International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
June 2025, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
Impedance matching and power recovery in response to coil misalignment in wireless power transmission Lunde Ardhenta1.
Ichijo Hodaka2.
Kazuya Yamaguchi3.
Takuya Hirata2 Department of Materials and Informatics.
Interdisciplinary Graduate School of Agriculture and Engineering.
University of Miyazaki.
Miyazaki.
Japan Department of Electrical and Electronic Engineering.
University of Miyazaki.
Miyazaki.
Japan Department of Control Engineering.
National Institute of Technology.
Nara College.
Yamatokoriyama.
Japan
Article Info
ABSTRACT
Article history:
The improper alignment of the coils between the transmitter and receiver has a significant impact on wireless power transfer.
If designers carefully calculate the parameters of inductance, capacitance, coupling coefficient, and working frequency and precisely implement these parameters into actual components, the system can optimize power transfer.
However, it is evident that such a precise realization is often unachievable.
This paper proposes a symbolic condition to maintain significant power despite the misalignment of transmitter and receiver coils.
These symbolic conditions constrain parameters by simplifying some variables.
This matching condition develops in the inequality of coupling coefficient, working frequency and quality factor, which are a crucial reference for maintaining power transfer.
This condition is considered an additional one to the well-known impedance matching condition.
Received Jul 17, 2024 Revised Dec 16, 2024 Accepted Jan 16, 2025 Keywords:
Coils misalignment Impedance matching Maximum power transfer Symbolic optimization Wireless power transfer This is an open access article under the CC BY-SA license.
Corresponding Author:
Ichijo Hodaka Department of Electrical and Electronic Engineering.
University of Miyazaki 1-1.
Gakuen-Kibanadai-Nishi.
Miyazaki, 889-2192.
Japan Email: hijhodaka@cc.
miyazaki-u.
INTRODUCTION
The electrical system in every electric device becomes quite complex and has several possible changes in properties when operational conditions change as technology advances.
Wireless power transfer (WPT) is innovative and unlike conventional because it delivers power wirelessly from a power supply as a transmitter side to the load as a receiver side.
Using the electromagnetic induction principle, the WPT system can eliminate traditional cable connections, providing electrical equipment with excellent safety and flexibility while resisting dynamic environments .
, .
This technology is utilized in various practical applications in everyday life, such as electric vehicles .
Ae.
, biomedical devices .
, .
, digital household appliances .
, .
, and industrial electricity .
In its application, the phenomenon of induction in the form of compensation plays a vital role in providing power.
Therefore, based on the pairing configuration of coils and capacitors in each transmitter and receiver side, these systems can be categorized into four types: both sides in series (S-S), series in transmitter-parallel in the receiver (S-P), parallel in transmitter-series in the receiver (P-S), and both sides in parallel (P-P) .
Ae.
Some more complicated developmental compensation topologies can be formed from these four topologies.
The most important thing to consider is the selection of appropriate compensation for a particular application determined by the transfer properties of the WPT system.
Therefore, choosing compensation topology is crucial to evaluate by comparing the influence of different transmission characteristics on the Journal homepage: http://ijece.
Int J Elec & Comp Eng
ISSN: 2088-8708
power-transferred.
Shevchenko et al.
has not presented a comprehensive analytical review of the power transfer of each topology, but they have provided suggestions on the values of inductors and capacitors for some topologies.
Dai et al.
discusses a topology selection method based on robustness, voltage gain, and efficiency, as well as optimizing the parameters.
However, they do not explain how the power is transferred in each topology.
Sagar et al.
analyzed the mutual inductance, load, and working frequency in S-S and S-P voltage gain topologies only.
Movagharnejad and Mertens .
stated that S-S and S-P topologies are the two most economical configurations coupled with choosing the source and capacitor frequencies appropriately so that the load and coupling coefficients can vary though deliver maximum efficiency.
Detka and Gyrecki .
presents the general characteristics of WPT, especially the energy transmission mechanism, discusses its advantages and disadvantages, and also discusses its application in certain industrial fields.
Mahesh et al.
describes several topologies in general without explaining how to choose the correct topology for an application.
Rehman et al.
investigated two basic topologies.
S-S and S-P, for unsymmetrical and symmetrical coils and calculated system efficiency.
Using fundamental topology.
Wang et al.
proposed a method to evaluate power transfer capability and analyze bifurcation Venkatesan et al.
investigated the basic topology and its development, especially the transmitter side and output characteristics.
From this valuable research, topology selection is one of the most challenging aspects of building a WPT system.
In order to make a preference of the topology based on the unknown maximum power distribution, we have to compare each topology and its characteristics in terms of power quantity.
In actual conditions, it may not be easy to achieve the maximum power, particularly if the coils for power transfer are not properly aligned.
This paper proposes a symbolic impedance matching method to adapt to dynamically moving coils for basic topologies.
The proposed method is demonstrated by two parameters that greatly influence the reaching of maximum power transfer: the power supply frequency and a coupling coefficient.
The operating frequency can be adjusted more quickly from a technical perspective, and the coupling coefficient represents the coil misalignment in the power transferred of the WPT system.
This investigation is intended to provide a comprehensive and straightforward overview of power transfer, given a general comparison of simulation results.
This approach is also applied to some topologies in order to deliver maximum power to the load, which is the main objective of the WPT system.
METHOD
This research employs a fundamental WPT circuit combined with impedance matching.
Impedance matching plays a key role in maximizing power transfer efficiency.
It ensures that the input impedance, including the voltage source, aligns with the output impedance, representing the load.
Significant power losses can occur without proper impedance matching, decreasing system performance.
Wireless power transfer Paired inductors act as the core of the system WPT and are fundamental to wireless power systems.
Ampyre's law states that the current flow through an inductor generates a magnetic field.
It indicates that a stable current induces a stable magnetic field, and a dynamic current induces a dynamic magnetic field.
the same time, the inductor pair will produce a current when varying magnetic flux penetrates the inductor.
The basic electrical circuit used in this model comprises two closed loops, as shown in Figure 1.
A particular coil has self-inductance ya1 and ya2 combined with mutual inductance ycA, where this mutual inductance is an inductive coupling that takes into interpretation the character of the coil and the distance between them.
ycIyc is the resistance within a power source, and ycIya is the load resistance used in the system.
ya1 and ya2 refers to capacitors combined with inductors in series or parallel to create resonance.
The power source, ya, is an alternating current (AC) supply.
The following equation represents the voltages across the inductor and capacitor, respectively.
ycOya1 = ycOya1 yaya1 ycOycAyaya2 ycOya2 = ycOycAyaya1 ycOya2 yaya2 yaya1 ycOya1 = ycOya2 yaya2 ycOya2 = ycOya2 and ycA is defined as Impedance matching and power recovery in response to coil misalignment A (Lunde Ardhent.
A ISSN: 2088-8708 ycA = ycoya1 ya2 In general, the WPT circuit consists of resistors, inductors, capacitors, and voltage sources, which have a simple configuration whose behavior is represented by Kirchhoff's Law .
oltage and curren.
and Ohm's Law.
Based on these laws, the equation for each configuration is derived in the following.
Series-series (S-S) A series-series topology uses two capacitors, which are in series with each coil, as illustrated in Figure 1.
This topology is the simplest configuration in the basic WPT topology.
The current through the transmitter circuit has the same value for each component .
aycIyc = yaya1 = yaya1 ), and the receiver has the same condition .
aycIya = yaya2 = yaya2 ).
yaycIyc represents the transmitter loop current, which started from the voltage source through the capacitor and the coil, while yaycIya has the opposite direction from the transmitter side.
it begins from the load to the coil in a counterclockwise direction.
Based on these laws, the equation for each phenomenon of series-series topology is derived as.
ya ycyuiya1 yaya1 ycyuiycAyaya2 ycyuiya1 ya1 0 = ycIya yaycIya ya ycyuiya2 yaya2 ycyuiycAyaya1 ycyuiya2 ya2 ya = ycIyc yaycIyc By separating the equation based on voltage and current, the impedance is obtained as following equation .
Oe ycs= yc ycyuiya1 ycIyc yuiya1 ycycAyui ycycAyui Oe yc ycIya ycyuiya2 yuiya2 Series-parallel (S-P) Figure 1.
shows that the coil in the transmitter is paired with a capacitor as a previous topology, whereas the receiving coil is paired with a capacitor in parallel.
This configuration is called a series-parallel On the transmitter side, the current for each component is the same, but on the receiver side, the current is different for each element.
The following is the circuit equations.
ya ycyuiya1 yaya1 ycyuiycAyaya2 ycyuiya1 ya1 0 = ycIya yaycIya ycyuiya2 yaya2 ycyuiycAyaya1 yaycIya = yaya2 yaya2 ya = ycIyc yaycIyc The impedance Z of series-parallel is, ycyui3 ya2 ya1 ya2 Oe ycycA2 yui3 ya2 Oe ycyuiya1 ycyuiya2 ya2 ycn Oe ycIyc yui 2 ya2 ya2 Oe 1 ya1 .
ui 2 ya2 ya2 Oe .
ui 2 ya2 ya2 Oe .
ycs= ycycAyui Oe 2 yui ya2 ya2 Oe 1 ycycAyui yui 2 ya2 ya2 Oe 1 ycyuiya2 ycIya Oe 2 yui ya2 ya2 Oe .
Oe Parallel-series (P-S) In a parallel-series circuit, illustrated in Figure 1.
, the circuit configuration is opposite to the previous circuit.
The current generated from the source will be directly split into the capacitor and inductor.
The circuit equations are:
ya = ycIyc yaycIyc ycyuiya1 yaya1 ycyuiycAyaya2 yaycIyc = yaya1 yaya1 0 = ycIya yaycIya ya ycyuiya2 yaya2 ycyuiycAyaya1 ycyuiya2 ya2 The impedance Z of parallel-series is.
Int J Elec & Comp Eng.
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Int J Elec & Comp Eng
yui 2 ya1 ya1 Oe 1
ycs= ycycAyui
Oe 2
yui ya1 ya1 Oe 1
ycIyc Oe
ISSN: 2088-8708
ycycAyui yui 2 ya1 ya1 Oe 1 ycyui3 ya1 ya1 ya2 Oe ycycA2 yui3 ya1 Oe ycyuiya2 ycyuiya1 ya1 yc Oe ycIya yui ya1 ya1 Oe 1 ya2 .
ui ya1 ya1 Oe .
ui ya1 ya1 Oe .
Oe Parallel-parallel (P-P) The last basic topology that will be observed is parallel-parallel, where the current in each component will be different, but the voltage will be the same in each component.
The equations below are derived from the circuit diagram shown in Figure 1.
ya = ycIyc yaycIyc ycyuiya1 yaya1 ycyuiycAyaya2 yaycIyc = yaya1 yaya1 0 = ycIya yaycIya ycyuiya2 yaya2 ycyuiycAyaya1 yaycIya = yaya2 yaya2 The impedance Z of parallel-parallel is, ycyuiya1 ycycA2 yui3 ya2 ycyui3 ya2 ya1 ya2 ycIyc ya ycs= ycycAyui Oe yaA ycycAyui ya ycyui3 ya1 ya1 ya2 Oe ycyuiya2 Oe ycycA 2 yui3 ya1 ycIya ] yaA ya = yui4 ya1 ya2 ya1 ya2 Oe yui2 ya1 ya1 Oe yui2 ya2 ya2 Oe ycA2 yui4 ya1 ya2 1 yaA = Oeyui4 ya1 ya2 ya1 ya2 yui2 ya1 ya1 yui2 ya2 ya2 ycA2 yui4 ya1 ya2 Oe 1 .
Figure 1.
WPT system in .
series-series topology, .
series-parallel topology, .
parallel-series topology, and .
parallel-parallel topology Impedance matching using symbolic condition Research in WPT primarily focuses on achieving maximum power transfer.
One requirement for realizing maximum power transfer is considering systemAos impedance as a maximum power transfer theorem.
Therefore, the impedance between source and load is determined by the impedance matching method in various WPT scenarios.
Typically, the impedance matching process in a WPT system covers two parts, as Impedance matching and power recovery in response to coil misalignment A (Lunde Ardhent.
A ISSN: 2088-8708 shown in Figure 2.
The first part is the power source along with its impedance, while the second is the load's impedance as illustrated in equivalent circuit.
Maximum power transfer is obtained when the two parts have the same value or are perfectly matched.
The ycs1 is stated as impedance of the input side .
oltage sourc.
and the impedance of the load is ycs2 , it delivers the maximum power to the load if ycs1 = i ycs2 .
Figure 2.
Impedance setting for every topology The ycs2 impedance is an impedance equation for each topology as in Figure 2, where the ycs1 value must be the same as the conjugate value of ycs2 and ycs1 .
he source impedanc.
is assumed to be a purely resistive load.
In order to simplify the calculations and consider the cases of actual conditions where parameters are not always given and kept constant, the following equation is used, ycE1 = ycIyc ya ycIya Ooya1, ycE2 = ya2 Ooya , yui1 = Ooya ya , yui2 = Ooya ya The following equations show that the source and load impedance equality are separated into the resistive and reactive components.
Table 1 shows two equations for each topology in impedance matching conditions where the value equals 0 and the number of parameters is reduced.
Table 1.
Impedance matching condition for each topology Topology S-S S-P
P-S
P-P
Impedance matching condition 0 = yco 2 yui4 ycE1 ycE2 Oe yui4 ycE1 ycE2 yui2 ycE1 ycE2 yui12 yui2 ycE1 ycE2 yui22 Oe ycE1 ycE2 yui12 yui22 Oe yui2 yui1 yui2
0 = OeycE2 yui2 yui1 ycE1 yui2 yui2 ycE2 yui1 yui22 Oe ycE1 yui12 yui2
0 = Oeyco 2 yui2 ycE1 ycE2 yui2 yui2 ycE1 ycE2 yui2 Oe ycE1 ycE2 yui12 yui2 yui2 (Oeyui1 ) yui1 yui22
0 = Oeyco 2 yui4 ycE1 yui4 ycE1 Oe yui2 ycE1 yui12 Oe yui2 ycE1 yui22 yui2 ycE2 yui1 yui2 ycE1 yui12 yui22
0 = Oeyco 2 yui2 ycE1 ycE2 yui1 yui2 ycE1 ycE2 yui1 Oe ycE1 ycE2 yui1 yui22 Oe yui2 yui2 yui12 yui2
0 = yco 2 yui4 ycE2 Oe yui4 ycE2 yui2 ycE2 yui12 yui2 ycE2 yui22 Oe yui2 ycE1 yui1 yui2 Oe ycE2 yui12 yui22
0 = Oeyco 2 yui2 ycE1 ycE2 yui1 yui2 Oe yco 2 yui4 yui2 ycE1 ycE2 yui1 yui2 yui4 Oe yui2 yui12 Oe yui2 yui22 yui12 yui22
0 = yco 2 yuiycE1 yui1 Oe yco 2 yui2 ycE2 yui2 Oe yui2 ycE1 yui1 yui2 ycE2 yui2 ycE1 yui1 yui22 Oe ycE2 yui12 yui2
RESULTS AND DISCUSSION
The wireless power transfer system comprises resistors, inductors, capacitors, and voltage sources.
Table 2 shows the notation used in the circuit.
In designing a WPT, knowing the values of these parameters is required to fulfill maximum power.
This paper aims to help provide considerations for determining the component value based on the impedance matching method.
Based on simplified equation in the previous section, we can simplify the equation by substituting several variables, such as ya1 , ya2 , ya1 , and ya2 .
Many other papers state that the values of these parameters are determined to be the same to make calculations more straightforward.
Still, selecting the component values that are precisely the same would be tough.
This paper proposes the specific conditions for the impedance matching condition, which are ycE1 = ycE2 = ycE0 and yui1 = yui2 = yui0 .
This equality is arranged to simplify the equation by minimizing the number of variables addressed in the previous section, as shown in Table 3.
When considering the equations as in Table 3 alongside the inequality 0 < yco 2 < 1, which must always physically hold true for the coupling coefficient, it becomes mathematically evident that yui and ycE0 must satisfy the following inequalities.
It is understood that in order to maximize power, these parameters must be chosen to fulfill the following inequalities.
Int J Elec & Comp Eng.
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No.
June 2025: 2556-2566
Int J Elec & Comp Eng
ISSN: 2088-8708
Table 2.
Notation Symbol ya ycIyc , ycIya ya1 , ya2 ya1, ya2 ycOO yaO yce Representation Voltage source Resistor Capacitor Inductor Voltage of component* Current of component* Frequency of power supply Table 3.
Proposed equation and selecting condition for four basic topologies Topology S-S Proposed equation 0 = yco 2 yui4 ycE02 Oe yui4 ycE02 2yui2 ycE02 yui02 Oe ycE02 yui04 Oe yui2 yui02
Selecting condition O4 ycE02 Oe 2O2 ycE02 O20 ycE02 O40 O2 O20
0<yco = O4 ycE02
yui> O0
, ycE02 > O2
2O2 OeO20
yui2 yui02 Oe yui4
ycE0 = yui04
cE Oe
Oe O20 ) 0 < yco2 = O ycE0
S-P
0 = Oeyco 2 yui4 ycE0 yui4 ycE0 Oe yui2 ycE0 yui02 ycE0 yui04
0 = yco 2 yui2 ycE02 Oe yui2 ycE02 ycE02 yui02 Oe yui02 yui2
P-S
0 = yco 2 yui4 ycE0 Oe yui4 ycE0 yui2 ycE0 yui02 Oe ycE0 yui04
0 = yco 2 yui2 ycE02 Oe yui2 ycE02 ycE02 yui02 Oe yui02 yui2
P-P
0 = Oeyco 2 yui2 ycE02 yui02 yui2 ycE02 yui02 Oe 2yui2 yui02 yui04 Oe yco 2 yui4 yui4
Oo2
O2 O20 Oe O4
O40
cE Oe Oe O20 ) 0 < yco2 = O ycE0 ycE02 = 0 < yco2 = O2 ycE02 O20 Oe 2O2 O20 O40 O4 O2 ycE02 O20 O4 Oo2 The values of each component using the impedance matching conditions in Table 1 and the proposed ones in Table 3 are shown in Table 4.
The maximum average power calculation, ycEycaycycoycaycu = .
8ycIyc , is utilized to validate the result obtained from the proposed method.
Here, the resistance in power supply .
cIyc ) is 1 , and using 10 for the load resistance .
cIya ).
By selecting the input voltage magnitude ya = 2Oo2V, the maximum possible power is normalized to 1 W.
Figure 3 shows the optimum WPT power for components obtained according to Table 3, demonstrated in the Aumagic regimeAy .
For ease of investigation regarding whether the power transfer matches the systemAos ideal power, measurement intervals above 80% are colored red.
Table 4.
System parameter Topology S-S S-P
P-S
P-P
Impedance matching Inductance (AAH) Capacitance (AAF) ya1 =244.
ya1 =0.
ya2 =476.
ya2 =0.
ya1 =267.
ya1 =49.
ya2 =26.
ya2 =488.
ya1 =0.
ya1 =488.
ya2 =238.
ya2 =0.
ya1 =53.
ya1 =488.
ya2 =48.
ya2 =531.
Proposed impedance matching Inductance (AAH) Capacitance (AAF) ya1 =54.
ya1 =1.
ya2 =544.
ya2 =0.
ya1 =3.
ya1 =15.
ya2 =38.
ya2 =1.
ya1 =3.
ya1 =15.
ya2 =38.
ya2 =1.
ya1 =2.
ya1 =20.
ya2 =20.
ya2 =2.
The maximum power of 1 W can be achieved by using impedance-matching method calculations.
the series-series topology in Figure 3.
the maximum power received is at a frequency of 14.
75 kHz, while in the series-parallel topology in Figure 3.
and parallel-series in Figure 3.
, it is at 1.
39 and 14.
75 kHz In Figure 3.
, the parallel-parallel topology reaches its maximum power value at 0.
999 kHz.
From these results, the first method is not able to deliver maximum power at frequencies beyond that and cannot satisfy maximum power either because the coupling coefficient shifts from the critical point of maximum power.
In this condition, power cannot be maintained optimally even though the frequency is adjusted adaptively.
Impedance matching and power recovery in response to coil misalignment A (Lunde Ardhent.
A ISSN: 2088-8708 In contrast to the previous method, the maximum power value provided by the second method is shown in Figure 3.
By using suitable components obtained from the proposed method based on impedance matching, a maximum power value of 1 W can be achieved.
In Figure 3, especially the result of proposed impedance matching with the specific conditions, there are differences compared to the previous method, which are the uniformity of the maximum power value that can be performed.
In the S-S configuration, it can be seen that the change in frequency from 12 to 30 kHz has a uniform maximum power value, as in Figure 3.
The S-P and P-S topologies have the same output power characteristics and work in the frequency range 14 to 21 kHz, as in Figure 3.
In Figure 3.
, the P-P has maximum power at a frequency of 14 to 30 kHz.
Figure 3.
Average power of WPT using impedance matching for .
S-S, .
S-P, .
P-S, and .
P-P.
Average power of WPT using proposed impedance matching with the specific conditions for .
S-S, .
S-P, .
P-S, and .
P-P Int J Elec & Comp Eng.
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ISSN: 2088-8708
This scenario illustrates that if a coil misalignment occurs, the first matching condition cannot accept a significant change in the value of yco because the estimate does not account for yco.
Therefore, it cannot compensate for the misalignment.
Meanwhile, the proposed method can compensate for shifts in yco values by adjusting the frequency adaptively.
In terms of compensating shifts in yco, the P-P has the best response because it can tolerate changes in the value of k that are more significant than other topologies.
The series topology is the second-best alternative in dealing with the same problem.
By selecting the frequency accurately, maximum power can still be executed even if the transmitter and receiver are misaligned.
The next issue appears when determining the component value to be used because the calculated value differs from the actual value.
The previous calculation provides generated maximum power options for the S-S and P-P topologies better than the other topologies.
Therefore, these two topologies are suitable for investigating further properties by adding random values to the variables ya1 , ya2 , ya1 , and ya2 as a component tolerance and the tolerances are defined under three conditions.
A 1%.
A 5%, and A 10%.
Figure 4 presents the responses of these two topologies with the values of yce and yco chosen respectively, yce = 22 kHz and yco = 0.
35 because they produce more than 80% power for either S-S or P-P.
Figure 4.
depicts a tolerance of 1%.
the working area of the P-P and S-S topologies is 95% and 85% of the maximum power, respectively.
With a tolerance of 5%, the maximum power of the P-P topology achieves 70%, and the S-S topology reaches 50% of the maximum power, as shown in Figure 4.
Using a tolerance of 10% for both topologies is the last condition to investigate the properties of these two the output power produced by the P-P topology is greater, i.
, with a working area of 40% and the S-S topologyAos 20% of the maximum power value as depicted in Figure 4.
Therefore, the comparison results indicate that the proposed method generates higher output power than the basic method.
Additionally, the P-P topology offers the advantage that modifying the frequency simplifies reaching the maximum power transfer.
Figure 4.
Comparison of the average power due to component tolerances .
1%, .
5%, and .
10% This paper demonstrates several crucial points: the optimal frequency and distance of wireless power systems can be developed by considering components based on symbolic conditions.
By incorporating these symbolic conditions, it becomes possible to fine-tune the system for various scenarios, ensuring maximum power transmission under different operational settings.
Furthermore, using this approach, which adjusts the power transmission frequency, the distance settings have greater tolerance, which allows them to adapt effectively to dynamic environmental changes, such as inconsistent obstacles or interference.
Impedance matching and power recovery in response to coil misalignment A (Lunde Ardhent.
A ISSN: 2088-8708
CONCLUSION
By using fundamental topologies, an analytical review of WPT is presented throughout this paper.
Optimization of transferred power with an impedance matching technique has been discussed.
Beyond conventional impedance matching approaches, we have proposed a special condition besides impedance matching, where the maximum power can be recovered by tuning the working frequency for a variable coupling coefficient.
This tuning is based on special conditions derived from the inequalities involving the coupling coefficient, frequency, and quality factor.
This means that we can maximize the output power even under uncertain positions and orientations of transmitter and receiver coils.
This adaptability is crucial for real-world applications were, precise alignment of coils cannot always be guaranteed.
FUNDING INFORMATION
This research was conducted without financial support from external sources.
AUTHOR CONTRIBUTIONS STATEMENT
This journal uses the Contributor Roles Taxonomy (CRediT) to recognize individual author contributions, reduce authorship disputes, and facilitate collaboration.
Name of Author Lunde Ardhenta Ichijo Hodaka Kazuya Yamaguchi Takuya Hirata C : Conceptualization M : Methodology So : Software Va : Validation Fo : Formal analysis ue ue ue ue ue ue ue ue ue ue ue ue I : Investigation R : Resources D : Data Curation O : Writing - Original Draft E : Writing - Review & Editing ue ue ue ue ue ue ue ue ue ue ue ue ue Vi : Visualization Su : Supervision P : Project administration Fu : Funding acquisition CONFLICT OF INTEREST STATEMENT Authors state no conflict of interest.
DATA AVAILABILITY
Data availability is not applicable to this paper as no new data were created or analyzed in this study.
REFERENCES