BB ADC gain and multiplicity calculation

From: Michael Murray Tel 409 845 1411,FAX 1899, Home 823 3386 (MURRAY@cycomp.tamu.edu)
Date: Sun Sep 03 2000 - 02:53:53 EDT

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        Dear Yuri,
               I found you note on  the BB counters very informative and the data very 
    exciting. However I think that there is a small problem with the extraction of the ADC gain and
     multiplicity related to your use of the Pedestal RMS in section 1.1
    
    You define the gain AdcGain0 as the first peak in the distribution of 
    
                   ADC - Ped - 2*PedRMS                                   Eqn 1
    
    and     then you define as 
                 MultPerTube = <ADC - Ped - 2*PedRMS>/AdcGain0            Eqn 2
    
    where < > denotes an average over a given class of events.
    
    Let us say we have a tube whose ADC spectrum shows 4 peaks corresponding to the 
    Pedestal at  50
    1 MIP    at  80
    2 MIPS   at 110 and
    3 MIPS   at 140    
    
    Then suppose that PedRMS = 10. (This is extreem but bear with me)
    
    
    Eqn 1 gives   AdcGain0 = 80 - 50 - 2*10 = 10.
    
    Then for a given event if say you have an ADC value of 80 corresponding to 1 MIP then
    
    Eqn 2 implies 
                     MultPerTube = (80 - 50 -20)/10 = 1  which is correct.
    
    However if for the next event ADC = 110 (ie 2 MIPs)
                     MultPerTube = (110 - 50 -20)/10 = 4  which is incorrect.
    
    The problem is even worse for higher values. If ADC = 140 (ie 3 MIPS)
                     MultPerTube = (140 - 50 -20)/10 = 7                     
    
    Of course the magnitude of the problem is probably much  smaller in your analysis  since the  
    width of the pedestal is probably a small fraction of the distance  between peaks. 
    
    The problem can   be corrected by not plotting ADC - Ped - 2*PedRMS but simply
    ADC and looking for the first peak above Ped+2*PedRMS and calling this AdcGain1
        
    Then 
                      MultPerTube = <ADC - Ped>/AdcGain1            Eqn 3
     
    I beleive that this will   lead to   more correct and lower dN/dEta values.
                               Yours Michael              
    : 
    : Michael Murray murray@comp.tamu.edu
    : Cyclotron Institute, Texas A&M University, TX 77843-3366
    : Telephone (979) 845 1411, FAX 1899
    



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