1. 1 Commissioning meeting, Cascina, 5.12.2005 LA electronics noise budget ● Sources of electronic noise ● C7 electronic noise ● Electronic noise for optimized power ● Some conclusions

2. 2 Commissioning meeting, Cascina, 5.12.2005 Scheme of LA electronics ADC noise Preamp. noise Shot noise Low-pass filter AC: Gain 200 DC: Gain 1 diff. sig. non-diff.sig. Non-optimal treatment of DC signals dominated by ADC noise (but were not foreseen as error signals) VME QD box

3. 3 Commissioning meeting, Cascina, 5.12.2005 Principles of calculation Calculate electronic noise at each quadrant diode AC and DC signals Reconstruct error signals Using C7 matrix Pass through DSP correction filters Obtain mirror motions through suspension transfer functions LA loops closed Suppose asymmetry (10, 1, 0.2 mm) => length noise Two cases 1. C7 using measured QD DC powers 2. Optimized DC powers 50% of saturation power

4. 4 Commissioning meeting, Cascina, 5.12.2005 C7 matrix ThetaX PR BS NI NE WI WE B2_q1_DC 2.5 -4.5 -6.4 15 B5_q1_DC 10 B2_q1_ACp -24 9.41 17.9 5.38 B1p_q1_ACp 0.052 -0.108 0.0375 1 0.0729 B7_q1_ACq 0.042 -0.035 0.375 -0.027 B7_q2_ACq 0.042 -0.035 0.375 -0.027 B8_q1_ACp -0.25 0.65 0.052 0.071 B8_q1_ACq -0.25 -0.65 -0.052 -0.071 ThetaY PR BS NI NE WI WE B2_q1_DC 1 B5_q1_DC 10 B1p_q1_ACq 1 B7_q1_ACp 0.33 0.36 B7_q2_ACp 0.68 0.36 B7_q2_ACq -0.36 -0.36 B8_q1_ACp -0.46 -1 -0.36 B8_q2_ACp 1 ThetaX has undergone second diagonalization => mixing of all signals

5. 5 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (WE tx)

6. 6 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (WE ty) Pure DC signal

7. 7 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (NE tx) ?

8. 8 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (NE ty)

9. 9 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (NI tx)

10. 10 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (NI ty)

11. 11 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (BS tx)

12. 12 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (BS ty)

13. 13 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (PR tx)

14. 14 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (PR ty)

15. 15 Commissioning meeting, Cascina, 5.12.2005 Total LA electronics noise (C7, calculated) WE ty pure DC error signal => no extra noise vs. AC WI under local control Simulated WI LA curves for comparison C7 noise not limited by LA electronics noise (but: excess noise)

16. 16 Commissioning meeting, Cascina, 5.12.2005 Influence of QD power Can gain ~ factor 10 by increasing QD powers

17. 17 Commissioning meeting, Cascina, 5.12.2005 Noise budget (C7) ADC noise (= DC noise) is not dominating, but close => second diagonalization (tx) has spoiled signals by reintroducing DC signals everywhere ?

18. 18 Commissioning meeting, Cascina, 5.12.2005 Influence of mirror centering (optimized powers) Without optimized matrix nor optimized filters: => need LIGO centering precision (0.2 mm)

19. 19 Commissioning meeting, Cascina, 5.12.2005 Noise budget (optimized, 0.2 mm) Still some effort needed at low frequencies

20. 20 Commissioning meeting, Cascina, 5.12.2005 Contribution of mirrors (optim. powers) NI ty filter difficult to improve? => try combination of EM + HH optimizations

21. 21 Commissioning meeting, Cascina, 5.12.2005 Conclusions I We can go quite far => LF design sensitivity using present matrix and filters but improvements hopefully possible using DC signals if optimizing QD power if centering mirrors very well Maximization of power on QD's is important DC signals don't have more electronic noise than AC signals Typical levels: AC 50 µV/rtHz DC 3 µV/rtHz Lower DC electronic gain is not compensated by higher matrix gain B2 DC signal seems to have high sensitivity (good SNR) "second diagonalization" seems to spoil some signals but still same order of magnitude than AC signals Other reasons for getting rid of DC signals Get rid of laser technical noise at 6 MHz ? Seismic noise ?

22. 22 Commissioning meeting, Cascina, 5.12.2005 Conclusions II Extra noise observed on NI, BS, PR mirrors Not limited by electronic noise at 50 Hz C7 observation: NI ty injected noise into dark fringe => filter roll-off had to be improved Origin of extra noise - Related to WI local control? - Diffused light? same noise seen on B7, and on reconstr. signals using B7/B8 - QD miscentering? same noise seen in longitudinal noise (GV)

23. 23 Commissioning meeting, Cascina, 5.12.2005 Conclusions III Problems Feedback gains not well known Optical matrix not calibrated PR, BS influence on length noise not yet included To be done Develop optimized correctors for the 10-20 Hz range Find optimized matrix Understand DC-AC noise question Include PR, BS contributions to length noise

24. 24 Commissioning meeting, Cascina, 5.12.2005 End

25. 25 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (WI tx) Local control

26. 26 Commissioning meeting, Cascina, 5.12.2005 Electronics noise vs. C7 noise (WI ty) Local control