Report on recent work Wenli Zhao Department of Physics University of Michigan, Ann Arbor May 2014 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 1 / 20
Outline Setup 1 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 2 / 20
Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 2 / 20
Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Analysis of the rise time 3 Definitions Correction for risetime Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 2 / 20
Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Analysis of the rise time 3 Definitions Correction for risetime Conclusion 4 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 2 / 20
Setup Setup Goal: Study of the sensitivity of VPI panel depeding on 1 Voltage (Voltage Scan) 2 Time (Long term data) Collimated 3.7 mCi 90 Sr source right upon a RO line connected to an oscilloscope and a digital counter. Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 3 / 20
Setup Setup Detail Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 4 / 20
Measurements with VPI panel Voltage Scan measurement Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Analysis of the rise time 3 Definitions Correction for risetime Conclusion 4 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 5 / 20
Measurements with VPI panel Voltage Scan measurement Voltage Scan The background and signal rates are measured seperately. HV range 950-1005V with increments of 5V. At 1005V the background is more than 20% of the signal → STOP Basic parameters: Gas AAT0001 at 744 torr R(HV) = 200MΩ for 30 HV lines 24 RO lines discriminated at -700 mV Measurement on the 19 th from the first HV line. Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 6 / 20
Measurements with VPI panel Voltage Scan measurement Voltage Scan Data Fit: Rate ( HV ) = 2 . 915 × 10 − 27 · e 0 . 0635 x Background < 1% whereas the lowest total error is 6.8% = ⇒ background not plotted. Conclusion: in the range above, insignificant background contribution. Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 7 / 20
Measurements with VPI panel Voltage Scan measurement Voltage Scan On the Scope Waveforms captured on the oscilloscope (triggerd in single mode) for the illuminated line and the two nearest neighbors. First set: 100 measurements every 10V starting from 950V. From 950V to 990V no second fire in the trigger line. However, there was a second fire seen at 1000V. Second set: 700 measurements (to enhance the accuracy of the results). Left Trigger Right Counts 2 12 2 Percentage 0 . 3% 1 . 7% 0 . 3% The recorded numbers are much less than the errors → the signals we counted are the ones produeced singlely in a statistically convincing sense. Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 8 / 20
Measurements with VPI panel Long Term Measurements Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Analysis of the rise time 3 Definitions Correction for risetime Conclusion 4 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 9 / 20
Measurements with VPI panel Long Term Measurements Long term measurement Goal: measure the recording rate of VPI with respect to time. Setup: same as the Voltage Scan but fix the HV=980V. Plot of the daily number of hits: the data suggests a fluctuation which does not influence the ratio between different channels. Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 10 / 20
Measurements with VPI panel Long Term Measurements Long Term Measurements Ratio Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 11 / 20
Analysis of the rise time Definitions Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Analysis of the rise time 3 Definitions Correction for risetime Conclusion 4 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 12 / 20
Analysis of the rise time Definitions Some simple calculations Definition(Transfer function) Let x ( t ) y ( t ) be integrable functions appropriate for bilateral Laplace transform. Define the transfer function H for x , y to be a map H s : R → Hom ( C 0 , C 0 ) such that L ( x ( t )) �→ L ( y ( t )). Practically x ( t ) is the input and y ( t ) is the output. Remark For a system with input x ( t ) and output y ( t ), the transfer function is just H ( s ) = L y ( t ) L x ( t ) . Thus if we know the differential equation of input and output signal, we can directly write the transfer function of the system by taking bilateral Laplace transform. Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 13 / 20
Analysis of the rise time Definitions Some simple calculations Frequently, since the transfer function is not trivial, the measured signal has a different rise time than the actual signal. To see the difference, let’s consider the following example Example k Let H s be s + a (this transfer function corresponds to a low pass RC circuit). Let x = u ( t ) the step function. Then s ( s + a ) = k k k y ( t ) = k a (1 − e − at ) u ( t ) L{ y ( t ) } = as − → a ( s + a ) The signal has t rise to be positive risetime whereas originally t rise = 0. Since a = 1 RC ,then t rise = τ ( ln ( 1 1 0 . 1 ) − ln ( 1 τ = 0 . 9 )) ≃ 2 . 197 τ . Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 14 / 20
Analysis of the rise time Definitions Cutoff frequency Definition: The cutoff frequency of a system is defined as the frequency at which P output = 1 2 P passband . A simple calculation reveals that for low pass RC circuit 1 1 f cutoff = 2 π RC = 2 πτ Thus for single pole system t rise = 0 . 35 f cutoff Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 15 / 20
Analysis of the rise time Correction for risetime Outline Setup 1 Measurements with VPI panel 2 Voltage Scan measurement Long Term Measurements Analysis of the rise time 3 Definitions Correction for risetime Conclusion 4 Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 16 / 20
Analysis of the rise time Correction for risetime Correction for Risetime In reality, an oscilloscope is a complicated device and in order to find the correction we need to look at its circuit. However, since it consists of a probe and a scope, we may assume each part is approximately a single pole system, so the total rise time is given by � t 2 scope + t 2 probe + t 2 t rise = 1 . 1 signal where 1.1 is an empirical constant and t scope , t probe , t signal are respectively the risetime for scope, probe and signal. The first two can be calculated by knowing their cutoff frequency. In our measurement, the bandwidths of the cable and probe are small compared to that of the scope → we only need to consider the cutoff frequency of the scope: 350 MHz Thus the correction may be given by � t 2 rise 1 . 21 − 10 − 18 t signal = Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 17 / 20
Analysis of the rise time Correction for risetime Difference between Real and Measured Risetime The graph of the difference between the real risetime and the measured risetime difference between measured risetime [ns] 1 0.8 0.6 0.4 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 Real risetime [ns] Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 18 / 20
Analysis of the rise time Correction for risetime Risetime Error The percentage of the error is also plotted below. The graph of the ratio of the difference between the real risetime and the measured risetime Ratio 9 8 7 6 5 4 3 2 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Real risetime [ns] Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 19 / 20
Conclusion Conclusion Voltage Scan Long term measurement Correction on risetime t rise = 0 . 35 f cutoff � t 2 1 . 21 − 10 − 18 rise t signal = Wenli Zhao (University of Michigan, Ann Arbor) Report on recent work May 2014 20 / 20
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