JDS Uniphase JDS Uniphase 1,5 µm = Contrôleur de polarisation Photodiode DSC40S Déphaseur Ampli DC Analyseur FFT (HP 3561A)

Coupleur 10 dB

Ampli RF

3dB

Ampli AML 8-12GHz

LO RF 5 dBm 10 dBm

Fibre 2 Km

laser EOM SiGe ampli phase 2 km sapphire oscillator

Att FFT

DC JDS Uniphase JDS Uniphase 1,5 µm = Contrôleur de polarisation Photodiode DSC40S Déphaseur Ampli DC Analyseur FFT (HP 3561A)

Coupleur 10 dB

Ampli RF

3dB

Ampli AML 8-12GHz

LO RF 5 dBm 10 dBm

Fibre 2 Km

laser EOM SiGe ampli phase 2 km sapphire oscillator

The effect of AM noise and RIN

5

Background noise measured with =0

1 • sapphire oscillator & laser #1 2 • sapphire oscillator & laser #2 3 • synthesizer (Anritsu) & laser #1

S

• f,

dBrad

2

/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 oscillator

6

• The instrument noise scales as 1/τ, yet

the blue and black plots overlap magenta, red, green => instrument noise blue, black => noise of the sapphire

• scillator under test
• We can measure the 1/f3 phase noise

(frequency flicker) of a 10 GHz sapphire

• scillator (the lowest-noise microwave
• scillator)
• Low AM noise of the oscillator under test

is necessary

Att FFT

DC JDS Uniphase JDS Uniphase 1,5 µm = Contrôleur de polarisation Photodiode DSC40S Déphaseur Ampli DC Analyseur FFT (HP 3561A)

Coupleur 10 dB

Ampli RF

3dB

Ampli AML 8-12GHz

LO RF 5 dBm 10 dBm

ISO ISO

Fibre 2 Km

laser EOM SiGe ampli phase 2 km sapphire oscillator

Phase noise measurement

7

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) measurement

8

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

!'" !(" !%" !#" !"" '" (" %" #" ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5 6A.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 S(f), dBrad2/Hz 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

y = 10–12 baseline

Dual-channel (correlation) measurement

9

F F T a v e r a g e e f f e c t

the residual noise is clearly limited by the number of averaged spectra, m=200

F F T a v e r a g e e f f e c t F F T a v e r a g e e f f e c t

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 – operation

12

Σ

+ + A

free noise

• V’(s)

Vo(s) V

i(s)

initial conditions, noise, or locking signal βf(s) selector βd

τd

e−s = (s) delay

τd

e−s model output

• utput
• scillator

true in practice, delay + selector delay = (s) β

+2π/τd . . . . H(s) . . . . σ l=+3 l=+2 l=+1 l=0 l=−1 l=−2 l=−3 . . . . . . . . j ω τd ln(A) 1 +6π/τd −6π/τd +4π/τd −2π/τd −4π/τd

1 2 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

f * tau transfer function |H(jf)|^2 A=1 A=0.75 A=0.71 A=0.65 A=0.50 A=0.30

file le−calc−hdly−flt src allplots−leeson

delay−line loop, no selection filter

General feedback theory H(s) = Vo(s) Vi(s) = 1 1 − Aβ(s) Delay-line oscillator H(s) = 1 1 − Ae−sτd Location of the roots sl = 1 τd ln(A) + j 2π τd l integer l ∈ (−∞, ∞)

• E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge 2008, ISBN13 9780521886772

Barkhausen condition for oscillation: Aß = 1

Delay-line oscillator – phase noise

13

1000 10000 1e+05 1e+06 0.01 0.1 1 10 100 1000 10000 1e+05 1e+06 1e+07 1e+08

phase noise |H(jf)|^2 delay−line oscillator with selector

frequency, Hz

parameters: tau = 2E−5 s m = 2E5 nu_m = 10 GHz Q = 2000

file le−calc−dly−hphase src allplots−leeson

1

Σ

+ +

(s) Ψ (s) Φ free noise (s) B

f

τ 1 / (1+s ) = (s) B

τd

e−s = delay (s) B

τd

e−s = delay phase noise input phase noise

• utput

selector in practice, delay + selector ω m σ µ=0 µ=−1 µ=−2 . . . . . . . . µ=+2 µ=+1 = j ωm 2Q µ m τd Δω = − 2Q µ m τd Δω = − 2Q ωm (2π/τd) 2Q2 µ m

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) = Φ(s) Ψ(s) = 1 1 − B(s) Delay-line oscillator H(s) = 1 + sτf 1 + sτf − e−sτd Location of the roots sµ = −2Q2 τd µ m 2 + j 2π τd µ − 2Q τd µ m

Delay-line oscillator – expected flicker

14 fL = 1 4π2τ 2 fL = ν0 2Q Qeq = πν0τ Qeq=3×105 ← L=4km Sϕ(f) ≃ f 2

L

f 2 Sψ(f) for f ≪ fL fL=8kHz

Leeson formula

σy ≃ 2.9×10−12

10–11 Allan deviation h−1 = b−3/ν2 6.3×10–24 8.8×10–24 σ2

y = 2 ln(2) h−1

b–3 = 6.3×10–4 (–32 dB)

Delay-line oscillator – measured noise

15 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)‏
• ur 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

S(f), dBrad2/Hz

Phase noise of the opto-electronic oscillator (4 km)

frequency, Hz

• E. Rubiola, apr 2008

OEO: 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 discussions Grants from ANR, CNES, and Aeroflex

home page http://rubiola.org