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

Application of the optical fiber to generation and measurement of low-phase-noise microwaves K. Volyanskiy Ω ß , J. Cussey Ω † , H. Tavernier Ω , P. Salzenstein Ω ,G. Sauvage ¥ , L. Larger Ω , E. Rubiola Ω 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 • Basics • Single-channel phase noise measurements • Cross-spectrum phase noise measurements • Opto-electronic oscillator home page http://rubiola.org

2 The delay-line as a discriminator The delay line turns a frequency into a phase delay line resonator slope 2 �� 0 � slope 2Q arg H(f) arg H(f) f f � 0 � 0 comparing the slope: Q eq = πν 0 τ Virtues Problems & solution • • Works at any frequency ν = n/ τ , Coax cable: 50 dB attenuation limits to • integer τ (the resonator does not) 950 ns @ 1 GHz (Q=3000) - RG213 ✔ • • S φ measurement of an oscillator 300 ns @ 10 GHz (Q=11500) - RG402 ✔ • • Dual-channel S φ measurement Optical fiber: of an oscillator • max delay is not limited by the • Stabilization of an oscillator attenuation ✔ • • Opto-electronic oscillator 1-100 μ s delay is possible (Q=10 5 –10 7 @ 31 GHz)

3 Opto-electronic delay line optics microwaves delay τ d laser EOM iso iso P ( t ) = P (1 + m cos ω µ t ) intensity modulation i ( t ) = q η N s = 2 q 2 η h ν P (1 + m cos ω µ t ) photocurrent shot noise h ν PR 0 � q η � 2 P µ = 1 2 m 2 R 0 P 2 microwave power thermal noise N t = FkT 0 h ν shot thermal � 2 � 1 � � 2 � � h ν λ 2 h ν λ P + FkT 0 2 1 total white noise S ϕ 0 = m 2 R 0 q η P η flicker phase noise • amplifier GaAs: b –1 ≈ –100 to –110 dBrad 2 /Hz, SiGe: b –1 ≈ –120 dBrad 2 /Hz • photodetector b –1 ≈ –120 dBrad 2 /Hz [Rubiola & al. MTT/JLT 54(2), feb. 2006 • (mixer b –1 ≈ –120 dBrad 2 /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 optical-fiber phase noise? still an experimental parameter

4 Opto-electronic frequency discriminator Rubiola-Salik-Huang-Yu-Maleki, JOSA-B 22(5) p.987–997 (2005) τ d = 1.. 100 µ s Laplace transforms P λ phase (0.2−20 km) detector laser EOM Φ ( s ) = H ϕ ( s ) Φ i ( s ) v o (t) _ ∼ µ m τ d 0 1.55 R 0 20−40 out (calib.) dB analyz. 100 | H ϕ ( f ) | 2 = 4 sin 2 ( π f τ ) FFT 10 mW microwave mW input _0 τ∼ 52 dB 90° adjust power ampli S y ( f ) = | H y ( f ) | 2 S ϕ i ( s ) Note that here one arm is a microwave cable | H y ( f ) | 2 = 4 ν 2 f 2 sin 2 ( π f τ ) 0 Laplace transforms τ mixer −s e − Φ i (s) o (s) k ϕ Φ o (s) V = Φ o (s) k ϕ Σ + −s τ Φ o (s) ) Φ i (s) = (1−e • 10 GHz, 10 μ s delay –> frequency-to-phase conversion 10 GHz, 10 μ s • 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

5 The effect of AM noise and RIN The AM noise turns into Vos Ampli JDS Uniphase Photodiode JDS Uniphase EOM SiGe ampli AML laser 1,5 µm fluctuation, which may limit the DSC40S = 8-12GHz P μ (t) → V OS (t– τ ) sensitivity Analyseur FFT Contrôleur 2 km Fibre 2 Km 5 dBm (HP 3561A) de polarisation RF AM noise The delay de-correlates the AM Att FFT 3dB DC sapphire oscillator LO noise. Thus there is no null of Ampli DC 10 dBm sensitivity P μ (t) → V OS (t) Déphaseur phase Coupleur 10 dB Ampli RF The laser RIN turns into Vos P λ (t) → Ampli JDS Uniphase Photodiode JDS Uniphase EOM SiGe ampli AML laser 1,5 µm DSC40S = fluctuation, which may limit the 8-12GHz V OS (t– τ ) sensitivity Analyseur FFT Contrôleur 2 km Fibre 2 Km 5 dBm (HP 3561A) de polarisation RF Att FFT 3dB DC Laser RIN sapphire oscillator LO Ampli DC 10 dBm � f � , S � Background noise measured with � =0 Déphaseur phase Coupleur 10 dB dBrad 2 /Hz 1 • sapphire oscillator & laser #1 2 • sapphire oscillator & laser #2 Ampli RF 3 • synthesizer (Anritsu) & laser #1 Instrument background measured at zero-length fiber Lowest AM noise and Lowest RIN give the lowest background noise frequency, Hz

6 Measurement of a sapphire oscillator Ampli JDS Uniphase Photodiode JDS Uniphase EOM SiGe ampli AML laser 1,5 µm DSC40S = 8-12GHz Analyseur FFT Contrôleur 2 km Fibre 2 Km 5 dBm (HP 3561A) de polarisation RF Att FFT 3dB DC sapphire oscillator LO Ampli DC 10 dBm Déphaseur phase Coupleur 10 dB Ampli RF ISO ISO • 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 oscillator under test • We can measure the 1/f 3 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

7 Phase noise measurement 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/ μ s) A.L. Lance, W.D. Seal, F. Labaar ISA Transact.21 (4) p.37-84, Apr 1982

8 Dual-channel (correlation) measurement Improvements • Understanding flicker (photodetectors and amplifiers) • SiGe technology provides lower 1/f phase noise • CATV laser diodes exhibit lower AM/FM noise • Low V π EOMs show higher stability because of the lower RF power • Optical fiber sub-mK temperature controlled derives from: E. Salik, N. Yu, L. Maleki, E. Rubiola, Proc. Ultrasonics-FCS Joint Conf., Montreal, Aug 2004 p.303-306

9 Dual-channel (correlation) measurement J.Cussey 20/02/07 Mesure200avg.txt –20 #" residual phase noise (cross-spectrum), ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5 short delay ( � � 0), m=200 averaged spectra, 6A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51 –40 %" unapplying the delay eq. with � =10 � s (2 km) � y = 10 –12 baseline –60 (" –80 '" –100 !"" S � (f), dBrad 2 /Hz T F –120 F !#" e g a r e T v F a F t c e e g f f a e r e v a –140 t !%" c e f f e T F F e g –160 a !(" r e v a t c e f f e –180 !'" Fourier frequency, Hz J.Cussey, feb 2007 10 1 10 2 10 3 10 4 10 5 the residual noise is clearly limited by the number of averaged spectra, m=200

10 Measurement of the delay-line noise (1) • 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 Measurement of the delay-line noise (2) b –1 = 10 –11 ( –110 dB) • The method enables only to assess an upper bound of the delay- line noise b –1 ≤ 5 × 10 –12 rad 2 /Hz for L = 2 km (–113 dBrad 2 /Hz) • We believe that this residual noise is the signature of the two GaAs power amplifier that drives the MZ modulator

12 Delay-line oscillator – operation j ω H(s) model output V o (s) . . . . . . . . noise V i (s) free V’(s) l=+3 +6 π / τ d + o Σ A initial conditions, +4 π / τ d + l=+2 noise, or locking true signal oscillator output l=+1 +2 π / τ d delay l=0 0 e −s τ d β (s) = σ − 2 π / τ d l=−1 in practice, delay + selector Barkhausen condition delay selector − 4 π / τ d l=−2 τ d e −s β d β f (s) (s) = for oscillation: Aß = 1 l=−3 − 6 π / τ d . . . . . . . . General feedback theory 1 ln(A) τ d H ( s ) = V o ( s ) 1 V i ( s ) = 1 − A β ( s ) 20 delay − line loop, no selection filter 19 A=1 file le − calc − hdly − flt 18 src allplots − leeson 17 transfer function |H(jf)|^2 16 Delay-line oscillator A=0.75 15 14 13 1 12 A=0.71 H ( s ) = 11 10 1 − Ae − s τ d 9 8 A=0.65 7 6 Location of the roots 5 4 A=0.50 3 s l = 1 ln( A ) + j 2 π 2 A=0.30 integer l ∈ ( −∞ , ∞ ) l 1 0 τ d τ d 0 1 2 3 f * tau E. Rubiola, Phase Noise and Frequency Stability in Oscillators , Cambridge 2008, ISBN13 9780521886772