Application Note
Behavior of the MCA 166 at different Temperatures and
Gain settings and limits of centroid accuracy
10.1.2001
Jörg Brutscher
GBS Elektronik GmbH
1. Problem
2. Basic limits
3. Centroid error
4. Temperature drift of the MCA 166
5. Temperature drift of detectors
6. Stabilisation
7. Linearity and accuracy of gain setting
8. Conclusions
1. Problem
For very accurate measurements, all possible influences on measurement performance have to be known and
understood. This helps to estimate errors and to improve measurement conditions. In this document, the
temperature drift and the linearity of the gain and its dependence on settings have been examined.
2. Basic limits
Gamma spectroscopy can be a very accurate measurement method in terms of measuring photon energy. The
limits are mostly given by detector resolution. For example, the FWHM of the Co60 1333 keV peak with
measured with a HPGe (High purity Germanium) detector is typical 1.85 keV. A useful assumption is that the
centroid of a peak can be calculated with an error of 10% of its FWHM. This is a measurement error in this case
of 1.4E-4=140 ppm.
With other detectors the error is larger.
Table 1: typical photon energy measurement errors for different detectors.
detector
condition
relative error
HPGe
1.85 keV FWHM at 1333 keV 1.4E-4
CZT
12 keV FWHM at 662 keV
1.8E-3
NaI
7.5% FWHM at 662 keV
7.5E-3
Gamma spectroscopy with semiconductor or scintillation detectors is a relative measurement method which relies
on calibration by standard photon sources. So main requirements are linearity and stability. The most interesting
point is the peak drift caused by temperature change. Temperature drift may be caused by the detector crystal, the
preamplifier and the main amplifier within the MCA. For accurate measurements it is desirable to keep
conditions such that the drift does not exceed the relative errors mentioned in table 1.
Absolute values of gain are not critical because the MCA has to be calibrated anyway. The absolute accuracy of
the MCA166 gain setting is a few percent.
2. Centroid error
h
The peak centroid is the sum of the background corrected channel
i * Spectrumi
contents multiplied by the channel number and divided by the sum of
i =l
(1)
Centroid = h
the background corrected channel contents. Only the channels above
the half maximum are used (MCA measurement software algorithm).
Spectrumi
From this definition it can be derived that there is a systematical and a
i =l
statistical component of the centroid error.
Statistical error
The measurement of a peak in a spectrum can be seen as N repeated measurements of the corresponding photon
energy, where N is the peak area. The standard deviation of a single measurement is 42.5% of the FWHM of the
gaussian distribution. The standard deviation of the average is normally the standard deviation of a single
measurement divided by the square root of the number of single measurements. In the definition only the
∑
∑
channels above half maximum are used, which represent 76% of the total peak area. This yields in a statistical
∆E ≅ 0.5 ×
centroid error depending on peak area N of
FWHM
N
(2).
systematic error: From the definition above, it can be derived that the centroid is not a linear function of the
photon energy, but has some discontinuities. This discontinuities occur, when a channel at the edge has about half
of the maximum counts and it is decided whether to include it into the centroid calculation or not. The difference
when including another channel is ∆n =
∑ is
∑s
i
−
m ⋅ sm + ∑ isi
i
.
sm + ∑ si
The edge channel m is about 0.5*FWHM from the centroid:
∑ is
∑s
i
− m = 0.5 ⋅ FWHM ,
i
(i − n )2
(i − n )2 *8 ln 2
0
0
area
area ⋅ 8 ln 2 2 FWHM
2
2
the gaussian distribution s of the peak is si =
,
e 2σ =
e
σ 2π
FWHM 2π
the sum of the channels above FWHM is ∑ si = 0.76 ⋅ area , the content of the edge channel is just half of the
maximum channel
sm =
2 ⋅ ln 2
0.618
sm
1 area ⋅ 8 ⋅ ln 2
and the ratio is
.
=
=
2 FWHM 2π
∑ si 0.76 ⋅ FWHM 2π FWHM
Assuming now that the FWHM (in channels) is large (>4), the difference can be estimated as
0.5 ⋅ FWHM ⋅
∆n =
1+
sm
∑ si
sm
∑ si
≅ 0.5 ⋅ FWHM ⋅
0.618
= 0.309 (3)
FWHM
So almost independent from FWHM, this centroid calculation algorithm causes discontinuities of about 0.3
channels, which can be seen as an systematic error of +/- 0.15channels. As this discontinuities are caused both by
channels on the left and the right side of the peak, it is better to multiply this value with
error of +/- 0.21 channels to be assumed.
2 which results in an
11 1 8 .3
1
C e n tro id e rro r (in F W H M u n its)
FW H M 3 ch a n n els
FW H M 1 1 .5 c h an n e ls
FW H M 4 6 ch a n n e ls
3 51 .99
0.1
6 0 9 .1 4
6 0 9.2 3
3 5 2.0 7
35 1 .9 6
0.01
10
100
1000
P e a k a re a
Fig. 1. Centroid error dependend on peak area using peaks which are large compared to background. If the
FWHM is only a few channels, the formula derived for statistical centroid error can be applied. If FWHM is too
large, then the centroid error is increased due to strong fluctuations of the channels used for evaluation.
In an experimental study of the centroid error it was found that there is a third contribution to the centroid error if
the peak area is distributed to many channels. In this case, the statistics of a single channel content is very bad.
This causes the FWHM determination algorithm to work incorrect and the fluctuation of channels used for
centroid calculation is much larger than one channel. This also leads to an increased centroid error. To avoid this,
it is recommended to adjust the MCA resolution in a way that the FWHM is about 4 - 8 channels.
To reduce the range of possible centroid errors, it can be stated that peaks with an area <30 counts are hardly
recognizable and centroid errors < 5%FWHM seem hard to believe. So for practical purposes the following may
be assumed (if FWHM=3...12channels and the peak is large compared to background):
Table 2
Area
peak area<30
30<peak area <400
Centroid error
not a peak
peak area>400
FWHM*0.05
∆E ≅
FWHM
peak area
4. Temperature drift of the MCA 166
At first, it is evaluated how the drift changes with time. Knowing the thermal time constant allows to judge how
long it necessary to wait until the MCA runs stable.
It also tells that for measurement times short compared to the time constant, resolution losses due to gain drift can
be reduced.
1
C e ntroid d rift
0.998
0.996
M CA 166 w arm ing up from about -7°C
0.994
0.992
0.99
0.988
0
50
10 0
1 50
200
25 0
30 0
350
40 0
T im e (m in )
Fig. 2. Reaction of the MCA166 on a sudden temperature change from -7°C to +20°C. The thermal time
constant (1/e) can be evaluated as 33 minutes. planar high resolution HPGe detector type GL0310 which was
kept at constant temperature measuring a Co60 source was connected to the MCA.Spectra were taken in 5
minute intervals and the drift of the 1333 keV peak was evaluated. Shaping time was 2µs, Gain =5*0.6.
The drift reaction caused by switching on the device is similar to that on a thermal change of 4-7°C. So, for
perfect stability it is a good idea to leave the MCA at least 3 hours running to come to a thermal equilibrium. For
short measurements (few minutes) drift will not affect resolution, as drift is very slow. However, energy
calibration may have to be readjusted a few times.
In the next experiment it was measured how gain changes with temperature and if there are other dependencies.
For this experiment a GL1015R with a Ra226 source was used. The MCA was serial number 140 (one of the first
series). The count rate was about 6500 cps and 13% dead time (2µs shaping time). The MCA was in a climatic
chamber and all the time connected to the charger. After temperature adjustments the next measurement was
started earliest after 4h to allow the MCA to find its thermal equilibrium. This temperature test was also meant to
check the reliability of the MCA electronics. Below -10°C, the battery voltage was too low to allow correct MCA
operation without charger. The tests were stopped at -40°C due to lack of time and because this is far out of
specifications (normal minimum temperature -5°C).
In first order and within the specified temperature range, the gain change with temperature can be considered
linear. Only at very low temperatures there seems to be a nonlinear effect. Much more interesting is that the drift
depends strongly on the gain setting. The drift is sometimes positive, sometimes negative and sometimes nearly
negligible.
Fig. 3. Gain change depending on temperature. The drift depends very much on the gain setting.
This behavior was evaluated a bit closer. So the drift between 20°C and 0°C was measured for gain settings
between 2.7 and 560 using logarithmic steps of the E12 series. A second measurement was made for the drift
between 10°C and -10°C using values between 10 and 150 and smaller steps (E24 series).
A few measurements were additionally performed using a different MCA (serial number 366, recent series) and a
different detector (GL0310)
6E -4
T em pe rature D rift 1/°C
4E -4
2E -4
0
1
10
100
G a in
-2E -4
D rift 2 0 °C - 0 °C
D rift 1 0 °C - -1 0 °C
-4E -4
D rift M C A #3 6 6, D et. G L0 3 10
-6E -4
Fig. 4. Temperature drift dependence on gain setting.
At the first glance, the drift dependence on gain seems to be absolutely erratic. It becomes only understandable
by knowing about the internal hardware of the MCA166. The most temperature sensitive component within the
MCA is the adjustable gain amplifier [1]. This contains internally a 6dB step (factor 2) attenuation ladder and a
circuit for interpolating between the interpolation steps. This corresponds to the drift coefficient oscillating with a
factor 2 period. At the gain of 15 and the gain of 30 this oscillation is disturbed. This can be explained by
additional attenuators which are switched at these gains.
The results also seem to be reproducible within 100 ppm/°C between different MCAs. But this was not further
examined as these measurements are quite time consuming.
5. Temperature drift of detectors
For practical purposes, it is useless to look only at the MCA drift; the drift of detectors have always to be taken
into account. For this experiment, a CZT 500 detector was warmed up from -5°C to 22°C and a HPGe was
cooled down from 22°C to 12°C.
re lative peak shift
1.01
1
0.99
C ZT500 detector w arm ing up
from -5°C to +22°C
0.98
-20
-10
0
10
20
30
40
50
T im e (m inutes)
Fig. 5. The thermal time constant of a small CZT 500 is in the order of 5 minutes. The peak drift is about 1E-3
/°C
1.0006
1.0 004
P e a k sh ift o f th e C o 6 0 1 3 3 3 ke V P e a k w he n
th e d e te cto r (G L 0 3 1 0 ) is co o le d d o w n fro m
2 2 °C to 1 2 °C . T h e M C A is ke p t a t co n sta n t
te m p e ra tu re . M C A g a in : 5 *0 .6 , 2 µ s sh a pin g tim e .
relative pe ak sh ift
1.0002
1
0.9998
0.9 996
0.999 4
0.9992
Tem perature coefficent
detector: ~1E-4/°C
0 .99 9
0.9988
0
20
40
60
80
10 0
T im e (m inu te s)
Fig. 6. The time constant of a planar HPGe detector is around 25 minutes. The drift is about 1E-4 /°C
It can be seen that the time constant of a CdZnTe detector is quite short, which corresponds to its small size. The
thermal time constant of a HPGe detector is comparable to that of the MCA, and the drift is small, but not
negligible. It has to be mentioned that the drift of a HPGe is always the drift of its preamp, as the detection
crystal is always at liquid nitrogen temperature.
6. Stabilisation
If for a certain measurement task, a well known peak is always present, then the method of peak stabilization can
be applied to compensate peak drift regardless if caused by the detector or by the MCA. For stabilization, the
reference peak has to be marked with a special stabilization ROI. The centroid of this ROI is evaluated
periodically and the gain is adjusted correspondingly.
1
D rift (re lative )
w ith sta b iliza tio n
0.99 8
0 .9 96
w ith o ut stab iliza tio n
0 .99 4
0
30
60
90
1 20
T im e (m in )
Fig. 7. Peak drift of the MCA166 with detector GL0310 and a gain of 2.8 when exposed to a sudden temperature
change of 10°C, with and without stabilization.
The period of stabilization is determined for the MCA166 by the counts in the ROI. Default is at the moment a
stabilization cycle every 25000 counts, only in newer versions of WinSpec this area can be adjusted.
The stabilization cycle time is something which can be optimized. If the stabilization cycle time is too long, then
the drift may be faster and may not be fully compensated. If the stabilization cycle time is too short, then the error
of centroid evaluation acts as spectrum broadening noise and adds to the FWHM. The centroid evaluation error
FWHM
(4)
N
E ⋅ϑ ⋅ N
The centroid drift within a stabilization cycle is: ∆E D = E ⋅ ϑ ⋅ t =
(5)
n
depending on FWHM and area N is assumed as: ∆E c
=
with the gain drift rate ϑ, the stabilisation peak photon energy E and the stabilization peak count rate
optimum can be found where the sum of both contributions is minimized.
n . An
d (∆Ec + ∆E D )
FWHM E ⋅ ϑ
(6)
= 0 = − 21
+
3
dN
n
N2
2
 FWHM ⋅ n  3
This leads to an area N opt = 
 (7)
 2 ⋅ E ⋅ϑ 
Examples:
-For the example of Fig. 7 a maximum drift rate of 4 ppm/s can be assumed. For stabilization a peak at 352 keV
with a FWHM of 1 keV and a peak area count rate of 52 cps is used. So the optimum stabilization area is
2
N opt

3
1keV ⋅ 52cps
=
= 700
−6 
 2 ⋅ 352 keV ⋅ 4 ⋅ 10 1s 
This means that a stabilisation cycle here is 13s and a 4% peak broadening due to centroid calculation error has
to be accepted.
-A HPGe is to be stabilized on the weak K40 1460 keV peak for environmental measurements. FWHM at 1460
keV is 2 keV and a peak count rate of 0.4 cps can be assumed. As drift rate the maximum drift rate immediately
after switching on (1.6 ppm/s, same as a temperature change of 5°C) is assumed. Here, an optimum stabilization
2
area of
N opt

3
2 keV ⋅ 0.4cps
=
 = 30
. ⋅ 10 −6 1s 
 2 ⋅ 1460keV ⋅ 16
is calculated. This is near the lower limit for detection of the peak. Areas lower than 30 should not be used at all.
Here, the stabilization time is 125s and a peak broadening of 18% has to be accepted.
-For U235 enrichment measurement with a NaI, the 186 keV peak used for stabilization. FWHM there is 22 keV,
the peak rate is assumed with 1400cps and the NaI is considered ten times less stable than the MCA (16 ppm/s).
In this case, the optimum area calculates as:
2
N opt
 22 keV ∗1400cps  3
=
 = 30000
. ⋅ 10 −5 1s 
 2∗186keV ∗16
The stabilization cycle time is here 21s and the expected peak broadening is neglible (0.6%).
The default value for stabilization cycle area of 25000 seems to be rather at the upper end of useful values.
Especially with low count rate applications, it is very much recommended to use a newer version of WinSpec and
decrease the stabilization area value.
C h an n e ls/ke V
7. Linearity and accuracy of gain setting
In the scope of this study, also the absolute accuracy of the gain setting was investigated (Do not mix this with
the linearity of the ADC!). This measurement was also done with the MCA166 #141 and a GL1015R detector.
The absolute value of the scale / gain ratio depends severely on detector type and preamplifier. Even the
variations between several detectors of the same type may be large. E.g. the typical variation of signal amplitude
for CZT500 detectors from Ritec is about 20% [2]. Compared with that, the gain variation of different MCA166
units (typical 2-3%) can be neglected.
10
1
10
100
G ain settin g
Fig. 8. gain setting vs. energy scale using a GL1015 planar HPGe detector
S ca le /G a in ra tio (ch a n n e ls/ke V /g a in )
0 .1 2 8
0.1 2 4
0 .1 2
0 .1 1 6
10
100
G a in
Fig. 9. variation of the scale / gain ratio in dependence of the gain setting. The absolute gain setting is correct
within +/- 3%.
The nonlinearity of the gain shows the same oscillating behavior as the temperature drift coefficient, which shows
that the most critical component here is the adjustable gain amplifier.
8. Conclusions
-The temperature drift of the MCA166 is a complex oscillating function of the gain setting. Positive as well as
negative values for the drift are found.
-A positive aspect of this complicated behavior may be that it is possible to find a point with almost no gain drift
by varying the gain in a range of only +/- 30%.
-The MCA166 temperature drift gets important when doing optimum resolution germanium detector
spectrometry. With CdZnTe- and NaI-detectors, the temperature drift of the detectors will dominate.
-The thermal drift time constant of the MCA166 is about half an hour. If the measurement time is short compared
to this thermal time constant, then resolution will not degrade by drift, but it may be necessary to redo the energy
calibration. For long time measurements with best resolution it is recommended to switch on MCA and detector
a few hours before starting the measurement.
-Peak stabilization can do in some applications a great job of drift compensation, especially when stabilisation
parameter settings are optimized.
-The MCA166 works principally also at temperatures much deeper (-40°C) than specified; the primary limit is
the battery performance at low temperatures.
[1] A. Wolf, FZR, private communication
[2] Alexander Braun, diploma thesis, dated 16.9.2000; Hochschule für Technik, Wirtschaft und Sozialwesen
Zittau/Görlitz (FH) and JRC Ispra.
GBS -Elektronik GmbH, Bautzner Landstr. 22,
01454 Großerkmannsdorf / b. Dresden
Tel.: (0351) 217007-0 Fax: (0351) 217007-21
homepage: http://www.gbs-elektronik.de/
email: contact@gbs-elektronik.de