By applying detector bias an electric field is created, which causes the charge carriers to migrate and be collected. During the charge collection a small current flows, and the voltage drop across the bias resistor is the pulse voltage.
From point of distribution of dc voltage across detector and load resistor RL practically whole high dc voltage is laid on detector. Current flowing through the load resistor is practically independent from value of HV power supply -> it is property that specifies the current sources.
Most detectors can be displaced with
- model, consisting of pulse current source with yours internal
resistance Rd and capacitor, which figures capacitance Cd
of the detector.
In most cases high resistance Rd of reverse-biased junction, or other internal detector resistance effects negligible. Equivalent detector circuits works then with parallel combination Rd and RL => RL||Rd~RL.
Current signal from detector can be delivered to preamplifier directly (dc-coupling) or via isolating capacitor. (For high charge transfer efficiency admittance representing capacitance of coupling capacitor => differentiate capacitance of shaping amplifier.)
Because the maximal output voltage
the detector (Umax= QD/Cd) is
by the capacitance Cd, for the shaping purpose we can use
resistance RL in time constant RLCd,
which depends acceptable counting rates of detector events (according
collection time of charge carriers - ti) .
On figure above pulse height is Id and pulse duration ti. If the load resistance RL is very height, e.g RL~iinfinite and so tin=RLCd=infinite, then in time of the pulse duration tiis capacitor Cd charged with full charge Q=Idti=Uin_mCd, and the maximal pulse height Uin_m=Q/Cd can be reached by decreasing the capacitance Cd.
In real detector output circuit
be pick up in accordance with the time resolution of the detector but
minimal drop off pulse amplitude. From the next figure you can see
with given pulse duration ti and detector capacitance Cd,
the determinate drop off pulse height depends on time constant tin,
respectively on resistance RL.
Time constant tin=RLCd>> ti (case RL> 100MW) can increase collecting pulse amplitude but makes long decay time constant.
Time constant tin=RLCd<< ti (case RL~ 50-100W) shortens pulse duration (useful for high counting rates) but decreases pulse high.
For most scintillation
It was already mentioned that for most scintillation spectrometer is acceptable tin=RLCd~ ti, whith some drop off pulse amplitude. For better quality comparing, concept of "ballistic error" D A=Amax-A0 was established.
In next illustration figure the light flash from scintillation cause current pulse id=I*exp(-t/TS), which charges capacitor Cd in ideal case (RL~infinite ) to voltage Amax.
Amax representeds maximally possible pulse height when time constant tin=RLCd=infinite . In real detector the resistance RL<>infinite and pulse height A0 is occurred.
From this figure you can see that for scintillation spectrometer applications has no reason to make tin= RLCd shorter than 10TS, e.g. in scintillator NaI(Tl) (TS=0,3ms) with Cd~5pF and RL=0,5MW preserves time constant tin=RLCd~3ms.
Before amplification, the pulse-shaping amplifier must replace the long decay time of the preamplifier output pulse with a much shorter decay time (with preserving the energy information representing by pulse amplitude). Otherwise the acceptable counting rate would be severely restricted.
Possible ways to short pulse duration:
Best pulse shape from point of noise/signal (S/N) consideration is theoretical calculated pulse form in next figure (a).
To improve S/N ratio in amplifiers typically is set shaping time constant:
This noise performance (case - e in next fig.) is only 36% worse than optimum filter with the same time constant. The simple arrangement is useful for estimates, since simple to evaluate.
By replacing the
simple RC integrator with more complicated
active network => S/N improved by 17% to 19% at noise corner time
Drawback of CR-RC shaping is much longer pulse duration compared with delay-line shaping.
Simple delay line
clipping of scintillator pulses
illustrates next figure. Goal is to short pulses for improved count
pulse is obtained when 2 differentiate
chains are inserted. Double CR -differentiate shaping produces a
pulse with equal area in its positive/ negative lobes. CR-RC-CR shaping
case to undershoot and loss of resolution due to baseline fluctuations.
At medium to high counting rates a substantial fraction of the
pulses will ride on the undershoot from the previous pulse, pulse have
longer duration and worse S/N ratio, what cause broadening of the
capacitance in charge sensitive preamp must
be discharged too. Conventionally it is done with resistor. Output is
longer a step, but decays exponentially. Exponential decay superimposed
on shaper output. Small amplitude overshoot decays back to baseline,
long time constant, provided by the preamplifier output pulse often
conventional CR-RC shaping case to undershoot
and loss of resolution due to baseline fluctuations in Pole-Zero
(PZC) the resistor Rpzis
added in parallel with capacitor. Resistance Rpz must be
adjusted for good baseline recovery (=> simple exponential
to baseline) especially at high counting rates.
The bipolar shape is useful in minimizing baseline shift with varying counting rates when ac-coupling is used. Electronic resolution with bipolar shaping is typically 25-50% worse than for corresponding unipolar shaper. However:
capacitor in system prevents transmission
of DC component. A sequence of unipolar pulses has a DC base line
that depends on duty factor, i.e. event rate.
restorer (BLR) reduces baseline shift.
BLR are originally performed with diodes (passive restorer), today BLR circuits tend to include active loops with adjustable thresholds to sense presence of signal ("gated" restorer) + asymmetric charge and discharge time constants for the "memory" capacitor.
false amplitude measurement.
When 2 gamma-rays (according to figure above) arrive at the detector within the width of the spectroscopy amplifier output pulse a pulse pile-up to form an output pulse of distorted amplitude can occur.
The pile-up rejector is implemented by adding a "fast" pulse-shaping amplifier with very short shaping time constant in parallel with the "slow" spectroscopy amplifier.
Fast discriminator is set above the much higher noise level => digital logic pulses.
The trailing edge of fast output triggers an inspection interval TINS pulse , that covers the width TW of the slow pulse.
If second fast
pulse arrives during TINS
an inhibit pulse is generated (prevents A/D analysis of the pile-up
contribute to dead time of the spectrometry system:
In almost every area of measurement the ultimate limit of detectability of weak signals is set by noice - unwanted signals that obscure the desired signal. Even if the quantity being measured is not weak, the presence of noise degrades the accuracy of the measurement.
Noise- random variation in the output current of electronics circuits and amplifiers. These fluctuations in current are primarily due to the inherent particle nature of electrical current, and to variations in path, recombination rates, and diffusion caused by the randomness of charge movement. While the statistical average of diffusion current may be constant, on an instant-by-instant basis the diffusion rate may vary. At very low signal levels the signal current may be comparable in magnitude to the variation produced by such noise.
The noise has no specific frequency. Each impact of charges with atoms produces a very short energy pulse, which represents a very broad band of frequencies. Being random in nature, the distribution has a statistical effective power Pn .(Usefully interpreted signal has on time interval tj - ti its mean value, different from zero, but mean value of noise is zero!) Measurement of noise must be made over specified frequency band on power or voltage-square basis.
The noise power can be stated as Pn/D f - effective power per Hz at a center frequency, or Vrms/D f - effective voltage per Hz at a center frequency .
In a multistage amplifier, the noise power is attenuated by circuits or stages of amplifier. Because additive contribution of noise from the second stage to all noise is less than contribution of the first stage, it is conventional to refer noise rms voltage to the input an amplifier.
In this conclusions we suppose a proper grounding and shielding and the elimination of interface and pickup. Then the noise is applied to anything that obscures a desired signal, the term describing "random" noise of physical (often thermal) origin. Noise can be characterized by its:
generates a noise voltage across its terminals.
The thermal noise is developed by the random thermal motion and impacts
of the charges and atoms in all conductors. Since is due to thermal
this noise is temperature dependent. It is also found to be uniformly
over all frequencies presently in use. (Noise whit a flat spectrum is
noise") The thermal noise due to a resistance R is:
The term SnR=4kTR
is called spectral
density of noise and is often used by describing properties of
type of noise too. (T - absolute temperature in degrees Kelvin, k -
constant, Df is
bandwidth in hertz). In graphical mapping of noise is often used
units like Vn/(Hz)0.5 (- Vn per root
or Vn2/Hz (- volts squared per Hz).
For example 10kW resistor has on open-circuits rms voltage of 1.3mV, measured with bandwidth Df=10kHz. A real resistor may be considered as equivalent thermal noise generator of rms voltage Vn (or source In ) in series (parallel) with noiseless resistor R.
of thermal noise is that
it sets a lower limit on the noise voltage in any detector or
having resistance. The noise
power is dependent on the frequency band Df
noise => The bandwidth should be made as small as possible to get
current is the flow of discrete
charges. The finiteness of the charge quantum result in statistical
of the current. The noise is uniformly distributed over frequency
(white noise as "the rain in a tin roof"). The noise energy increases
the current in device, so collector currents are maintained at a
for low noise application (IC min) :
noise and Johnson noise are irreducible
forms of noise generating according to physical principles. Real
have in addition to thermal and shot
various sources of "excess
depends on many factors having to do with the construction of the
resistor, including the resistive material (carbon-composition, metal
wire-wound) and especially the end-cap connections. This noise has
a 1/f spectrum and is sometimes called "pink noise".
=> Base current noise in transistor is reduced to low level by
fabrication techniques. Flick noise seems largely confined bellow
and varies inversely with frequency.
conventional to refer noise
to the input of an amplifier (although the measurements are
at the output), i.e., to describe source noise and amplifier noise in
of microvolts at the input that would generate the observed output
This makes sense when you want to think of the relative noise added by
the amplifier to a given signal, indipendent of amplifier gain;
also realistic, because most of the amplifier noise is usually
by the input stage.
The noise generated by an amplifier is easily described by a simple noise model (fig. above in which :
Transistor (or amplifier in general) is assumed noiseless, and simply amplifies the input noise voltage it sees. Total noise voltage ea, referred to the input of transistor:
The two terms are the amplifier input noise voltage and the noise voltage generated by the amplifier's input noise current passing through the source resistance RS .Since the two terms are usually uncorrelated , their squared amplitudes add to produce the effective noise voltage seen by the amplifier. For low value of resistance RS noise voltage en dominates, whereas for high RS the noise current generally dominates. The fact that en drops and in rises with increasing collector current provides a simply way to optimize transistor operating current to give lowest noise whit given source.
voltage en is
essentially thermal noise of channel resistance given approximately by
According the figure bellow noise current and voltage sources can be described by their spectral densities, which depends on:
The amplifiers adds resulting noise vn12 (its "parallel" noise component source resistance is Rp) to the JFET noise voltage en2=4kTRS (its "serial" noise component source resistance is RS=0.7/gm). Resulting noise voltage v2n0 on the output of the amplifier (after amplification A=1 and filter shaper CR-RC (what means time constant ti=td=t, which supplies max signal/noise relationship) can be expressed by means of the followed equivalent circuits:
equivalent noise charge:
consist of parts:
The optimal value of the noise corner time constant t=t0 can be calculated from condition:
True in general must be experimentally checked, e.g. for system with Si - barrier detector can be optimal t~0,5 - 1ms , and for germanium or Si(Li) detector t~6 - 20ms.
illustrates dependence parallel and series
component to total noise of the preamplifier. Short time constant t
is dominant for series component of the noise and long time constant
for parallel component (which depends on thermal Rp~R, thus
on detector leakage Ib or gate leakage current of FET).
For comparing purpose the system noise can be expressed:
The next figure illustrates the dependence noise vs. input capacitance of 2 type of preamp.
located close to the detector
and accepting signal from detector preserves max S/N ratio whit
shaping, or sometimes a fast rise time output pulse for good time
The optimum configuration of preamplifier in system depends on characteristics of the detector and type of signal processing following after.
There are generally used 3 type of preamplifiers:
It has high impedance input. It accept the signal from circuit of parallel combination of detector capacitance and its input resistance and responds with a low-impedance output signal, suitable for driving a long cable to the linear amplifier. It is not widely used for energy spectroscopy applications because its gain dependent on detector capacitance (CD does not remain constant during bias voltage change) => makes broader the peak width.2. Current - sensitive preamplifier:
It has low impedance input (R~100W) to convert fast current pulses (f.e. from the anode of a PM to a voltage pulse). It is used when fast timing is desired. The output accepts several meter coax without shape distortion. e.g. the input resistance 100W preamplifier with the gain 10 has sensitivity Uout/Iin=500 mV/mA (Uout - voltage amplitude of the output pulse, Iin-- current amplitude of the input pulse.)3. Charge - sensitive preamplifier:
It is preferred for most energy spectrometric applications. Preamplifier is mounting close to detector, thus reducing input capacitance caused by cabling, decreasing microphone noise, ground loop and radio-frequency pickup. The signal from a semiconductor detector or ion chamber is a quantity of charge, delivered as a current pulse, lasting from 1ns to 10us, depending on type of detector and its size. For most applications the quantity of charge and/or the time of occurrence of an event are the parameter of interest.
Charge sensitive preamplifier integrates the charge QD on its feedback capacitor Cf . Its gain Aq~Vo/QD~1/CF is not sensitive to variations of detector capacitance. The rise time of its output pulse is equal to the detector current pulse width in ideal case.
preamplifier output Vo~QD/CF.
The decay time constant tF=RFCF
(CF~0.1 to 5pF). Feedback resistor RF is a noise
source and is made as large as possible with the signal energy rate
and the detector leakage current in the direct-coupled system.
Sensitivity (usually is expressed in mV/MeV ) Vo/E =e/(eCF) to energy E deposited in given detector material. The charge released by the detector is a function of the gamma - ray or particle energy and the detector material QD=eE/e (e - the amount of energy required to produce e.g. an electron-hole par in the detector.)
Preamplifier noise depends on FET, resistance to the input, input leakage current from detector and FET and total capacitance at the input (CF, CD).
The noise can be
measured in the system shown on
Linear pulse-shaping amplifier is special type of wide-band amplifier, which is used with scintillation, silicon charge particle detectors for energy spectroscopy measurement.
Linear amplifier must accept preamplifier pulse shapes. Each pulse consist of rapidly rising step (amplitude ~ energy of detected radiation), followed by a slow exponential decay (determined by feed back resistor RF parallel with CF timing constant RFCF~ 50us).
For detector with very short charge collection times, the rise time of the preamplifier output pulse is controlled by the amplifier itself, and the rise time is usually in the range from 10ns to 100ns.
For detector with
long charge collection times, such
as NaI(Tl) detectors, proportional counters, coax Ge - detectors, the
rise time of the preamplifier is controlled by the detector charge
time. The output rise time can range up to 700ns, for large Ge -
and ~500ns for NaI(Tl) detectors.
Conflict with the need of handling high counting rates and optimum energy resolution
The fast amplifiers – tries for minimal degradation of rise time => good time resolution.
The slow or wide-band linear amplifiers, used with scintillation, silicon charge particle detectors for energy spectroscopy purpose apart from magnify the amplitude of the preamplifier pulses are assign to :