About Amplifier

1. INTRODUCTION
Alpha or beta particle or photon hits the semiconductor detector and is absorbed in it.
Inside the sensitive volume of the detector we have the electric charge. Detector is
connected to the electric voltage. The positive charge is moved in the direction of the
negative voltage and the negative charge is moved toward the positive electrode.
In the preamplifier the generated charge is put inside the capacitor with the value of
few pF. As the consequence, the voltage across capacitor rises.
The energy spent for the creation of an electron-hole pair inside a typical
semiconductor detector is about 2 eV. The particle with the energy of 100 000 eV will
produce 50 000 electrons and 50 000 holes, each with a charge of 1.60 . 10-19
As. The
total charge 1.60 . 10-19
As . 5. 104
= 8.10-15
As yields a voltage change of 4 mV on the
2 pF capacitor.
In measurement of radiation from 1 keV to 1 MeV we can expect voltage responses
from 0.05 mV to 500 mV. In order to bring signals to 5V level, suitable for further
analysis we need amplification.
The upper amplification factor should be somewhere 1000, and the lower about 10.
Some gain we can get already within the PREAMPLIFIER, while the main amplification
is done done by the SPECTROSCOPY AMPLIFIER.
However, besides of the amplification many other tasks should be done. The signal
from the charge sensitive preamplifier with the voltage span about 10 volts cannot be
amplified without overloading the amplifier. The information about separate pulse is the
height of each step. We can get it by making the difference between the original signal,
and slightly delayed (or time-shifted) signal. Unfortunately, this treatment increases the
noise, and makes results less reliable. The difference between the original signal, and
the time-shifted signal is, and this we know from mathematics, also proportional to the
time derivation of the signal, or as we also call the differentiation. This is completely
true if the time shift tend to go to zero.
To improve the signal to noise ratio some filtering must be applied. We can calculate
the average value of the noise within the time interval T. Longer the averaging time,
smaller the average value. The signal is less reduced by the averaging. Run
TRIFILTER program to prove this statement.
The conclusion is that we need amplification, differentiation and filtering. Which is the
order of separate operations? It was already our conclusion that we should start with
the differentiation. As the next we can add either amplification, or filtering.
For the input signal processing, it makes no difference; the final result will be the
same. However, we have the real system in which also additional noise is generated. If
we put amplification stages at the end of the processing chain, the noise from amplifier
will appear at the output. If amplification is made before filtering, then also the noise
generated inside the amplifier will be filtered.

2. This is a typical configuration:
The amplification of 1 to 2 thousands cannot be achieved in one stage because of the
limited frequency response of operational amplifiers.
Also the efficient output filtering should be performed in few stages.
At the output the power stage is added to be able to drive coaxial cables with typical
impedancy of 50 ohms.
The described system is still far from the commercial spectroscopy amplifier. Better
name for the first stage is pseudo-differentiator. The real differentiator is unstable
circuit. In addition, the differentiation increases noise while does not change the signal
amplitude. Differentiator is always used together with the smoothing filter. The circuit is
called pseudo-differentiator or the approximate differentiator.
All stages are DC-coupled. Any small offset voltage of the input stage provides a large
shift of the output base line. Even when properly compensated, the long-term
temperature drift will affect the base line position later. The simplest, and the most
efficient solution is to add at the end the second differentiator. Single polar bell-shaped
pulses (named pseudo-gaussian) are converted into the bipolar pulses, and the base
line is absolutely stable. However, each differentiation increases the noise and
deteriorates the energy resolution of the system. This is quite acceptable when our
detector is a scintillation counter, with the resolution not better than 6 or 7 percent.
Analysing signals from contemporary semiconductor detector the resolution might be
below 0.2 percent. The second differentiation cannot be applied. We use sophisticated
system for the correct base line position maintenance. System is called BLR (base line
restorer). The most sophisticated version of the BLR is the gated BLR. The idea is
simple. We observe the base line position when it is free from pulses. The servo
system compares the reading with the reference zero, and pushes it back toward the
zero position when its deviates from zero. In the feedback loop we use an integrator
and high gain. This base line regulation system acts around the output stage. Even
this is not enough. If deviation is too big, the system can be blocked. Therefore
spectroscopy amplifiers have a similar, simpler feedback loop after the amplifiers. Its
name is the DC-restorer.
The race to improve the resolution led to the development of the gated integrator. The
output signal is integrated. Instead of measuring the pulse amplitude we measure the
peak surface. Integration is an additional filtering and improves the signal to noise
ratio. When pulse is over, the integrator output voltage is returned to zero by the reset.

3. However, the resolution improvement becomes negligible by adding further filters. On
the other hand, the base line deviation has stronger influence one the accuracy of the
energy determination. The base line error DUo versus pulse amplitude Ao causes the
relative error DUo/Ao. This error is doubled when pulse is processed through the gated
integrator. The great hit of '70th
disappears from the last generation of spectroscopy
amplifiers.
In the first amplifiers few low-pass single real pole filters (called also: pseudo-
integrators, approximate integrators or first order filters) were used. The disadvantage
of such filters was the existence of rather long exponential tail following the pulse
peak.
Later introduced the complex pole filtering became widely used. It offers better signal
to noise ratio and almost symmetrical pulses. However, it can be proved that the
triangular output pulse shape enable the ultimate signal to noise ratio. Therefore
further attempts were made in this direction.
By using three two complex pole filtering stages, and by making the linear combination
of all three stages the output signal closer to the triangular form, can be shaped.
Although the difference in resolution measured by using the pseudo-gaussian and
pseudo-triangular pulse shaping is small the pseudo-triangular pulse shaping seems to
dominate in the present generation of spectroscopy amplifiers.
Have you gained some knowledge?
Run the following program to test yourself. You are qualified for further travel through the nuclear
electronics.

4. IAEA TOURS
Is announcing direct flights to many useful destinations
Differentiation and pole-zero
compensation.
How to prepare signals from the preamplifier for the
successful amplification?
Amplifiers
Making signals bigger by using various circuits and
operational amplifiers
DC controller
How to correct the base line deviation?
Complex pole filtering
Time to start fighting with the noise
Base line restoration
Last chance to put the base line into exact zero position
Base line restorer gating
BLR is not a simple task. We should handle with the base
line only between pulses. How to define these intervals?
Noise level detection
By using the discriminator with the level set slightly above
the noise level we can eliminate pulses. How much is the
noise level?
Single channel analyser
Analyser select pulses of the same height class
Timing single channel analyser
We know the number of pulses within the same height
class but the exact time information hase been lost. How
to keep it?
Constant fraction discriminator
Still fighting for the exact timing of selected pulses
Preamplifier
How to collect charge from the detector and how to pump
it into well defined capacity?
CLICK AND FLY…
TO TERMINAL 2

5. FROM DETECTOR TO SPECTROSCOPY AMPLIFIER
Preamplifier response
Voltage sensitive mode
Charge sensitive mode
Charge sensitive preamplifier with the resistor feedback
Preamplifier structure
HOW TO START?
From staircase to pulses
From step, or long-tailed exponential to decent pulse
Undershoot follows the pulse. Pole-zero cancellation
Pole-zero adviser in Silena spectroscopy amplifier
ABOUT AMPLIFICATION
Operational amplifier
Frequency response of few operational amplifiers. The gain influence.
FILTERING REDUCES THE NOISE
Making mathematical average. Expected in the new generation?
RC filters. From white to filtered noise
RC filters. Improving resolution
Too long tail when using RC filters
Complex pole filtering
TAKING CARE FOR THE PROPER POSITION OF THE BASE LINE
Good and bad features of the AC coupling
Pulse clipping improves the operation
Feedback gain and the response time of the base line restorer system (BLR)
Gated BLR. Gating operated manually
HOW TO PREPARE GATING PULSES?
Let us try with discriminator
Hysteresys improves the response
HOW TO SET THE OPTIMAL LEVEL?
Charging capacitor through diode
Diode threshold problems avoided. Circuit too nervous
Noise level detector; final approach
SINGLE CHANNEL ANALYZER:
Two comparators set at different levels.
Response of two comparators set to two levels
Can we XOR responses to get an answer?
Problem solved, but more logics added
Watching signals through the single channel analyzer
Modified version of single channel analyzer
LOST TIMING INFORMATION kept in TIMING SINGLE CHANNEL ANALYZER
Peak position by differentiation…
Peak position by constant fraction discriminator…
TIMING SCA but not good…
Good TIMING SCA
SOME SPECIAL TREATMENT
Bipolar output
Gated integrator
CHECK YOUR KNOWLEDGE. REFRESH BASIC LINEAR OPERATIONS
Operational amplifier
Test1 Test 2 Test3 Frequency response
Integrator for pedestrians
Integrator
Pseudo-integator for pedestrians
Pseudo-integrator (RC filter, approximate integrator, single real pole filter…)
How good I am in pseudo-integrator?
Pseudo-differentiator
Comparator
Hysteresis
Designing system…
BACK TO TERMINAL 1

6. Our intention is to study in details the
educational version of the spectroscopy
amplifier. The main difference between
the present apectroscopy amplifier and
commercially available amplifiers is in
the use of only one pulse shaping time.
Note the main spectroscopy chain, the DC
controller inside the left dashed box and
the gated BLR circuit inside the right
dashed box.
The wiring diagram is on the next figure
while the detailed description of the
separate sub-units you can find in the
corresponding chapters of the book.

7. Spectroscopy amplifier;
educational version.
If you replace cheap operational
amplifiers LM318 with faster
LT1220 (as shown with U9)and
TL081 in the first two stages with
ultralow noise CLC425 as shown
in APPENDIX 1 you can reach
the commercial quality.