Volume 02 Issue 06-2022
59
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
The article examines the large inductance difference passing through adjacent busbars and the new induction
converter errors designed to measure the symmetry of three-phase currents using the parametric structure method.
The additive components of the error are shown in the variable parametric structure diagram as a correction to the
output size, and the multiplicative components - in the form of a transmission coefficient or correction to the
parameter. It has been found that the input of errors in the form of corrections to the inter-chain transmission
coefficients, magnitudes and parameters in the parametric structure scheme is the effect of interfering physical
effects that link the different physical nature of the variable to the main parameter, magnitude and transmission
coefficients. It was found that the regular component of the error of the variable studied does not exceed 0.68%, and
its random component does not exceed 1.28%.
KEYWORDS
Induction converter, large alternating current difference, symmetrical three-phase current, parametric structure
circuit, magnetomodulation mode, transformer mode, error, additive error, multiplicative error.
Research Article
THE RESEARCH OF CURRENT DIFFERENCE MEASURE ERRORS OF NEW INDUCTION
CONVERTER
Submission Date:
June 02, 2022,
Accepted Date:
June 12, 2022,
Published Date:
June 24, 2022
Crossref doi:
https://doi.org/10.37547/ajast/Volume02Issue06-09
S.F. Amirov
Tashkent state university of transport, Address: 1 Temiryo
ʻ
lchilalar str., 100167 Tashkent city, Republic of
Uzbekistan
S.X. Jumaboev
Tashkent state university of transport, Address: 1 Temiryo
ʻ
lchilalar str., 100167 Tashkent city, Republic of
Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 02 Issue 06-2022
60
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
INTRODUCTION
Currently, more than 30% of electricity generated in the
country is distributed in low-voltage zero-wire
networks [1]. Numerous studies on the operating
modes of such networks show that the quality of
electricity in them often does not meet the
requirements of the standards.
One of the main factors in the deterioration of voltage
regimes in electricity consumers and the increase in
power losses in low-voltage networks is the
occurrence of current symmetry in three-phase
circuits. In such chains, automatic symmetry devices
are widely used to restore the symmetric mode [2].
A single-phase gravity load in an electrified railway
system is a source of symmetry for an external three-
phase power supply system. Therefore, high-precision
measurement of current symmetry in three-phase
alternating current circuits is one of the important and
topical issues.
Non-contact electromagnetic measuring converters
(MC) are mainly used to measure the difference in
currents flowing through the busbars [3, 4, 5].
However, the existing MCs do not meet the
requirements for them in terms of functional
capabilities.
At the Department of "Power Supply" of our university
developed a new design of induction converter (IC),
which measures the difference in current in the bus
(Figure 1) [6]. The device detects the symmetry of
three-phase currents or large alternating currents
passing through three can change the difference in
proportion to the alternating voltage. When an IC is
designed to measure a large value of alternating
current difference, its modulation coils are supplied
from an industrial frequency alternating current
source, resulting in an alternating magnetic flux of
𝑄
𝜇м
value in each modulation circuit.
𝑄
𝜇𝐴
,
𝑄
𝜇𝐵
,
𝑄
𝜇𝐶
magnetic fluxes on non-adjacent rods of a three-
contour magnetic conductor when alternating
currents pass through busbars 1, 2, 3, and
∆𝑄
𝜇𝐴𝐵
=
𝑄
𝜇𝐴
− 𝑄
𝜇𝐵
,
∆𝑄
𝜇𝐵𝐶
= 𝑄
𝜇𝐵
− 𝑄
𝜇𝐶
,
∆𝑄
𝜇𝐶𝐴
= 𝑄
𝜇𝐶
− 𝑄
𝜇𝐴
currents on adjacent rods is formed. When the currents
in the tires are equal to each other,
𝑄
𝜇𝐴
= 𝑄
𝜇𝐵
= 𝑄
𝜇𝐶
the differences in the magnetic fluxes of the adjacent
rods are zero, ie.
∆𝑄
𝜇𝐴𝐵
= 0
,
∆𝑄
𝜇𝐵𝐶
= 0
,
∆𝑄
𝜇𝐶𝐴
= 0
.
As a result, the voltages generated by the modulated
magnetic currents in the measuring coils on the non-
adjacent rods are proportional to the magnitude of the
current flowing through the corresponding bus, and
the signals at the outputs of the measuring coils on the
adjacent rods are zero.
If the magnitude of the currents in the tires differs from
each other (or the current in one of them from the
currents in the others), then at the outputs of the
measuring coils on the corresponding adjacent rods
are generated signals proportional to the difference in
currents in two adjacent tires.
When the generated IC is installed in three-phase
alternating current circuits, the measuring coils on the
adjacent and non-adjacent rods are connected to each
other in an open triangular manner, and the
modulation coils are disconnected from the
corresponding current source. When the three-phase
circuit operates in symmetrical mode, the signals at the
corresponding common outputs of the 16, 17, 18 and 19,
20, 21 coils connected in the open triangle method are
zero. If a symmetrical mode occurs in a three-phase
circuit, then the output signals are proportional to the
symmetry of the three-phase currents at the
corresponding common outputs of the IO bands and
their values are equal to the effective values of the sum
of the following complex voltages:
𝑈̇
э.чиқ.1
= 𝑈̇
э𝐴
+
𝑈̇
э𝐵
+ 𝑈̇
э𝐶
,ва
𝑈̇
э.чиқ.2
= 𝑈̇
э𝐴𝐵
+ 𝑈̇
э𝐵𝐶
+ 𝑈̇
э𝐶𝐴
.
The
signals induced in the measuring coils on non-adjacent
rods are proportional to the alternating current in the
corresponding busbar.
Volume 02 Issue 06-2022
61
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
Figure 1. Construction of a new electromagnetic
converter measuring the symmetry of three-phase
currents: 1, 2,3 - current tires; 4, 5, 6 and 7, 8, 9 - non-
adjacent and adjacent rods of a three-contour magnetic
conductor, respectively; 10, 11, 12 and 13, 14, 15 -
modulation coils on non-adjacent and adjacent rods; 16,
17, 18 and 19, 20, 21 - measuring rings on adjacent and
non-adjacent rods, respectively; δ is the air gap in the
non-adjacent rods
When the generated IC is installed in three-phase
alternating current circuits, the measuring coils on the
adjacent and non-adjacent rods are connected to each
other in an open triangular manner, and the
modulation coils are disconnected from the
corresponding current source. When the three-phase
circuit operates in symmetrical mode, the signals at the
corresponding common outputs of the 16, 17, 18 and 19,
20, 21 coils connected in the open triangle method are
zero. If a symmetrical mode occurs in a three-phase
circuit, then the output signals are proportional to the
symmetry of the three-phase currents at the
corresponding common outputs of the IO bands and
their values are equal to the effective values of the sum
of the following complex voltages:
𝑈̇
э.чиқ.1
= 𝑈̇
э𝐴
+
𝑈̇
э𝐵
+ 𝑈̇
э𝐶
,ва
𝑈̇
э.чиқ.2
= 𝑈̇
э𝐴𝐵
+ 𝑈̇
э𝐵𝐶
+ 𝑈̇
э𝐶𝐴
.
The
signals induced in the measuring coils on non-adjacent
rods are proportional to the alternating current in the
corresponding busbar.
The advantage of the created IC over existing devices
of this type is that, firstly, it can be used to measure the
asymmetry of currents in three-phase AC circuits, as
well as to measure the difference of alternating
currents passing through two or three busbars,
secondly, the device simultaneously can measure the
current difference, thirdly, it can give information
about the symmetry of the currents in the circuit from
two outputs that are not galvanically connected to
each other in a three-phase alternating current circuit,
and fourthly, the measuring chains on non-adjacent
rods (due to the presence of air gaps δ).
Before recommending the generated IC for
widespread use, it is necessary to study its basic
technical characteristics.
One of the main characteristics of MCs is its
measurement error. This is because the accuracy class
of MCs, including ICs, is precisely measured by the
measurement error [7].
Elements of measurement error theory are often used
to identify, analyze, and quantify the sources of IC
errors [8]. However, there are some difficulties in
identifying the sources of error and taking into account
the interactions of the parameters of different chains
Volume 02 Issue 06-2022
62
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
of MC in the derivation of error equations, as well as in
evaluating the results.
RESEARCH METHOD AND RESULTS
Therefore, it is more convenient to use the method of
parametric structure schemes (PSS) based on the
energy information model of different physical chains
in the study of errors of measuring converter(MC or
transducers) based on events and processes occurring
in different physical chains, especially the principle of
operation
.
[9].
In the PSS for the theoretical study of measurement
errors of IC, additive errors consisting of regular and
random components are in addition to the output size
of each elementary link, and multiplicative errors
consisting of regular and random components are
added to each elemental link in the PSS (inter-chain
physical effect (PhTE). ) or chain parameter) is
considered in addition to the transmission coefficient
or parameter. The causes of errors in the PSS in the
form of additions to the magnitudes, parameters and
coefficients of interconnection of chains of different
nature are directly related to the physical effects that
link the sizes of chains of different physical nature to
the parameters and coefficients of the chain.
The sequence for calculating IC measurement errors
using the PSS method is as follows [9]: 1) the PSS is
divided into elementary links configured for the static
mode of the device; 2) the regular and random (mean
square deviation) components of additive and
multiplicative errors for each elementary link that
reflects this or that physical effect are taken into
account in the structural scheme; 3) the sources of
errors and their values are determined and evaluated
using PSS, taking into account the inter-chain sizes and
inter-chain effects between the parameters in the
structural scheme, as well as external quantities of
different physical nature; 4) are regular and random
organizers of additive and multiplicative errors for
each elementary link (variable); 5) The error of the PSS
elementary links is calculated using the equations of
the theory of errors, taking into account the methods
of their interconnection in the circuit.
It should be noted that the accuracy of the assessment
of regular and random components of additive and
multiplicative errors largely depends on the degree of
detection of sources that cause the coefficients,
parameters and magnitudes in the PSS to deviate from
their true values.
1. Identify sources of IC error operating in
magnetomodulatory mode (to measure the difference
in alternating currents in tires). For this mode, its
sources of error are shown in Figure 2 of the PSS.
The following PhTE and parameters were used in the
above PSS: 1) PhTE, which converts electric current into
magnetic voltage (ampere-winding effect):
𝑈
𝜇𝑥𝐴
=
𝐾
𝐼
э𝑥𝐴
𝑈
𝜇𝑥𝐴
𝐼
э𝑥𝐴
, here is
𝐼
э𝑥𝐴
,
𝑈
𝜇𝑥𝐴
–respectively, the
electric current passing through the bus A and the
magnetic driving force (MDF) generated by it in the
corresponding contour of the magnetic circuit around
the bus (x) is included in the indices of magnitude and
parameters of electrical and magnetic circuits
corresponding to the difference between the
measured currents and (or) currents [A];
𝐾
𝐼
э𝑥𝐴
𝑈
𝜇𝑥𝐴
=
𝑤
𝑥𝐴
= 1
-
𝐴
the number of windings on the tire, [-]; 2)
internal PhTE, which correlates the reduced magnetic
voltage (
𝑈
𝜇𝑥𝐴𝛿
) in the air gap in a non-adjacent branch
of a three-contour magnetic circuit with the magnetic
flux (
𝑄
𝜇𝑥𝐴
) in it through the magnetic capacitance
parameter (
𝐶
𝜇𝑥𝐴𝛿
):
𝑄
𝜇𝑥𝐴
= 𝑈
𝜇𝑥𝐴𝛿
𝐶
𝜇𝑥𝐴𝛿
; 3) internal
PhTE:
𝑈
𝜇𝑥𝐴п
= 𝑄
𝜇𝑥𝐴
𝑊
𝜇𝑥𝐴п
; which correlates the
reduced magnetic voltage (
𝑈
𝜇𝑥𝐴п
) in the magnetic
conductor (steel) part of the non-adjacent branch of
the magnetic chain with the magnetic flux (
𝑄
𝜇𝑥𝐴
) in it
through the magnetic hardness parameter (
𝑊
𝜇𝑥𝐴п
); 4)
internal PhTE:
𝑈
𝜇𝑥𝐴𝐵
= 𝑄
𝜇𝑥𝐴𝐵
𝑊
𝜇𝑥𝐴𝐵
, which correlates
the reduced magnetic voltage (
𝑈
𝜇𝑥𝐴𝐵
) with the
magnetic flux (
𝑄
𝜇𝑥𝐴𝐵
) in the magnetic conductor
(steel) part of the adjacent branch of the magnetic
chain through the magnetic hardness parameter
(
𝑊
𝜇𝑥𝐴𝐵
); 5) PhTE (ampere-winding effect), which
converts the electric current
(𝐼
эм
)in the modulation
Volume 02 Issue 06-2022
63
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
circuit to magnetic voltage
𝑈
𝜇м
= 𝐾
𝐼
эм
𝑈
𝜇м
𝐼
эм
, where
𝐾
𝐼
эм
𝑈
𝜇м
= 𝑤
м
is the number of windings in the
modulation circuit, [- ];
Volume 02 Issue 06-2022
64
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
Figure 2. PSS scheme of EMC, which measures the
symmetry of three-phase currents, taking into account
all sources of error internal PhTE, which interconnects
the MYuK (
𝑈
𝜇м
)generated by the
𝐼
эм
current in the
modulation magnetic circuit by the magnetic flux (
𝑄
𝜇м
)
in it through the magnetic capacitance parameter
(
𝐶
𝜇м
),
𝑄
𝜇м
= 𝑈
𝜇м
𝐶
𝜇м
; where
𝐶
𝜇м
= 𝜇𝜇
0
𝑆
𝜇
𝑙
𝜇
, [𝐻]
; 6)
magnetomodulation
effect:
𝑄
𝜇𝐴𝐵∑
=
𝐾
𝑄
𝜇м
𝑄
𝜇м
𝑈
𝜇𝑥𝐴𝐵
𝑄
𝜇м
, where is
𝐾
𝑄
𝜇м
𝑄
𝜇м
=
1
𝑙
𝜇м
∙
𝑑(𝜇𝜇
0
)
𝑑𝐵
м
,
[
𝐻
𝑊𝑏
]
, and here
𝑙
𝜇м
,
𝐵
м
– the average length of the
magnetic flux path along the modulation magnetic
circuit and the magnetic induction in it, respectively,
[𝑚]
;
[𝑇]
; 7) magnetic flux (
𝑄
𝜇𝐴𝐵∑
) interacts with
differential
operation
that
(
𝐼
𝜇𝐴𝐵∑
):
𝐼
𝜇𝐴𝐵∑
=
𝑑
𝑑𝑡
𝑄
𝜇𝐴𝐵∑
, [𝑉];
8) electromagnetic induction ФТЭ:
𝑈
э𝐴𝐵
= 𝐾
𝐼
𝜇𝐴𝐵∑
𝑈
э𝐴𝐵
𝐼
𝜇𝐴𝐵∑
, where is
𝐾
𝐼
𝜇𝐴𝐵
𝑈
э𝐴𝐵
= 𝑤
ўл
–
the inter-chain PhTE coefficient that converts the
magnetic current (
𝐼
𝜇𝐴𝐵∑
) into an electrical voltage - the
number of windings of the output coil,
[−]
.
It should be noted that the tires and the modulation
coil heat up as a result of the passage of appropriate
currents. As a result, the active resistance of the
modulation coil cable increases. However, since this
coil is supplied from a current source, a change in the
electrical resistance of the wire under the influence of
temperature does not lead to a change in the source
current. The current in the output coil is also close to
zero because the corresponding element (load) of the
measuring instrument or control system connected to
the output coil has a large input resistance. Therefore,
the change in resistance of these wires under the
influence of temperature of the IC in the PSS was not
taken into account [10].
Although the PSS IC structure shown in Figure 1 is
structured taking into account all sources of errors
affecting each elementary link in the structure
diagram, the process of calculating the IO error based
on it poses some difficulties. This is because for one
column of the PSS (for example, to derive the equation
of dependence of the measured current difference on
the output voltage generated in the measuring strip on
the rod between busbars A and B, taking into account
all sources of error), the effect of magnetic chain sizes
on the other column must be taken into account.
Therefore, in order to simplify the calculations a bit,
using the equations generated in the study of static
and dynamic characteristics of IC, we replace the part
of the PSS in Figure 2 with a dashed line in each column
with a single elemental link and examine each column
separately (Figure 3). . In this case, for each segment of
the PSS separated by dashed lines, for example, for the
segment in column 1, we can write the following
equation:
𝑄
𝜇𝐴𝐵Ʃ
= 𝑈
𝜇𝐴𝐵
𝐶
𝜇𝐴𝐵Ʃ
=
𝑈
𝜇𝐴𝐵
𝑊
𝜇1
+ 3𝑊
𝜇2
,
(1)
here is
𝐶
𝜇𝐴𝐵Ʃ
= 1 (𝑊
𝜇1
+ 3𝑊
𝜇2
)
⁄
– the resulting
magnetic capacity of the chain in the path of the
magnetic flux generated by the currents in the
adjacent tires in the rod between them, [H];
𝑊
𝜇1
=
𝑊
𝜇𝛿
+ 𝑊
𝜇𝐴п
;
𝑊
𝜇𝛿
;
𝑊
𝜇𝐴п
– the resultant, non-adjacent
branch of the three-contour magnetic chain,
respectively,
𝛿
air gap and the magnetic stiffness of the
steel part (magnetic resistance by classical analogy),
[
1 H
⁄
];
𝑊
𝜇2
= 𝑊
𝜇𝐴𝐵
= 𝑊
𝜇𝐵𝐶
= 𝑊
𝜇𝐶𝐴
- the magnetic
stiffness of the adjacent branches of a three-contour
magnetic chain, [
1 H
⁄
];
𝑈
𝜇𝐴𝐵
= 𝐾
𝐼
э
𝑈
𝜇
(𝐼
э𝐴
− 𝐼
э𝐵
)
- A and
B MYuK formed by the difference in currents in the
busbars, [
𝐴
].
For each elementary link (transducer) in the PSS, we
write the equation of static characteristic, taking into
account the sources of error in it as follows:
𝑈
э𝐴𝐵
= (𝐾
40
+ ∆𝐾
4
± 𝜎𝐾
4
)𝐼
𝜇𝐴𝐵ƩƩ
,
(2)
It is
𝐾
4
= 𝐾
𝐼
𝜇
𝑈
э
= 𝑤
ўл
, [
−
] – coefficient of inter-chain
physical-technical effect (elemental link) that converts
magnetic current
𝐼
𝜇
to electric voltage;
𝐾
40
,
∆𝐾
4
,
±𝜎𝐾
4
-
𝐾
𝐼
𝜇
𝑈
э
the value of the coefficient in the ideal state
(without errors), respectively, its gains from
Volume 02 Issue 06-2022
65
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
systematic and random sources of error (in the
following elementary links, the corresponding
coefficient "0" in the index, the ideal value of a
parameter or quantity, preceded by “
∆
” and “
±𝜎
” –
regular and random components of the error,
respectively;
𝑤
ўл
– the number of wrappings.
Figure 3. A simplified parametric structure diagram of the PSS 1 column shown in Figure 2
𝐼
𝜇𝐴𝐵ƩƩ
= ∆𝐼
𝜇𝐴𝐵
±𝜎𝐼
𝜇𝐴𝐵
+ 𝑗(𝜔
0
+ ∆𝜔 ± 𝜎𝜔)𝑄
𝜇𝐴𝐵ƩƩ
,
(3)
𝑄
𝜇𝐴𝐵ƩƩ
= ∆𝑄
𝜇𝐴𝐵Ʃ
± 𝜎𝑄
𝜇𝐴𝐵Ʃ
+ 𝑈
𝜇𝐴𝐵Ʃ
𝐶
𝜇𝐴𝐵Ʃ
,
(4)
𝐶
𝜇𝐴𝐵Ʃ
= (𝐾
20
+ ∆𝐾
2
± 𝜎𝐾
2
)𝑄
𝜇мƩ
,
(5)
𝑄
𝜇мƩ
= ∆𝑄
𝜇м
± 𝜎𝑄
𝜇м
+ (𝐶
𝜇м0
+ ∆С
𝜇м
± 𝜎С
𝜇м
)𝑈
𝜇мƩ
,
(6)
𝑈
𝜇мƩ
= ∆𝑈
𝜇м
± 𝜎𝑈
𝜇м
+ (𝐾
30
+ ∆𝐾
3
± 𝜎𝐾
3
)𝐼
эмƩ
,
(7)
𝐼
эмƩ
= 𝐼
эм
+ ∆𝐼
эм
± 𝜎𝐼
эм
,
(8)
𝑈
𝜇𝐴𝐵Ʃ
= ∆𝑈
𝜇𝐴𝐵
± 𝜎𝑈
𝜇𝐴𝐵
+ (𝐾
10
+ ∆𝐾
1
± 𝜎𝐾
1
)𝐼
э𝐴𝐵
,
(9)
𝐼
э𝐴𝐵
= 𝐼
э𝐴
− 𝐼
э𝐵
.
(10)
On the basis of PSS, change the magnitude of the IC
output in the order of derivation of the equation of
dependence on its input size [9], equation (3) and
subsequent equations, respectively, and multiplication
of two or more multiplications by a measuring device
operating in magnetomodulation mode we obtain the
Volume 02 Issue 06-2022
66
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
following equation of the function formed by taking
into account the sources of errors in it::
𝑈
э𝐴𝐵.Ʃ(мм)
= ∆𝐼
𝜇𝐴𝐵
𝐾
40
± 𝜎𝐼
𝜇𝐴𝐵
𝐾
40
+ 𝑗∆𝑄
𝜇𝐴𝐵Ʃ
𝜔
0
𝐾
40
± 𝑗𝜎𝑄
𝜇𝐴𝐵Ʃ
𝜔
0
𝐾
40
+
+𝑗∆𝑈
𝜇𝐴𝐵
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝜔
0
𝐾
40
± 𝑗𝜎𝑈
𝜇𝐴𝐵
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝜔
0
𝐾
40
+
+𝑗∆𝐾
1
𝐼
э𝐴𝐵
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝜔
0
𝐾
40
± 𝑗𝜎𝐾
1
𝐼
э𝐴𝐵
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝜔
0
𝐾
40
+
+𝑗∆𝑄
𝜇м
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
± 𝑗𝜎𝑄
𝜇м
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+
+𝑗∆𝑈
𝜇м
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
± 𝑗𝜎𝑈
𝜇м
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+
+𝑗𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+ 𝑗∆𝐾
3
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
±
±𝑗𝜎𝐾
3
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+ 𝑗∆𝐼
эм
𝐾
30
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
±
±𝑗𝜎𝐼
эм
𝐾
30
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+ 𝑗∆С
𝜇м
𝐾
30
𝐼
эм
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
±
±𝑗𝜎С
𝜇м
𝐾
30
𝐼
эм
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+ 𝑗∆𝐾
2
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
±
±𝑗𝜎𝐾
2
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
𝐾
40
+ 𝑗∆𝜔𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝐾
40
±
±𝑗𝜎𝜔𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝐾
40
+ 𝑗∆𝐾
4
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
±
±𝑗𝜎𝐾
4
𝐾
30
𝐼
эм
𝐶
𝜇м0
𝐾
20
𝐾
10
𝐼
э𝐴𝐵
𝜔
0
(13)
For the ideal case, that is, the analytical equation for
the static characteristics of the device under study
without a source of error is written as follows on the
basis of PSS:
𝑈
э𝐴𝐵.0(мм)
= 𝐾
10
𝐾
20
𝐾
30
𝐾
40
𝑗𝜔
0
𝐶
𝜇м0
𝐼
эм
𝐼
э𝐴𝐵
(14)
The accuracy class of a measuring transducer is mainly
determined by its reported error. Therefore, we
conduct an analysis of the IC error under investigation
for its reported error. The given error is found on the
basis of the following formula [11]:
𝛾
кел.𝑈
э𝐴𝐵(мм)
=
𝑈
э𝐴𝐵.Ʃ(мм)
− 𝑈
э𝐴𝐵.0(мм)
𝑈
э𝐴𝐵.0(мм)
∙ 100 % =
= [
∆𝐼
𝜇𝐴𝐵
𝐼
𝜇𝐴𝐵
±
𝜎𝐼
𝜇𝐴𝐵
𝐼
𝜇𝐴𝐵
+
∆𝑄
𝜇𝐴𝐵Ʃ
𝑄
𝜇𝐴𝐵Ʃ
±
𝜎𝑄
𝜇𝐴𝐵Ʃ
𝑄
𝜇𝐴𝐵Ʃ
+
∆𝑈
𝜇𝐴𝐵
𝑈
𝜇𝐴𝐵
±
𝜎𝑈
𝜇𝐴𝐵
𝑈
𝜇𝐴𝐵
+
∆𝐾
1
𝐾
1
±
𝜎𝐾
1
𝐾
1
+
+
∆𝑄
𝜇м
𝑄
𝜇м
±
𝜎𝑄
𝜇м
𝑄
𝜇м
+
∆𝑈
𝜇м
𝑈
𝜇м
±
𝜎𝑈
𝜇м
𝑈
𝜇м
+
∆𝐾
3
𝐾
3
±
𝜎𝐾
3
𝐾
3
+
∆𝐼
эм
𝐼
эм
±
𝜎𝐼
эм
𝐼
эм
+
∆𝐶
𝜇м
𝐶
𝜇м
±
±
𝜎𝐶
𝜇м
𝐶
𝜇м
+
∆𝐾
2
𝐾
2
±
𝜎𝐾
2
𝐾
2
+
∆𝜔
𝜔
±
𝜎𝜔
𝜔
+
∆𝐾
4
𝐾
4
±
𝜎𝐾
4
𝐾
4
] ∙ 100 % =
= [𝛾
кел.𝑈
э𝐴𝐵(мм)
мун.
(∆𝑈
ҳ
, ∆𝑈
𝜇
, ∆𝐼
э
) + 𝛾
кел.𝑈
э𝐴𝐵(мм)
тас.
(±𝜎𝑈
ҳ
, ±𝜎𝑈
𝜇
, ±𝜎𝐼
э
)] ∙ 100 %,
(16)
Where
is
𝛾
кел.𝑈
э𝐴𝐵(мм)
мун.
(∆𝑈
и
, ∆𝑈
𝜇
, ∆𝑈
э
)
and
𝛾
кел.𝑈
э𝐴𝐵(мм)
тас.
(±𝜎𝑈
и
, ±𝜎𝑈
𝜇
, ±𝜎𝑈
э
)
- respectively regular
and random components of the given error of the IC
operating in the mode of magnetomodulation; (
∆𝑈
𝜇
ва
±𝜎𝑈
𝜇
), (
∆𝑈
ҳ
ва
±𝜎𝑈
ҳ
) and (
∆𝐼
э
ва
±𝜎𝐼
э
) – sources of
additive and multiplicative errors in the studied IC due
to deviations from the normal values of the source
current parameters that provide the external
alternating and constant magnetic fields, temperature
and modulation chain, respectively.
Volume 02 Issue 06-2022
67
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
59-67
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
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978-1-7281-2564-
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