This study tries to answer two main questions:
(1) What is the SVT noise level (in mV)?
(2) What is the best procedure to subtract the pedestals (i.e., the one that minimises the noise level): whether to subtract the pedestal with relation to the time bin or whether to subtract the pedestal with relation to the capacitor (or both)?

Figure 2 shows the RMS distribution of all pixels from one hybrid calculated over 400 events (file st_cluster2_0351056_raw_0008.daq). The X-axis is presented in ADC channels, where each channel corresponds to 4 mV. The hybrid is divided into 3 analog outputs (AO), thus each histogram (red, blue and green) corresponds to the pixels from one AO. Each AO has 127 X 80 = 10160 pixels. The mean of this distribution is quoted as our noise level. In this case, NO pedestal subtraction was performed.

This calculation shows a ~7.5 mV noise level for RAW data.

Figure 2: RMS distribution of all pixels from one hybrid calculated over 400 events.

If the pedestals are calculated and subtracted only on a time bin basis, this result won't change, since the pedestal will represent only a constant offset subtraction (it does not vary in a event by event basis).

Next, the pedestals are calculated and subtracted based on the SCA capacitor instead of the time bin, in order to eliminate the variations due to the SCA capacitor read out fluctuations. So, in this case, there is one pedestal value for each (SCA capacitor, anode) pair, instead of (time bin, anode) pair as before. The pedestal for each (time bin,anode) pixel will vary in a event by event basis, depending on which capacitor read out that specific time bin in that specific event.

Figure 3 shows the result of such procedure for the same hybrid and the same 400 events as in figure 2.

Figure 3: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted given the read out capacitor instead of the time bin.

This procedure results in a noise level, approximately, 1.5% higher than the previous one. It shows clearly that the ADC read out fluctuations due to time bin variations are greater than the fluctuations due to SCA capacitor variations.

An additional procedure can still be performed. The pedestals could be labelled or identified as a function of the pixel (time bin, anode) AND the SCA capacitor. In other words, instead of having 128(time bins) X 240(anodes) pedestals per hybrid, one would have 128 X 240 X 128(SCA capacitors) pedestals per hybrid, and event by event fluctuations due to the SCA capacitors variation could be corrected.

The result of such procedure is illustrated in figure 4 for the same 400 events from the two previous results. In this case, the pedestal calculation demands a much higher statistics, that was obtained analysing 2,550 events from files st_cluster2_0351056_raw_0007.daq, st_cluster2_0351056_raw_0006.daq and st_cluster2_0351056_raw_0005.daq.

Figure 4: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted given the read out capacitor AND the time bin.

In this case, the noise level is, approximately, 1.5% lower than the first case.

Therefore, the improvement obtained is very small. And, given the high statistic demanded by this procedure and the fact that it increases a factor of 128 the number of pedestals to be stored (128*248*128*4 bytes = 15 Mbytes/per hybrid), the cost-benefit ratio prohibits such procedure to be used during the analysis.

During this analyses, an additional problem was observed. In order to identify the SCA capacitor number for each time bin in a event by event basis, the capacitor corresponding to the zeroth time bin is obtained from the header received via the fiber, stored in the Receiver Board Bank.

An important (and time consuming) step of this study was to check whether this information was correct or not. In order to do that, a feature presented in the data, that depends exclusively on the SCA capacitors was identified. Given the time bin of such feature and the zeroth time bin capacitor number, one could verify if the correlation between time bin and capacitor number was correct. The feature identified was a small step present in all events that corresponds to the end of a cycle of the SCAs(???). Figure 5 shows such feature as seen in the data. Figure 5: ADC values as function of anode number (X-axis) and time bin (Y-axis) for a typical event, demonstrating the SCA feature around time bin 100. The same feature can be seen on time bin axis projection (the small "step" seen around time bin 100).

Using an automatic procedure to identify such feature (that agrees with a visual inspection, at least for few events checked), it was possible to identify events where the zeroth SCA capacitor was read correctly. From a sample of 4250 events, ~82% of the events had a correct zeroth capacitor reading.

Using only these events, the two procedures to calculate the pedestal described above (figure 3 and figure 4) were repeated, and the result can be observed in figures 6 and 7, respectively.

Figure 6: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted given the read out capacitor instead of the time bin, only for events where the zeroth capacitor was read correctly (following the procedure described in the text).

Figure 7: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted given the read out capacitor AND the time bin, only for events where the zeroth capacitor was read correctly (following the procedure described in the text).

The results show no improvement in the noise level. Therefore, this problem does not impact the pedestal calculation or the noise level evaluation.

HOWEVER, it would be nice to have it CORRECTED...

Following Helen's suggestions, I calculated the pedestals taking in account an extra detail. The first two time bins have always a higher value than the other time bins. Although they are stable, when one tries to calculate the pedestal relative to the first capacitor, the "capacitor bin" corresponding to the first time bins will have an anomalous high value, that makes the pedestals fluctuate sensibly. Therefore, the procedure here is just to exclude the capacitor bin that correspond to the first two time bins from the pedestal calculation. Figure 8 shows the RMS obtained from this procedure.

Figure 8: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted given the read out capacitor, taking care of excluding the first two time bins from the pedestal calculation.

As seen from figure 8, a small improvement (~2.5%) was achieved relative to the time bin pedestal subtraction (figure 2). This result changes completely the previous conclusion, where a higher noise level has been obtained with the pedestal subtraction relative to the first capacitor (figure 3). It shows that the ADC read out fluctuations are higher due to the SCA capacitors than pixel variations. The higher ADC values of the first two time bins were introducing extra fluctuation that "hides" this conclusion.

The first and last SCA capacitors seem to have the same feature as the first two time bins,i.e., they present an anomalous ADC value (the "step" of figure 5) that can influence the pedestal calculation. Therefore, the same exercise as above was performed for the pedestal calculation relative to the first time bin. Time bins corresponding to the first and last capacitors were excluded from the pedestal calculation. Figure 9 shows the result of such procedure.

Figure 9: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted relative to the first time bin, taking care of excluding the first and last capacitors from the pedestal calculation.

The noise level obtained is similar to the first procedure (figure 2). Therefore, no improvement was achieved. Actually, this result was expected, since the amplitude variation due to the first and last capacitors is much lower than the variation due to the first time bins.

Still another test can be performed repeating the procedure shown in figure 4, but this time taking care of excluding the first time bins AND the first and last capacitors from the pedestal calculation. Figure 10 shows the result obtained.

Figure 10: RMS distribution of all pixels from one hybrid calculated over 400 events. The pedestals are calculated and subtracted given the read out capacitor AND the time bin, taking care of excluding the first two time bins AND the first and last capacitors from the pedestal calculation.

An extra ~2% improvement can be achieved with this procedure relative to procedure shown in figure 8 or a ~4.5% improvement relative to the first procedure (figure 2). But, again, the high memory demanding of this procedure and the low improvement factor does not justify its application during the data analysis.

A final study of the noise level corresponds to the common mode noise subtraction off the data. The common mode noise is given by the mean value of the ADC calculated for each time bin over all anodes. The common mode noise calculation and subtraction is performed in a event by event basis.

Figure 11 shows the result obtained for one hybrid over 400 events.

Figure 11: RMS distribution of all pixels from one hybrid calculated over 400 events, performing the common mode noise calculation and subtraction event by event.

This result shows the noise level ~25% lower than all previous procedures (~5.5 mV). Although it corresponds to a significant improvement, this method cannot be used for a zero suppressed data taken mode, unless we can make the calculation and subtraction of the c.m.n. fast enough. However, it shows the source of a significant fraction of the SVT noise.

So far, the questions that motivated this study can be answered as following:
(1) The SVT noise level obtained with the cosmic data from Dec. 99 is ~7mV using the best pedestal subtraction procedure, and ~5.5mV performing the common mode noise subtraction.
(2)The most appropriate method to calculate and subtract the pedestals in order to achieve the lowest noise level, correspond to the calculation of the pedestal relative to the first capacitor, but excluding the first and second time bins from the calculation.

Suggestion and comments are very welcome and important in order to get a more definte answer to these questions

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