hw:lab:spectrochain:script
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hw:lab:spectrochain:script [2009/09/14 23:19] marek.idzik |
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| ====== spectrometric chain ====== | ====== spectrometric chain ====== | ||
| ===== Introduction ===== | ===== Introduction ===== | ||
| - | 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. In next step you will measure the basic parameters like gain or noise of such readout chain. | + | 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 ===== | ===== Circuit description ===== | ||
| - | |||
| ==== Building blocks ==== | ==== Building blocks ==== | ||
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| operational amplifiers is of the order <latex>10^5-10^6</latex>). | 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> | <latex> | ||
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| - | 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 | 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 | for two purposes: first to set the DC level of the preamplifier input and | ||
| Line 190: | Line 189: | ||
| where <latex>\Gamma</latex> is the Gamma function. | where <latex>\Gamma</latex> is the Gamma function. | ||
| - | |||
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| ====Sensor, Preamplifier and Shaper - Signal to Noise==== | ====Sensor, Preamplifier and Shaper - Signal to Noise==== | ||
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| \tau_{opt} = (C_{in}+C_f) \sqrt{\frac{v_{eqw}^2}{(2n - 1)(i_{eqw}^2 + 2qI_{leak} + 4kT/R_{f})}} | \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} | \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> | </latex> | ||
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| The noise dependence on 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 | 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 a function of peaking time, for different shaping orders. This is done below setting all required parameters to reasonable values corresponding to this laboratory setup. | + | |
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| Assuming that the further signal processing stages add negligible contribution | 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 electrons, 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>. | ||
| - | 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 realization ==== | ==== Practical realization ==== | ||
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| <latex>Q_{in}=\frac{R_2}{R_1+R_2} C_{test} V_{in}</latex>. | <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. 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 is realized with 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). | + | 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 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. | ||
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| ==== Observing the preamplifier 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 formula "x". | + | 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". | 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". | ||
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| ==== Linearity check of pre amplifier ==== | ==== Linearity check of pre amplifier ==== | ||
| - | Perform the measurements of output pulse amplitude at the preamplifier output for the set of input test pulse amplitudes. The obtained results write to file ''preamp.dat'' in following format: | + | 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> | <code> | ||
| #vin[mv] vout[v] | #vin[mv] vout[v] | ||
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| ==== Observing shaper output ==== | ==== Observing shaper output ==== | ||
| - | Look at first stage shapers output. Check if displayed time constant corresponds to peaking time (time after pulse has its maximum). Look at pulses at the output of subsequent stages. Find pulses peaking time and compare it with shaping time constant. Try to compare pulse shapes witch same peaking time for different orders. | + | 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 ==== | ==== Noise performance ==== | ||
| - | Measuring noise performance is two phase process. At the begining one has to measure output amplitude <latex>V_{out}</latex> being response to input current pulse carrying charge <latex> Q_{in}</latex> (use cursors on oscilloscope to this measurement). In second phase voltage root mean square <latex> V_{rms}</latex> at the output is measured by HP3400 True RMS meter. During this measurement input pulse should be disabled. Important is also to keep circuit setting (shaping time, observed output) same for both measurements. | + | 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. |
| - | Equivalent noise charge (ENC) is given by: | + | The equivalent noise charge (ENC) is given by: |
| <latex> ENC[C]=\frac{V_{rms}}{V_{out}} Q_{in}</latex> | <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 Yours results to file ''noise.dat'' in following format: | + | 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> | <code> | ||
| #order time_const[us] v_out[mv] v_rms[mv] | #order time_const[us] v_out[mv] v_rms[mv] | ||
| Line 367: | Line 339: | ||
| </code> | </code> | ||
| - | To analyse measured data use script ''noise.gnu''. Results at file ''noise.png''. Are You able to show optimum shaping time for each filter order? Does it pay off to use higher shaper orders for noise reduction ? | + | 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==== | ==== Discussions topics==== | ||
| - | * What is main uncertainty source during gain measurements in such setup? | + | * 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 world ? | + | * 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? |
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| E. Gatti i P.F. Manfredi, Processing the Signals from Solid-State Detectors in | E. Gatti i P.F. Manfredi, Processing the Signals from Solid-State Detectors in | ||
| Elementary-Particle Physics, Revista Del Nuovo Cimento (1986). | Elementary-Particle Physics, Revista Del Nuovo Cimento (1986). | ||
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