The smallest strip pulse comes from interactions near the cathode (Z=0). The 100ns diff-int shaping is sensitive to the falling edge so it is inherently noisier than looking at the longer duration peak.
The simulated signals show that a 100ns differentiator-integrator gives a reasonably uniform pulse height over most of the volume of unit cell. This shaping narrows the bandwidth so it will improve the signal to noise relative to the unfiltered preamp output. However the signal to noise is expected to be quite poor in comparison to the pixel signal which can be filtered with a much longer time constant (2usec).
A comparison of noise can be calculated assuming that the contribution from random noise will be proportional to the square root of the noise bandwidth. The effective noise bandwidth of a single stage RC filter is 1.57/(2pi RC). The following table gives the expected noise compared to the pixel signal. Noise is based only on relative bandwidth assuming a 2usec single stage shaper on the pixel signal. The strip signal noise may be even higher due to the difference in preamp input capacitance. The table shows that the due to the lower signal and wider bandwidth, the 100ns diff-int output is expected to have a factor 67 worse signal/noise than the pixel signal.
| Filter | Bandwidth | Pulse (Z=0) | Relative noise/sig |
|---|---|---|---|
| pixel 2usec int | 125KHz | 0.91 | 1.00 |
| fall 50ns diff-int | 2.97MHz | 0.054 | 82.1 |
| fall 100ns diff-int | 1.49MHz | 0.047 | 66.8 |
| peak 100ns int | 2.5MHz | 0.179 | 22.7 |
| peak 200ns int | 1.25MHz | 0.134 | 21.5 |
The signal strength is based on simulated detector signals run through simulated filters.
The smallest strip pulse comes from interactions near the cathode (Z=0). The 100ns diff-int shaping is sensitive to the falling edge so it is inherently noisier than looking at the longer duration peak.
For depths near Z=0, filtering the positive peak would have a better signal to noise.
For Z of about 1.6mm (or greater) the negative residual would have the best signal to noise ratio. The amplitude is still fairly low but the duration would allow filtering with long time constants.
The depth where the filtered resid signal becomes better than the peak is at about 1.6mm. The signal/noise at this crossover point is about 30 times worse than the pixel signal. A factor of 30 is about the best that can be done at this depth regardless of shaping choice.
Using the resid would give good signal/noise for most of the cell but can not cover the entire depth. This signal is very depth dependent and would require handling a very large dynamic range of pulse heights.
Using either the peak or resid signal depending on depth theoretically gives is the best possible signal/noise over the entire unit cell.
The 100ns diff-int is about a factor of 2 worse for noise but it gives a signal over the entire depth.