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Determination of The Degree of Non Linearities In the Charge to
Digital V265 ADC Using The Known Photomultiplier Tube and
Possible Calibration
Atanu Nath
Project Supervisor: Prof. Gobinda Majumder
Department of High Energy Physics, Tata Institute of Fundamental Research.
Abstract
In a typical high energetic particle detection exper-
iment, the generated signal has to be passed through a
number of electronics circuits before getting stored in
a memory for analysis. During those processes signal
can get modified due to circuit non-linearities and/or
various noises can get added to the signal resulting in
a great loss of information. This project deals with the
test of response of the PMT plus V265 ADC (Charge
to Digital Converter) for signals at various applied high
voltages applied to the PMT. Search for possible non-
linearities have been done and possible calibration is
suggested.
Introduction
Most of the particle detection and determination of
various relevant physical quantities of interest are based
on the measurement of current and/or voltage signal
produced by the Photo Multiplier Tubes as a result of
incident photons created by the high energetic parti-
cles in the scintillator which is fed to the electronics
modules and will be finally digitized to store for anal-
ysis. Usually several steps are there in this process
and maintaining the original form of the signal is ex-
tremely important so that the actual physical quantities
of the particles can be reproduced. In these steps var-
ious noise and also the circuit non-linearity can enter
leading to the distortion of the signal . A step by step
test is necessary before one runs a real experiment.
The calibration for the type of the experiment that
we were doing can be schematically represented as fol-
lows:
Distortion can enter in the PMT and/or in the
later electronics (various circuits inside the ADC) and
also from coaxial cable connections if proper impedance
matching (50 Ω) is not done . We have studied the
Most Probable Value of the ADC distribution as a
function of the High Voltage applied to the PMT and
checked for possible non-linearity and attempted a
remedy for that.
Instruments Used and Their De-
tails
Scintillator Paddles: We have used 4 scintillator
paddles from Bicron (BC408) of dimension 20x15x1
cm3
, the material is Polyvinyltoluene doped with
PBD. It has Light Output 64 (% of Anthracene ),
has a refractive index 1.58 and pulse width (FWHM)
2.5 ns. It emits maximum photon at 425nm. The
scintillator is connected to the PMT via a light guide
(Perspex) which helps to match the geometry so
that the light loss is lowest. Emission spectra of the
scintillator is shown in the figure below:
Photomultiplier Tubes: Four PMTs (9807B,
Electron Tubes Limited) for four paddles are used.
It is a 51 mm diameter, end window photomultiplier
with blue-green sensitive bialkali photocathode and
have 12 stages of BeCu dynodes. It is of linear focused
design for good linearity and timing. The curve for
quantum efficiency and the electrical circuit diagram of
the PMT are displayed in Fig.2 and Fig.3 respectively.
Constant Fraction Discriminator (V814): It
is a low threshold constant fraction discriminator
with negative input signals and ECL output. The
threshold of which can be varied from -1mV to -255
mV, in our experiment we set it at 30 mV as the
signals due to Muons are much stronger ( typically
more than 100 mV I have observed), but signal due to
other possible events like scintillation due to electron
strike or PMT dark current are much below 30 mv.
More over P1, P3 and P4 AND Gated pulse was
given as a trigger to the GATE os the ADC to reduce
chance coincidence due to noise trigger. CFD has
got maximum input frequency of 60 MHz, output
width can be varied in the range 6ns-95ns, I have
used 72 ns and that includes most of the significant
part of the signal even including some tail part, an
oscilloscope image describing the situation can be seen
in Fig.4(B). Time delay of this module is 10.5 ± 1.5 ns.
NIM-ECL/ECL-NIM Translator And Fan Out
(V538A): 8 channel accepts ECL/NIM signals and
converts it to NIM/ECL respectively. For each input
there corresponds four output options. ECL signal
frequency < 300MHz (NIM) and < 250MHz (ECL)
signal is accepted in the inputs. Time delay for
ECL-NIM is 2.5-3 ns and for NIM-ECL 3.5-4ns.
Four-fold Coincidence Fan-in/out Translator
(V976): This has 16 inputs and 16 outputs 2-fold, 3-
fold and 4-fold adjustable AND/OR gating is possible,
minimum signal width and also minimum coincidence
width is 2ns, time delay of operation is of 11.5 ns.
Charge Integrating ADC (V265): this has got 8
channels and full-scale of it is 800 pC(12 bit ADC
range), conversion gain 5 counts/pC.
Scematic Diagram of The Experiment
Notations: We use the following notations for clarity:
Signal from PMT-1 of Paddle-1 ≡ P1
Signal from PMT-2 of Paddle-2 ≡ P2
Signal from PMT-3 of Paddle-2 ≡ P3
Signal from PMT-4 of Paddle-2 ≡ P4
All the voltages are in Volts
Details of the connections and operating volt-
ages are given in the table below:
Constant Fraction Dis-
criminator (V814)
Threshold = 30 mV.
Gate width 72 ns.
P1, P3 and P4 are in
the inputs.
PMT-1 of Paddle-1
(Lower most)
HV= 1411 V.
PMT-2 of Paddle-2
(2nd from the bottom)
HV = Variable in my
experiment 1254 V -
1788 V
PMT-3 of Paddle-3
(3rd from the bottom)
HV = 1498 V.
PMT-4 of Paddle-4
(Top most)
HV = 1500V.
Four-fold Coincidence
Fan in Fan out Trans-
lator (V976)
P1, P3 and P4 com-
ing out of the CFD
outputs are three-fold
AND-gated.
Quad Linear Fan in Fan
out (PS Mod.740)
P2 is in the input and 4
outputs are taken in the
output which are P21,
P22, P23, P24.
Charge Integrating
ADC (V265)
P21, P22, P23 and P24
are conncetd to the four
channels ch0, ch2, ch4
and ch6. Three-fold
AND-gated output is
fed to the GATE of
the CFD after match-
ing the delays such that
P21, P22, P23, P24 are
well inside 72 ns GATE
trigger pulse.
Linearity Check of PMT and ADC
P21, P22, P23 and P24 are conncetd to the
four channels ch0, ch2, ch4 and ch6, actually out of
the 8 channels odd numbered ones (ch1, ch3, ch5 and
ch 7) happened to be not working well that was tested
in the beginning of this experiment and it was seen
that these odd channels posses no pedastal values
and hence the pedestal positions were undetermined
therefore the even numbered channels were chosen
for the experiment. Typical signal distribution and
corresponding pedestal distribution are displayed in
Fig.5(B) and Fig.5(A) respectively. Where the
signal distribution is fitted with Landau function
and the pedestal is fitted with Gaussian distribution
function, pedestal mean values for the channels 0,2,4
and 6 have been shown in the Table.2.
Channel No Pedestal Value
0 208.2
2 143.5
4 170.00
6 239.4
Two sets of data were taken, in the
first set, for 10 different voltages ADC was
run and the results are shown in Fig.6
First of all these four channels have identical inputs as
these were the 4 outputs of fan-out of the same signal
from Paddle-2, but the graphs shows they are giving
different results, thing to notice is that the points are
differing more and more as we go to higher and higher
voltages, so this clearly show that the channels are
working differently.
Suppose there are N-stages of dynodes in the PMT
and gi and Ri are the gain and resistance for each
stage respectively then the total gain (G) is given by:
G ∝
N
i
gi ∝
N
i
RiV α
ΣRi
= A0V Nα
Final gain of the PMT is the product of gain in each
dynode stage gain, and gain of a stage is proportional
to the applied voltage to that dynode and its previous
stage. This voltage dependence can take complicated
non-linear form but we consider a simple power law for
for this dependence,
M = B0Gβ
= B0(A0V Nα
)β
=> log(M) = p1 log(V ) + p0
Where, p1 = Nαβ and p0 = B0Aβ
0 .
To test our assumption we plot our results in
Log-Log, which is shown in Fig. 7 below.
This shows that p1 = Nαβ 7.4 on the average which
is far from 12 and approximately p1 vary 8 %. p1 closed
to 12 (as N=12) was rather expected. So to be sure
of the results we take second set of data considering
the same connections by reconnecting them again.
Second set consists of 6 different voltages but the range
of voltage change kept the same as that of first set,
results for this case are displayed in Fig.8 and Fig.9.
Results (p1 7.5) are not much different from the
first set. Now the question that we can ask is:Is
ADC/PMT Nonlinear ? if yes then both of them
or one of them are non-linear ? And at what extent
they are non-linear?
For a better understanding we needed an al-
ready calibrated ADC. Fortunately we had and
already calibrated QDC (V792N 16 channel QDC)3
,
we repeated our experiment for three channels 6,8 and
14 keeping the earlier situation intact. The result that
we got is displayed in Fig.10 and Fig.11.
Above graphs say p1 11.14 and the point to
notice is that it is the same PMT so α has not changed
its the β that has changed by a factor of 1.5 hence
non-linearity is mainly entering due to the V265 ADC.
So for QDC V792N, p1 = Nα = 11.14 and hence
β 0.673 on the average and particularly for the
channel no. 2 it is 0.665 (which we will need later).
One can think that the Fan-in/out may also contribute
to this results. But this is certainly not the case,
because of two facts, first: the oscilloscope image
shows exactly identical signals, second: 10 shows that
indeed they are identical.
PMT Independent Measurement
This time we took a signal generator and cho-
sen a square pulse of width 10 ns and frequency 10 Hz
(oscilloscope image is shown in Fig.12 ) and fan-out it
two four signals which were finally fed to channel no.
2 of V265ADC and data were taken.
A typical ADC distribution along with Gaussian fit
is displayed in Fig.13 below:
Though the pulse was supposed to be 10 ns wide but ac-
tually it is 16 ns at the top and 8 ns at the bottom, the
estimated area under this signal is 16H − 4H = 12H
so charge contained in this puls is 12H/R (where
R = 50Ω) finally for V265 ADC charge contained in
one bin = 0.2 pC hence this pulse will correspond
to ADC bin number 12H/(50 × 0.2) = 1.2H taking
logarithm we get log(ADCPeak) = log(H)+constant.
This line, we expect to describe the ADC be-
haviour in principle, but practically we consider
log(ADCPeak) = β log(H) + constant, but we expect
the slope β to be 1 if the ADC is linear. Following are
the experimental results:
Clearly β 0.651 for channel no. 2. This again
shows that this ADC is non-linear and the QDC
V792N is indeed a good one as we obtained the slope
11.14 for that QDC with PMT from where we obtained
the value of β to be 0.665. But to check V792N with
this pulse method we repeated the same experiment
with this same signal generator pulse and the result is
displayed in Fig.16:
The slope is 1 which strongly suggest that QDC
V792N is definitely linear.
Conclusion
The conclusions those we can draw are:
˙ ADC V265 is non linear.
˙ Our assumed power law successfully describes
the ADC V265 data.
M = B0Gβ
with β 0.651 for channel 2 and each channel
have different β. Through beta we have
quantified the amount of non-linearity.
˙ QDC V265 is linear whcih confirms that the
earlier calibration was right.
Appendix
Tables
set-I V265 ADC (Channel 0)
Voltage Pedestal Separated MPV Error
1254 109.824 ±0.464915
1303 134.957 ±0.524712
1371 198.181 ±0.700580
1422 257.639 ±0.843207
1503 386.879 ±1.22332
1567 508.655 ±1.45834
1604 593.924 ±1.61694
1682 872.7 ±2.29109
1706 976.86 ±2.54258
1788 1410.6 ±3.82075
set-I V265 ADC (Channel 2)
Voltage Pedestal Separated MPV Error
1254 126.089 ±0.447923
1303 153.767 ±0.513254
1371 224.716 ±0.699892
1422 291.173 ±0.818525
1503 444.27 ±1.160030
1567 595.159 ±1.476380
1604 698.94 ±1.870770
1682 1025.95 ±2.427240
1706 1151.98 ±3.020200
1788 1677.44 ±4.618830
set-I V265 ADC (Channel 4)
Voltage Pedestal Separated MPV Error
1254 102.79 ±0.432258
1303 129.296 ±0.507708
1371 199.964 ±6.982120
1422 266.028 ±8.269300
1503 416.064 ±1.170170
1567 564.506 ±1.591390
1604 663.295 ±1.661750
1682 983.63 ±2.429470
1706 1107.79 ±2.905850
1788 1673.2 ±5.885160
set-I V265 ADC (Channel 6)
Voltage Pedestal Separated MPV Error
1254 135.661 ±0.456602
1303 168.906 ±0.584004
1371 243.123 ±0.786308
1422 313.5 ±0.992811
1503 485.405 ±1.42406
1567 647.032 ±1.88967
1604 750.664 ±2.16090
1682 1064.3 ±3.17085
1706 1180.07 ±3.92885
1788 1661.43 ±5.95805
set-II V265 ADC (Channel 0)
Voltage Pedestal Separated MPV Error
1254 141.877 ±0.870509
1327 195.783 ±1.12879
1422 314.283 ±1.79578
1567 652.614 ±2.21524
1682 1149.31 ±4.63862
1788 2006.61 ±6.58844
set-II V265 ADC (Channel 2)
Voltage Pedestal Separated MPV Error
1254 155.677 ±0.818286
1327 214.096 ±1.08029
1422 345.711 ±1.17669
1567 726.372 ±3.55726
1682 1329.76 ±3.76888
1788 2042.23 ±3.71988
set-II V265 ADC (Channel 4)
Voltage Pedestal Separated MPV Error
1254 131.147 ±0.562506
1327 188.955 ±1.05711
1422 320.272 ±1.14969
1567 694.193 ±3.51232
1682 1353.2 ±4.38374
1788 1935.97 ±3.26153
set-II V265 ADC (Channel 6)
Voltage Pedestal Separated MPV Error
1254 169.344 ±0.599008
1327 238.002 ±1.186170
1422 377.562 ±1.441890
1567 797.23 ±2.918080
1682 1516.18 ±5.300040
1788 2164.34 ±6.228640
V792N QDC (Channel 6)
Voltage Pedestal Separated MPV Error
1343 103.8 ±0.6
1409 239.8 ±0.5
1484 433.1 ±0.7
1566 796.9 ±1.8
1659 1463.9 ±3.5
V792N QDC (Channel 8)
Voltage Pedestal Separated MPV Error
1343 108.7 ±0.6
1409 245 ±0.6
1484 446.4 ±0.8
1566 820.1 ±1.9
1659 1509.1 ±3.7
V792N QDC (Channel 14)
Voltage Pedestal Separated MPV Error
1343 104.7 ±0.6
1409 236.2 ±0.6
1484 433 ±0.7
1566 796.2 ±1.8
1659 1467.2 ±3.5
Acknowledgement
I would like to thank Prof. Gobinda Majumder for
his sincere guidance through out the project and for
his help to understand every bit of the experiment. I
am also thankful to Deepak Samuel (Project Scientist)
for his help to understand his codes written for some
of the VME modules. I would also like to thank
my senior Research Scholar Esha Kundu for valuable
discussions and for her earlier calibration of QDC
V792N which helped me to calibrate the V265 ADC. I
thank my colleague Soureek Mitra for his co-operation
and understanding for sharing the same high voltage
supply and for important conceptual discussions.
References
[1] Glenn F. Knoll, Radiation Detection and
Measurement, Third Edition, Reprint 2009.
[2] W. R. Leo, Techniques for Nuclear and
Particle Physics Experiments, Second Revised
Edition, Indian Reprint 2010.
[3] Esha Kundu, Calibration of Versa Module
Europa (VME) Modules , Experimental Project,
February 2011.
[5] CAEN, V265 ADC User Manual.
[6] CAEN, V814 CFD User Manual.
[7] CAEN, V538A ECL-NIM/NIM-ECL Translator
User Manual.
[8] CAEN, V976 Four Fold Coincidence Fan In
Fan Out Translator User Manual.
[9] Phillips Scientific, Quad Linear Fan In Fan Out
User Manual.
[10] CAEN, V792N QDC User Manual
[11] http://my.et-enterprises.com/

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finalreport

  • 1. Determination of The Degree of Non Linearities In the Charge to Digital V265 ADC Using The Known Photomultiplier Tube and Possible Calibration Atanu Nath Project Supervisor: Prof. Gobinda Majumder Department of High Energy Physics, Tata Institute of Fundamental Research. Abstract In a typical high energetic particle detection exper- iment, the generated signal has to be passed through a number of electronics circuits before getting stored in a memory for analysis. During those processes signal can get modified due to circuit non-linearities and/or various noises can get added to the signal resulting in a great loss of information. This project deals with the test of response of the PMT plus V265 ADC (Charge to Digital Converter) for signals at various applied high voltages applied to the PMT. Search for possible non- linearities have been done and possible calibration is suggested. Introduction Most of the particle detection and determination of various relevant physical quantities of interest are based on the measurement of current and/or voltage signal produced by the Photo Multiplier Tubes as a result of incident photons created by the high energetic parti- cles in the scintillator which is fed to the electronics modules and will be finally digitized to store for anal- ysis. Usually several steps are there in this process and maintaining the original form of the signal is ex- tremely important so that the actual physical quantities of the particles can be reproduced. In these steps var- ious noise and also the circuit non-linearity can enter leading to the distortion of the signal . A step by step test is necessary before one runs a real experiment. The calibration for the type of the experiment that we were doing can be schematically represented as fol- lows: Distortion can enter in the PMT and/or in the later electronics (various circuits inside the ADC) and also from coaxial cable connections if proper impedance matching (50 Ω) is not done . We have studied the Most Probable Value of the ADC distribution as a function of the High Voltage applied to the PMT and checked for possible non-linearity and attempted a remedy for that. Instruments Used and Their De- tails Scintillator Paddles: We have used 4 scintillator paddles from Bicron (BC408) of dimension 20x15x1 cm3 , the material is Polyvinyltoluene doped with PBD. It has Light Output 64 (% of Anthracene ), has a refractive index 1.58 and pulse width (FWHM) 2.5 ns. It emits maximum photon at 425nm. The scintillator is connected to the PMT via a light guide (Perspex) which helps to match the geometry so that the light loss is lowest. Emission spectra of the scintillator is shown in the figure below:
  • 2. Photomultiplier Tubes: Four PMTs (9807B, Electron Tubes Limited) for four paddles are used. It is a 51 mm diameter, end window photomultiplier with blue-green sensitive bialkali photocathode and have 12 stages of BeCu dynodes. It is of linear focused design for good linearity and timing. The curve for quantum efficiency and the electrical circuit diagram of the PMT are displayed in Fig.2 and Fig.3 respectively. Constant Fraction Discriminator (V814): It is a low threshold constant fraction discriminator with negative input signals and ECL output. The threshold of which can be varied from -1mV to -255 mV, in our experiment we set it at 30 mV as the signals due to Muons are much stronger ( typically more than 100 mV I have observed), but signal due to other possible events like scintillation due to electron strike or PMT dark current are much below 30 mv. More over P1, P3 and P4 AND Gated pulse was given as a trigger to the GATE os the ADC to reduce chance coincidence due to noise trigger. CFD has got maximum input frequency of 60 MHz, output width can be varied in the range 6ns-95ns, I have used 72 ns and that includes most of the significant part of the signal even including some tail part, an oscilloscope image describing the situation can be seen in Fig.4(B). Time delay of this module is 10.5 ± 1.5 ns. NIM-ECL/ECL-NIM Translator And Fan Out (V538A): 8 channel accepts ECL/NIM signals and converts it to NIM/ECL respectively. For each input there corresponds four output options. ECL signal frequency < 300MHz (NIM) and < 250MHz (ECL) signal is accepted in the inputs. Time delay for ECL-NIM is 2.5-3 ns and for NIM-ECL 3.5-4ns. Four-fold Coincidence Fan-in/out Translator (V976): This has 16 inputs and 16 outputs 2-fold, 3- fold and 4-fold adjustable AND/OR gating is possible, minimum signal width and also minimum coincidence width is 2ns, time delay of operation is of 11.5 ns. Charge Integrating ADC (V265): this has got 8 channels and full-scale of it is 800 pC(12 bit ADC range), conversion gain 5 counts/pC. Scematic Diagram of The Experiment Notations: We use the following notations for clarity: Signal from PMT-1 of Paddle-1 ≡ P1 Signal from PMT-2 of Paddle-2 ≡ P2 Signal from PMT-3 of Paddle-2 ≡ P3 Signal from PMT-4 of Paddle-2 ≡ P4 All the voltages are in Volts Details of the connections and operating volt- ages are given in the table below: Constant Fraction Dis- criminator (V814) Threshold = 30 mV. Gate width 72 ns. P1, P3 and P4 are in the inputs. PMT-1 of Paddle-1 (Lower most) HV= 1411 V. PMT-2 of Paddle-2 (2nd from the bottom) HV = Variable in my experiment 1254 V - 1788 V PMT-3 of Paddle-3 (3rd from the bottom) HV = 1498 V. PMT-4 of Paddle-4 (Top most) HV = 1500V. Four-fold Coincidence Fan in Fan out Trans- lator (V976) P1, P3 and P4 com- ing out of the CFD outputs are three-fold AND-gated. Quad Linear Fan in Fan out (PS Mod.740) P2 is in the input and 4 outputs are taken in the output which are P21, P22, P23, P24.
  • 3. Charge Integrating ADC (V265) P21, P22, P23 and P24 are conncetd to the four channels ch0, ch2, ch4 and ch6. Three-fold AND-gated output is fed to the GATE of the CFD after match- ing the delays such that P21, P22, P23, P24 are well inside 72 ns GATE trigger pulse. Linearity Check of PMT and ADC P21, P22, P23 and P24 are conncetd to the four channels ch0, ch2, ch4 and ch6, actually out of the 8 channels odd numbered ones (ch1, ch3, ch5 and ch 7) happened to be not working well that was tested in the beginning of this experiment and it was seen that these odd channels posses no pedastal values and hence the pedestal positions were undetermined therefore the even numbered channels were chosen for the experiment. Typical signal distribution and corresponding pedestal distribution are displayed in Fig.5(B) and Fig.5(A) respectively. Where the signal distribution is fitted with Landau function and the pedestal is fitted with Gaussian distribution function, pedestal mean values for the channels 0,2,4 and 6 have been shown in the Table.2. Channel No Pedestal Value 0 208.2 2 143.5 4 170.00 6 239.4 Two sets of data were taken, in the first set, for 10 different voltages ADC was run and the results are shown in Fig.6 First of all these four channels have identical inputs as these were the 4 outputs of fan-out of the same signal from Paddle-2, but the graphs shows they are giving different results, thing to notice is that the points are differing more and more as we go to higher and higher voltages, so this clearly show that the channels are working differently. Suppose there are N-stages of dynodes in the PMT and gi and Ri are the gain and resistance for each stage respectively then the total gain (G) is given by: G ∝ N i gi ∝ N i RiV α ΣRi = A0V Nα Final gain of the PMT is the product of gain in each dynode stage gain, and gain of a stage is proportional to the applied voltage to that dynode and its previous stage. This voltage dependence can take complicated non-linear form but we consider a simple power law for for this dependence, M = B0Gβ = B0(A0V Nα )β => log(M) = p1 log(V ) + p0 Where, p1 = Nαβ and p0 = B0Aβ 0 . To test our assumption we plot our results in Log-Log, which is shown in Fig. 7 below.
  • 4. This shows that p1 = Nαβ 7.4 on the average which is far from 12 and approximately p1 vary 8 %. p1 closed to 12 (as N=12) was rather expected. So to be sure of the results we take second set of data considering the same connections by reconnecting them again. Second set consists of 6 different voltages but the range of voltage change kept the same as that of first set, results for this case are displayed in Fig.8 and Fig.9. Results (p1 7.5) are not much different from the first set. Now the question that we can ask is:Is ADC/PMT Nonlinear ? if yes then both of them or one of them are non-linear ? And at what extent they are non-linear? For a better understanding we needed an al- ready calibrated ADC. Fortunately we had and already calibrated QDC (V792N 16 channel QDC)3 , we repeated our experiment for three channels 6,8 and 14 keeping the earlier situation intact. The result that we got is displayed in Fig.10 and Fig.11. Above graphs say p1 11.14 and the point to notice is that it is the same PMT so α has not changed its the β that has changed by a factor of 1.5 hence non-linearity is mainly entering due to the V265 ADC. So for QDC V792N, p1 = Nα = 11.14 and hence β 0.673 on the average and particularly for the channel no. 2 it is 0.665 (which we will need later). One can think that the Fan-in/out may also contribute to this results. But this is certainly not the case, because of two facts, first: the oscilloscope image shows exactly identical signals, second: 10 shows that indeed they are identical. PMT Independent Measurement This time we took a signal generator and cho- sen a square pulse of width 10 ns and frequency 10 Hz (oscilloscope image is shown in Fig.12 ) and fan-out it two four signals which were finally fed to channel no. 2 of V265ADC and data were taken.
  • 5. A typical ADC distribution along with Gaussian fit is displayed in Fig.13 below: Though the pulse was supposed to be 10 ns wide but ac- tually it is 16 ns at the top and 8 ns at the bottom, the estimated area under this signal is 16H − 4H = 12H so charge contained in this puls is 12H/R (where R = 50Ω) finally for V265 ADC charge contained in one bin = 0.2 pC hence this pulse will correspond to ADC bin number 12H/(50 × 0.2) = 1.2H taking logarithm we get log(ADCPeak) = log(H)+constant. This line, we expect to describe the ADC be- haviour in principle, but practically we consider log(ADCPeak) = β log(H) + constant, but we expect the slope β to be 1 if the ADC is linear. Following are the experimental results: Clearly β 0.651 for channel no. 2. This again shows that this ADC is non-linear and the QDC V792N is indeed a good one as we obtained the slope 11.14 for that QDC with PMT from where we obtained the value of β to be 0.665. But to check V792N with this pulse method we repeated the same experiment with this same signal generator pulse and the result is displayed in Fig.16: The slope is 1 which strongly suggest that QDC V792N is definitely linear. Conclusion The conclusions those we can draw are: ˙ ADC V265 is non linear. ˙ Our assumed power law successfully describes the ADC V265 data. M = B0Gβ with β 0.651 for channel 2 and each channel have different β. Through beta we have quantified the amount of non-linearity. ˙ QDC V265 is linear whcih confirms that the earlier calibration was right. Appendix Tables set-I V265 ADC (Channel 0) Voltage Pedestal Separated MPV Error 1254 109.824 ±0.464915 1303 134.957 ±0.524712 1371 198.181 ±0.700580 1422 257.639 ±0.843207 1503 386.879 ±1.22332 1567 508.655 ±1.45834 1604 593.924 ±1.61694 1682 872.7 ±2.29109 1706 976.86 ±2.54258 1788 1410.6 ±3.82075
  • 6. set-I V265 ADC (Channel 2) Voltage Pedestal Separated MPV Error 1254 126.089 ±0.447923 1303 153.767 ±0.513254 1371 224.716 ±0.699892 1422 291.173 ±0.818525 1503 444.27 ±1.160030 1567 595.159 ±1.476380 1604 698.94 ±1.870770 1682 1025.95 ±2.427240 1706 1151.98 ±3.020200 1788 1677.44 ±4.618830 set-I V265 ADC (Channel 4) Voltage Pedestal Separated MPV Error 1254 102.79 ±0.432258 1303 129.296 ±0.507708 1371 199.964 ±6.982120 1422 266.028 ±8.269300 1503 416.064 ±1.170170 1567 564.506 ±1.591390 1604 663.295 ±1.661750 1682 983.63 ±2.429470 1706 1107.79 ±2.905850 1788 1673.2 ±5.885160 set-I V265 ADC (Channel 6) Voltage Pedestal Separated MPV Error 1254 135.661 ±0.456602 1303 168.906 ±0.584004 1371 243.123 ±0.786308 1422 313.5 ±0.992811 1503 485.405 ±1.42406 1567 647.032 ±1.88967 1604 750.664 ±2.16090 1682 1064.3 ±3.17085 1706 1180.07 ±3.92885 1788 1661.43 ±5.95805 set-II V265 ADC (Channel 0) Voltage Pedestal Separated MPV Error 1254 141.877 ±0.870509 1327 195.783 ±1.12879 1422 314.283 ±1.79578 1567 652.614 ±2.21524 1682 1149.31 ±4.63862 1788 2006.61 ±6.58844 set-II V265 ADC (Channel 2) Voltage Pedestal Separated MPV Error 1254 155.677 ±0.818286 1327 214.096 ±1.08029 1422 345.711 ±1.17669 1567 726.372 ±3.55726 1682 1329.76 ±3.76888 1788 2042.23 ±3.71988 set-II V265 ADC (Channel 4) Voltage Pedestal Separated MPV Error 1254 131.147 ±0.562506 1327 188.955 ±1.05711 1422 320.272 ±1.14969 1567 694.193 ±3.51232 1682 1353.2 ±4.38374 1788 1935.97 ±3.26153 set-II V265 ADC (Channel 6) Voltage Pedestal Separated MPV Error 1254 169.344 ±0.599008 1327 238.002 ±1.186170 1422 377.562 ±1.441890 1567 797.23 ±2.918080 1682 1516.18 ±5.300040 1788 2164.34 ±6.228640 V792N QDC (Channel 6) Voltage Pedestal Separated MPV Error 1343 103.8 ±0.6 1409 239.8 ±0.5 1484 433.1 ±0.7 1566 796.9 ±1.8 1659 1463.9 ±3.5 V792N QDC (Channel 8) Voltage Pedestal Separated MPV Error 1343 108.7 ±0.6 1409 245 ±0.6 1484 446.4 ±0.8 1566 820.1 ±1.9 1659 1509.1 ±3.7 V792N QDC (Channel 14) Voltage Pedestal Separated MPV Error 1343 104.7 ±0.6 1409 236.2 ±0.6 1484 433 ±0.7 1566 796.2 ±1.8 1659 1467.2 ±3.5
  • 7. Acknowledgement I would like to thank Prof. Gobinda Majumder for his sincere guidance through out the project and for his help to understand every bit of the experiment. I am also thankful to Deepak Samuel (Project Scientist) for his help to understand his codes written for some of the VME modules. I would also like to thank my senior Research Scholar Esha Kundu for valuable discussions and for her earlier calibration of QDC V792N which helped me to calibrate the V265 ADC. I thank my colleague Soureek Mitra for his co-operation and understanding for sharing the same high voltage supply and for important conceptual discussions. References [1] Glenn F. Knoll, Radiation Detection and Measurement, Third Edition, Reprint 2009. [2] W. R. Leo, Techniques for Nuclear and Particle Physics Experiments, Second Revised Edition, Indian Reprint 2010. [3] Esha Kundu, Calibration of Versa Module Europa (VME) Modules , Experimental Project, February 2011. [5] CAEN, V265 ADC User Manual. [6] CAEN, V814 CFD User Manual. [7] CAEN, V538A ECL-NIM/NIM-ECL Translator User Manual. [8] CAEN, V976 Four Fold Coincidence Fan In Fan Out Translator User Manual. [9] Phillips Scientific, Quad Linear Fan In Fan Out User Manual. [10] CAEN, V792N QDC User Manual [11] http://my.et-enterprises.com/