Chapter No. 18

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Multichannel Pulse Analysis
Chapter No. 18 Radiation Detection and
Measurements, Glenn T. Knoll, Third edition
(2000), John Willey .
2
Ch 18 GK I ? SINGLECHANNEL METHODS II ?
GENERAL MULTICHANNEL CHARACTERISTICS III ? THE
MULTICHANNEL ANALYZER IV ? IV. SPECTRUM
STABILIZATION AND RELOCATION V ? V. SPECTRUM
ANALYSIS VI
3
Multichannel Pulse Analysis A measurement of the
differential pulse height spectrum from a
radiation detector can yield important
infonnation on the nature of the incident
radiation or the behavior of the detector itself
and is therefore one of the most important
functions to be perfonned in nuclear
measurements. By definition (see Chapter 4), the
differential pulse height spectrum is a
continuous curve that plots the value of dN/dH
(the differential number of pulses observed
within a differential increment of pulse height
H) versus the value of the pulse height H. The
ratio of the differentials can never be measured
exactly, but rather all measurement techniques
involve a determination of I1N/I1.H (the discrete
number of pulses observed in a small but finite
increment of pulse height H). The increment in
pulse height I1H is commonly called the window
width or channel width. Provided I1H is
small enough, a plot of 11N/11H versus H is a
good discrete approximation to the
continuous curve that represents the actual
differential pulse height spectrum. As a
practical matter, a distiBction is seldom made
between the continllolls distribution and its
discrete approxi mati on, and all such plots are
generally referred to as differential pulse
height distributions or pulse height spectra. It
SINGLECHANNEL METHODS The differential
discriminator (single-channel analyzer SCA)
described in the previous chapter can be used to
record a steady-state pulse height spectrum. The
window is set to a small width I1H and the number
of output pulses produced over a measurement
period is recorded as 11N. In a somewhat tedious
process, this window can then be moved
stepwise over the pulse height range of interest.
Sequential measurements of t.N/I1H plotted at
the midpoint H value of the window will then
trace out the shape of the differential
distribution. This serial process is inefficient,
in that most pulses are ignored during a given
measurement since they lie outside the specific
window chosen. However, before the days
of multichannel analyzers, this manual procedure
was often the only method available to measure
pulse height spectra. A better approach is to
employ multiple SCAs as in Fig. 18.1. Here the
measurement is converted from one that is serial
to one that is parallel, and every pulse can now
contribute to the measured spectrum. All the
inputs are connected together and each output fed
to a separate counter. The lower level of the SCA
at the bottom of the stack is set to zero, and
that for the top SCA is set to correspond to the
largest pulse height of interest. The lower level
of the intermediate SCAs are arranged at equal
intervals between these extremes. The window
width of each SeA is identical and is set equal
to the spacing between adjacent discrimination
levels. This arrangement thus provides a series
of contiguous pulse height windows of equal
width, as illustrated in Fig. 18.2. 685 686
Chapter 18 Multichannel Pulse Analysis Input Figur
e 18.1 An array of stacked single-channel
analyzers, Windows A. B. C. ' .. are assumed to
be contiguous and of equal width llH. with A at
the bottom of the pulse height scale. An input
pulse presented to this array will fall into one
and only one of the multi windows set by the
SCAs. Therefore, each input pulse results in an
increment of one added to the corresponding SCA
counter, One can therefore view the overall
pro the sorting of each input pulse into the
proper window and incrementing the content that
counter by one. A small pulse will correspond to
a window near the bottom of . stack, whereas a
large pulse will faIl into a window near the top.
At the end of a meas ment period, the sum of all
the counters will simply be the total number of
pulses present' . to the input. If we now plot
the number of recorded pulses M/ in each counter
divided by the wi.tii dow width tJi versus the
average pulse height for each window, we derive a
discrete rePA resentation of the differential
pulse height distribution. In this context, each
window is coni ventionally called a channel and
is numbered in increasing order from left to
right. The iovr.J. est channel corresponds to the
pulse height window at the bottom of the range
and recordl"" only those pulses whose amplitudes
are very small. The largest channel numbers are
plot1 ted at the right of the horizontal axis and
record only the pulses of largest amplitudes.
' This process of sorting successive signal
pulses into parallel amplitude channels is
commonly called multichannel pulse height
analysis, As a practical matter, schemes based
on, A B C D SC wind A ow Channel
Channel Channel Channel 1 2 3 4 Pulse height
H Figure 18.2 A pointwise representation of the
differential pulse height distribution
obtained from the stacked SCA array of Fig. 18.1
by plotting the content of each counter llN
(normalized to the window width llH) versus the
midpoint of the corresponding SCA window. Chapter
18 General Multichannel Characteristics
687 stacked independent SCAs are seldom
attractive because of complications introduced
by drifts in the various discrimination levels
and window widths. These drifts can lead to
overlapping or noncontiguous channels whose width
may also not be constant. As a result, other
approaches have evolved for accomplishing the
same purpose. The standard device designed to
carry out this function is known as a
multichannel analyzer (MCA), an,d.the1QIlowing sec
tions discuss some general properties and
functions of these instruments. n. GENERAL
MULTICHANNEL CHARACTERISTICS A. Number of
Channels Required In any pulse height
distribution measurement, two factors dominate
the choice of the number of channels that should
be used for the measurement the degree of
resolution required and the total number of
counts that can be obtained. If an arbitrarily
large number of counts can be accumulated, there
is no disadvantage in making the number of
channels as large as one wishes. By providing a
large number of channels, the width of anyone
channel can be made very small and the resulting
discrete spectrum will be a close
approximation to the continuous distribution. For
a faithful representation, the true
distribution should not change drastically over
the width of one channeL If peaks are present in
the spectrum, this requirement translates into
specifying that at least four or five
channels should be provided over a range of pulse
height corresponding to the FWHM (full width at
half maximum) of the peak. Figure 18.3b shows a
hypothetical differential distribution taken
under conditions in which the number of channels
is too small to meet this criterion. The
resulting distortions and loss of resolution in
the spectrum are obvious. The channel
requirements can also be expressed in terms of
detector resolution R. For a peak with a mean
pulse height H FWHM R--- H FWHM or
H--- R (18.1) We can express both Hand FWHM in
terms of numbers of channels, and furthermore,
we now reqUire that at least five channels be
provided over the FWHM of the peak. The
position of H in units of channels is therefore 5
channels peak position H ---R (18.2) and at
least this number of channels must be provided. A
detector whose energy resolution is 5 therefore
requires a minimum of 100 channels, and a
detector with 0.2 resolution would require 2500
channels. This argument is valid only in those
cases in which the full range of pulse amplitude
is recorded with constant channel width ranging
from zero to the maximum pulse height. The
channel requirement can be reduced by selectively
recording only a portion of the spectrum with a
large value of zero offset discussed in the next
section. The above arguments would suggest that
one should always use the maximum number of
channels possible. A second factor arises,
however, when the available measurement time
limits the total number of pulses that contribute
to the recorded spectrum. Because the number of
events that fall within anyone channel will vary
in proportion to its width, the content of a
typical channel varies inversely with the total
number of channels provided over the spectrum.
Choosing a larger number of channels will
consequently cause the relative statistical
uncertainty of each content to increase, and the
channel-to-channel fluctuation of the data over
smooth portions of the spectrum will become more
noticeable. If these fluctuations are large
enough, they can begin to interfere with the
ability to discern small features in the
spectrum. Very small peaks can become lost in
statistical noise. These effects are illustrated
in Fig. 18.3d. 688 Chapter 18 Multichannel Pulse
Analysis dN iii CONTINUOUS SPECTRUM PULSE HEIGHT
"H" Cal 10 CHANNELS CHAHNE l NUMBER (bl 50
CHANNELS .. .. -......... .. .. '0 CHANNEL
NUMBER (el . " .t' t, CHANNEL NUMBER (en ,
. !' ,.' , \ Figure 18.3 An illustration of the
effect of varying the number of channels used to
record the differential distribution at the top
left. A total of 15.000 counts were accumulated
for each of the three multichannel spectra In (b)
the number of channels is too small to show
sufficient detail. in (c) the choice is about
right. and too many channels were used in (d).
The low average number of counts per channel in
spectrum (d) leads to large statistical fluctuatio
ns that could obscure small additional peaks if
they were present. Another factor in choosing the
number of channels across the width of typical
peaks in the spectrum is the behavior of the
software used to locate the peak and quantify
its properties. Even if the underlying data were
to follow a perfect Gaussian distribution,
the "binning" effect of sorting the data into
channels with finite width results in a series
of points that do not fall on a perfect Gaussian
curve because of the averaging effect that takes
place within each channel. Neglecting statistical
fluctuations. the contents of the channels would
become closer to a true Gaussian as a larger
number of channels are provided across the peak
width. Thus if the analysis software assumes that
the data in the region of a peak (after
subtraction of any underlying continuum) follow a
true Gaussian or some variant thereof (as most
do), it may be better to allocate 9 to 12
channels across the FWHM to minimize the errors
that are introduced due to the binning effect) B.
Calibration and Linearity The ideal MeA would
perform a perfectly linear conversion of pulse
height to channel number. Under these conditions,
a plot of pulse height versus channel number
would be a Pul .. height Chapter 18 General
Multichannel Characteristics 689 Figure 18.4
Typical calibration plot for a linear MCA with
and without zero offset. simple straight line, as
illustrated in Fig. 18.4. In addition, it is
usually convenient to introduce some zero offset
shift of the origin, such that a nonzero
amplitude is required for storage in the first
channel. The zero offset is sometimes desirable
to suppress high count rates from very small
noise pulses, which may appear with the signal,
or to assign the available channels only to the
upper portion of a spectrum to be recorded. The
zero offset is adjustable through front panel
controls or as a software selection on many
commercial MCAs. In many situations, the signal
pulses are first sent through a linear amplifier
with variable gain. Then the slope of the
calibration plot can also be varied by changing
the gain factor. For example, Fig. 18.5 shows the
calibration plots for an ideal MCA for three
different values of amplifier gain. The same
effect can also be achieved if the MeA allows
selection of the conversion gain of its
analog-ta-digital converter (see next
section). The user is generally interested in an
initial calibration of an MCA that will
determine the energy scale of the pulse height
distribution. Assuming the analyzer is
sufficiently linear, two parameters need to be
determined the slope and intercept of the
calibration line shown in Fig. 18.4. The easiest
calibration method is to place sources of known
energy at the detector and record the channel
number into which the centroid of the resulting
fullenergy peak falls. Because two points
completely determine a straight line, only
two energies are, in principle, required.
However, other sources are often used to
provide additional points along the line for
confirmation purposes and a test of linearity. If
peaks of known energy cannot conveniently be
provided, a pulse generator may also be used
to Channel number Figure 18.5 Different MCA
calibration plots for three values of amplifier
gain. 690 Chapter 18 Multichannel Pulse
Analysis provide points for a calibration plot.
Only pulses of known relative amplitude are to
test linearity and determine the zero offset, but
some other means must then be relate
independently the pulse height scale to
energy. The linearity of the MCA can be measured
or quoted in several different most direct method
is to make a measurement of the channel number in
WIJ!),iJJ...pl known amplitude are stored, and
then make the plot of pulse amplitude
versus number shown in Fig. 18.6. The maximum
deviation of the measured curve from a straight
line is a measure of the integral linearity and
is conventionally quoted as centage of the full
MCA range. Nonlinearities are most often observed
at either height extreme and are typically less
than 0.1 for well-designed analyzers. A more
sensitive method of detecting nonlinearities is
to employ a source of with a uniform distribution
in amplitude. If the MCA is connected to
accumulate pulses over a period of time, a
uniform or flat distribution of counts in all
channels result (see Fig. 18.6). Sufficient
counting time must be allowed so that the
statistical ations in channel content are small
compare with the desired measurement accuracy. a
calibration measures the differential linearity
of the MCA. Deviations from uniformity a few
percent are typical of good MCAs. The integral
and differential calibrations are interrelated,
because the differential plot will be simply
proportional to the slope of the integral plot at
any point. In Fig. 18.6, th two calibrations
are intended to be consistent and illustrate the
same nonlinearity. The diti ferential
calibration, although more difficult to set up,
is obviously a more sensitive test of MCA
linearity. .. The differential nonlinearity of an
MCA is not a serious issue in most applications
if it is small and varies smoothly from channel
to channel. More significant problems can
be created in pulse height analysis if the
differential nonlinearity plot of the type shown
in Fig. 18.6 has abrupt discontinuities or
"bumps" that sometimes occur. These artificial
features will appear superimposed on smooth
regions of all pulse height spectra recorded
by the analyzer and can easily be misinterpreted
as true structure in the spectrum. Such
discontinuities will show up in the measurement
using a uniformly distributed pulse
source, Pulse height Counts Integral linearity Dif
ferential linearity Channel number Channel
number Figure 18.6 Examples of integral and
differential linearity measurements for an
MeA. Chapter 18 The Multichannel Analyzer 691 but
they can also be detected in a much simpler
test.2 The pulse height distribution from many
types of detectors is known to be smoothly
varying over an extended amplitude interval (for
example, a plastic scintillator responding to a
gamma-ray source). The amplifier gain can be
adjusted to spread this interval over the full
range of the MCA, and a large number of counts
are recorded to minimize the channel-to-channel
statistical fluctuations. Even though the
resulting recorded spectrum will not be uniform
over the full range, it U still show any sudden
discontinuities or periodic structures that are
the most trome features of differential
nonlinearity. Although not as widely used as the
nonlinearity tests, measurements of the
channel profile discussed in Chapter 17 can also
be applied in the performance testing of
MCAs. Precision pulse generators whose amplitude
can be continuously varied with a very
fine vernier control are used to trace out the
type of profile illustrated on p. 651. The
probability that a typical pulse is stored in a
preselected channel is plotted versus the pulse
amplitude as it is varied from below to above the
channel range. Ideally, these channel
profJ.les have sharply defined limits, and there
are no tails extending substantial distances
beyond the nominal channel boundaries. MCAs with
overly broad channel profiles that overlap with
neighboring channels have a reduced resolution,
and the effective number of channels is actually
smaller than the nominal value. Any differential
nonlinearity of the analog-todigital converter
will also be reflected in a corresponding
departure from constant channel width over its
range as measured by individual channel
profiles. m. THE MULTICHANNEL ANALYZER A. Basic
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m. THE MULTICHANNEL ANALYZER A. Basic Components
and Function The multichannel analyzer (MCA) is
comprised of the basic components illustrated in
Fig. 18.7. Its operation is based on the
principle of converting an analog signal (the
pulse amplitude) to an equivalent digital number.
Once this conversion has been accomplished, the
extensive technology available for the storage
and display of digital information can be brought
to bear on the problem of recording pulse height
spectra. As a result, the analogto- digital
converter (ADC) is a key element in determining
the performance characteristics of the analyzer.
The flash and subranging ADCs previously
discussed in Chapter 17 produce a continuous
series of digital output values at a fixed clock
frequency. In contrast, the ADCs intended for use
in MCAs operate in a different mode. They are
designed to produce only a single output value
for each pulse presented to their input that is
proportional to the peak amplitude of that pulse.
They are therefore often called peak sensing
ADCs. The input circuitry Input Input gate (Open
when ADC is not busy) "Not busy" -IT' Ch.l Live
time Figure 18.7 Functional block diagram of a
typical MCA. 692 Chapter 18 Multichannel Pulse
Analysis for these ADCs must include a capability
to sense the arrival of an input pulse pie and
hold the maximum amplitude of that pulse for a
time needed to carry version to a digital value.
The output of the ADC appears in a
rpolt.t..-rt, address a standard digital
memory that has as many addressable locations as
the number of channels into which the spectrum
can be subdivided. The memory locations is
normally made a power of 2, with memories of 1024
to 8192 mon choices. The maximum count capacity
of anyone channel is set by the bit memory, and
in commercially available units can be as high as
232, or over 4 X The basic function of the MCA
involves only the ADC and the memory. For poses
of illustration, we imagine the memory to be
arranged as a vertical stack of able locations,
ranging from the first address (or channel number
1) at the bottom the maximum location number
(say, 1024) at the top. Once a pulse has been
prclcesell the ADC, the analyzer control
circuits seek out the memory location
corresponding digitized amplitude stored in the
address register, and the content of that
location is mented by one count. The net effect
of this operation can be thought of as one in
which pulse to be analyzed passes through the ADC
and is sorted into a memory location corresponds
most closely to its amplitude. This function is
identical to that described for the stacked
single-channel analyzers illustrated in Fig.
18.1. Neglecting dead time, input pulse
increments an appropriate memory location by one
count, and therefore total accumulated number of
counts over all memory is simply the total number
of presented to the analyzer during the
measurement period. A plot of the content
of channel versus the channel number will be the
same representation of the differential height
distribution of the input pulses as discussed
earlier for the stacked smgle-cnaDller analyzers.
A number of other functions are normally found in
an MCA.As illustrated in Fig.18.7 an input gate
is usually provided to block pulses from reaching
the ADC during the time it is "busy" digitizing
a previous pulse. The ADC provides a logic signal
level that holds the input gate open during the
time it is not occupied. Because the ADC can be
relatively slow. high counting rates will result
in situations in which the input gate is closed
for much of the' time. Therefore, some fraction
of the input pulses will be lost during this dead
time, and any attempt to measure quantitatively
the number of pulses presented to the analyzer
must take into account those lost during the dead
time. To help remedy this problem, most MCAs
provide an internal clock whose output pulses are
routed through the same input gate and are stored
in a special memory location,. The clock output
is a train of regular pulses synchronized with an
internal crystal oscilla tor. If the fraction of
time the analyzer is dead is not excessively
high, then it can be argued that the fraction'of
clock pulses that is lost by being blocked by the
input gate is the same as the fraction of signal
pulses blocked by the same input gate. Therefore,
the number of clock pulses accumulated is a
measure of the live time of the analyzer or the
time over which the input gate was held open.
Absolute measurements can therefore be based on
a fixed value of live time, which eliminates the
need for an explicit dead time correction to the
data. Further discussion of the dead time
correction problem for MCAs is given later in
this chapter. Many MCAs are also provided with
another linear gate that is controlled by a
singlechannel analyzer. The input pulses are
presented in parallel to the SCA and, after
passing through a small fixed delay, to the
linear pulse input of this gate. If the input
pulse meets the amplitude criteria set by the
SCA, the gate is opened and the pulse is passed
on to the remainder of the MCA circuitry. The
purpose of this step is to allow rejection of
input pulses that are either smaller or larger
than the region of interest set by the SCA
limits. These limits, often referred to as the
LLD (lower-level discriminator) and ULD
(upperlevel discriminator), are chosen to exclude
very small noise pulses at the lower end and very
large pulses beyond the range of interest at the
upper end. Thus, these uninteresting Chapter 18
The Multichannel Analyzer 693 pulses never reach
the ADC and consequently do not use valuable
conversion time, which would otherwise increase
the fractional dead time. If an MCA is operated
at relatively high fractional dead time (say,
greater than 30 or 40), distortions in the
spectrum can arise because of the greater
probability of input pulses that arrive at the
input gate just at the time it is either opening
or closing. It is therefore often advisable to
reduce the counting rate presented to the input
gate as much as possible by excluding noise and
othificant small-amplitude events with the LLD,
and if significant numbers of large-ampliude back
ground events are present, excluding them with an
appropriate ULD setting. The contents of the
memory after a measurement can be displayed or
recorded in a number of ways. Virtually all MCAs
provide a CRT display of the content of each
channel as the Y displacement versus the channel
number as the X displacement. This display
is therefore a graphical representation of the
pulse height spectrum discussed earlier. The
display can be either On a linear vertical scale
or, more commonly, as a logarithmic scale to show
detail over a wider range of channel content.
Standard recording devices for digital data,
including printers and storage media, are
commonly available to store permanently the
memory content and to provide hard copy
output. Because of the similarity of many of the
MCA components just described to those of the
standard personal computer (PC), there is a
widespread availability of plug-in cards that
will convert a PC into an MCA. The card must
provide the components that are unique to the MCA
(such as the ADC), but the normal PC memory,
display, and I/O hardware can be used directly.
Control of the MCA functions is then provided in
the form of software that is loaded into the PC
memory. Some compromises in performance of the
plug-in boards are often necessary because the
noisy electronic environment inside the PC
produced by the many digital switching operations
is somewhat hostile to the sensitive
analog operations required in ADCs. Thus there
are also units in which the ADC operations
are housed within an external NIM module that
communicates with the PC through an
interface cable. In some cases, the MCA is
incorporated in a computer-based spectroscopy
system that allows software control of the MCA
functions as well as other settings such
as detector voltage supply and parameters of the
shaping amplifier such as gain, shaping
time, pile-up rejection, and spectrum stabilizer
operation (see later section in this chapter). B.
The AnalogtoDigital Converter 1. GENERAL
SPECIFICATIONS The job to be performed by the ADC
is to derive a digital number that is
proportional to the amplitude of the pulse
presented at its input. Its performance can be
characterized by several parameters 1. The speed
with which the conversion is carried out. 2. The
linearity of the conversion, or the faithfulness
to which the digital output is proportional to
the input amplitude. 3. The resolution of the
conversion. or the "fineness" of the digital
scale corresponding to the maximum range of
amplitudes that can be converted. The nominal
value of the resolution depends on the number of
bits provided by the ADC, and is specified as the
maximum number of addressable channels. Thus a
12-bit ADC will provide 212, or 4096 channels of
resolution. From the previous discussion of
ADC properties in Chaper 17, the effective
resolution may be less than this value if
electronic noise or instability result in typical
channel profiles that are overly broad. For the
types of ADCs generally chosen for use in MCAs,
the effective resolution should not
deviate greatly from the nominal value. 694
Chapter 18 Multichannel Pulse Analysis The
voltage that corresponds to full scale is
arbitrary, but most ADCs nuclear pulse
spectroscopy will be compatible with the output
of typical linear Zero to 10 V is thus a common
input span. Shaping requirements will also
usually ified for the input pulses, and most ADCs
require a minimum pulse width of a of a
microsecond to function properly. The conversion
gain of an ADC specifies the number of channels
over amplitude range will be spread. For example,
at a conversion gain of 2048 channels, to lO-V
ADC will store a 10 V pulse in channel 2048,
whereas at a conversion gain that same pulse
would be stored in channel 512. At the lower
conversion gain, a fraction of the MCA memory can
be accessed at anyone time. On many ADCs,
the version gain can be varied for the purposes
of a specific application. The resolution ADC
must be at least as good as the largest
conversion gain at which it will be used. The
conversion speed or dead time of the ADC is the
critical factor in determining overall dead time
of the MCA. Therefore, a premium is placed on
fast conversion, but tical limitations restrict
the designer in speeding up the conversion before
linearity to suffer. The fastest ADCs, the flash
or subranging type discussed in Chapter 17,
are used in MCAs because of their poor
differential linearity. Two other types dominate
in temporary MCAs linear ramp converters and
successive approximation ADCs. The first these,
although the slowest, generally has the best
linearity and channel profile specifications compa
red with the other types and has gained the most
widespread application in MCAs. Successive
approximation ADCs offer faster conversion times,
but generally with poorer linearity and channel
uniformity. 2. THE UNEAR RAMP CONVERTER
(WILKINSON TYPE) The linear ramp converter is
based on an original design by Wilkinson3 and is
illustrated in Fig. 18.8. The input pulse is
supplied to a comparator circuit that
continuously compares the amplitude with that of
a linearly increasing ramp voltage. The ramp is
conventionally generated by charging a capacitor
with a constant-current source that is started at
the time the input pulse is presented to the
circuit. The comparator circuit provides as its
output a gate pulse that begins at the same time
the linear ramp is initiated. The gate pulse is
maintained "on" until the comparator senses that
the linear ramp has reached the amplitude of
the input pulse. The gate pulse produced is
therefore of variable length, which is directly
proportional to the amplitude of the input pulse.
This gate pulse is then used to operate a Ramp
comparator Pulse input Figure 18.8 Block diagram
of a linear ramp (Wilkinson type) ADC. Chapter 18
The Multichannel Analyzer 695 linear gate that
receives periodic pulses from a
constant-frequency clock as its input. A
discrete number of these periodic pulses pass
through the gate during the period it is open
and are counted by the address register. Because
the gate is opened for a period of time
proportional to the input pulse amplitude, the
number of pulses accumulated in the
address register is also proportional to the
input amplitude. The desired conversion between
the analog amplitude and a digital equivalent has
therefore been carried out. Because the clock
operates at a constant frequency, the time
required by a Wilk!!lsontype ADC to perform the
conversion is directly proportional to the number
of pt11SeS accumulated in the address register.
Therefore, under equivalent conditions, the
conversion time for large pulses is always
greater than that for small pulses. Also, the
time required for a typical conversion will vary
inversely with the frequency of the clock. In
order to minimize the conversion time, there is a
premium on designing circuits that will reliably
handle clock pulses of as high a frequency as
possible. Clock frequencies of 100 MHz are
representative of present-day commercial
designs. The WJ.lkinson-type ADC leads to
contiguous pulse height channels, all ideally of
the same width. Because the linear ramp
generation can be very precise, this design is
characterized by good linearity specifications,
accounting for its widespread popularity in
MCAs. Variants of the Wilkinson design that lead
to some improvement in speed are described
by Nicholson,4 and a clock frequency of up to 400
MHz can be achieved in advanced designs. 3. THE
SUCCESSIVE APPROXIMATION ADC The second type of
ADC in common use is based on the principle of
successive approximation. Its function can be
illustrated by the series of logic operations
shown in Fig. 18.9. In the first stage, a
comparator is used to determine whether the input
pulse amplitude lies in the upper or lower half
of the full ADC range. If it lies in the lower
half, a zero is entered in the Hrst (most
significant) bit of the binary word that
represents the output of the ADC. If the
amplitude lies in the upper half of the range,
the circuit effectively subtracts a value equal
to one-half the ADC range from the pulse
amplitude, passes the remainder on to the second
stage, and enters a one in the most significant
bit. The second stage then makes a . Bit
.alue for example shown -r----Full-scale
amplitude R .------ --RI2 -R/4 -Rill -R/16 o Fig
ure 18.9 Illustration of the operational sequence
for a successive approximation ADC. Four stages
are shown which generate the four-bit word shown
at the bottom as the digital output. 696 Chapter
18 Multichannel Pulse Analysis similar
comparison, but only over half the range of the
ADC. Again, a zero entered in the next bit of the
output worQ depending on the size of the
rfgtrn""nrl, from the first stage. The remainder
from the second stage is then passed to the and
so on. If 10 such stages are provided, a 10-bit
word will be produced Lua ...... 'ti1'"l range of
210 or 1024 channels. In its most commOn circuit
implementation, the successive approximation
ADC multiple use of a single comparator that has
two inputs one is the sampled and held voltage
and the other is produced by a digital-ta-analog
converter (DAC). For the stage comparison, the
input to the DAC is set to a digital value that
is half the put range. Depending on the result of
the initial comparison, the second-stage is then
carried out with the digital input to the DAC set
to either 25 or 75 of the and so on. In this
way, analog subtractions are avoided but the
functional operation equivalent to that described
above. For a given successive approximation ADC,
the conversion time is constant and
in4fl pendent of the size of the input pulse.
For typical converters with a lO-bit output, the
cOh version time can be a few microseconds or
less. Adding stages to increase the
resolutiod only increases the conversion time in
proportion to the number of total stages or in
pro'' portion to the logarithm of the maximum
number of channels. Their speed advantage
is therefore most pronounced when the number of
addressed channels is large. The major
dis advantage of typical successive
approximation ADCs is a more pronounced
differential nonlinearity compared with linear
ramp ADCs. Some refinements to their design to
help overcome this limitation are described in
Refs. 5-7. 4. THE SLIDING SCALE PRINCIPLE The
linearity and channel width uniformity of any
type of ADC can be improved by employing a
technique generally called the sliding scale or
randomizing method. Originally suggested in 1963
by Gatti and co-workers,8 the method has gained
popularity (e.g., Refs. 9 and 10) through its
implementation using modern IC technology. It has
been particularly helpful in improving the
performance of both successive approximation and
flash ADCs. Without the technique, pulses of a
given amplitude range are always converted to
a fixed channel number. If that channel is
unusually narrow or wide, then the differential
linearity will suffer in proportion to the
deviation from the average channel width. The
sliding scale principle is illustrated in Fig.
18.10. It takes advantage of the averaging
effect gained by spreading the same pulses over
many channels. A randomly chosen analog
voltage is added to the pulse amplitUde before
conversion and its digital equivalent
subtracted after the conversion. The net digital
output is therefore the same as if the voltage
had not Digital output Figure IS.10 Functional
diagram of the sliding scale principle for
ADCs. C. The Memory Chapter 18 The Multichannel
Analyzer 697 been added. However, the conversion
has actually taken place at a random point along
the conversion scale. If the added voltage covers
a span of M channels, then the effective channel
uniformity will improve as \1M if the channel
width fluctuations are random. The implementation
of Fig. 18.10 derives the added voltage by first
generating a random digital number and converting
this number to an analog voltage in a DAC. The
same digital number is then subtracted after the
conversion. One of the disadvantages of the
technique is that the original ADC scale
of-H"C1iannels is reduced to N - M. If a pulse
occurs that would normally be stored in a
channel number near the top of the range, the
addition of the random voltage may send the
sum off scale. Other designslo.11 avoid this
limitation by using either upward averaging
(as described above) or downward averaging (by
subtracting the random voltage) depending on
whether the original pulse lies in the lower or
upper half of the range. The choice of M can then
be as large as N /2 to maximize the averaging
effect without reducing the effective ADCscale. Be
cause the sliding scale method involves
converting a fixed pulse amplitude
through different channels whose width may vary,
a potential disadvantage is a broadening of
typical channel profiles. If this broadening is
severe enough, it will compromise the
resolution of the ADC. Another potential problem
is that, if the addition and subtraction steps
are not perfectly matched in scale factor,
periodic structures can be generated in the
differential nonlinearity that appear as
artifacts in recorded spectra. The memory section
of an MCA provides one addressable location for
every channel. Any of the standard types of
digital memory can be used, but there is
sometimes a preference for "nonvolatile" memory,
which does not require the continual application
of electrical. power to maintain its content.
Then, data acquired over long measurement periods
will not be lost if the power to the MCA is
accidentally interrupted. Most MCAs make
provisions for subdividing the memory into
smaller units for independent acquisition and
storage of multiple spectra. In this way a 4096
channel analyzer can be configured as eight
separate 512 channel memory areas for storing
low-resolution spectra, or as a single 4096
channel memory for a high-resolution spectrum. In
most analyzers, provision is made for the
negative incrementing of memory content as well
as additive incrementing. In this "subtract"
mode, background can conveniently be taken away
from a previously recorded spectrum by analyzing
for an equal live time with the source
removed. IAncillary Functions . 1. MEASUREMENT
PERIOD TIMING Virtually all MCAs are provided
with logic circuitry to terminate the analysis
period after a predetermined number of clock
pulses have been accumulated. One often has the
choice between preset live time or clock time,
which are distinguished by whether the clock
pulses are routed through the input gate (see
Fig. 18.7). Normally, quantitative comparisons
or subtraction of background are done for equal
live time periods, and this is the usual way
of terminating the analysis period. 2.
MULTISCALING Multichannel analyzers can be
operated in a mode quite different from pulse
height analysis, in which each memory location is
treated as an independent counter. In this
multiscaling mode, all pulses that enter the
analyzer are counted, regardless of amplitude.
Those that 698 Chapter 18 Multichannel Pulse
Analysis arrive at the start of the analysis
period are stored in the first channel. After
a time known as the dwell time, the analyzer
skips to the second channel and pulses of all
amplitudes at that memory location. Each channel
is sequentially One such dwell time for
accumulating counts, until the entire memory
has The dwell time can be set by the user, often
from a range as broad as from 1 f.lS to minutes.
The net effect of this mode is to provide a
number of independent to the number of channels
in the analyzer, each of which records the total
number of Over a sequential interval of time.
This mode of operation can be very useful in the
behavior of rapidly decaying radioactive sources
or in recording other urrle-llec,eul11 phenomena.
3. COMPUTER INTERFACING Stand-alone MCAs share
many features with general purpose computers. In
its most I' form, the MCA can only increment and
display the memory, but more elaborate
operatic" can be carried out if it is provided
with some of the features of a small computer.
", example, one of the most useful functions is
to allow summation of selected portions
of." spectrum, generally called regions of
interest (ROIs). Cursors are generated whose
position ."' the displayed spectrum can be used
to define the upper and lower bounds of the
channel n bers between which the summation is
carried out. This operation has obvious practical
use fof simple peak area determination in
radiation spectroscopy. Other operations, such as
additiori or subtraction of two spectra or other
manipulations of the data can also be provided.
. More complex computer-based systems are also
widely available that are based on p with an
appropriate ADC under software control. In this
approach, the functions ment tioned above can be
duplicated through software routines that may be
modified or supplemented by the user. Useful
operations of this type can range from simple
smoothing of the spectra to damp out statistical
fluctuations, to elaborate spectrum analysis
programs in which the position and area of
apparent peaks in the spectrum are identified and
measured. Current manufacturer's specification
sheets are often the best source of
detailed information in this rapidly eVOlving
area. 4. MULT/PARAMETER ANALYSIS The simplest
application of multichannel analysis is to
determine the pulse height spectrum of a given
source. This process can be thought of as
recording the distribution of events over a
single dimension-pulse amplitude. In many types
of radiation measurements, additional experimental
parameters for each event are of interest, and
it is sometimes desirable to record
simultaneously the distribution over two or more
dimensions. One example is in the case in which
not only the amplitude of the pulse carries
information, but also its rise time or shape.
Categories of events can often be identified
based on unique combinations of amplitUde and
shape, while a clean separation might not be
possible using either parameter alone. In the
example shown in Fig. 18.11, both the amplitude
and shape (measured from the rise time) of each
pulse from a liquid scintillation counter
are derived in separate parallel branches of the
pulse processing system. The object will now
be to store this event according to the measured
values of both these parameters. In any unit
designed for multiparameter analysis, at least
two separate inputs with dedicated ADCs must be
provided, together with an associated coincidence
circuit. The memory now consists of a
two-dimensional array in which one axis
corresponds to pulse amplitude and the other to
pulse shape. Because both parameters are derived
from the same event, they appear at the two
inputs in time coincidence. The multiparameter
analyzer recognizes the coincidence between the
inputs and increments the memory location
corresponding to the intersection of the
corresponding pair of digitized addresses. As
data accumulate, the intensity distribution then
takes the form of a two-dimensional surface with
local peaks representing combinations of
amplitude and shape that occur most frequently.
The data are Chapter 18 The Multichannel Analyzer
699 PM tube Pulse shape samPle Sample holder and
reflector Two-dimensional multichannel analyzer /"
alphas enws Pulse height Figure 18.11
Example of a two-parameter analysis of the pulses
from a photomultiplier tube viewing a liquid
SCintillator vial. Events build up into a surface
represented by the contour lines on the display
of the two-dimensional memory. sometimes
displayed as a surface contour plot, or as an
isometric view of the surface from a perspective
that can be changed using software routines for
best viewing. Multiparameter analyzers generally
require a much larger memory than
singleparameter analyzers because, for equal
resolution, memory requirements for two
parameters are the square of the number of
channels required for only one parameter. Often,
however, one of the two parameters need not be
recorded with the same degree of resolution so
that nonsquare (rectangular) memory
configurations will suffice. Three or more
parameters require multidimensional memory
allocations that can be impractical in size.
In experiments in which many parameters are of
interest for each event (for example,
from multiple detectors recording coincident
events), it may no longer be possible to dedicate
a large enough memory to sort all the information
in real time. An alternative mode of
data recording called list mode acquisition can
then be employed. Each of the multiple
parameters is digitized with a separate ADC in
real time, and the results are then quickly
written to memory. A clock may also be read to
provide a "time stamp" to record the time of
occurrence of the event. As the measurement
proceeds, the collection of data grows with
each observed event but requires a memory whose
size is only the product of the total number of
events mUltiplied by the number of recorded
parameters. After the conclusion of
the measurement, the data can then be sorten
off-line based on arbitrary criteria involving
any or all of the recorded parameters. I. MeA
Dead Time The dead time of an MCA is usually
comprised of two components the processing time
of the ADC and the memory storage time. The first
of these was discussed earlier and, for
a Wilkinson-type ADC, is a variable time that is
proportional to the channel number in which the
pulse is stored. The processing time per channel
is simply the period of the clock oscillator. For
a typical clock frequency of 100 MHz, this time
is 10 ns per channel. Once the pulse has been
digitized, an additional fixed time of a few
microseconds is generally required to store the
pulse in the proper location in the memory. Thus,
the dead time of an MCA using an ADC of this type
can then be written N 'T - B (18.3) v 700
Chapter 18 Multichannel Pulse Analysis where v is
the frequency of the clock oscillator, N is the
channel number in which is stored, and B is the
pulse storage time. The analyzer control circuits
will hold gate closed for a period of time that
equals this dead time. A dead time meter driven
by the input gate to indicate the fraction of
time the gate is closed, as experimenter. One
normally tries to arrange experimental conditions
so that the dead time in any measurement does not
exceed 30 or 40 to prevent possible distortions.
The automatic live time operation of an MCA
described earlier is usually quite s factory for
making routine dead time corrections.
Circumstances can arise, howeve which the
built-in live time correction is not accurate.
When the fractional dead tim high, errors can
enter because the clock pulses are not generally
of the same shape duration as signal pulses. One
remedyI2,13 is to use the pulser technique
described on p. to produce an artificial peak in
the recorded spectrum. If introduced at the
preamp' the artificial pulses undergo the same
amplification and shaping stages as the signal
pu The fraction that are recorded then can
account for both the losses due to pileup
and analyzer dead time. Several authors14,15 have
reviewed the live time correction proble and
suggested conditions under which the pulser
method is not accurate. To avoid pote tial
problems, the pulse repetition rate must not be
too high, and the use of a random ratherl than
periodic pulser is preferred. Under these
conditions, the pulser method can success fully
handle virtually any conceivable case in which
the shape of the spectrum does notl change during
the course of the measurement. Additional
complications arise if spectrum shape changes
occur during the measurement, which lead to
distortions and improper dead time corrections
with the pulser method. A better method first
suggested by Harms16 can accommodate spectrum
changes but requires a nonstandard mode of MCA
operation. In this method, the analysis is run
for a fixed clock time. If a pulse is lost
because the analyzer is dead (this can be sensed
externally), compensation is made immediately by
assigning a double weight to the next pulse and
incrementing the corresponding memory location by
two. Spectra that change during the course of the
measurement are properly accommodated because the
correction automatically takes into account the
amplitude distribution of signal pulses at the
time of the loss. This correction scheme has been
tested by Monte Carlo simulation for a wide
variety of spectrum shapes and time variations
and has proved to be quite accurate in all
casesP At higher rates, however, the assumption
breaks down that only one pulse was lost
during the dead time, and the Harms method begins
to undercorrect for losses. One remedy is
to modify the correction process by first
calculating the expected number of counts lost
during a dead period from a running measurement
of the input pulse rate. The memory
location corresponding to the next converted
pulse is then incremented, not by two counts
as above, but by one plus the calculated number
of lost pulses. These artificial counts do
not have the same statistical significance as the
same number recorded normally, but they
do maintain the total spectrum content as if
there had been no losses. Normally called loss
free counting,IS this technique is applicable in
situations in which the dead fraction of the
MCA is as high as 80.19 It is particularly
helpful in measurements from short-lived
radioisotopes from which the counting rate may
change by many orders of magnitude over
the measurement period. IV. SPECTRUM
STABILIZATION AND RELOCATION A. Active
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