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Electrometers: Instructions for electrical calibration of measurement of
charge
Prepared by:
(Signature)
(E.g. Quality Management Supervisor)
(Title)
(Date)
Revised:
(Signature)
(E.g. Electronics Group Head)
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Approved by:
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EG.CI.01
DATE/REVISION
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EG.CI.01
DATE/REVISION
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1.
Title:
ELECTROMETERS: INSTRUCTIONS FOR ELECTRICAL
CALIBRATION OF MEASUREMENT OF CHARGE
2.
Purpose:
To define the set of procedures for the implementation of
calibration of electrometers for the measurement of electric
charge.
3.
Scope:
The scope of this instruction extends to the calibration of
electrometers using an operational amplifier for the
measurement of charge. This instruction is also applicable to
the electrical calibration of dosemeters based on the use of an
ionization chamber and an electrometer for dose measurement.
4.
Definitions:
Calibrator: Electronic device generating an electrical signal
which main property can be used as a measure of an electrical
magnitude. This property is characterized by a reference value
whose uncertainty is known.
Control measuring instrument: Electronic device allowing to
measure the value of the magnitude of a calibrator generated
signal (reference value) with uncertainty no greater than that
of the reference value.
Zero bias: Sudden change in indication at the beginning of the
electrometer measuring scale.
Zero spread: Continuous changes in the reading indication in
the absence of an input signal.
Minimal effective value of reading: Minimal value of the
reading complying with the electrometer relevant
specifications of performance (resolution, repeatability, nonlinearity, variation due to mains power changes).
Minimal effective input current: Minimal value of the input
current complying with the electrometer relevant
specifications of performance (zero bias, zero spread, charge
leakage, non-linearity, variation due to temperature, humidity
and mains power changes).
5.
Symbols and abbreviations:
CL
The following symbols and abbreviations are
adopted in this calibration instruction:
- leakage current (CF)
CLM
- mean leakage current (CFM)
di
- departure from linearity (i)
Dm
- zero spread
FC
- electrometer calibration factor
I
- electric current
Imef
- minimal input effective current
IR
- reference current generated by the calibrator
m0,5
- instrument indication when charge q0,5 is applied
mevi
- minimal effective value of indication
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q0,5
- electric charge leading to an indication value
corresponding to half of the maximum of the selected
scale for measuring.
QE
- electrometer indication when charge QR is applied.
QEIL (C) - initial electrometer reading indicación in leakage
testing.
QEFL(C) - final electrometer reading indicación in leakage
testing.
QR
- reference charge generated by the calibrator
S
- experimental standard deviation of a set of readings
Dm
- zero drift caused by variation in the conditions of zero
adjustment
Sza.m
- shift in zero indication caused by switching from zero
adjustment to measurement mode (Sdz.m)
t0,5
- time required to obtain a reading value equal to half of
the selected scale when current i is applied.
t(s)
- time (seconds)
tM
- measuring time (TM)
6.
References: IEC –Medical electrical equipment - Dosimeters with ionization
chambers as used in radiotherapy (IEC 60731:1997), Swiss Society
of Radiobiology and Medical Physics.
Järvinen H., Rantanen E. and Jokela K. “Testing of radiotherapy
dosimeters in accordance with IEC specification”. Finnish Centre
for Radiation and Nuclear Safety. Helsinki, Finland 1986.
ISO GUM: 1995, Guide to the expression of uncertainty in
measurement.
EA-4/02, Expression of the uncertainty of measurement in
calibration, European Co-operation for accreditation, December
1999.
7.
Responsibilities: The EG Technical staff members are responsible for the
implementation and validation of electrical calibration of
measurement of charge.
The Head of EG has the responsibility of reviewing and
approving any changes or modifications introduced to this
calibration instruction.
The EG Quality Manager is responsible for addressing the
internal quality control measurements, for reviewing the
obtained results and keeping documented evidences of the
IQC.
7.
Procedure:
7.1
General considerations.
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Electrometers are instruments designed to measure very low electric current
or charge, very high resistance or electric potential with an instrument of
very high impedance.
The circuits designed for the measurement of charge and current are
commonly based on an operational amplifier in inverting configuration,
having either a feedback resistor for the measurement of charge or a
feedback capacitor for the measurement of charge. The function of the
resistor or the capacitor is to transform the electric current or charge in a
voltage signal (accordingly to the Ohm law U=RI or Coulomb law Q=CU,
respectively).
The operational amplifiers used in the electrometers have a very high input
impendance, low output impedance and allow the establishment of a virtual
ground level. In some cases the electrometer input circuits are designed to
transform the current or charge into a frequency signal, but still acting as an
operational amplifier with very high input impedance.
The principle of work of some dosemeters is based on the measurement of
the electric charge accumulated in an ionization chamber by using an
electrometr. In some cases, the electrometer indication is provided in dose
units. This instruction can be used for the calibration of such dosemeters,
providing that a proportionality factor is established for the conversion
from dose to charge units and viceversa.
7.1.1 Fundamentals.
Operational amplifiers used in inverting configuration have a very
small difference between the inverting and non-inverting (connected
to earth) inputs. That is the reason why the non-inverting input is
usually called “virtual ground” (see Figure 1).
If a tension UR is applied on CR an electric charge qR  CRU R will be
produced, since the potential difference between the non-inverting
and inverting inputs is practically nill. This current or charge is
converted into tension by the feedback elements and appears at the
output, where the operational amplifier impedance is low (~ 100
Ohm) and can be measured with a conventional voltmeter. The
generation of small charge or current by using a voltage source and
employing resistors and capacitors serves for the purpose of
electrometer calibration. If a suitable capacitor is not available, the
generation of charge can be accomplished by integrating continuous
current during a priori defined interval of time ( q  I  t ).
EG.CI.01
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RR
RM
(Measurement of current)
CM
(Measurement of charge)
-
CR
Output
+
Both inputs are at the same
potencial  “virtual ground”
To voltmeter
ELECTROMETER
FIGURE 1: Schematic representation of an operational amplifier with inverting
configuration.
Therefore, the reference charge can be produced by using a calibrator
generator for the generation of a reference tension and a reference air
capacitor for the charge accumulation. The capacitor CR shall have
not only a small uncertainty for the reference value, but also a
neglictible variation due to environmental changes (temperature,
humidity)
Note: This calibration instruction is prepared for the work with
electrometers based on operational amplifier and may not be
applicable to old electrometers for which the assumption of a “virtual
ground” condition is not valid.
7.1.2 Electrometer burden conditions.
It must be taken into account that each electrometer model can be
used for a limited maximal variation of charge (dQ/dt or current).
Some electrometers will indicate false readings when the charge
applied to the input, and which is generated by applying tension to a
capacitor, exceeds the maximal value of input current at the
electrometer input. In such cases, an additional resistor shall be added
in serial connection to the capacitor to limit the value of dQ/dt to
acceptable level.
7.2
Interconection.
Since the type of connectors varies from model to model, it is advisable to
have a set of conector adapter cables to allow the use of the available
sources of charge and current.
7.3
Electrometer initial verification.
This section adressess the main tests than must be performed for the
verification of the work performance of the electrometer before its
calibration. The provided recommendations are adapted from IEC 60731
and constitute a preliminary step before electrical calibration.
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The concept of minimal effective value of indication (mevi) is defined as the
value of the reading complying with the electrometer relevant specifications
of performance (resolution, repeatability, non-linearity, variation due to
mains power changes). Usually this value is not provided by the instrument
manufacturer and can be considered as no less than 200 times the
instrument resolution [Järvinen, 1996].
The leakage current values specified by the manufacturer are very low but
in practice the effective values depend on environmental conditions,
especially on environmental humidity. A survey on the specifications of
different models of dosimeters used in radiotherapy revealed a maximal
value reported for leakage current of 60 fA. The mevi for current
corresponding to this value is therefore of 12 pA (200 x 60 fA).
Changes in environmental temperature and humidity affect the electrometer
measurements. The calibration must be carried out at a temperature as close
as possible to that indicated for the specifications provided (200 C). The
limit values for the environmental temperature are 150C and 250C, whereas
humidity must be kept around 50 %.
7.3.1 Zero drift evaluation.
Electrometer zero drift shall not exceed +1% (+ 0,5% in the case of
reference electrometers) of the value indicated when the input
minimal effective current is measured. The procedure for zero drift
evaluation comprises the following steps:
a) Switch on the electrometer and wait for stabilization period.
b) If the electrometer has a minimal input current discriminator, it
must be adjusted to zero.
c) Switch the electrometer to measuring mode, annotate the value of
indication and calculate the charge equivalent to this indication
Q1(C)
d) Maintain the electrometer in measuring mode, and after an
interval of time t annotate the value of indication and calculate
the charge equivalent to this indication Q2(C). The interval of
time t shall be not less than that required for the minimal
effective input current to produce the minimal effective value of
indication. An interval of 15 min is a practical choice for t.
e) Calculate the zero drift Dm in measuring mode as
Dm 
f)
Q2  Q1 
t
Express this zero drift as percentage of the minimal effective
input current for the selected scale and compare with accepted
limit (1%)
(1)
7.3.2 Zero shift evaluation.
Electrometer zero shift shall not exceed +1% (+ 0,5% in the case of
reference electrometers) of the minimal effective value of indication
for any scale whenever the electrometer is switched from zero
adjustment or reset to measurement mode.
The procedure for zero shift evaluation comprises the following steps:
a)
If the electrometer has a minimal input current discriminator, it
must be adjusted to zero.
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b)
After the electrometer has been stabilized and the zero level
adjusted, annotate the value of indication and calculate the
charge equivalent to this indication as Q1(C). If the electrometer
zero adjustment is automatic, assume Q1(C) as zero.
c)
Swith the electrometer to measuring mode, annotate the value
of indication and calculate the charge equivalent to this
indication as Q2(C).
d)
Calculate the shift of the zero resulting from the change in
mode of operation as
S dz,m  Q2  Q1
(2)
f) Express this zero shift as percentage of the minimal effective
input current for the selected scale and compare with accepted
limit (1%).
7.3.2 Leakage test.
This test is carried out for electrometers using a charging capacitor
for the measurement, and which might present some discharge
leakage. The discharge rate (leakage current) shall not exceed 0,5%
of the minimal effective input current.
The procedure for leakage test comprises the following steps:
a)
If the electrometer has a minimal input current discriminator, it
must be adjusted to zero. For electrometers that have an
automatic measuring sequence, the electrometer must be
maintaned in the measurement mode.
b)
The electrometer must be maintained on for the required
stabilization period.
c)
If the electrometer has different measuring scales, select the
scale with lowest maximal value.
d)
Connect the calibrator to the electrometer using a suitable
connection cable, make the zero adjustment, switch to
measurement mode and apply a charge producing an indication
of approximately 50 % of the scale.
e)
Keeping the electrometer in measurement mode, disconnect the
calibrator, the capacitor and any other external connection that
might serve as external leakage path for the input connector.
Cover the input connector with its metallic cap. Usually a
change occurs in the indication when the calibrator is
disconnected.
f)
Further, annotate the indication and observe its variation during
the following 15 minutes.
g)
Calculate the discharge rate in amperes as intial reading minus
final, divided by the time and express it as percentage of the
minimal effective input current for the selected scale.
h)
Repeat the steps from d) to g) for each of the measurement
scales.
7.3.2 Non-linearity test.
The indication variation due to non-linearity in the scale range shall
not exceed 0,5 %. This test evaluation is of more impoprtance for
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old electrometer models using a potentiometer associated to a
numeric dial for the indication reading.
For electrometers with a a selectable scale, the test for non-linearity
evaluation must be carried out at 5 equidistant values within each of
the scales or if such selection is not possible, at values corresponding
to 5%,10%, 20%, 50% and 100% of the scale. For electrometers with
a single scale or with automatic scaling the evaluation must be carried
out at 5 equidistant values within each decade or if such selection is
not possible, at values corresponding to 5%,10%, 20%, 50% and
100% of the decade.
The procedure for non-linearity evaluation comprises the following
steps:
a)
If the electrometer has different measuring scales, select the
scale with lowest maximal value.
b)
Connect the calibrator to the electrometer using a suitable
connection cable.
c)
The electrometer must be switch on and maintained on for the
required stabilization period. Make zero adjustment.
d)
Apply a charge q0,5 to produce to an indication value
corresponding to half of the maximum of the selected scale.
Anottate the value of the reading m0.5 and return the
electrometer to the mode of zero adjustment.
e)
Swith con to measurement mode and apply a charge q1(C)
sufficient to produce an indication close to the first value of the
series. Annotate the reading as m1 and return the spectrometer
to the mode of zero adjustment.
f)
Calculate and annotate the value of the factor d1 (percentage of
deviation from linearity for value q1 as
g)
h)
7.3


d1  100   m1
 1
(3)
m
0,5


Repeat the steps e) to f) for each of the values from the
measurement sequence to obtain the values d2, d3, d4 and d5.
The non-liinearity value is taken from the maximum value from
d1, …, d5.
Charge measurement calibration.
Changes in environmental temperature and humidity affect the electrometer
measurements. The calibration must be carried out at a temperature as close
as possible to that indicated for the specifications provided (200 C). The
limit values for the environmental temperature are 150C and 250C, whereas
humidity must be kept around 50 %.
The calibration comprises the following steps:
a)
Connect the calibrator to the electrometer using a suitable connection
cable.
b)
Switch on the electrometer and keep it on for the required
stabilization period.
c)
Follow the manufacturer instructions for zero calibration
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d)
e)
f)
g)
.g)
Select the measuring scale and switch to measurement mode. Apply a
charge q0,5 to produce to an indication value corresponding to half of
the maximum of the selected scale. Annotate the reading as m0,5
Repeat the steps d) and e) to obtain 10 replicate readings
Calculate the mean ( m ) and standard deviation of the ten replicate
readings.
The calibration factor for the electrometer is calculated as
q
CU
(4)
CF  R  R R
m
m
where UR is the reference DC voltage supplied by a calibrator, CR is a
reference capacitance.
The uncertainty of the calibration factor CF is calculated following
the specifications provided in the specific procedure EG.OP.004
According to eqn. (4) and the recommendations for uncertainty estimation,
the absolute combined uncertainty of the calibration factor can be
calculated as
u (C F ) 
qR
m
u 2 (q R )
q R 2

u 2 (m )
(5)
m 2
Several sources contribute to the uncertainties of the reference value qR and
the mean of measurements m :
u (q R )  u 2 (C R )  U R2  u 2 (U R )  C R2
(6)
2
u (m )  u 2prec (mi )  u res
(mi )
(7)
2
u(U R )  u abs
(U R )  uch2 (U R )
2
u(C R )  u abs
(C R )  uch2 (C R )
`
(8)
(9)
The meaning of each the contributions in eqn (6) and (7) are:
u abs (U R ) is the absolute absolute uncertainty of the DC voltage reference
value reported by the calibrator manufacturer
u ch (U R ) is the additional uncertainty of the DC voltage reference value
reported by the calibrator manufacturer for the cases when changes
in environmental conditions exceed the working interval assumed
for operation
u abs (C R ) is the absolute uncertainty of the capacitor reference value
reported by the manufacturer (it is assumed that additional
uncertainty of the reference value due to changes in
environmental conditions in reference air capacitors is
neglictible).
u ch (C R ) is the additional uncertainty of the capacitor reference value
reported by the calibrator manufacturer for the cases when changes
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in environmental conditions exceed the working interval assumed
for operation
u prec (m ) 
s(m)
n

n
1
(mi  m ) 2

n(n  1) i
(9)
u res (mi ) is the uncertainty of the electrometer resolution indication, that
can be calculated for a rectangular probability distribution as:
u res (C R ) 
1
12
(resolution ) elect
(10)
Assuming a normal probability distribution for the calculated calibration
factor, a coverage factor k=2 ensures 95 % of coverage probability, and the
calibration result is reported from expressions (4) and (5) as
CF 
EG.CI.01
CR
 2  u(C R )
m
DATE/REVISION
(9)
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