Re: Back of the envelope Dynamic range

["Fernando J. Barbosa" <barbosa@jlab.org>]

Hi Gerard,

    This discussion started with the presentation and summary table 
showing a typical charge of 1.5 pC for the FDC anodes and the preamp 
dynamic range of 400fC (with a few % linearity) for point ionization.

    We wanted to get a ballpark figure, without going into much detail. 
I agree with you that at some point someone needs to go through a 
simulation and get all the factors in place, including all the detector 
details, inefficiencies, cell geometries and so on.  I don't think 
anybody has done this in the collaboration. Maybe a nice project?

    I used the classical capacitance matching to group all the 
unaccounted factors, although this is strictly a construct on my part - 
the losses due to parasitic capacitances, etc can account for about 20% 
or so of the losses - not much of a difference in the numbers on the 
slide. It could be even worse for the FDC given the geometry and edge 
effects on the cells and their variable length, capacitance, etc. In 
other words, our quick, back of the envelope calculations agree with 
what has been on the summary table for years.

    I suggest, following your feedback, that we need to back up all of 
these numbers with realistic data, perhaps from your and Simon's work on 
the FDC prototype. Then, we can finalize the specifications for Mitch 
before the final design of the preamp.

Regards,
Fernando

Gerard Visser wrote:
> Hi folks,
>     There are a couple of misconceptions I think lurking around 
> here... First a small factor: naively treating the ion drift in the 
> FDC as a cylindrical chamber, applying standard formulas for instance 
> from a paper of Radeka, I get the signal charge is
> Q(t)=Q0 * ln(1+t/t0) / ( 2*ln(rc/ra) ).
> Here Q0 is the _total_ signal charge to time infinity;
> rc is the "cathode radius", I'll use 5mm;
> ra is the effective anode radius, I'll use 13um (it must be a little 
> larger than the wire, the mean radius of ion production in the 
> avalanche is what you put here);
> t0 is the time scale parameter, t0=ra/(2*mu*V), I'll use mu=1.62e-4 
> and V=1650, then t0=1.88ns;
> With this Q(10ns) = 15% of Q0. 20% is too high a figure I think.
>     Secondly, it is all a little too simplistic to pretend that the 
> preamp measures just a charge and that it is exactly the charge 
> delivered in 10ns. Both the signal and the preamp/shaper/ADC system 
> have a frequency response to consider here, and the overall response 
> to detector current is not simply an integration (g(s)=1/s) response 
> over all the relevant frequencies. We are not measuring precisely the 
> charge or the current but something in between. Back-of-the-envelope 
> "charge" discussions about the signal size may be useful to set the 
> rough scale, but we need someday to converge on a real specification, 
> and that can only come from a calculation or simulation that includes 
> the less trivial time/frequency response of the system.
>     Thirdly, it is obvious both a priori and from a quick look at 
> signals from the prototype, that not all the electrons arrive at the 
> anode wire simultaneously. Of course details of the arrival time 
> distribution depend on the track parameters, but I _guess_ it's 
> probably fair to assume a fluctuating fraction maybe 10% to 50% of the 
> signal charge actually arrives at the preamp in "the largest" 10 ns 
> interval. I think all the FDC/CDC signal size calculations I have seen 
> written so far have been ignoring this...
>     Fourth: a capacitance match on the preamp (Cdet=Camp) is in 
> reference to the _open_-loop amplifier; the closed-loop preamplifier 
> is supposed to have a much lower input impedance than that. _All_ of 
> the charge is supposed to go into the preamp (if the far side of the 
> detector is not having a termination resistor, of course; and of 
> course this is also ignoring the non-infinite coupling capacitance and 
> charge sharing between preamp and detector due to that). [I'm also not 
> sure that this ASIC is subject to this capacitive match rule, it does 
> not directly apply for such short peaking times, maybe?] In any case, 
> this means a factor of 1/2 for "capacitance match" is _not_ present 
> and should be dropped out of Fernando's slide.
>     [Ok Elton also already addressed this one by now...]: Fifth, I 
> don't know much about it but the figure of 100 (or 90) e-ion pairs 
> produced by the track, is the mean, isn't it? And the distribution of 
> it (Landau distribution?) has a significant tail. The implication 
> being, we can't just use the mean value to set the signal range of the 
> readout electronics or else it's going to saturate on a lot of events. 
> Some factor needs to be included, to account for the ratio between 
> point where remaining tail is ignorable and the mean. Unless I goofed 
> the math, I find a factor 2.2 should be included, for 5% of events are 
> more than a factor 2.2 greater than the mean. [Elton says 3.0.]
>
>     Gerard
>
> p.s. Elton in your summary, you don't mention the CDC track 
> inclination (path length) contribution. Isn't that important? What is 
> the distribution of track lengths in the CDC? (I think Ryan produced a 
> plot of this for us once... I don't know if it is still accurate today.)
>
>
> Elton Smith wrote:
>> HI Fernando,
>>
>> Thanks for the plot. We had ignored your Cdet/Camp factor of 0.5. Your
>> gain for the FDCs should be updated to 8^10^4. We agree that the dynamic
>> range is fine for the FDCs.
>>
>> Curtis should comment on 1) operating gain of the CDCs (2x10^4?), and 2)
>> the required dynamic range. My guesstimate is factor of 10 for dE/dx 
>> and a
>> factor of 3 for Landau fluctuations, giving a total of 30. Linearity of
>> this entire range is probably not required, as even saturation would
>> identify slow protons. Clearly the region of linearity is most important
>> for the FDC cathodes which matches the dynamic range.
>>
>> Thanks, Elton.
>>
>>
>>
>>
>> Elton Smith
>> Jefferson Lab MS 12H5
>> 12000 Jefferson Ave
>> Suite # 16
>> Newport News, VA 23606
>> elton@jlab.org
>> (757) 269-7625
>>
>> On Wed, 14 Feb 2007, Fernando J. Barbosa wrote:
>>
>>
>>> Hi Elton,
>>>
>>> I made a slide which I am attaching. Please check the numbers as I show
>>> what a MIP in the chamber corresponds to the charge into the preamp.
>>>
>>> Regards,
>>> Fernando
>>>
>>> Elton Smith wrote:
>>>
>>>> Hi Fernando,
>>>>
>>>> Yesterday during your presentation you showed the dynamic range of the
>>>> preamp to saturate at 400 fC. We are a little confused about the range
>>>> required. I know that there was quite a bit of discussion at the 
>>>> time the
>>>> range was decided, but simple estimates give higher numbers and we 
>>>> need to
>>>> know what we are missing.
>>>>
>>>> Fernando was correct in that the induced signal on the wire on the 
>>>> wire
>>>> coming from the electron signal is only about 20% of the avalanch 
>>>> charge
>>>> (in the first say 10 ns). Therefore, we obtain the following for a 
>>>> minimum
>>>> ionizing track:
>>>>
>>>> Simon says that the gain of the FDC is about 0.8x10^5.
>>>>
>>>> assume: 100 ions, 20% of Qtot, Gain=10^5, e=1.6x10^-19.
>>>> Signal charge (anode) = 0.2 x 100 x 10^5 x 1.6x10^-19 ~ 300 fC
>>>> Signal charge (cathode) ~ 300 fC x 1/2 x 1/4 ~ 40 fC.
>>>>
>>>> My preliminary (rough) estimate concludes that this should work for 
>>>> the
>>>> FDC cathodes. The FDC anodes under the nominal design do not use the
>>>> FADCs, but would likely saturate if they do.
>>>>
>>>> For the CDC, the anode signal will also be used for dE/dx, so a 
>>>> factor of
>>>> at least 30 is needed in dynamic range. These would clearly 
>>>> saturate at a
>>>> Gain of 10^5, but we might want to run them at lower gain.  At G=10^4
>>>> gain, and 30 dynamic range, we get a maximum signal of 900 fC, also
>>>> saturating the preamp.
>>>>
>>>> Comments? What am I doing wrong?
>>>>
>>>> Thanks, Elton.
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Elton Smith
>>>> Jefferson Lab MS 12H5
>>>> 12000 Jefferson Ave
>>>> Suite # 16
>>>> Newport News, VA 23606
>>>> elton@jlab.org
>>>> (757) 269-7625
>>>>
>>>
>>
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