Possibilities of precision ohmmeter calibration in the exploitation condition

Abstract

Increasing of ohmmeter metrological reliability by a resistive code-control measure-imitator under the exploitation conditions is proposed in this article. The correction algorithm of additive errors for both an ohmmeter and a code-control resistive measure-imitator is proposed, which provides invariance to the impact of connecting lines and also remaining commutator parameters. The extreme metrological possibility of remote express ohmmeter checking in the exploitation conditions has been discussed.

Full text

The 7th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications
12-14 September 2013, Berlin, Germany
Possibilities of Precision Ohmmeter Calibration
in the Exploitation Condition
V. Yatsuk, R. Yanovych, Yu. Yatsuk, V. Zdeb
Lviv Polytechnic National University, S. Bandery 12, Lviv, Ukraine, vyatsuk@lp.edu.ua , www.lp.edu.ua,
romanyanovych@rambler.ru, zvbl@polynet.lviv.ua
Abstract—Increasing of ohmmeter metrological
reliability by a resistive code-control measure-imitator
under the exploitation conditions is proposed in this article.
The correction algorithm of additive errors for both an
ohmmeter and a code-control resistive measure-imitator is
proposed, which provides invariance to the impact of
connecting lines and also remaining commutator
parameters. The extreme metrological possibility of remote
express ohmmeter checking in the exploitation conditions
has been discussed.
Keywords—ohmmeter; code-control measure; remote
calibration; error correction; exploitation condition;
I. INTRODUCTION
Measurements made during monitoring the course of
technology processes should be considered as a holistic
process starting from the perception and transformation
of measuring information taken from an object to its
processing, storage, transmission and utilization, to
produce a feedback effect on controlled technological
objects. In modern terms to assure one of the most
important parameters of measurement devices (MD),
required metrological reliability, in practice the processes
of measurement are constantly supervised [1]. Reliable
measurement information of necessary accuracy can be
obtained only by technically proved choice of
measurement devices, which includes the following
information [2]: availability of object controlling and
measuring parameters; allowable values of object
controlled and measurement parameter deviations as well
as permissible errors of parameter measurement;
acceptable probability of false and unknown failure for
each controlled parameter and confidence values for
measured parameters; the distribution laws of measured
(controlled) parameters and their measurement errors that
may occur while using devices of parameter measurement
(control); measurement conditions: mechanical stress
(vibration, shock, acceleration etc.); climatic influences
(temperature, humidity, pressure etc.); the presence or
absence of actively harmful environment (aggressive
gases and liquids, high temperature or electrical voltage,
fungi, mold, electromagnetic fields, radioactive and other
radiation etc.), where means of measurement or their
elements should be exploited.
Considering this information, exact specifications of a
necessary measurement device (allowable limits for
primary and secondary errors) are calculated.
II. EXPLOITATION TASK ESTABLISHMENT
A. Metrological reliability of measuring devices
Accuracy of measurement (control) parameters,
which indicates the probability that the measurement
error value will not exceed the allowable values at a
specified likelihood, is one of the main metrological
characteristics of measurement devices during periodic
monitoring. Today national and international normative
documents recommend systematic and complete control
of the measurement process in order to guarantee the
required quality level of goods, products and services
produced by using measuring devices. This control is
treated as a separate and lengthy procedure [1]. The
proposed standard recommends the monitoring of
measuring control processes with statistical processing of
measurement results and documenting. It is necessary to
determine the frequency of checking the measurements
for each individual process, in particular as a technical
and economic compromise between the value of
metrological checks (with the removal or replacement of
means from a measurement process, or with halting a
production process, transportation of a measuring device
to a testing laboratory, and calibration conductance, in the
case of irreplaceability) and importance of precision of
the measured parameters for quality assurance. It depends
on the following four main factors [1] – the number of
inspections, required degree of security, degree of
importance of measurement error sources, stability of the
process.
Frequency of metrology inspection is primarily
determined by the metrological reliability of
measurement. To improve the reliability of measurement,
frequency should be increased. On the other hand, the
implementation of metrological verification is associated
with significant economic costs and therefore its period
should be maximized. Consequently the problem of
establishing optimal verification intervals stays

complicated and partly solvable. For example, in Canada
and the United States, laboratories of national reference
service do not indicate expiration of the metrological
verification, thus implying temporal changes in the values
of the error, and leaving the next issue of the metrological
verification to the consumer [2-5].
B. Express checking of metrological conditions of
measuring devices
The ultimate goal of efficient control of measurement
processes is to improve the metrological reliability.
Implementation of this procedure is connected with two
scientific and technical aspects. The first is a quantitative
characteristic – the reliability of control, and the second –
the frequency of the monitoring.
To ensure high reliability of control D = 1, one should
in practice provide symmetrical limits of a permissible
measurement error with the mathematical expectation
М(Δх) = 0. The equality of the mathematical expectation
of a measurement tool error to zero in real operating
conditions can be achieved only with correcting a
systematic error component.
In terms of a modern element base, the code-control
measures of electrical quantities can easily be made
compact and portable [2, 3], and therefore controlling the
errors of measurements can be hold arbitrarily, often at
the place in question. Frequency of control operations
will depend on the time drift of measurement device
metrological characteristics, and control results can be
fixed in a special card. A conclusion about suitability of a
measurement device or need for its metrological
verification can be made on the basis of analyzing card
data. Of course, while determining the boundaries of
permissible values of error ΔXP of measurement devices,
the values of impact variables should be monitored, and
the corresponding values of additional errors should be
calculated in working conditions.
III. DESIGN OF A PRECISION OHMMETER
CALIBRAT ION UNIT
A. Measurement device errors correction by code-
control measure means
In a general case, the error value depends on the input
informative signal R and to analyze it a polynomial model
is the most applicable [2, 3].
The additive error component (AEC)
x0
∆
,
multiplicative
sx
δ
and nonlinear
x
ε
coefficients of this
model are variables or processes that depend on the
Q

vectors of parameters measuring circuit and
ζ

factors of
errors, but do not depend on the informative parameter X.
Unfortunately, there is no universal method of adjusting
systematic errors, because of variety of methods, tools
and conditions of measurement [2, 3]. Prediction of
temporal changes of errors requires a large set of
experiments for a particular type of measurement devices
in the exploitation conditions [6].
Since the use of modern microelectronic and
information technology enables us to implement small-
size code-control measures, to measure electrical
quantities, differential or compensation methods are the
most appropriate [2, 3].
B. Possibilities of ohmmeters remote calibration
There are many different devices produce for the
sensors resistance simulation [7-9]. But it has some
disadvantages especially large values of permissible error
and small resolution and stationary fulfillment provides to
significantly complicate the ohmmeter calibration
procedure on the exploitation place.
To carry out an efficient control of MD, being
exploited, it is advisable to use portable code-control
measures (calibrators) of electrical quantities [5]. It is
known that for high control accuracy, the limit of
admissible error values of code-control measures should
be several times less than the limits of acceptable error
values of controlled MD [2, 3]. In exploitation
conditions, the functioning of serial calibrators of
electrical quantities requires periodic manual adjustment
of an AEC. It increases the complexity of metrology
operations and the time of their conduction, which, in
some cases, is virtually unacceptable because of the very
limited time for involving an operator at such
technological objects, for example, as nuclear power
plants [4]. Therefore the calibrators of electrical
quantities are expected to be provided with an automatic
AEC adjustment, or one can apply the method of
commutation inverting during measuring electrical
quantities [2, 3].
If the implementation of voltmeters calibrating
methods, based on the voltages calibrated sources, using
the double inversion method the precision ohmmeters
calibration process is not so obvious [2, 3]. During the
ohmmeters remote calibration by electrical resistance
measure-simulators using, one should, first of all, provide
invariance to the influence of connecting line resistances
[2, 3]. Obviously, the practical invariance to impact of
connecting line resistance can be assured only by four-
wired sensors’ connection, although in practice various
structures of ohmmeters with three-wired sensor
attaching are used [2-5]. Another important problem
during calibration of an ohmmeter in exploitation
condition is the effect of resistance simulator errors,
especially of equivalent AEC, whose value depends on
the value of the control code [2, 3].
Considering the expounded before, calibrating the
precision ohmmeters should be made with involving the
resistance simulators according to the structure shown in
Fig. 1.
The principle of this calibration scheme consists in
adding the two ohmmeter measurement results obtained
at different values of measuring current flowing through
the code-control measure-simulator of resistance.

In a regular work mode, the measured resistance RX is
connected to the ADC entrance through the connected
key SХ hereby both calibrating keys S1K and S2K are
disconnected. During calibration, the measuring key SХ is
disconnected, and the calibrating resistor RK is connected
to the ADC entrance by the switched on key S1K (S2K is
disconnected) or the connected key S2K (S1K is
disconnected). Alternating connection of keys S1K and S2K
provides the flowing of measuring current Іі through the
calibrating resistor RK in opposite directions.
A similar structure of electrical resistance calibration
should be employed for precision ΣΔ ADC of the type
AD7792 (AD7793) [10]. Owing to four-wired connection
of the measuring RХ and calibrating RK resistors to these
ADC, the possibility of remote efficient control of a
whole measuring tract of the ohmmeters built on their
basis is assured. Hereby, the switchers SХ, S1К, S2К of four-
pole commutation should be realized on the basis of
complementary metal-oxide-semiconductor transistors,
for example ADG419 Analog Device.
The code-controlled measure-simulator of electrical
resistance is suggested being implemented according to
the scheme in Fig. 2 [2, 3, 11].
The code-control resistance simulator based of Ohm
law reproducing for the electrical circuit part. The
simulator current Ii flows through the input terminal 1, an
precision resistor RN, operational amplifier (OA) output
A3 and terminal 2 (fig. 2). The simulator active part
include voltage buffer A1, multiplying DAC1 with output
OA A2, and voltage inverter A3 and DAC2 and
reproduce at the A3 output voltage opposite to drop
voltage of precision resistor RN and their value is
depended of control code μ. As a result between 1 and 2
simulator terminal reproduce resistance Ri, which ideal
value can be found from the expression [11]
( ) ( )
mRImRIRIIUR
NiNiNiii
µµ
−=−==
1
12
,
(1)
here U12 – voltage drop between 1 and 2 simulator
terminal; Ii – measuring current which flows between
simulator terminal; μ – DAC1 control code; m=λ2G2/
(1-λ2)G2=0,5/(1-0,5)=1 – inverter amplifier A3
conversion coefficient if DAC2 control code is equal
λ2=0,5.
In this case the multiplying DAC2 is used as
conductivities of OA A3 feedback.
Experimental investigation results had shown that
least signification value of reproduced resistance by
simulator measure was near 0,0001 Ohm at several
miliamperes of measuring current value and resolution
which dependent of used DAC1 type.
Having analyzed the circuit of a code-control
resistance simulator, we could find the voltage U12
between the terminals "1" and "2":
( )( )
[
( ) ( )
]
( )
( )
me
kmek
MkeRIRIU
NiNi
++ +++++× ×+++−=
1
11111
111
3
322
11112
µµ
,
(2)
here e1, e2, e3 – equivalent value of AEC of OA A1, A2,
A3; k1, k2, k3 – conversion coefficient of OA A1, A2, A3
accordingly; M1 – common mode rejection ratio of OA
A1.
Then the resistance Ri of an simulator is defined by
the formula (3):
( )
[
( )( ) ( )
]
( ) ( )
mIekm
IeIeRk
MkRIUR
i
iiN
Nii
+++× ×++++× ×++−==
111
111
111
33
212
1112
µµ
. (3)
Adjustments of AEC code-control measures is carried
out by finding with the help of measurement devices an
arithmetic mean of its two values R11 and R12 at the
forward and reverse flows of current Ii through a measure
of resistance
( ) ( )
( ) ( )
i
K
KNNN
i
K
KNNN
I
mRRR
I
mRRR
∆
−+++=
∆
++++=
δµδ
δµδ
11
11
21
12
, (4)
L
X1
P
X1
S
X
P
X2
L
X2
L
K1
P
K1
S
1K
P
X2
L
X2
L
K2
P
K2
S
2K
P
K1
L
K1
R
X
R
K
ADC
KNTR
IND
Figure 1. Block-scheme of ohmmeter calibration with adjustment of
an additive error component.
DAC1
DAC2
R
N
e
1
e
2
e
3
μ
μ
m
A1
A2
A3
I
i
1
2
Figure 2. Structure-scheme of code-control resistance measure.

here δK – a multiplicative error component (MEC) of the
code-control simulator resistance; δN – MEC of a scale
resistor resistance; μ1 – DAC1 control code; m –
control code DAC2; ΔK – ACE of a code-control
measure-simulator of electrical resistance, Іі –
measuring current of ohmmeter.
In many practical cases, the limits of permissible error
values of precision ohmmeters
[ ]
R
SPPXP
δ+∆±=∆
0
and code-control measures
[ ]
R
SMPMPMP
δ+∆±=∆
0
are normalized by a binomial model, where Δ0P and Δ0MP
– AEC permissible values and δSP, δSMP – permissible
coefficients values of MEC of precision ohmmeters and
code-control measure accordingly, R – measuring or
reproducing resistance values. Let us assume that during
the process of measurement, both exploitation conditions
and errors of the ohmmeter and calibrator remain
unchanged. To determine the ohmmeter error, only four
measurements at two values of an output calibrator signal
R1 and R2 should be made and their results must be
processed. If transformation function of digital ohmmeter
is showed as
( )
RkR
SXHXX
δ∆
++=
1
0
, where Δ0X, kH,
δSX – that unit AEC, nominal transformation coefficient
and coefficient of MEC accordingly, we should find such
measurement results system:
( ) ( ) ( )
[ ]
( ) ( ) ( )
[ ]
( ) ( ) ( )
[ ]
( ) ( ) ( )
[ ]
KKNNNSXHX
KKNNNSXHX
KKNNNSXHX
KKNNNSXHX
mRRkR
mRRkR
mRRkR
mRRkR
02022
02021
01012
01011
111
111
111
111
∆δµδδ∆ ∆δµδδ∆ ∆δµδδ∆ ∆δµδδ∆
−+−+++= ++−+++= −+−+++= ++−+++=
(5)
here, R11, R12, R21, R22 – checking ohmmeter indicators for
opposite polarities connection of a resistance measure-
imitator and for two different values of the DAC1
control code μ1 та μ2, respectively; Δ0K – equivalent
AEC of resistance measure-simulator.
From the equation (5), the coefficients of
multiplicative and additive error components of a
checking ohmmeter are determined as:
( ) ( )
( )
1
2
12
22211211
−
µ−µ +−+
=δ
NH
SX
mRk
RRRR
, (6)
( ) ( )
( )
2
1
1
2
1211
12
22211211
10
RR
m
RRRR
X
+
+





−×
×
µ−µ +−+
µ−≈∆
, (7)
As seen from the formulas (6) and (7), AEC of code-
control resistance simulator is adjusted by commutation
inverting, and ACE and MCE of a checked (calibrated)
ohmmeter are quite simply determined in exploitation
conditions.
Moreover, the multiplying DACs by the R-2R
matrices based have very small value of a conversion
temperature coefficient of the degree ±15·10-6 %/0С [12].
Then they are proposed to be used reproduce ohm values
by an resistive measure simulator at exploitation
conditions. In this case, the invariance to the temperature
influence of reproduced resistance values within the
whole range of environmental temperature altering is
provided [3, 11, 12]. The use of a resistor RN with
thermo-compensation unit allows this measure
application as precision code-control resistance at the
whole ohmmeter exploitation conditions [2, 3, 13].
IV. CONCLUSIONS
The algorithm of solving the problem of calibration of
precision ohmmeters in exploitation condition is
proposed. The scheme of calibrating the meters of
electrical resistance with additive error component
measures’ adjustment by commutation inverting has been
developed. The structure scheme of a code-control
measure-simulator of electrical resistance has been
designed.
The conducted analysis of structural schemes and the
procession of the results of conversion after the method
of commutation inverting enable us to calibrate precision
ohmmeters on the spot and evaluate their metrological
parameters in exploitation conditions.
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