7.3.4 TIMING LINEARITY AND RESOLUTION
The timing linearity and resolution were determined relative to a Philips
Scientific 10C6 FASTBUS 10-bit TDC with a least significant bit (LSB) of 100
ps. This module was tested by recording 500 NIM-signals with various delays
between 30 and 100 ns. A resolution of about 50 ps (rms) was found for
these pulses. From a calibration curve [PS 89] a maximum deviation of
0.15 ns from linearity was found.
An "analog" NIM pulse was delayed relative to the trigger signals by 10 values
between 30 and 100 ns (Fig 7.5). The trigger signal started the TDC and
triggered the DSM100. The "analog" pulse was delayed and used as TDC stop and
input for the DSCs. For each delay value 500 events were recorded for which the
FB TDC tref value is known and the leading edge of the DSC
waveform (called DSC TDC value td) is calculated. The DSC TDC
plotted as a function of the FB TDC is displayed in Fig 7.10.
The timing linearity lt of the DSCs is determined from the
maximum deviation of the linear fit. Since it includes the non-linearity of the
FB TDC of 0.15 ns the value is
lt <±0.3 ns (max). (
7.5)
Figure
7.10:
DSC TDC td plotted as a function of FB TDC tref (left).
Each point is the mean value of 500 events. The maximum deviation of the linear
fit is 0.3 ns (right). The error bars are the rms-values of the mean
values.
For each event the difference [Delta]t between the FB TDC value and the
DSC value
(
7.6)
is calculated. The resulting histograms for 4 DSCs are shown in Fig. 7.11.
Figure
7.11:
Distribution of [Delta]t as defined in eq 7.6 for four DSCs.
The timing resolutions [Delta]tr are defined as the
rms-values of the histograms and are between 0.1 and 0.2 ns. As final value for
the timing resolution the maximum is taken:
[Delta]tr<0.2 ns (rms). (7.7)
It should be mentioned that this value includes the 50 ps timing resolution of
the FB TDC.