J. Kissel

Investigating the DAC saturations I've been hearing this morning from H1 SUS ETMY, I've taken a live ASD of the requested DAC outputs (which are not yet in the frames -- see E1500323) to see if / where we're close to saturating. If looks like the only place where we're "in danger" of saturation is the PUM around the microseism (~0.05 - 0.5 [Hz]). I put "in danger" in quotes because the RMS is still at ~8000 [ct_RMS] or ~11000 [ct_Pk], which is only 8% of the 2^17 = 131072 [ct_Pk] range of the DAC, but this still doesn't seem to be enough.

 
We've recently put lot of good effort has been put into rolling off the PUM faster (LHO aLOG 19859), and I think as such we've been focused on the ~above 1 [Hz] RMS levels (since the (L2/PUM) - (L3/TST) "crossover" is at "30 [Hz]").

Since there's *plenty* of range left in the UIM, I suggest we roll-off the low frequency end of the PUM drive better.

It's surprising really, because Brett put together a paper on a more sophisticated metric for determining the probability of saturations in a given time period (see P1000101), which suggests that the probably of saturation in one sample is

p_{i} = 1 - erfc( 1 / (sqrt(2)*dacMargin) )

and the probably over a given time period T is

p_{T} = 1 - p_{i}^(T / Ts)

where dacMargin is the ratio of ( measured RMS / DAC limit [in RMS] ), the DAC limit (in RMS) is (2^17 [ct_Pk]) / sqrt(2) =  92681.9 [ct_RMS], Ts is the sample time = 1/16384 = 61 [us], and erfc is the complementary error function (see Wikipedia and more importantly Matlab's definitions). (Note -- there's a bug in Brett's Eq. (4) of the paper I cite -- the "scale factor" of 10 was intended to represent the DAC range in aLIGO, but 10 is the peak voltage limit; the RMS voltage limit is 7.07 [V_RMS]. I've accounted for this bug in my (re)definition of dacMargin and in the calculations below.)

I've calculated this for the RMS at each stage for the probability of saturating in 1 hour,
                           L1/UIM      L2/PUM       L3/TST
dacOutput_rms [ct_RMS] =  1618.2       7658.3       4623.7
dacMargin              =  0.01746      0.08263     0.049888
probSat_oneTs          =  0            1.09e-33    2.23e-89
probSat_1hour          =  0            0           0
i.e. matlab ran out of numerical precision to give us an estimate of the probability since its so small.