F. Clara, J. Kissel, D. Sigg

While the team had the OMC DCPD's AA chassis out in the shop, I gathered transfer functions each channel,
    (a) to confirm their functionality after the ECR change (E1900105)
    (b) to understand the DC gain of the chassis better, given the recent confusion about AA chassis gains (see LHO aLOG 48272 and IIET Ticket 12642)

It turns out, in the heat of battle, I measured the wrong channels for the low-frequency (i.e. gravitational wave channel) versions of the OMC DCPDs -- CH13 and 14, I measured 4 channels over, CH09 and 10. 
But I still learned a lot.

Here're my conclusions:
(1) The low-frequency channels I measured (CH09 and CH10 of the AA chassis) behave as expected, with a DC gain of 1.0 +/- 0.04%, and a butterworth lowpass with a notch at *roughly* 65 kHz (measured minimum magnitude's frequency within 2% of 2^16 Hz), and suppression *at* 2^16 Hz for both channels is -90 dB = 3e-5 V/V.
(2) The PI channels for the OMC DCPD (CH15 and 16 of the AA chassis) have had all anti-aliasing removed, and the through-signal has no modification of signal from DC to 10 kHz, and above 10 kHz, at MOST a 0.25% / 1 deg change up to 100 kHz.
(3) As far as measuring the low-frequency "DC" gain of the AA channels, electrical grounding of measurement equipment is very important. If one does *not* properly reference all equipment to a common ground, i.e. leaves the ground floating, then the data will errantly suggest that the DC gain of the AA chassis is 0.99, the frequency of the notch will shift, and the depth of the notch will also shift.

Check out the first attachment 2019-04-09_H1OMC_AAChassisTFs.pdf. 
The first two pages shows the "final answer" for CHs 09, 10, 15, and 16 for the OMC AA chassis, as reported with correctly grounded test equipment.
The legend label "CHSGND" stands for "properly referencing the measurement equipment to the AA CHaSsis GrouND." "FLTGND" stands for "the ground of the measurement equipment is FLoaTing with respect to the chassis GrouND."
The third page shows what happens what you measure the coil driver test box (D1000931) with proper grounding (as was done in today's measurement) vs. the ground floating (i.e. as shown in all of the diagrams in -v1 of D1900027-v1). One can clearly a reported gain of 1.983 V_{se}/V_{diff} when the ground properly referenced, and a reported gain of 2.002 V_{se}/V_{diff} when floating.
The fourth page shows what happens when you measure the anti-aliasing channels with proper grounding (as was done in today's measurement) vs. with the ground floating. Here, one can clearly see that with the floating ground, the AA notch has far less Q and the notch frequency is much more variable.

Unfortunately with today's measurement, we had the rare treat of being able to pull the chassis out of the rack, pull off the lid, and directly access test points and grounding pins the filter board (D070081). Rarely do we get this luxury, as we're often stuck in the rack, at an end station, having to use the clumsy SCSI breakout board.

The second attachment (AAChassisSetup_20190409.pdf) shows the proposed method of performing this clumsy technique while paying much better attention to referencing a common electrical ground.

The third attachment (2019-04-09_AAChassis_Meas_Pics.pdf) shows some pictures of what it was like today, comparing properly grounded configurations and floating configurations that correspond to

I believe the lack of attention to (3) is what has lead LHO to measure a low-frequency gain of 0.99 back in ER7/ER8 (i.e. in 2015), and we've been using the model from that data set for both AA and AI filters for *anything* that has one since then. That model is 
    ^/trunk/Runs/ER8/H1/Scripts/AAAI/20150813_H1ER7_AA_upto10kHzFitLTI.mat
which we used for O1 and O2, and has now been unceremoniously dumped into a new .mat file in a python compatible format, but in doing so lost its origin story, 
    ^/trunk/Common/pyDARM/H1aa.mat
which is now used for O3.

I've followed the rabbit hole of that model, which lead me to the last time we systematically measured the PCAL AA chassis, in May 2015 (see LHO aLOG 18658), during Pre ER7 times, which was processed by the script 
    ^/trunk/Runs/PreER7/H1/Measurements/ElectronicsMeasurements/process_H1PCALEX_AA_Measurements_20150527.m
which reveals a plot that I re-attach because I couldn't find the aLOG in which I said I'd write about it.
Check out the fourth attachment, 2015-05-26_H1PCALEY_AAChassis_S1203519.pdf.
It has a DC gain of 1.0 +/- 0.02%, which is *not* the case for the model we've been using for the AA chassis since ER7.

That model, came from Kiwamu's processing script, 
     ^/trunk/Runs/ER8/H1/Scripts/AAAI/gen_H1ER7_AA_upto10kHzFitLTI.m
which took data from  
     ^/trunk/Runs/PreER7/H1/Measurements/ElectronicsMeasurements
which just like above, uses the Coil Driver Test Box to create a differential signal, whose transfer function, 
     ^/trunk/Runs/PreER7/H1/Measurements/ElectronicsMeasurements/TESTBOX_CH1In_Pins1-6Out_2015-05-19_092805.txt
you can clearly see has a gain of 2.002 V_{se}/V_{diff} instead of the properly grounded 1.983 V_{se}/V_{diff}.

No bueno!!

Well -- hopefully now this lesson has been learned -- we'll update our calibration group documentation in such a way that hopefully this mistake will never happen again. AND we'll save a new python-friendly model, likely based on the data that Joe / LLO originally put together in 
     ^/trunk/Common/Documents/T1500165/
or we'll go around and measure every AA and AI chassis properly.

The message: AA and AI filters have a DC gain of 1.0 +/- 0.0(something)%, so we should stop treating them as otherwise.

Wrapping up loose ends from O3, I've plotted the 2019-04-09 measurements for channel 09 and 10 (i.e. OMC DCPD A and B) against the model of the AA chassis that we used throughout O3 in the calibration models. 

While one might immediately get alarmed by the 1.01 gain discrepancy with the measurement and the H1aa.mat model -- this is again a relic of the poorly grounded measurement that Kiwamu took as described above. 

The calibration group has danced around this H1 model issue by dividing out the DC gain of the model every time it appears in calculation of the sensing function or the corrections to the PCAL channels, as discussed in originally in IIET Ticket 12642, which has now been closed and transferred to the pyDARM 2.0 git repo's Issue 11.

This is why I show the L1aa.mat model too -- which was created with the correct gain -- but is otherwise identical in frequency response.

The conclusion remains the same: using the either model, as long as the DC gain normalized out, provides a good model of H1's measured response for either channel with negligible systematic error (growing with frequency only to 1.0005% / 0.1 deg by 1 kHz and only 1.004% / 0.6 deg at 5 kHz).

In fact, because the systematic error for each channel coincidentally are in opposite directions, when averaged as is done in the control system (balanced with gains as mentioned in LHO aLOG 47217 and then further tweaked with the preceding filter modules as described in 47257), the frequency dependence of the two channels probably "cancels" to even smaller systematic error (tracing out all the digital gains, doing the math, and making some further plots is probably in order, but not worth it at this time.)

Since the world has moved to python, the script to produce these plots is in the same folder as the previous study, but y'know, in python: 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Common/Electronics/H1/Scripts/
    plot_omcaachassis_20190409meas_vs_O3Bmodel_20200624.py

(and, of course, uses the same properly grounded AA chassis data, divided by the properly grounded test box data.)

The models live in
/ligo/svncommon/CalSVN/aligocalibration/trunk/Common/pyDARM/
    H1aa.mat
    L1aa.mat


EDIT: As a bonus, I also plotted the H1 EY PCAL RXPD AA chassis channel as well (just modifying the python script called out above, which now isn't so accurately named, but so be it). I only divided it against the L1 model, since we now know the H1 model is just different by a gain. The H1 EY PCAL RXPD AA chassis channel is similarly, negligibly different from the L1 model.
Note -- have this also be negligible is important for sensing function measurements, for which we divide DARM_IN1 by PCAL, and in doing so, we sneakily assume (because we assume AA chassis channels are the same) that the AA's cancel, and we don't have to account for this frequency dependence.