Digitiser Effects

In order to investigate the effect of the digitiser specifications, the noise and non-linearities of the electronics were removed. This allowed the limits imposed on the resolution by the digitiser noise to be determined. A simulation was run with the same parameters as in ClicSigProc but with a position sweep in x with a single train at each point so that the minimum resolution of the digitiser is visible. The minimum offset visible above the digitiser noise was also determined. This came to 170 nm and is the same for both deconvolution and DDC processing algorithms. The bandwidth of the digital filter used for the DDC was 45 MHz in both cases.

The plot on the left shows the results of the position sweep using the sample at 75 ns from the start of the beam signal. The plot on the right shows the resolution determined from the points in the sweep where the signal was large enough to be observed for each sample that measured a signal from the beam.

Timing

The timing of the single bunch waveform used for the deconvolution was varied between 20 ns before the start of the multibunch waveform up to 30 ns after. It can be seen that the start time of the deconvolved waveform that is shown in the plot in the left is at t_{0,deconvolved}=t_0,multibunch-t_0,single. When this goes negative, the deconvolved waveform rolls round to the end of the window. Therefore, it is desired that the arrival time of the single bunch waveform is earlier than the arrival time of the multibunch waveform.

New Resolution Measure

A measure of resolution that may be useful in simulation is calculated from the difference between the measurement at a particular sample number and the interpolated bunch position at that time. A simple illustration of the measured and interpolated positions with a DDC filter bandwidth of 80 MHz is shown below.

This measure is constant when normalised by the level of bunch to bunch jitter. It doesn't vary a low but shows noticeable changes with the DDC filter bandwidth.

This measure of resolution (dubbed 'averaging resolution') goes above 1.0 (the value it would take if simply averaging over the whole bunch) when the bunch to bunch jitter dips below the BPM resolution.