Re: BB ADC gain and multiplicity calculation

From: Yury Blyakhman (Yury_B@physics.nyu.edu)
Date: Sun Sep 03 2000 - 10:59:32 EDT

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    Hello, Michael and everybody.

      Yes, it looks like that was the reason of my a little bit high
multiplicity numbers. Flemming already pointed it out to me on Friday.
The other thing , which is wrong in my formulae is, that I should assign
0 multiplicity to all events coming before the half-width of the 1st MIP
peak. Anyway, I really appreciate your comment. It turns out, from the
discussion with Flemming, that everybody are aware of that mistake, it's
just nobody mentioned it yet to me ;-)))

      Thanks again, and new, corrected numbers are underway. These
two corrections makes multiplicity values to be lower by about 10%, keeping
the shape of it's distribution.

    "Michael Murray Tel 409 845 1411,FAX 1899, Home 823 3386" wrote:

        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
    


    -- 
        Yury Blyakhman.
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