SiPM Amplifier Signal Analysis - Revision history

Senderovich at 16:15, 2 October 2009

2009-10-02T16:15:36Z

Senderovich at 16:05, 2 October 2009

2009-10-02T16:05:10Z

Senderovich: /* Single pixel signal shaping */

2009-10-02T15:31:20Z

Single pixel signal shaping

Senderovich: /* Single pixel signal shaping */

2009-10-01T19:54:33Z

Single pixel signal shaping

Senderovich at 01:01, 30 September 2009

2009-09-30T01:01:30Z

Senderovich at 00:42, 30 September 2009

2009-09-30T00:42:21Z

Senderovich at 20:06, 1 March 2009

2009-03-01T20:06:20Z

Senderovich: /* Modeling of realistic signals */

2009-02-12T20:31:57Z

Modeling of realistic signals

Senderovich at 20:30, 12 February 2009

2009-02-12T20:30:00Z

Senderovich at 20:29, 12 February 2009

2009-02-12T20:29:35Z

@@ Line 22: / Line 22: @@
 </math>
-* T_1 = 14.9ns
-* p_1 = 99.2
+where,
-* T_2 = 2.54&mu;s
+{|
-* p_2 = 2.50
-* t_o = -0.206&mu;s
+{|
-* T_3 = 0.125&mu;s
+| T<sub>1</sub> || = || 14.9ns
-* p_3 = 0.642
+|-
-* t_1 = 9.57ns
+| p<sub>1</sub> || = || 99.2
-* sigma_1 = 1.50ns
+|-
-* a = 0.258
+| T<sub>2</sub> || = || 2.54&mu;s
-* t_2 = 13.0ns
+|-
-* sigma_2 = 1.53ns
+| p<sub>2</sub> || = || 2.50

@@ Line 18: / Line 18: @@
 e^{-\left(\frac{t}{T_2}\right)^{p_2}}
 \cos \left[ \left(\frac{t-t_3}{T_3} \right)^{p_3} \right] +
-\exp \left[ \frac{-(t-t1)}{2 \sigma_1^2} \right] +
+e^{ \frac{-(t-t1)}{2 \sigma_1^2} } +
-\exp \left[ \frac{-(t-t2)}{2 \sigma_2^2} \right]
+a e^{ \frac{-(t-t2)}{2 \sigma_2^2} }
 </math>
-* T_1 =
+* T_1 = 14.9ns
-* p_1 =
+* p_1 = 99.2
-* T_2 =
+* T_2 = 2.54&mu;s
-* p_2 =
+* p_2 = 2.50
-* t_o
+* t_o = -0.206&mu;s
-* T_3
+* T_3 = 0.125&mu;s
-* p_3
+* p_3 = 0.642
-* sigma_1
+* t_1 = 9.57ns
-* sigma_2
+* sigma_1 = 1.50ns
 === Modeling of realistic signals ===

@@ Line 13: / Line 13: @@
 The spectral response of the modeled amplifier in its low and high gain setting (see [[SiPM Amplifier Optimization]]) is shown in Fig.&nbsp;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&nbsp;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
+A reasonable approximation of this slightly pulse, including ringing tail is a follows:
 <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]
+e^{-\left(\frac{t}{T_2}\right)^{p_2}}
-\cos \left[ \left(\frac{t-t_o}{T_3} \right)^{p_3} \right] +
+\cos \left[ \left(\frac{t-t_3}{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 ===

@@ Line 13: / Line 13: @@
 The spectral response of the modeled amplifier in its low and high gain setting (see [[SiPM Amplifier Optimization]]) is shown in Fig.&nbsp;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&nbsp;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
 === Modeling of realistic signals ===

← Older revision		Revision as of 01:01, 30 September 2009
Line 13:		Line 13:
	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^{~~cfrac~~{-(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>e^{\frac{-t}{2 \sigma_1^2}} + a e^{\frac{-(t-t_0)}{2 \sigma_2^2}}</math>

← Older revision		Revision as of 00:42, 30 September 2009
Line 11:		Line 11:
	The speed of the amplifier response is one of the chief challenges. The transistors themselves, at a bandwidth of ~4 GHz, cover the expected signal spectrum well enough. However, points in the amplifier circuit where currents are injected present integrators with the RC time set by the effective AC coupling capacitance and input impedance of the following stage. Since reduction of effective capacitance at the SiPM circuit stage is not an option (the effective charge deposited per SiPM pixel discharge decreases) the input impedance was minimized. This is accomplished both in the amplifier and summing circuit input stages with injection on the transistor emitter (as opposed to base.) The effective resistance is thus on the order of 20 Ω (generally a quiescent current-dependent value) as opposed to a parallel combination of order 1 kΩ resistors and the effective βR<sub>E</sub> resistance looking into the base.		The speed of the amplifier response is one of the chief challenges. The transistors themselves, at a bandwidth of ~4 GHz, cover the expected signal spectrum well enough. However, points in the amplifier circuit where currents are injected present integrators with the RC time set by the effective AC coupling capacitance and input impedance of the following stage. Since reduction of effective capacitance at the SiPM circuit stage is not an option (the effective charge deposited per SiPM pixel discharge decreases) the input impedance was minimized. This is accomplished both in the amplifier and summing circuit input stages with injection on the transistor emitter (as opposed to base.) The effective resistance is thus on the order of 20 Ω (generally a quiescent current-dependent value) as opposed to a parallel combination of order 1 kΩ resistors and the effective βR<sub>E</sub> resistance looking into the base.

−	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^{cfrac{-(t-t_0)}{2 \sigma_2^2}}</math>

@@ Line 16: / Line 16: @@
 === Modeling of realistic signals ===
-[[Image:Scint_Amp_resp.png|thumb|395px|Figure 3: Comparison of the naive superposition of simultaneous single-pixel events with the expected pulse shape taking into account scintillators response. The decay time of an excitation in the scintillator is 2.7&nbsp;ns]]
+[[Image:Scint_Amp_resp.png|thumb|395px|Figure 3: Comparison of the naive superposition of simultaneous single-pixel events with the expected pulse shape taking into account scintillator's response. The decay time of an excitation in the scintillator is 2.7&nbsp;ns]]
 Figure 3 presents multi-pixel signals expected on the output of the amplifier. Simple superposition of 500 simultaneous pixel discharges is compared with a realistic signal shape. The single-pixel pulse shaped by the amplifier as described above has been convolved with the exponential distribution of photons from the scintillator. This is due to the cascade of optical excitations and decays initiated by the high-energy tagging electron passing through the scintillator bulk. The overall light flash decay time in BCF-20 is 2.7&nbsp;ns. Thus we may expect the arrival of the photons to be distributed as an exponential distribution with this characteristic time. (The differences in optical path are thought to be negligible on this scale.) Of course, the smooth distribution assumes sampling of infinitely many photons. The expected signal in the hundreds of activated pixels is sufficient or, at the very least this convolution with the ideal distribution presents the mean shape of the resulting signals.
 Note the significant attenuation when the scintillator decay time is taken into account. The dynamic range of the readout is a concern for the expected signals: about 300 pixels, exceeding 500 with proposed reflection coating on the upstream end of scintillating fibers. Since the integral of the pulse is preserved (being proportionate to the charge deposited in the SiPM), the effort to shorten the pulses lead to amplification, threatening that the full intensity signals will exceed the full range (currently 1.5&nbsp;V in the amplifier design). This upper-range estimate of 500 pixels for the signal is safely within range.

← Older revision		Revision as of 20:29, 12 February 2009
Line 15:		Line 15:

	=== Modeling of realistic signals ===		=== Modeling of realistic signals ===
		+
		+	[[Image:AmpResp.png\|thumb\|395px\|Figure 3: Comparison of the naive superposition of simultaneous single-pixel events with the expected pulse shape taking into account scintillators response. The decay time of an excitation in the scintillator is 2.7 ns]]
		+
		+	Figure 3 presents multi-pixel signals expected on the output of the amplifier. Simple superposition of 500 simultaneous pixel discharges is compared with a realistic signal shape. The single-pixel pulse shaped by the amplifier as described above has been convolved with the exponential distribution of photons from the scintillator. This is due to the cascade of optical excitations and decays initiated by the high-energy tagging electron passing through the scintillator bulk. The overall light flash decay time in BCF-20 is 2.7 ns. Thus we may expect the arrival of the photons to be distributed as an exponential distribution with this characteristic time. (The differences in optical path are thought to be negligible on this scale.) Of course, the smooth distribution assumes sampling of infinitely many photons. The expected signal in the hundreds of activated pixels is sufficient or, at the very least this convolution with the ideal distribution presents the mean shape of the resulting signals.
		+
		+	Note the significant attenuation when the scintillator decay time is taken into account. The dynamic range of the readout is a concern for the expected signals: about 300 pixels, exceeding 500 with proposed reflection coating on the upstream end of scintillating fibers. Since the integral of the pulse is preserved (being proportionate to the charge deposited in the SiPM), the effort to shorten the pulses lead to amplification, threatening that the full intensity signals will exceed the full range (currently 1.5 V in the amplifier design). This upper-range estimate of 500 pixels for the signal is safely within range.