```CALIBRATION OF CURRENT
INTEGRATORS USED WITH
IONIZATION CHAMBERS
V. Spasić Jokić, I. Župunski, B. Vujičić, Z.
Mitrović, V. Vujičić, Lj.Župunski
Faculty of Technical Sciences, University
SPECIFIC AIMS
 Purpose
: trace the harmonization of
uncertainty evaluation within accreditation
framework
 Uncertainty estimation in accordance with
the GUM but it is necessary to establish the
method more suitable for the measurements
in calibration laboratories
 Good metrology practice : evaluation of Type
B uncertainty is particularly important and
requires proper use of the available
information is based on experience and skill.
DOSIEMETERS BASED ON
IONIZATION CHAMBERS
device
• The typical order of magnitude of ion
currents: (10-6 to 10-14 ) A
Voltmeter function: The input resistance of an
integrator is greater than 100 TΩ , the input offset
current is less than 3fA.
 Ammeter function: can detect currents as low as 1fA
 Coulombmeter Function: Current integration and
measurement as low as 10fC, has low voltage burden,
(less than100μV).Currents as
IC self capacitance = 100 pF
IC
low as 1fA may be detected
HV
using this function

C2
R2
R3
R1
Relay
+
C1
INPUT
C6
C5
Low current
source
R4
RLY1
C3
C4
+
-
U1
CURRENT INTEGRATOR
For current
measurement
For charge
measurement
• Capacitor in the feedback: (10-5 - 10-11) F
(calibrated within 0.1%)
•Conventional carbon resistors are available in
values up to 108 
CALIBRATION: WHICH SOLUTION IS THE ‘BEST’
• Ionization chambers are used together with current
integrators and they should be calibrated together
•Chamber is standard instrument
•Integrator is standard instrument
•Calibrated together as the same rank instruments
Good reason for separate
calibrations is that, one
integrator is used with a
number of chambers, so it
would be inconvenient to
calibrate it with every
chamber.
IAEA 398 SOLUTION
•
Assumes user has a calibration factor for exposure ND
for the ion chamber/ integrator combination in use
But allows
Dw,Q= MQ ND,w,Qo kQ,Qo
corrected
instrument
M  Pion PT P Pelec Ppol M raw
•
calibration
coefficient
at Qo
(C or rdg)
Pelec a factor allowing for separate calibration of the integrtor here 1
beam
quality
factor
Calibration method for a current-measuring
feedback-controlled integrator
The output impedance of the current source must be
large compared to R.
Verification of dosimeters used
protection is a legal requirement
in Serbia
Verification is a subject of
accreditation
according
to
SRPS/ISO 17025
ISO 17025: GENERAL REQUIREMENTS FOR
THE COMPETENCE OF TESTING AND
CALIBRATION LABORATORIES
EUROMET Project n. 830,
“Comparison of small
current sources”
Laboratory for metrology at the
Faculty of Technical Sciences,
accredited in terms of SRPS/ISO
17025 for verification of current
integrators
CALIBRATION OF CURRENT
INTEGRATORS
 Suitable
direct current source that
simulate the output from ionizing radiation
detectors.
 Range: 100 fA - 100 mA (uncertainty better
than 0.05 %), depending of chamber type
 IEC 60731
 Calibration: using method of direct
measurement
SIMPLIFIED CALIBRATION SETUP
DC reference
voltage source
V+
V-
Relay
switching
unit
Device under test
Reference
capacitor
DMM
Ground
Guard
GPIB
- standard high impedance DC source Keithley 6220,
- various standard resistors and capacitors and
- digital multi-meter HP 3450 B
ACCREDITED METROLOGICAL
LABORATORY FTN UNS
CONCEPT OF UNCERTAINTY ESTIMATION

Model function for uncertainty estimation in the
calibration procedure for current integrator can be
expressed as
E x  ( I x  I x )  I e
Ix - current read by integrator under the test;
 δIx – error of reading obtained by integrator under the
test due to final resolution;
 Ie – preset current (on current source) derived from
the declaration of the manufacturer or calibration
certificate

CONCEPT OF UNCERTAINTY ESTIMATION

Sensitivity coefficient is derived from expressions
c  I x   E x /   I x  1 c Ie   E x /  I e   1
Calibration uncertainty for current
integrator can be expressed as
u  Ex  
 c
 u   I x     c  Ie  u   I e  
2
Ix
2
RESULTS
The main part of each calibration procedure is
uncertainty estimation and design of uncertainty
budget
 Uncertainty budget obtined during calibration
procedure of current integrator type NP 2000
manufactured in OMH, Hungary
 Preset value: 2 nA
 Rectangular probability
distribution was assumed

THE UNCERTAINTY OF THE CURRENT
SOURCE ITSELF
Comes from several contributions:
 Capacitance calibration (5 ppm)
 Temperature coefficient (4 ppm/K)
 ac-dc difference
 Triggering timing (1 ppm)
 Leak current compensation (2.10-5 I + 10 aA)

Preliminary uncertainty assessment for the current
generated by the source
I
100 fA
1 pA
10 pA
100 pA
UB (I)( k=2)
13 aA
48 aA
420 aA
4.2 fA
Only type B evaluation has been
considered
ESTIMATION OF TYPE B UNCERTAINTY
ASSUMPTIONS
 I = 2 nA
 Lower and Upper limit values: (I- =I – Δ, I+ =I+Δ)
 Rectangular distribution: there is 100 % probability
that the true value is found in the interval
I-
2 nA
I+
ESTIMATION OF TYPE B UNCERTAINTY
 Step

1.
Probability density p(x) for the distribution of
current values as
p(x)=C for I- Δ  x  I+Δ
p(x)= 0 in all other cases
ESTIMATION OF TYPE B UNCERTAINTY
 Step
2: Calculation of the best
estimated value and variance
Ex
UNCERTAINTY BUDGET
Quantity
Integrator
the test
Value
under
2,004 nA
Uncertainty
(Type)
0,00802 nA
(A)
ci
Uncertainty due to
final resolution of
100 fA
28,9 fA
(B)
1
Preset current on
DC source
2 nA
0,001 nA
(B)
-1
Uncertainty
integrator
of
0,0081 nA
UNCERTAINTY BUDGET OF THE CURRENT TO
VOLTAGE CALIBRATION FOR THE 100 PA, 10 PA
AND 1 PA
Uncertainty component
Voltage measurement
1 pA
[ppm]
50
10 pA
[ppm]
10
100 pA
[ppm]
10
Resistor value
1350
190
70
1/f noise
1300
130
13
10
10
10
1900
230
75
3800
460
150
Current source
Combined standard
uncertainty
Expanded uncertainty (k=2)
MEASUREMENT CAPABILITIES
WITH
UNCERTAINTY BUDGET
I
dV/dt
Reference
capacitor
u95 source
u95 integrator
calibration
100 fA
10 mV/s
1 pF
400 μA/A
2%
100 pA
100 mV/s
1 pF
100 μA/A
1 mA/A
1 pA
100 mV/s
10 pF
20 μA/A
500 μA/A
10 pA
100 mV/s
100 pF
18 μA/A
90 μA/A
100 pA
100 mV/s
1 nF
10 μA/A
70 μA/A
The expanded uncertainty U with the coverage factor k = 2, corresponding
to the 95% confidence level, is often used to represent the
overall uncertainty, which relates to the accuracy of the measurement of
the quantity Q.
CONCLUSION


The current uncertainty permits the calibration
of even the most accurate commercial meters
present on the market.
The source is simple, portable and based on lowcost electronics and equipment typically present
in most electrical metrology calibration
laboratory, where it could be efficiently
employed.
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