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--- hw:lab:spectrochain:script [2009/09/14 16:40]
szymon.kulis
+++ hw:lab:spectrochain:script [2019/03/08 14:08] (current)
@@ Line 1: / Line 1: @@
 ====== spectrometric chain ======
 ===== Introduction =====
-The aim of this laboratory course is to understand how spectrometric chain works. You will look at behavior of components like preamplier or shaper. Next step will be to measure basic parameters of such a chain like gain or noise performence.
+The aim of this laboratory is to understand how the spectrometric chain works. First, you will observe the operation of readout electronics blocks like preamplifier and shaper. The next step you will measure the basic parameters like gain or noise of such readout chain. At the we will try to observe pulses from Am61 radio active source.
 ===== Circuit description =====
 ==== Building blocks ====
-Schematic diagram of the spectrometric chain is shown below on <imgref sch_front>.
+Schematic diagram of the spectrometric chain is shown below in <imgref sch_front>.
@@ Line 14: / Line 13: @@
 </imgcaption>
-The most often used front-end electronics configuration consists of the charge
+The most often used front-end electronics configuration consists of a charge
-sensitive preamplifier and <latex>CR-(RC)^n</latex> the filter known as pseudo-gaussian shaper.
+sensitive preamplifier and a <latex>CR-(RC)^n</latex> the filter known as pseudo-gaussian shaper.
 The <latex>CR-(RC)^n</latex> filter is called pseudo-gaussian because the response of such
-filter to step function becomes exactly gaussian when its order n approches infinity.
+filter to step function becomes exactly gaussian when its order n approaches infinity.
 The pseudo-gaussian shaper is frequently used because of its simplicity and because
 it allows to obtain close to optimum S/N ratio [ref-gatti,radeka].
@@ Line 32: / Line 31: @@
 operational amplifiers is of the order <latex>10^5-10^6</latex>).
-The shaper output signal can be then writrten as:
+The shaper output signal can be then written as:
 <latex>
@@ Line 70: / Line 69: @@
 </latex>
-Usually, a very good assumption for sensor pulse shape is a dirac delta i.e. <latex>I_{in}(s)=Q_{in}</latex> with its integral equal to a total charge <latex>Q_{in}</latex> deposited in the sensor. This assumption reflects the fact that the charge collection time in the sensor is much shorter than the front-end electronics shaping time.
+Usually, a very good assumption for sensor pulse shape is a dirac delta, i.e. <latex>I_{in}(s)=Q_{in}</latex> with its integral equal to a total charge <latex>Q_{in}</latex> deposited in the sensor. This assumption reflects the fact that the charge collection time in the sensor is much shorter than the front-end electronics shaping time.
 Under this assumption the front-end response in time domain equals:
@@ Line 88: / Line 87: @@
-To pass from the theoretical considerations to a practical circuit the only
+To move from the theoretical considerations to a practical circuit the only
 thing needed is to add a resistance <latex>R_f</latex> in parallel to <latex>C_f</latex>. It is needed
 for two purposes: first to set the DC level of the preamplifier input and
 second, to assure that the feedback capacitance <latex>C_f</latex> gets discharged
-and so it will not saturate the preamplifier output after a number of
+and so the preamplifier output will not saturate after a number of
 subsequent pulses from the sensor. The derived above transfer function becomes
 practically unaffected if the <latex>R_f</latex> value is sufficiently large (<latex>\sim 1 G\Omega</latex>
-in this work).
+in this laboratory circuit).
@@ Line 102: / Line 101: @@
 in the proposed spectrometric system: the sensor noise and the front-end electronics
 noise. The sensor noise comes mainly from a shot noise caused by the sensor
-leakage current <latex>I_{leak}</latex> and its spectral power density is equal to:
+leakage current fluctuations <latex>I_{leak}</latex> and its spectral power density is equal to:
 <latex>
@@ Line 110: / Line 109: @@
 The front-end electronics noise is mainly due to the preamplifier and the feedback
-resistance <latex>R_f</latex>. In properly designed system the following shaper stages
+resistance <latex>R_f</latex>. In a properly designed system the following shaper stages
-give small contribution to the total noise (since the signal is already amplified).
+give small contribution to the total noise (since the signal is already amplified by the preamplifier).
@@ Line 190: / Line 189: @@
 where <latex>\Gamma</latex> is the Gamma function.
 ====Sensor, Preamplifier and Shaper - Signal to Noise====
@@ Line 211: / Line 208: @@
 \tau_{opt} = (C_{in}+C_f) \sqrt{\frac{v_{eqw}^2}{(2n - 1)(i_{eqw}^2 + 2qI_{leak} + 4kT/R_{f})}}
 \label{eq:tau_opt}
-</latex>
-In such case the minimum ENC equals:
-<latex>
-ENC_{min} = \frac{e^n n!}{q n^n} \\
- \sqrt{\frac{\Gamma(n - \frac{1}{2}) (C_{in}+C_f)}{8 \sqrt{\pi} \sqrt{n!}} \\
- \sqrt{ (2n-1) \cdot v_{eqw}^2 \cdot (i_{eqw}^2 + 2qI_{leak} + \frac{4kT}{R_{f}}) }\\
-+ (C_{in} + C_{f})^2 \frac{v_{1/f}^2}{2n}}
-\label{eq:enc_min}
 </latex>
@@ Line 239: / Line 226: @@
 of the peaking time <latex>T_{peak}</latex> can be done in order to equalize the
 contribution of voltage and current noise. As before the voltage component decreases
-with the increase of <latex>T_{peak}</latex> while the current component increases
+with increasing <latex>T_{peak}</latex> while the current component increases
 with increasing <latex>T_{peak}</latex>.
-The noise dependence on the shaping order is more complicated and in general it is
+The noise dependence on shaping order is more complicated and in general it is
 better seen with numerical simulations. Qualitatively one can only say that the ratio
-of voltage to current noise contribution increases with increasing shaping order.
+of voltage to current noise contribution increases with increasing shaping order. To get feeling about the real noise performance it is instructive to plot the ENC as a function of peaking time, for different shaping orders (Fig XX).
-To get feeling about the real noise performance it is instructive to plot the ENC
-as the function of peaking time, for different shaping orders.
-This is done below setting all required parameters to the reasonable values
-corresponding to this work.
-{{  :user:kulis:uspec:theory01.png|  }}
+{{:hw:lab:spectrochain:theory01.png|}}
-As expected the optimum peaking time exists.
-Reagarding the shaping order it is seen that in general the higher order
+As expected the optimum peaking time exists. Regarding the shaping order it is seen that in general the higher order the better noise performance.
-the better noise performance.
 Assuming that the further signal processing stages add negligible contribution
-to the overall system noise one can estimate the expected resolution of the spectrometric system in terms of the number of electrones, on the basis of eq. <latex>\ref{eq:enc2}</latex>.
+to the overall system noise one can estimate the expected resolution of the spectrometric system in terms of the number of electrons, on the basis of eq. <latex>\ref{eq:enc2}</latex>.
-For example one can assume second order shaping, <latex>C_{in} + C_f = \sim 10~pF</latex>, <latex>T_{peak} = 5~\mu s</latex>, <latex>R_f = 1~G\Omega</latex>, <latex>I_{leak} = 300~pA</latex> and spectral noise densities of Texas Instruments OPA657 operational amplifier <latex>v_{eq}^2 = 25~nV^2/Hz</latex>, <latex>i_{eq}^2 = 1.7~fA^2/Hz</latex>.
+==== Practical realization ====
-In such case the total system noise with ENC below 200 electrons may be expected.
-Requesting the S/N of 10 for good separation between the signal and noise one can expect
-that the signals corresponding to 2000 or more electrons realased in the sensor should be well seen by such system.
-As a practical example a copper(<latex>Cu</latex>) Xray fluorescence <latex>K_{\alpha} = 8.05~keV</latex> line  may be considered. Each Xray photon should release in silicon sensor about (8050 eV)/(3.7 eV)=2175 electron-hole pairs which is above the requested minimum
-for the given readout electronics specifications. It means that the specified readout
-system should be able to detect the <latex>Cu</latex> <latex>K_{\alpha}</latex> line
-and higher energy photons.
-==== Practical realisation ====
 Schematic diagram of the implemented spectrometric chain is shown below on figure## .
@@ Line 276: / Line 248: @@
 </imgcaption>
-One can see a few differenses betwen figures XX and ZZ.
+One can see few differences between figures XX and ZZ.
+At the input of the preamplifier charge adapter is added. Such a circuit allows injecting quasi dirac current pulses. Amount of charge is given by the amplitude of voltage step pulses. Rt resistor is added for line termination. Looking at the resistors R1 and R2 at voltage divider one can write the value of injected charge as:
+<latex>Q_{in}=\frac{R_2}{R_1+R_2} C_{test} V_{in}</latex>.
+All capacitances in the shaper are changeable in a wide range(mode than two orders of magnitude). Such a construction will allow to study the impact of the shaping time value on output signal shape and noise performance of the whole chain. Such a changeable capacitance are build from tens of binary weight capacitances cross-connected by switches. All switches are controlled by microcontroller. On front panel you may read the shaping time  value (<latex> \tau=RC </latex>) given in microseconds. To change it you should use the rotary switch (selector).
+The outputs of subsequent stages are routed via switches to one output connector. Those switches are controlled by the same digital circuit. The active output is displayed in the box OUTPUT. By clicking rotary knob you can select the active variable: shaping time or output.
+The laboratory module contains also few integrated voltage regulators to generate all needed voltages for both analog and digital blocks.
 ===== Laboratory Setup =====
-During this laboratory we use following equipment:
+During this laboratory we use the following equipment:
-  * laboratory module
+  * front-end electronics circuit
-  * digital sampling oscilospcope (TEKTRONIX TDS3034)
+  * digital sampling oscilloscope (TEKTRONIX TDS3034)
   * pulse generator (AGILENT 3320)
-  * True RMS meter (HP3400)
+  * true RMS meter (HP3400)
-  * Power Supply (AGILENT 3631A)
+  * power Supply (AGILENT 3631A)
   * cables
-  * PC wich proper software
+  * PC with dedicated software
 The connection of the setup is shown in the figure X.
@@ Line 294: / Line 277: @@
-After connecting setup do following steps:
+Ask the leading person to check all connections and do following steps:
   * set supply voltages to +/- 7V
-  * set chanel 1 input impedance to 50 Ohm
+  * set channel's one digital scope input impedance to 50 Ohm
   * set rectangular wave on pulse generator
-  * switch on pulse generators output
+  * switch on pulse generator output
-  * set triger to proper chanel
+  * set triger to proper channel
@@ Line 305: / Line 288: @@
 ===== Measurements =====
-==== Observing pre-amplifier output ====
+==== Observing the preamplifier output ====
+Select 0 as an active output. Try to find output pulse on oscilloscope. Set time base of oscilloscope to 400ns. Does signal look like voltage step? Try to estimate charge gain given by <latex> K_u = \frac{V_{out}}{Q_{in}} </latex> (having in mind formula "charge adapter") and compare it with value given by formula X ref wzmocnienie pream X.
+Try to look mode deeply on the pulse head (change time base to 40ns). How would you explain the non zero rising time? Then look at the pulse tail. Try to estimate time constant of this pulse and compare it to "y".
 ==== Linearity check of pre amplifier ====
+Perform measurements of pulse amplitude at the preamplifier output for the set of input test pulse amplitudes. The obtained results write to file ''linearity.dat'' in following format:
+<code>
+#vin[mv] vout[v]
+      XXX.Y
+     XXX.Y
+     XXX.Y
+     XXX.Y
+...
+</code>
+Then run script ''linearity.gnu'' and see results written in the file ''linearity.png''.
 ==== Observing shaper output ====
-==== Linearity check of shaper ====
+Look at the first shaper stage output. Check whether the displayed time is equal to the peaking time (time after which pulse reaches its maximum). Look at the pulses at the outputs of subsequent stages. Find their peaking times and see how they are related to the shaping time constant. Try to set the same peaking times for different shaping orders and compare the pulse shapes.
 ==== Noise performance ====
-===== References =====
+Measuring noise performance is two phase process. At the begining one has to measure the output amplitude <latex>V_{out}</latex> being response to input current pulse carrying charge <latex> Q_{in}</latex> (use cursors on oscilloscope for this measurement). In the second phase the voltage noise root mean square <latex> V_{rms}</latex> at the output is measured by the HP3400 true RMS meter. During this measurement input pulse should be disabled. It is important to keep circuit settings (shaping time, observed output) the same for both measurements.
-E. Gatti i P.F. Manfredi, Processing the Signals from Solid-State Detectors in
-Elementary-Particle Physics, Revista Del Nuovo Cimento (1986).
+The equivalent noise charge (ENC) is given by:
+<latex> ENC[C]=\frac{V_{rms}}{V_{out}} Q_{in}</latex>
+Repeat this measurements for several combinations of shaping time and shaping order. Write down your results to the file ''noise.dat'' in following format:
+<code>
+#order time_const[us] v_out[mv] v_rms[mv]
+      0.25           XXX       Y.YY
+      0.50           XXX       Y.YY
+      0.70           XXX       Y.YY
+      1.00           XXX       Y.YY
+...
+      0.25           XXX       Y.YY
+      0.50           XXX       Y.YY
+      0.75           XXX       Y.YY
+      1.00           XXX       Y.YY
+...
+      0.25           XXX       Y.YY
+      0.50           XXX       Y.YY
+      0.75           XXX       Y.YY
+      1.00           XXX       Y.YY
+...
+</code>
+To analyse the measured data use script ''noise.gnu''. See the results in the file ''noise.png''. Are you able to show the optimum shaping time for each filter order ? Does it pay off to use higher shaper orders for noise reduction ?
+==== Observing pulses from source ====
+Uda sie zorganizowac zrodlo ?
+==== Discussions topics====
+  * What is main uncertainty source during gain measurement in such setup?
+  * During this laboratory we were investigating electronic noises. You have to remember that in real experiments You also have to fight with disturbances. Can You give an example of disturbances in real experiment?
+===== References =====
+E. Gatti i P.F. Manfredi, Processing the Signals from Solid-State Detectors in
+Elementary-Particle Physics, Revista Del Nuovo Cimento (1986).

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