Stability Measurement of 3 CSOs with Tracking DDSs and Two-Sample - PowerPoint PPT Presentation

French and Italian National Research Councils Stability Measurement of 3 CSOs with Tracking DDSs and Two-Sample COV C. E. Calosso 1 , F . Vernotte 2 , V. Giordano 2,3 , C. Fluhr 4 , B. Dubois 4 , E. Rubiola 1,2,3 1 INRIM, Torino, Italy, 2 Besançon Observatory, France 3 FEMTO-ST Institute, France, 4 FEMTO Engineering, France http://rubiola.org Motivations and Outline 10 GHz CSOs TDDS Statistics • 2 × 10 –16 …10 –15 ADEV 
 • 2 × 10 –14 / τ ADEV 
 • Scalable at 1…10 5 s at 100 MHz • Challenging instrument 
 • Not tested at 100 MHz • Statistical limit? and oscillators Let’s put all things together and play � 1

� 2 Liquid-He Sapphire Oscillator Cr 3+ Fe 3+ doped Paramagnetic temperature Al 2 O 3 mono crystal Whispering Gallery compensation H mode ϕ ≈ 5 cm, H ≈ 3 cm T1 n ESR 10 GHz resonance H T2>T1 Q ≈ 2 × 10 9 at 5–7 K n ESR Magnetic E Susceptibility frequency T Pound-Galani Oscillator n ESR WGH 16,0,0 mode at 11.565 GHz ν 0 ∆ ƒ, Hz 0 0.2 ppm Q oscillator loop 10 0.1 ppm 20 out 30 PM temperature, K 40 power 5 6 7 8 detector VCO • 3 units operational ƒ m • Transportable unit –> stability & control noise validated after roundtrip V ~ ν – ν 0 • 1 unit in progress • Pound frequency lock to the cavity • µHz-resolution synthesis • The same cavity is used in the VCO (2 more units delivered to other labs)

� 3 Mechanical & Thermal Engineering Low-vibe cryogenerator Low acceleration sensitivity < 2 µm displacement @ 1Hz Cold head Thermal ballast Top flange Cold finger temperature stability 100 mK pk low thermal conductance 70K stage supporting rods copper 4K stage braids Temperature stabilised plate Gold plated cavity First generation: 6kW three-phase Current generation: 3 kW mono-phase

� 4 Frequency Synthesis Direct 9.99 GHz 10 GHz output CSO –10±3 MHz 10 GHz 10 GHz input 10 GHz outputs LP DC 2.5 GHz heterodyne x4 PLL BP LP 10±3 MHz 10 GHz DRO frequency DDS control 10±3 MHz DDS ÷4 ÷10 word offset 250 MHz 48 bit DDS 100 MHz outputs 9x10 –17 resolution LP 100 MHz HF/VHF out 0.9 µHz at 10 GHz ÷10 distribution 5 MHz ÷20 outputs LP 5 MHz • Resonator engineering —> 10 GHz – 10 MHz ±3 MHz • Small frequency o ff set —> DDS is OK • Uneven frequencies —> No crosstalk

� 5 Tracking DDS —> Digital PLL ϕ i 100 MHz noise budget b –1 = –110 dBrad 2 /Hz Tracking DDS A A D 9 9 1 2 Clock distribution DDS Mixer, Amplifier, and ADC ADC ϕ m Servo b 0 = 154 dBrad 2 /Hz estimator FPGA ^ x(t) DDS Noise —> C. E. Calosso, Y. Gruson, E. Rubiola, Proc 2012 IFCS p.777-782 TDDS —> M. Calligaris, G. A. Costanzo, C. E. Calosso, Proc 2015 IFCS pp.681-683

� 6 AD9912 —> Time-PM Noise at ≥ 5 MHz ϕ i Flicker: √ k -1 = 5 fs Tracking DDS A DDS ADC σ y ( τ )=1.5 × 10 -14 @ 1 s ϕ m f h = 5 Hz Servo estimator FPGA Jitter = 700 fs rms ^ x(t) DDS Noise —> C. E. Calosso, Y. Gruson, E. Rubiola, Proc 2012 IFCS p.777-782 C. E. Calosso, E. Rubiola, Phase Noise and Jitter in Digital Electronics, arXiv:1701.00094 [physics.ins-det]

� 7 The 6-Channel TDDS Mixer DDS RS-232 Ethernet DC/DC & Clock voltage regulator Ethernet VoCore2 Linux computer (back side) Thermally 12 V, 10 W supply Cyclone III FPGA symmetric design SMA input connectors 6 TDDSs, control unit, and interface in a small instrument

� 8 Thermal Image Small dissipation and thermal symmetry improve phase stability

� 9 Statistics Time Interval Counters Oscillator Instrument ϕ t ( ) Output Noise A x 12 x ( t = ) 1 TIC / ϕ M Single Delta Single Delta 2 2 πυ 0 x x x x x B 2 x BA 21 n 21 d ( t ) B x 34 3 y ( t ) TIC / ϕ M = 4 d t y y y y y C x 56 B 2 BA 21 n 21 y ( t ) y ( t ) 5 − − τ TIC / ϕ M z ( t , ) τ ≡ 6 2 z z z z z B 2 BA 21 n 21 AVAR 2-Sample COV 2 2 2 2 2 σ σ σ σ σ BA 1 21 n 21 B 2 2 ( ) E [ z z ] ( ) E [ z ] σ τ = σ τ = B A y y , y A B σ B , A

� 10 Statistical Tools 3-cornered hat with A x 12 1 TIC / ϕ M noise-free instruments 2 B 2 2 x 34 E [ z ] ⎧ 3 σ = TIC / ϕ M AB 12 1 4 ⎪ 2 2 2 2 2 2 E [ z ] E [ z z z ] σ = ⇒ σ = + − ⎨ BC 34 B 12 34 56 2 C 2 2 x 56 ⎪ E [ z ] 5 σ = TIC / ϕ M CA 56 ⎩ 6 Noisy Instruments 1 1 2 2 2 2 2 2 2 3-Cornered Hat E [ z z z ] [ ] + − = σ + σ + σ − σ 12 34 56 B n 12 n 3 4 n 56 2 2 2 E [ z z ] 2-Sample COV background noise —> 0 = σ 21 34 B At 100 MHz the Time Interval Counter is not an option

� 11 2-Sample COV with TDDS x 1 1 Channels remapping 2 E [ z z ] A σ B = Tracking DDS 32 45 x 2 6-channel 2 x 3 3 • Expand all terms B x 4 4 • Look at convergence laws x 5 5 • Room for improvement C x 6 6 First improvement z z + j k 2 z z E [ z z ] ← = − σ B = i i jk 3 12 4 56 2 Second improvement 1 2 We use this —> E [ z z z z ] σ = + B 3 12 4 56 4 12 3 56 2

� 12 Experiment x 1 2-sample COV A Synth. Tracking DDS x 2 6-channel • INRIM 6-Ch TDDS x 3 Synth. B • 100 MHz outputs x 4 • 2-sample covariance x 5 Synth. C x 6 ϕ AB 3-cornered hat Counter ϕ BC • Lange / K&K counters ϕ CA • 10 GHz outputs • Different beat notes 
 prevent crosstalk

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� 14 Time Domain and ADEV correlated thermal e ff ects drift not removed CSOs CSOs drift removed TDDS

� 15 2-COV vs 3-CH ≈ 10 GHz outputs 100 MHz outputs HF beat notes (1 … 10 MHz) 6-Ch TDDS Lange/K&K Counters 2COV Algorithm 3CH Algorithm 10GHz —> 100 MHz synthesizer 2COV algorithm and 3CH give the affects short-term ( ≤ 100 s) stability same result

� � 16 Conclusions 100 MHz carrier semi-major axes 1-m G shift ♇ at gnd level ☿ ♃ ♄ ♆ � ⛢ ♁ ☾ statistical processing limit τ , s • Full validation of the 100 MHz output • 5–400 MHz TDDS range • Next step: composite clock, 2 × 10 –14 / τ DDS limit