| A simplified circuit diagram of the ABCStar's FE. The distinct blocks are described in the text of section~\ref{sec:impulse}, with time constant $\tau_i$ matched to the corresponding block denoted by ``P$i$'' for $i=1,\ldots,7$. As discussed in the text, the preamplifier (P1/P2) is resolved as two first-order low-pass filters within the semi-empirical approach. The first-order low-pass filter with time constant $\tau_7$ is found at the input to the discriminator (P7). |
| Impulse response of the ABCStar's FE. In the upper plot, both a SPICE simulation and an analytical function are shown are shown. The analytical function lies entirely underneath the SPICE simulation. In the lower plot, the ratio of the function to the simulation is shown. For the analytical function, the peaking time is \unit[25.6]{ns}, the full width at half maximum is \unit[33.2]{ns}, the zero crossing is \unit[74]{ns}, and the ratio of the positive-to-negative maxima is 8.8. The asymptotic behaviour in the ratio at 0 and \unit[74]{ns} is due to the numerical precision at these zero crossings. |
| A picture of the measurement setup at the B16 Test Beamline at the Diamond Light Source. (a) A side view showing the beampipe (left), compound refractive lenses (centre left), and the module test box (centre right) mounted on precision translation stages (bottom). (b) An approximate $45^\circ$ view of the same setup. |
| A picture of the measurement setup at the B16 Test Beamline at the Diamond Light Source. (a) A side view showing the beampipe (left), compound refractive lenses (centre left), and the module test box (centre right) mounted on precision translation stages (bottom). (b) An approximate $45^\circ$ view of the same setup. |
| The hit efficiency as a function of the discriminator threshold and the beam intensity. The shape of a typical S-curve is overlaid for comparison. The colourbar uses a logarithmic scale except in the range of $[0, 1]\%$, where a linear scale is used instead. |
| The observed fraction of triggers which measure a hit as a function of the distance following a hit for a beam intensity of 89\% and a discriminator threshold of \unit[14]{DAC}. |
| The observed fraction of triggers which measure a hit as a function of the distance following a hit for nine combinations of beam intensities (89\%, 17.1\%, and 2\%) and discriminator thresholds (8, 14, and \unit[20]{DAC}). Also shown are the linear fits to the observed data. The error bars correspond to the Wilson confidence intervals. |
| : Slope |
| : Relative uncertainty on slope |
| : Signed $Z$ score |
| : Reduced $\chi^2 - 1$ |
| A demonstration of the ABCStar FE's output response for eight simulated events (i.e., triggers) at a beam intensity of 90\% and a discriminator threshold of \unit[20]{DAC}. The magenta stars indicate the arrival of photons. In the upper plot, the impulse response, equation~\ref{eqn:impulse_response}, is drawn at each of these times as a shaded blue area. The dashed blue line is drawn to emphasize the impulse response for the first photon. The solid blue line represents the total FE response, given by the linear sum of the impulse response for each photon across all time bins. All of these quantities are defined relative to the pedestal, which is indicated by the dotted blue horizontal line. N.B. the long tail of the impulse response which falls below the pedestal. In the lower plot, the total FE response is shown in relation to the relevant trigger thresholds. The dashed black vertical lines indicate trigger times (i.e., every \unit[25]{ns}). The dotted black horizontal line indicates the set threshold; the solid green horizontal lines indicate the set threshold plus the noise if the total FE response exceeds this sum at a trigger time (i.e, a hit), and the solid red horizontal lines indicate this same quantity if the total FE response does not exceed this sum at a trigger time (i.e., no hit). |
| The response curve used in the simulation. The gain at an input charge $q$ corresponds to the slope of the response curve at $q$. The value of each point in the response curve corresponds to value of the set threshold which results in a 50\% hit efficiency, determined by scanning the hit efficiency as a function of the set threshold and fitting equation~\ref{eqn:scurve}, as shown in the inset. The fitted mean corresponds to the value of the response curve and the fitted width corresponds to the value of the output noise. |
| The number of observed and simulated hits as a function of threshold for nine different beam intensities. Simulations including and excluding threshold bounce (``TB'') effects are both shown. The error bars correspond to the Poisson counting uncertainties. |
| : Including threshold bounce effects |
| : Excluding threshold bounce effects |
| The observed and simulated fractions of triggers which measure a hit as a function of the distance following a hit for nine combinations of beam intensities (89\%, 17.1\%, and 2\%) and discriminator thresholds (8, 14, and \unit[20]{DAC}). The simulation includes threshold bounce effects. The error bars correspond to the Wilson confidence intervals. |