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 Wed Apr 26 01:00:23 2017, gautam, Update, General, DRMI locking Fri Apr 28 02:04:36 2017, gautam, Update, General, DRMI locking Fri Apr 28 13:56:26 2017, rana, Update, General, DRMI locking Mon May 1 16:29:51 2017, gautam, Update, General, DRMI locking Mon May 1 21:45:54 2017, ericq, Update, General, DRMI locking Wed May 3 18:45:45 2017, rana, Update, General, DRMI locking Thu May 4 19:03:15 2017, gautam, Update, General, DRMI locking - preliminary MICH NB Fri May 5 10:13:02 2017, ericq, Update, General, MICH NB questions Fri May 5 12:10:53 2017, gautam, Update, General, MICH NB questions Sat May 6 21:52:11 2017, rana, Update, General, MICH NB questions Wed May 10 01:56:06 2017, gautam, Update, General, MICH NB - OL coupling Wed May 10 16:53:38 2017, rana, Update, General, MICH NB - OL coupling Wed May 10 17:17:05 2017, gautam, Update, General, DAC / Coil Driver noise Wed May 10 17:46:44 2017, gautam, Update, General, DAC / Coil Driver noise - SRM coil driver + dewhite board removed Thu May 11 09:45:46 2017, rana, Update, General, DAC / Coil Driver noise - SRM coil driver + dewhite board removed Thu May 11 18:59:22 2017, gautam, Update, General, SRM coil driver + dewhite board initial survey Fri May 12 01:36:04 2017, gautam, Update, General, SRM coil driver + dewhite board LISO modeling Fri May 12 12:34:55 2017, gautam, Update, General, ITM and BS coil driver + dewhite board pulled out Fri May 12 18:50:08 2017, gautam, Update, General, ITM and BS coil driver + dewhite board pulled out Mon May 22 13:37:01 2017, gautam, Update, General, DAC noise estimate Tue May 23 22:58:23 2017, gautam, Update, General, De-Whitening board noises Thu May 25 19:27:29 2017, gautam, Update, General, Coil driver board noises Mon May 29 16:47:38 2017, gautam, Update, General, Coil driver boards reinstalled Tue May 30 16:02:59 2017, gautam, Update, General, Coil driver boards reinstalled Thu Jun 1 00:10:15 2017, gautam, Update, General, Coil driver boards reinstalled Fri Apr 28 19:32:06 2017, gautam, Update, General, DRMI locking - PRCL angular FF
Message ID: 13003     Entry time: Mon May 22 13:37:01 2017     In reply to: 12990     Reply to this: 13010
 Author: gautam Type: Update Category: General Subject: DAC noise estimate

### Summary:

I've spent the last week investigating various parts of the DAC -> OSEM coil signal chain in order to add these noises to the MICH NB. Here is what I have thus far.

### Current situation:

• Coils are operated with no DAC whitening
• So we expect the DAC noise will dominate any contribution from the electronics noise of the analog De-Whitening and Coil Driver boards
• There is a factor of 3 gain in the analog De-Whitening board

### DAC noise measurement:

• I essentially followed the prescription in G1401335 and G1401399
• So far, I only measured one DAC channel (ITMX UL)
• The noise shaping filter in the above documents was adapted for this measurement. The noise used was uniform between DC and 1kHz for this test.
• For the >50Hz bandstops, I used 1 complex pole pair at 5Hz, and 1 compelx zero pair at 50Hz to level off the noise.
• For <50Hz bandstops, I used 1 compelx pole pair at 1Hz and 1 complex zero pair at 5Hz to push the RMS to lower frequencies
• I set the amplitude ("gain" = 10,000 in awggui) to roughly match the Vpp when the ITM local damping loops are on - this is ~300mVpp (measured with a scope).
• The elliptic bandstops were 6th order, with 50dB stopband attenuation.
• The SR785 input auto-ranging was disabled to allow a fair comparison of the various bandstops - this was fixed to -20 dBVpk for all measurements, and the SR785 noise floor shown is also for this value of the input range. Input was also AC coupled, and since I was using the front-panel LEMO for this test, the signal was effectively single-ended (but the ground of the SR785 was set to "floating" in order to get the differential signal from the DAC)
• Attachment #1 shows the results of this measurement - I've subtracted the SR785 noise from the other curves. The noise model was motivated by G1401399, but I use an f^-1/2 model rather than an f^-1 model. It seems to fit the measurement alright (though the "fit" is just done by eye and not by systematic optimization of the parameters of the model function).

### Noise budget:

• I then tried to translate this result into the noise budget
• The noises for the 4 face coils are added in quadrature, and then the contribution from 3 optics (2 ITMs and BS) are added in quadrature
• To calibrate into metres, I converted the DAC noise spectral density into cts/rtHz, and used the numbers from this elog. I thought I had missed out on the factor of 3 gain in the de-white board, but the cts-to-meters number from the referenced elog already takes into account this factor.
• Just to be clear, the black line for DAC noise in Attachment #2 is computed from the single-channel measurement of Attachment #1 according to the following relation: $\script{n}_{\mathrm{DAC}} ~ (m/\sqrt{Hz}) = n_{1-ch} (V/\sqrt{Hz}) \times (2^{15}/20) (cts/V) \times G_{act} \times 2 \times \sqrt{6}$, where G_act is the coil transfer function from the referenced elog, taken as 5nm/f^2 on average for the 2 ITMs and BS, the factor of 2 comes from adding the noise from 4 coils in quadrature, and the factor of sqrt(6) comes from adding the noise from 3 optics in quadrature (and since the BS has 4 times the noise of the ITMs)
• Using the 0.016N/A number for each coil gave me an answer than was off by more than an order of magnitude - I am not sure what to make of this. But since the other curves in the NB are made using numbers from the referenced elog, I think the answer I get isn't too crazy...
• Attachment #2 shows the noise budget in its current form, with DAC noise added. Except for the 30-70Hz region, it looks like the measured noise is accounted for.