Tsoulfanidis N. Measurement and detection of radiation

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338

MEASUREMENT

AND

DETECTION OF RADIATION

3102

H.V.

2015A

SCA

Amp/

TSCA

1446

2007 Universal

coincidence

802-4 constant start

2043

Nal(TI)

fraction

discr.

analyzer SCA

Out

timing delay

Logic

shaper

ADC

gate

Preamp

Delay

input

3105

H.V.

Figure

10.31

NaI-Ge(Li)

coincidence system (from Ref.

25;

numbers indicate Canberra

models).

essentially independent of the pulse amplitude but depends on the pulse shape,

is usually converted into a pulse by means of a TAC. The pulse from the TAC

may be used to gate the counting system. Figure

10.33

shows a block diagram for

such a counting system. The result of

n-y

discrimination is usually

spectrum

that resembles Fig.

10.34.

Actually, the

peak is due to electrons produced by

the gammas, and the neutron peak is due to protons recoiling after collisions

with the incident neutrons. More details of this method of neutron detection are

given in Chap.

14.

A second method, introduced by ~rooks," integrates the charge from the

early part of the pulse and compares it to the total charge.

third method,

introduced by Kinbara and ~umahara,'~ differentiates

n-y

pulses by

measure-

ment of the risetime of the pulse.

final example of a

PSD

technique is that

used by Burrus and ~erbinski,'~,'~ based on a design by

FortC.16

Details

the

circuitry are given in Refs.

and

15.

This

PSD

method produces a large

positive pulse output for neutrons and a small positive or a large negative pulse

for gammas.

ELECTRONICS

339

Stilbene

100 200 300 400

Time,

Figure

1032

The light produced by neutrons and gammas in stilbene and

213.

Light intensity is

shown at left: integrated light intensity is shown at right (based on data of Ref.

8).

10.10

PREAMPLIFIERS

In Sec.

1.5.5,

a few general comments were made about preamplifiers. It was

stated that the primary purpose of the preamplifier is to provide an optimum

coupling between the detector and the rest of the counting system.

secondary

purpose of the preamplifier is to minimize any sources of noise, which will be

transmitted along with the pulse and thus may degrade the energy resolution of

the system. This second objective, low noise, is particularly important with

semiconductor detectors, which are the counters offering the best energy

resolution.

There are three basic types of preamplifiers: charge-sensitive,

current-sensi-

tive, and voltage-sensitive. The voltage-sensitive preamplifier is not used in

spectroscopy because its gain depends on the detector capacitance, which in

turn depends on the detector bias. The charge-sensitive preamplifier is the most

340

MEASUREMENT

AND

DETECTION OF RADIATION

stop

Time diagram

::"

route

Channels

Figure

10.33

block diagram for a PSD system (reproduced from

Instruments

for

Research and

Applied Sciences

by permission of

ORTEC, Oak Ridge, Tennessee).

commonly used in spectroscopic measurements and the only type used with

semiconductor detectors.

To understand the basic features of a charge-sensitive preamplifier, con-

sider the basic circuit associated with a semiconductor detector, shown in Fig.

10.35. The high-voltage

(HV)

bias applied to the detector is usually connected

through the detector to the first stage of the charge-sensitive preamplifier. In

Fig. 10.35,

is the feedback capacitor

pF) and

is the feedback resistor

1000

MR)."

The triangle with the letter

indicates the first stage of the

preamplifier, which today is usually a field-effect transistor (FET). The FET is a

p-n junction with reverse bias, exhibiting extremely low noise. The type of

coupling shown in Fig. 10.35 is called dc coupling. There is an ac coupling, too,

Channel

Figure

10.34

The result of

y-n

using PSD.

discrimination

ELECTRONICS

341

Bias

in which the detector is coupled to the FET through a coupling capacitor (see

Nicholson, p. 110).

The detector sees the FET stage as a large capacitor of magnitude

ACf.

long as

ACf

Ci,

where

is the total input capacitance consisting of the

detector capacitance

C,,

the cable capacitance, etc., the voltage at the output of

the preamplifier is equal to

where

the charge produced in the detector, is given by

Detector

where

energy of the particle

electronic charge

1.6

10~'~ coulombs

average energy required to produce one electron-hole pair

The major components of

are the detector capacitance

and that of the

cables between the detector and the preamplifier. Both of these components are

controlled by the user to a certain extent.

The noise of the charge-sensitive preamplifier depends on three parameters:

the noise of the input FET, the input capacitance

Ci,

and the resistance

connected to the input. The noise can be determined by injecting

charge

equivalent to

into the preamplifier and measuring the amplitude of the

generated pulse. Commercial preamplifiers are provided with a test input for

that purpose. In general, the noise expressed as the width (keV) of

Gaussian

distribution increases as input capacitance increases (Fig. 10.36).

The

output pulse of the preamplifier has a fast risetime (of the order of

nanoseconds) followed by a slow exponential decay,

100 ps (Fig. 10.37). The

useful information in the pulse is its amplitude and its risetime. The risetime is

particularly important when the signal is going to be used for timing. The

observer should be aware that the risetime increases with external capacitance.

The preamplifier pulse is shaped in the amplifier by the methods described in

Sec. 10.6.

,pf

I I

Figure

1035

The first stage of a

To stage

charge-sensitive preamplifier

dc-coupled to the bias circuit.

342

MEASUREMENT

AND

DETECTION

RADIATION

Figure

1036

The dependence of noise on external

capacitance for a typical charge-sensitive preamplifier

l0U

10 100 1000

(from

permission

Instruments

for

Research

ORTEC,

and

Applied

Oak

Sciences

Ridge,

External capacitance (pF)

Tennessee).

The

sensitivity

(or

gain)

of a charge-sensitive preamplifier is expressed by

the ratio V/E, where V is given by

Eq.

10.31. For a 1-MeV particle in a

germanium detector, the sensitivity is (using

5 pF)

current-sensitive preamplifier is used to transform fast current pulses

produced by a photomultiplier into a voltage pulse. The current-sensitive pream-

plifier is an amplifying instrument. The sensitivity (or gain) of such a unit is

expressed as

V,,,/Zi,,

i.e., in mV/mA with typical values of the order of 500

mV/mA. The risetime of the pulse is

ns.

10.11

AMPLIFIERS

As explained in Sec. 1.5.6, the amplifier plays the two roles of amplifying and

shaping the signal. The need for amplification is obvious. The output signal of

the preamplifier, being in the range of a few millivolts, cannot travel very far or

be manipulated in any substantial way without losing the information it carries

or being itself lost in the noise. Commercial amplifiers consisting of many

amplification stages increase the amplitude of the input signal by as many as

2000 times, in certain models.

The need for shaping the signal was explained in

Sec. 10.6. The type of

shaping that is applied depends on the requirements of the measurement. For

spectroscopy measurements where good energy resolution is the important

Figure

1037

Typical

pulse from a charge-sensitive

preamplifier.

ELECTRONICS

343

parameter, pulse shaping should not decrease the signal-to-noise ratio. For

timing measurements, depending on the method of time pick-off, the signal may

be singly or doubly differentiated or be shaped by a single or double delay line.

For a good measurement, the amplifier should satisfy many require-

ment~.'~-~~ Not all types of measurements, however, require the same level of

performance. For example, if one measures only the number of particles and not

their energy, the precision and stability of the amplification process can be

relatively poor. It is in spectroscopy measurements, particularly measurements

using semiconductor detectors, that the requirements for precision and stability

are extremely stringent. Since the energy resolution of Ge detectors is of the

order of 0.1 percent, the dispersion of the pulses due to the amplification

process should be much less, about 0.01 percent.

ideal spectroscopy amplifier should have a constant amplification for

pulses of all amplitudes without distorting any of them. Unfortunately, some

pulse distortion is always present because of electronic noise, gain drift due to

temperature, pulse pile-up, and limitations on the linearity of the amplifier.

The effect of electronic noise on energy resolution was discussed in Sec.

9.6.2. Random electronic noise added to equal pulses makes them unequal (see

Fig. 9.12). Gain drift of an amplifier is caused by small changes in the character-

istics of resistors, capacitors, transistors, etc., as a result of temperature changes.

The value of the gain drift, always quoted by the manufacturer of the instru-

ment, is for commercial amplifiers of the order of 0.005 percent per

or less.

Since the time of arrival of pulses is random, it is inevitable that a pulse may

arrive at a time when the previous one did not fully decay. Then the incoming

pulse "piles up" on the tail of the earlier one and appears to have a height

different from its true one. Pulse pile-up depends on the counting rate.

The linearity of an amplifier is expressed as differential and integral.

Differential nonlinearity

is a measure of the change in amplifier gain as a

function of amplifier input signal. Referring to Fig.

10.38,

the differential

Figure

10.38

Diagram used for

the

defi-

nition

differential and integral linear-

ity of an amplifier.

The

output signal of a

perfect amplifier plotted versus input

signal should give the straight line shown

Amplifier input

(-.-.-.

344

MEASUREMENT

AND

DETECTION

RADIATION

nonlinearity in percent is given by

In Eq. 10.33, the numerator is the slope of the amplifier gain curve at the

point where the nonlinearity is measured, and the denominator is the slope of

the straight line as shown in Fig. 10.38.

Integral nonlinearity

is defined as the maximum vertical deviation between

the straight line shown in Fig. 10.38 and the actual amplifier gain curve, divided

by the maximum rated output of the amplifier. Referring to Fig. 10.38, the

integral nonlinearity in percent is given by

The integral nonlinearity is one of the specifications of commercial amplifiers

and has a value of about 0.05 percent or less over the range 0-10

There are many types

commercial amplifiers designed to fit the specific

needs of spectroscopic or timing measurements. Companies like Canberra,

G ORTEC, etc., offer a wide selection of such instruments.

10.12

ANALOG-TO-DIGITAL CONVERTERS (ADC)

As discussed in Sec. 9.9, the backbone of an MCA is the analog-to-digital

converter (ADC), the unit that digitizes the input pulse height and assigns it to a

specific channel. Many types of ADCs have been developed, but the most

frequently used is the Wilkinson

type.24

The Wilkinson-type ADC operates as shown in Fig. 10.39. When a pulse

enters the MCA, two events are initiated:

1. A capacitor starts charging.

input gate prevents the acceptance of another pulse until the previous

one is fully processed and registered.

The capacitor keeps charging until the peak of the pulse is reached. At that

point in time, two new events are initiated:

The voltage on the charged capacitor is discharged by a constant current.

oscillator clock starts. The clock stops its oscillations when the capacitor

is fully discharged.

The number of oscillations during this time-called

rundown

conversion time

-is proportional to the pulse height and constitutes the information that

determines the channel number in which that pulse will be stored.

Figure

1039

The processing of the

pulse in a Wilkinson ADC.

(a)

emery

cycle

Input pulse.

(b)

Charge capacitor

voltage.

(c)

Gate stops other

pulses.

(d)

Oscillator clock.

(e)

I-

Dead time

Pulse storage.

variation of this method is shown in Fig.

10.40.

The steps followed in this

case are

The input pulse is stretched in such a way that its flat portion is proportional

to its height.

At the moment the pulse reaches its maximum (time

t,),

a linear ramp

generator is triggered, producing

voltage

Figure

10.40

The processing of the pulse

the

ADC.

(a)

Input pulse.

(b)

Input

pulse stretched; flat part proportional to

pulse height.

(c)

Ramp voltage and oscilla-

tor clock start at

1,.

346

MEASUREMENT

AND

DETECTION

RADIATION

3. At the same moment (t,), a gate signal is produced and an oscillator clock is

turned on.

When the voltage ramp signal reaches the flat part of the stretched pulse

(PI,

the gate signal turns the clock off. Thus, the time interval (t,

t,) and,

therefore, the number of oscillations during (t,

t,) are again proportional to

the height of the pulse. This second method of ADC operation (Fig. 10.40) is not

favored because it is difficult to keep the pulse height constant for the time

interval (t,

t,).

Figure 10.39 shows, in addition to the principle of operation of the Wilkin-

son ADC, the reason for the dependence of the MCA dead time on the channel

number. The dead time consists of three components:

Pulse risetime

2. Conversion time

3. Memory cycle time (time it takes to store the digitized signal)

Of the three components, the second is the most important because it depends

on the channel number. One can reduce the size of the conversion time by using

a clock with higher frequency. Today's ADCs use quartz-stabilized clocks with a

frequency of

450

MHz.

Obviously, for a Wilkinson

ADC,

the higher the

clock frequency is, the shorter the dead time will be. The equation for dead time

is written as

where a typical value of

is 1.5 ps,

address (channel) count, and

effective digital offset." The digital offset is a capability offered by modern

ADCs of subtracting a certain number of channels from the converted channel

number before the data are introduced into the memory. One application of

digital offset is to enhance resolution in a measurement performed with a small

MCA. For example, with a 1000-channel MCA and an 8000 channel ADC, a

7000 digital offset allows data to be recorded for the top eighth of the spectrum

only. A fixed dead time

(FDT)

ADC has also been developed for certain

application^.^^

The resolution of an ADC is expressed in terms of channels. It represents

the maximum number of discrete voltage increments into which the maximum

input pulse can be subdivided. ADC resolutions range from 4096 to 16,384

channels. Since commercial amplifiers can provide a maximum 10-V pulse, an

ADC with a resolution of 4096 channels may subdivide 10

into 4096 incre-

ments. Another quantity used is the conversion gain of the ADC. The conver-

sion gain may be considered as a subset of the resolution.

ADC with a

resolution of 16,384 channels may be used, depending on the application, with a

conversion gain of 4096, or 8192, or 16,384 channels.

The accuracy of the ADC is expressed in terms of its differential and

integral nonlinearity. The differential nonlinearity describes the uniformity of

address widths over the entire range of the ADC. To make this point better

ELECTRONICS

347

understood, assume that a 1000-channel ADC is used to process pulses with

maximum height of 10

Then the average address width is

10/1000

lOmV/channel. The ideal ADC should provide a conversion of 10 mV/channel

at any channel. Any deviation between this width and the actual one is

expressed by the differential nonlinearity. Mathematically, if

average width

AVmax

maximum width

AVmin

minimum width

then the differential nonlinearity is given by the equation

Differential nonlinearity

AVmax

Avmin

(100)

(10.36)

Commercial ADCs have differential nonlinearity of the order of

0.5 percent

percent.

The

integral nonlinearity

is defined as the maximum deviation of any address

(ADC channel) from its nominal position, determined by a linear plot of address

(ADC channel) versus input pulse amplitude (Fig. 10.41). The maximum pulse

height

VmaX

corresponds to the maximum address

N,,,.

is the address

number with the maximum deviation between the actual and nominal pulse

heights, the integral nonlinearity is given by the equation

Vnom

Kc,

Integral nonlinearity

(100) (10.37)

vmax

Modern commercial ADCs have integral nonlinearity of the order of

0.05

percent over

98-99

percent of the full range.

The integral nonlinearity affects the centroid position of energy peaks,

which in turn affects the calibration of the system as well as the identification of

unknown energy peaks.

10.13

MULTIPARAMETER ANALYZERS

The MCA is an instrument that stores events by a single parameter, namely,

pulse height. When the need arises, however, there are many experiments for

ADC

channel

Figure

10.41

The definition

integral nonlinearity is based on a linear plot of

ADC

channel versus

pulse amplitude.