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SiPM Amplifier Signal Analysis (view source)
Revision as of 19:54, 1 October 2009
, 19:54, 1 October 2009→Single pixel signal shaping
The spectral response of the modeled amplifier in its low and high gain setting (see [[SiPM Amplifier Optimization]]) is shown in Fig. 2. Note the beginning of the roll-off in the response (due to the integration described above) within the spectral envelope of the input signal. The stretching seen in the time-domain plot is due to this attenuation of high frequency components. However, given the ADC's sampling rate of 250 MSps, shortening the pulse further (flattening the frequency response across the entire signal spectrum) is not necessary.
The spectral response of the modeled amplifier in its low and high gain setting (see [[SiPM Amplifier Optimization]]) is shown in Fig. 2. Note the beginning of the roll-off in the response (due to the integration described above) within the spectral envelope of the input signal. The stretching seen in the time-domain plot is due to this attenuation of high frequency components. However, given the ADC's sampling rate of 250 MSps, shortening the pulse further (flattening the frequency response across the entire signal spectrum) is not necessary.
A quick, 2-Gaussian model of this signal is a reasonable approximation of this slightly asymmetric pulse. So, to arbitrary vertical scale and time offset, the fit to <math>e^{\frac{-t}{2 \sigma_1^2}} + a e^{\frac{-(t-t_0)}{2 \sigma_2^2}}</math>
A quick, 2-Gaussian model of this signal is a reasonable approximation of this slightly asymmetric pulse. So, to arbitrary vertical scale and time offset, the fit to
<math> f(t) = \frac{A}{t} \left[1- e^{- \left( \frac{t}{T_1} \right) ^{p_1}}\right]
\exp \left[- \left(\frac{t}{T_2}\right)^{p_2} \right]
\cos \left[ \left(\frac{t-t_o}{T_3} \right)^{p_3} \right] +
\exp \left[ \frac{-(t-t1)}{2 \sigma_1^2} \right] +
\exp \left[ \frac{-(t-t2)}{2 \sigma_2^2} \right]
</math>
=== Modeling of realistic signals ===
=== Modeling of realistic signals ===