CN107766669A - A kind of Wireless charging coil self-induction and the unit for electrical property parameters computational methods of mutual inductance - Google Patents
A kind of Wireless charging coil self-induction and the unit for electrical property parameters computational methods of mutual inductance Download PDFInfo
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Abstract
The present invention proposes a kind of Wireless charging coil self-induction and the unit for electrical property parameters computational methods of mutual inductance, belongs to new-energy automobile field and electromagnetism field.This method obtains self-induction function, self-induction correction factor, mutual inductance function and the mutual inductance correction factor zoom table of different shape coil first；To any coil, the coil geometric parameter is obtained, including：Coil dimension, wire radius, coil turn, fore-and-aft distance and lateral shift between two coils, calculate dimensionless group；According to coil shape, using geometric parameter and dimensionless group, the self-induction function of the coil, self-induction correction factor, mutual inductance function and mutual inductance correction factor are obtained by zoom table；Formula is finally utilized, the unit for electrical property parameters of the coil is calculated, including：Electrodynamic capacity, mutual inductance and Mutual Inductance Coupling coefficient.The present invention utilizes coil geometric parameter, is calculated by tabling look-up with formula, you can obtains self-induction of loop coefficient and the accurate result of calculation of mutual inductance, method is easy, there is very high promotional value.
Description
Technical field
The invention belongs to new-energy automobile field and electromagnetism field, more particularly to a kind of Wireless charging coil self-induction and mutually
The unit for electrical property parameters computational methods of sense.
Background technology
With the continuous lifting of battery energy density, the continual mileage of electric automobile may no longer turn into problem.But how
Electric energy is transferred on car from power network, the bottleneck that electric automobile is promoted can be turned into.Electric automobile power battery charging presents following
A few class solutions：Wired charging, change electricity and wireless energy transfer (wireless charging).
Wireless energy transfer refers to not by wire, using electromagnetic induction principle or other associated AC induction technologies,
Realize the electric energy transmission of certain distance.Ease of use, charging security, car possessed by wireless charging-net electric energy transmission spirit
The particular advantages such as active, unmanned electric vehicle applicability so that wireless charging technology has more wide development space.
At present, automobile-used wireless energy transfer is mainly using magnet coupled resonant type wireless electric energy transmission (Magnetically-
Coupled Resonant Wireless Power Transfer) mode, this technology is existed by the Massachusetts Institute of Technology
It is proposed within 2007.For this technology, study hotspot main at present and technological difficulties concentrate on following three aspects：Wirelessly
The design of charge coil, the design of wireless charging circuit structure, power converter design and control.Wherein, Wireless charging coil
The purpose of design is the wireless energy transfer for realizing that high-power, efficient, anti-excursion capability is strong.And coil design needs to establish and counted
On the basis of calculation self-induction of loop coefficient and mutual inductance.
The computational methods of currently used self-induction of loop coefficient and mutual inductance have：1. calculated using empirical equation：This
In computational methods, calculate electrodynamic capacity and mutual inductance empirical equation be directed to mostly circular coil, square shaped coil etc. other
Shape is difficult to calculate, and part formula calculates complexity；2. calculated by establishing magnetic field model：This method is computationally intensive, process
Complexity, it is unsuitable for engineering technology application.
The content of the invention
The purpose of the present invention is to overcome the weak point of prior art, proposes a kind of Wireless charging coil self-induction and mutual inductance
Unit for electrical property parameters computational methods.The present invention utilizes coil geometric parameter, is calculated by tabling look-up with formula, you can obtains coil certainly
Feel coefficient, mutual inductance and the accurate result of calculation of Mutual Inductance Coupling coefficient, method is easy, has in Practical Project very high
Promotional value.
The present invention proposes a kind of Wireless charging coil self-induction and the unit for electrical property parameters computational methods of mutual inductance, it is characterised in that
Comprise the following steps：
1) self-induction function L corresponding to different shape coil difference is obtained0(r/a) zoom table, self-induction correction factor ε (n, r/
A) zoom table, mutual inductance function f (x/a, d/a) zoom tables and mutual inductance correction factor τ (n, r/a) zoom table；
2) any coil i is chosen, obtains the coil geometric parameter, including：Coil dimension ai, wire radius ri, coil turn
ni, fore-and-aft distance d between two coilsi, lateral shift x between two coilsi；
3) dimensionless group is calculated to the coil i that step 2) is chosen, including：Dimensionless line footpath ri/ai, dimensionless distance di/
ai, dimensionless skew xi/ai；
4) according to coil i shape, four zoom tables corresponding to the coil shape obtained by step 1), the line is utilized
The geometric parameter and dimensionless group of circle, table look-up to obtain function and correction factor corresponding to coil i, including：Self-induction function L0
(ri/ai), self-induction correction factor ε (ni, ri/ai), mutual inductance function f (xi/ai, di/ai), mutual inductance correction factor τ (ni, ri/ai)；
5) geometric parameter, function and correction factor corresponding to coil i are substituted into below equation, the coil oneself is calculated
Feel coefficient L, mutual inductance M and Mutual Inductance Coupling coefficient κ；Calculation formula is as follows：
Electrodynamic capacity：
Mutual Inductance Coupling coefficient：
Mutual inductance：M=L κ or
The features of the present invention and beneficial effect are：
A kind of Wireless charging coil self-induction of present invention proposition and the unit for electrical property parameters computational methods of mutual inductance can be used for a variety of
The coil of shape, it is applied widely, and calculating process is simple, the use of look-up table has versatility, for a kind of line of shape
Circle, only it need to once be obtained operation, lower secondary design, other people can be constantly reused when designing；Amount of calculation is small, easily realizes quick
Calculate, be more suitable for engineering field application.The computational methods of the present invention both can be used for the Wireless charging coil design phase, to line
Enclose size, error resilience capability carries out quick calculating and Computer Aided Design；Wireless charging system test is can also be used for, to wireless charging electric wire
Enclose anti-excursion capability, power-carrying and coil efficiency to be assessed, the analysis process of wireless charging system can be simplified.
Brief description of the drawings
Fig. 1 is a kind of Wireless charging coil self-induction of the present invention and the unit for electrical property parameters computational methods FB(flow block) of mutual inductance.
Fig. 2 is the wireless charging square coil geometric parameter schematic diagram of the embodiment of the present invention.
Embodiment
A kind of Wireless charging coil self-induction proposed by the present invention and the unit for electrical property parameters computational methods of mutual inductance, with reference to attached
Figure and specific embodiment are further described as follows.
A kind of Wireless charging coil self-induction proposed by the present invention and the unit for electrical property parameters computational methods of mutual inductance, overall flow is such as
Shown in Fig. 1, comprise the following steps：
1) self-induction function L corresponding to different shape coil difference is obtained0(r/a) zoom table, self-induction correction factor ε (n, r/
A) zoom table, mutual inductance function f (x/a, d/a) zoom tables and mutual inductance correction factor τ (n, r/a) zoom table；
In order to L in electrodynamic capacity, mutual inductance and Mutual Inductance Coupling coefficient formulas0(r/a), ε (n, r/a), f (x/
A, d/a), τ (n, r/a) these unknown quantitys are demarcated and are fabricated to zoom table, so as to other designs and test wireless charging
The engineer of system directly uses, and the present invention utilizes MathCAD softwares, establishes a magnetic field data simulation model, utilizes magnetic
The method of field distribution formula (Biot-Savart law) and magnetic flux integration, has obtained the zoom table of these unknown quantitys
(lookup table).Comprise the following steps that：
1-1) obtain self-induction function L0(r/a) zoom table；Comprise the following steps that：
Coil geometric parameter 1-1-1) is inputted into MathCAD documents；
(coil shape involved in the present invention includes the coil and circle of various regular polygons to the coil of selection any shape
Coil), by wire radius r (unit m, span and interval determine according to r/a range of needs and interval), single turn line
Circle size a=1m (refers to the square length of side for square coil, refers to diameter of a circle for circular coil, for regular polygon coil
Refer to polygonal side length), coil turn n=1 is input in MathCAD documents, and obtains r/a value；If primary coil and secondary
Coil is regular polygon coil, then into step 1-1-2)；If primary coil and secondary coil are circular coils, enter step
Rapid 1-1-3)；
Unified straight wire section magnetic field function 1-1-2) is established (if primary coil and secondary coil are circular coils, to jump
Cross this step).
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B
(x2, y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate, the function description magnetic direction
It is perpendicular to the direction (z directions) of coil plane.This function is piecewise function：Remember tested point P to conductor spacing be dP,：Work as dP
During ＜ r, it assumes that magnetic induction intensity was 0 (ignoring the magnetic field in line)；Work as dPDuring ＞ r, then Biot-Savart law meter is utilized
Calculate magnetic induction intensity：
Wherein：l0It is integration variable；lABIt is straight wire section AB length；D=2r, i.e. diameter of wire；I.e. On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2It is space permeability.
1-1-3) establish coil magnetic field function.
For square and other regular polygon coils, because coil is made up of a plurality of straight wire section, so coil magnetic field letter
Number Bz(x, y, z) is by multiple end to end straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil,
Wherein, θ is integration variable, and R is the radius of whole coil.
1-1-4) calculate self-induction of loop coefficient L；
To the magnetic field B of vertical direction in coil planar rangez(x, y, z) is integrated to obtain magnetic flux (x here, y, z
Span be the plane that coil is surrounded scope), then divided by 1 ampere of empty electric current, you can obtain length of side 1m single turn lines
Enclose electrodynamic capacity L, the result is step 1-1-1) in L corresponding to r/a0(r/a) value
1-1-5) repeat step 1-1-1) to 1-1-4), for different types of coil, the scope according to needed for application, respectively
Calculate L corresponding to different r/a0(r/a), result corresponding to every kind of coil is arranged into the self-induction function L of this kind of coil0(r/a) check quickly
Table.
1-2) obtain self-induction correction factor ε (n, r/a) zoom table；Comprise the following steps that：
Coil geometric parameter 1-2-1) is inputted into MathCAD documents；
Any type of coil is chosen, by wire radius r (unit m, demand model of the span with interval according to r/a
Enclose and be spaced determination), (unit m, refers to the square length of side for square coil to coil dimension a=1m, refers to circle for circular coil
Diameter, refer to polygonal side length for regular polygon coil), coil turn n it is (true according to design and test request it is required that n ＞ 1
It is fixed) it is input in MathCAD documents, and obtain r/a value.If primary coil and secondary coil are regular polygon coils, enter
Enter step 1-2-2)；If primary coil and secondary coil are circular coils, into step 1-2-3)；
1-2-2) repeat step 1-1-2), unified straight wire section magnetic field function is established (if primary coil and secondary coil
It is circular coil, skips this step)；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B
(x2, y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate, the function description magnetic direction
It is perpendicular to the direction (z directions) of coil plane.This function is piecewise function：Remember tested point P to conductor spacing be dP：Work as dP
During ＜ r, it assumes that magnetic induction intensity was 0 (ignoring the magnetic field in line)；Work as dPDuring ＞ r, then Biot-Savart law meter is utilized
Calculate magnetic induction intensity：
Wherein, l0It is integration variable；lABIt is the length of straight wire section；D=2r, i.e. diameter of wire；I.e. On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2, it is space permeability.
1-2-3) establish coil magnetic field function；
For square and other regular polygon coils, because coil is made up of a plurality of straight wire section, so coil magnetic field letter
Number Bz(x, y, z) is by multiple end to end straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil,
Wherein, θ is integration variable；R (n)=R-2 (n-1) r, it is the radius of each circle coil circle；R is the half of whole coil
Footpath；
1-2-4) calculate self-induction of loop coefficient L；
Magnetic field B in coil plane to each circle coil vertical direction of the 1st circle to the n-th circlez(x, y, z) is integrated,
And the integral result of the 1st circle to the n-th circle is added, obtain total magnetic flux, then divided by 1 ampere of empty electric current, you can obtain coil
Electrodynamic capacity L.
1-2-5) calculate self-induction correction factor ε (n, r/a).According to formula：L=an2·L0(r/a) ε (n, r/a), its
Middle L is by step 1-2-4) obtain, a and n are by step 1-2-1) obtain, corresponding L0(r/a) by L0(r/a) zoom table obtains, by
This can calculate corresponding ε (n, r/a).To n=1 situation, for every kind of coil, ε (n, r/a)=1 is directly made.
1-2-6) repeat step 1-2-1) to 1-2-5), for coil of different shapes, the scope according to needed for application, respectively
ε (n, r/a) corresponding to different n and different r/a is calculated, result corresponding to every kind of coil is arranged into the self-induction amendment system of this kind of coil
Number ε (n, r/a) zoom table.
Mutual inductance function f (x/a, d/a) zoom table 1-3) is obtained, is comprised the following steps that：
Coil geometric parameter 1-3-1) is inputted into MathCAD documents：
The coil of any shape is chosen, by wire radius r=2 × 10-3M, the coil dimension a=1m (selections of the two values
Result is influenceed it is little, but be closer to preferably with practical application), coil turn n=1, longitudinal direction between primary coil and secondary coil
Distance d (unit m, span and interval determine according to d/a range of needs and interval), lateral shift x is (single between two coils
Position is that m, span and interval determine according to x/a range of needs and interval) it is input in MathCAD documents, respectively obtain
X/a and d/a value.If primary coil and secondary coil are regular polygon coils, into step 1-3-2)；If primary coil and
Secondary coil is circular coil, then into step 1-3-3)；
Unified straight wire section magnetic field function 1-3-2) is established (if primary coil and secondary coil are circular coils, to skip
This step)；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B
(x2, y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate, the function description magnetic direction
It is perpendicular to the direction (z directions) of coil plane.This function is piecewise function：Remember tested point P to conductor spacing be dP,：Work as dP
During ＜ r, it assumes that magnetic induction intensity was 0 (ignoring the magnetic field in line)；Work as dPDuring ＞ r, then Biot-Savart law meter is utilized
Calculate magnetic induction intensity：
Wherein：l0It is integration variable；lABIt is the length of straight wire section；D=2r, i.e. diameter of wire；I.e. On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2, it is space permeability.
1-3-3) establish primary coil magnetic field function；
For square and other regular polygon coils, because coil is made up of a plurality of straight wire section, so primary coil magnetic
Field function Bz(x, y, z) is by multiple end to end straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z) it is added
Arrive；
For circular coil,
Wherein, θ is integration variable；R is the radius of whole coil.
1-3-4) mutual inductance M between calculating coil；
Primary coil magnetic field function B in secondary coil plane to vertical directionz(x, y, z) is integrated and is added, and is obtained
To magnetic flux of the primary coil magnetic field in secondary coil plane, then divided by 1 ampere of empty electric current, you can obtain mutual inductance between coil
Coefficient M.
M is step 1-3-1) in x/a, the value of the mutual inductance function f (x/a, d/a) corresponding to d/a.
1-3-5) repeat step 1-3-1) to 1-3-4), for coil of different shapes, the scope according to needed for application, respectively
F (x/a, d/a) corresponding to different x/a and different d/a is calculated, result corresponding to every kind of coil is arranged into the mutual inductance letter of this kind of coil
Number f (x/a, d/a) zoom table.
1-4) obtain mutual inductance correction factor τ (n, r/a) zoom table；Comprise the following steps that：
Coil geometric parameter 1-4-1) is inputted into MathCAD documents；
The coil of any shape is chosen, by wire radius r (unit m, demand model of the span with interval according to r/a
Enclose and be spaced determination), (unit m, refers to the square length of side for square coil to coil dimension a=1m, refers to circle for circular coil
Diameter, refer to polygonal side length for regular polygon coil), coil turn n it is (true according to design and test request it is required that n ＞ 1
It is fixed), lateral shift x=0m between two coils, fore-and-aft distance d=0.2m between two coils (d value with practical application close to)
It is input in MathCAD documents, and obtains r/a value.If primary coil and secondary coil are regular polygon coils, enter step
Rapid 1-4-2)；If primary coil and secondary coil are circular coils, into step 1-4-3)；
1-4-2) establish uniform magnetic field function (if primary coil and secondary coil are circular coils, skipping this step)；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B
(x2, y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate, the function description magnetic direction
It is perpendicular to the direction (z directions) of coil plane.This function is piecewise function：Remember tested point P to conductor spacing be dP, work as dP
During ＜ r, it assumes that magnetic induction intensity was 0 (ignoring the magnetic field in line)；Work as dPDuring ＞ r, then Biot-Savart law meter is utilized
Calculate magnetic induction intensity：
Wherein：l0It is integration variable；lABIt is the length of straight wire section；D=2r, i.e. diameter of wire；I.e. On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2, it is space permeability.
1-4-3) establish primary coil magnetic field function；
For square and other regular polygon coils, (included because coil is made up of a plurality of straight wire section from the 1st circle to the
All conducting line segments of n circles), so primary coil magnetic field function Bz(x, y, z) is by multiple end to end straight wire section magnetic field letters
Number Bz(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil,
Wherein, θ is integration variable；R (n)=R-2 (n-1) r, it is the radius of each circle coil circle；R is the half of whole coil
Footpath.
1-4-4) mutual inductance M between calculating coil.
Primary coil magnetic field function in secondary coil plane to each circle (from the 1st circle to the n-th circle) coil vertical direction
Bz(x, y, z) is integrated and is added, and obtains total magnetic flux of the primary coil magnetic field in secondary coil plane, then divided by 1 peace
The empty electric current of training, you can obtain mutual inductance M between coil.
Resulting M is step 1-4-1) in input n, the value of the τ (n, r/a) corresponding to r/a.
1-4-5) repeat step 1-4-1) to 1-4-4), for coil of different shapes, the scope according to needed for application, respectively
τ (n, r/a) corresponding to different r/a and different n is calculated, result corresponding to every kind of coil is arranged into the mutual inductance amendment system of this kind of coil
Number τ (n, r/a) zoom table.
Utilize above-mentioned calculating process, it is possible to obtain L0(r/a), ε (n, r/a), f (x/a, d/a), τ (n, r/a) value,
Four zoom tables are obtained.
2) any coil i is chosen, obtains the coil geometric parameter, including：Coil dimension ai(unit m), for square
Coil refers to the square length of side, refers to diameter of a circle for circular coil, refers to polygonal side length for regular polygon coil), wire half
Footpath ri(unit m, if conductor cross-section is not circular, being substituted using equivalent redius), coil turn ni(it is required that primary coil and
Secondary winding turns are identical), fore-and-aft distance d between two coilsi(unit m), lateral shift x between two coilsi(unit m).Each ginseng
Several acquisition modes depend on practical engineering application occasion：If tested for wireless charging system, all coils geometric parameters
Number is obtained by measuring；If designed for wireless charging system, all coils geometric parameter is rule of thumb or indirect assignment
Obtain.Assignment is such as needed, geometric parameter should not exceed the dimensionless group span in look-up table.
For the present embodiment by taking square coil as an example, schematic diagram is as shown in Figure 2；In Fig. 2, the coil positioned at downside is primary line
Circle, the coil positioned at upside is secondary coil；The geometric parameter of the coil includes：Coil dimension ai(it is herein square side
It is long), wire radius ri, coil turn ni(it is required that primary coil is identical with secondary winding turns), fore-and-aft distance d between two coilsi,
Lateral shift x between two coilsi。
3) dimensionless group is calculated to the coil that step 2) is chosen, including：Dimensionless line footpath ri/ai(unit should turn to mm/
M, in order to table look-up), dimensionless distance di/ai(unit should turn to mm/mm), dimensionless skew xi/ai(unit should turn to mm/
mm)；
4) according to coil i shape, four zoom tables corresponding to the coil shape obtained by step 1), including：L0
(r/a) zoom table, ε (n, r/a) zoom table, f (x/a, d/a) zoom table, τ (n, r/a) zoom table, the geometric parameters of the coil are utilized
Number and dimensionless group, table look-up to obtain function and correction factor corresponding to coil i, including：Self-induction function L0(ri/ai), self-induction
Correction factor ε (ni, ri/ai), mutual inductance function f (xi/ai, di/ai), mutual inductance correction factor τ (ni, ri/ai)；
5) geometric parameter, function and correction factor corresponding to coil i are substituted into below equation, the coil oneself is calculated
Feel coefficient, mutual inductance and Mutual Inductance Coupling coefficient；Calculation formula is as follows：
Electrodynamic capacity：
Mutual Inductance Coupling coefficient：
Mutual inductance：M=L κ or
Wherein, L is electrodynamic capacity, and κ is Mutual Inductance Coupling coefficient, and M is mutual inductance；Above coefficient is corresponding to the coil
Self-induction and the unit for electrical property parameters of mutual inductance.Each coefficient is selected according to demand in Practical Project by engineer or designer above
Take.
Formula and zoom table obtained by the inventive method, can be to two etc. of arbitrary dimension, the number of turn, distance and skew
Big square coil, circular coil or other regular polygon coils carry out electrodynamic capacity, mutual inductance and Mutual Inductance Coupling coefficient
Quick to calculate, for coil of different shapes, calculation formula is identical, but zoom table is different.
With reference to a specific embodiment, that the present invention is described in more detail is as follows：
In the test of certain wireless charging system, using square coil, measurement obtains primary coil and secondary coil length of side a=
0.400m, diameter of wire r=1.7 × 10-3M, number of turn n=8；Fore-and-aft distance d=0.150m between two coils, between two coils laterally partially
Move x=0.050m.
A kind of Wireless charging coil self-induction proposed by the present invention and the unit for electrical property parameters computational methods of mutual inductance, including following step
Suddenly：
1) self-induction function L corresponding to different shape coil difference is obtained0(r/a) zoom table, self-induction correction factor ε (n, r/
A) zoom table, mutual inductance function f (x/a, d/a) zoom tables and mutual inductance correction factor τ (n, r/a) zoom table；The present embodiment is square
Coil, then obtain self-induction function L corresponding to square coil0(r/a) zoom table, self-induction correction factor ε (n, r/a) zoom table, mutually
Feel function f (x/a, d/a) zoom tables and mutual inductance correction factor τ (n, r/a) zoom table；Wherein, self-induction function L0(r/a) zoom table
As shown in table 1, self-induction correction factor ε (n, r/a) zoom table is as shown in table 2；Mutual inductance function f (x/a, d/a) zoom table such as institute of table 3
Show, and mutual inductance correction factor τ (n, r/a) zoom table is as shown in table 4
2) coil is chosen, obtains the coil geometric parameter；The square coil geometric parameter that the present embodiment obtains is specific as follows：
Coil dimension a=0.400m；Wire radius r=1.7 × 10-3m；Coil turn n=8；Fore-and-aft distance d between two coils
=0.150m；Lateral shift x=0.050m between two coils；
3) dimensionless group is calculated to the coil that step 2) is chosen；The square coil dimensionless group of the present embodiment is specific such as
Under：
Dimensionless line footpath
Dimensionless distance
Dimensionless is offset
4) according to coil shape, four zoom tables corresponding to coil shape established by step 1), including L0(r/a)
Zoom table, ε (n, r/a) zoom table, f (x/a, d/a) zoom table, τ (n, r/a) zoom table, using the coil geometric parameter and
Dimensionless group, table look-up to obtain function and correction factor corresponding to coil i, including：Self-induction function L0(ri/ai), self-induction amendment
Coefficient ε (ni, ri/ai), mutual inductance function f (xi/ai, di/ai), mutual inductance correction factor τ (ni, ri/ai)；
Because the coil shape of the present embodiment is square, according to square coil zoom table, as shown in table 1 to table 4, must can be somebody's turn to do
Function corresponding to coil and correction factor are following (using linear interpolation)：
Self-induction function L0(r/a)=L0(4.25)=3.752 μ H
Self-induction correction factor ε (n, r/a)=ε (8,4.25)=0.646
Mutual inductance function f (x/a, d/a)=f (0.125,0.375)=0.0980
Mutual inductance correction factor τ (n, r/a)=τ (8,4.25)=1.6095
5) geometric parameter, function and correction factor corresponding to coil i are substituted into below equation, the coil oneself is calculated
Feel coefficient, mutual inductance and Mutual Inductance Coupling coefficient；Calculation formula is as follows：
Electrodynamic capacity：
Mutual Inductance Coupling coefficient：
Mutual inductance：The μ H of M=L × κ=9.78
By the inventive method, it is square coil to be calculated for primary coil and secondary coil, and length of side a=
0.400m, line footpath r=1.7 × 10-3M, number of turn n=8, fore-and-aft distance d=0.150m between two coils, lateral shift x between two coils
=0.050m, its electrodynamic capacity L=62.0 μ H, mutual inductance M=9.78 μ H, Mutual Inductance Coupling coefficient κ=0.1577.The result with
More complicated magnetic field model analysis result is very similar.
The square coil L of table 10(r/a) zoom table
Table 2 square coil ε (n, r/a) zoom table
Continued 2 square coil ε (n, r/a) zoom table
Continued 2 square coil ε (n, r/a) zoom table
Table 3 square coil f (x/a, d/a) zoom table
Continued 3 square coil f (x/a, d/a) zoom table
Continued 3 square coil f (x/a, d/a) zoom table
Continued 3 square coil f (x/a, d/a) zoom table
Continued 3 square coil f (x/a, d/a) zoom table
Continued 3 square coil f (x/a, d/a) zoom table
Table 4 square coil τ (n, r/a) zoom table
Continued 4 square coil τ (n, r/a) zoom table
Continued 4 square coil τ (n, r/a) zoom table
Claims (5)
1. a kind of Wireless charging coil self-induction and the unit for electrical property parameters computational methods of mutual inductance, it is characterised in that comprise the following steps：
1) self-induction function L corresponding to different shape coil difference is obtained0(r/a) zoom table, self-induction correction factor ε (n, r/a) quick checkings
Table, mutual inductance function f (x/a, d/a) zoom tables and mutual inductance correction factor τ (n, r/a) zoom table；
2) any coil i is chosen, obtains the coil geometric parameter, including：Coil dimension ai, wire radius ri, coil turn ni,
Fore-and-aft distance d between two coilsi, lateral shift x between two coilsi；
3) dimensionless group is calculated to the coil i that step 2) is chosen, including：Dimensionless line footpath ri/ai, dimensionless distance di/ai, nothing
Dimension offsets xi/ai；
4) according to coil i shape, four zoom tables corresponding to the coil shape obtained by step 1), the coil is utilized
Geometric parameter and dimensionless group, table look-up to obtain function and correction factor corresponding to coil i, including：Self-induction function L0(ri/
ai), self-induction correction factor ε (ni, ri/ai), mutual inductance function f (xi/ai, di/ai), mutual inductance correction factor τ (ni, ri/ai)；
5) geometric parameter, function and correction factor corresponding to coil i are substituted into below equation, the self-induction system of the coil is calculated
Number L, mutual inductance M and Mutual Inductance Coupling coefficient κ；Calculation formula is as follows：
Electrodynamic capacity：
Mutual Inductance Coupling coefficient：
Mutual inductance：M=L κ or
2. the method as described in claim 1, it is characterised in that self-induction function L in the step 1)0(r/a) zoom table, obtain
Step is as follows：
1-1) obtain self-induction function L0(r/a) zoom table；Comprise the following steps that：
Coil geometric parameter 1-1-1) is inputted into MathCAD documents；
The coil of any shape is chosen, by wire radius r, unit m, single-turn circular coil size a=1m, coil turn n=1 input
Into MathCAD documents, and obtain r/a value；If primary coil and secondary coil are regular polygon coils, into step 1-
1-2)；If primary coil and secondary coil are circular coils, into step 1-1-3)；
1-1-2) establish unified straight wire section magnetic field function；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B (x2,
y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate；Remember tested point P to conductor spacing be dP：
Work as dPDuring ＜ r, then magnetic induction intensity is 0；Work as dPDuring ＞ r, then Biot-Savart law calculated magnetic induction intensity is utilized：
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Wherein：l0It is integration variable；lABIt is straight wire section AB length；D=2r, i.e. diameter of wire；I.e. On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2It is space permeability；
1-1-3) establish coil magnetic field function；
For regular polygon coil, coil magnetic field function Bz(x, y, z) is by multiple end to end straight wire section magnetic field function Bz
(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil, Wherein, θ is integration variable, and R is the radius of whole coil；
1-1-4) calculate self-induction of loop coefficient L；
To the magnetic field B of vertical direction in coil planar rangez(x, y, z) integrated to obtain magnetic flux, then divided by 1 ampere
Empty electric current, obtain length of side 1m single-turn circular coil electrodynamic capacity L, the result is step 1-1-1) in L corresponding to middle r/a0(r/a)
Value；
1-1-5) repeat step 1-1-1) to 1-1-4), for different types of coil, the scope according to needed for application, calculate respectively
L corresponding to different r/a0(r/a), result corresponding to every kind of coil is arranged into the self-induction function L of this kind of coil0(r/a) zoom table.
3. the method as described in claim 1, it is characterised in that self-induction correction factor ε (n, r/a) is checked quickly in the step 1)
Table, obtaining step are as follows：
Coil geometric parameter 1-2-1) is inputted into MathCAD documents；
Any type of coil is chosen, by wire radius r, unit m, coil dimension a=1m, coil turn n, n ＞ 1, input
Into MathCAD documents, and obtain r/a value；If primary coil and secondary coil are regular polygon coils, into step 1-
2-2)；If primary coil and secondary coil are circular coils, into step 1-2-3)；
1-2-2) establish unified straight wire section magnetic field function；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B (x2,
y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate；Remember tested point P to conductor spacing be dP：
Work as dPDuring ＜ r, then magnetic induction intensity is 0；Work as dPDuring ＞ r, then Biot-Savart law calculated magnetic induction intensity is utilized：
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Wherein, l0It is integration variable；lABIt is the length of straight wire section；D=2r, i.e. diameter of wire；I.e.
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1-2-3) establish coil magnetic field function；
For regular polygon coil, coil magnetic field function Bz(x, y, z) is by multiple end to end straight wire section magnetic field function Bz
(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil,
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Wherein, θ is integration variable；R (n)=R-2 (n-1) r, it is the radius of each circle coil circle；R is the radius of whole coil, I
It is the empty electric current that size is 1 ampere；
1-2-4) calculate self-induction of loop coefficient L；
Magnetic field B in coil plane to each circle coil vertical direction of the 1st circle to the n-th circlez(x, y, z) is integrated, and by
The integral result of 1 circle to the n-th circle is added, and obtains total magnetic flux, then divided by 1 ampere of empty electric current, obtain self-induction of loop coefficient L；
1-2-5) calculate self-induction correction factor ε (n, r/a)；
According to formula：L=an2·L0(r/a) ε (n, r/a), wherein L is by step 1-2-4) obtain, a and n are by step 1-2-
1) obtain, corresponding L0(r/a) by L0(r/a) zoom table obtains, ε (n, r/a) corresponding to calculating；If n=1, for every kind of line
Circle, ε (n, r/a)=1；
1-2-6) repeat step 1-2-1) to 1-2-5), for coil of different shapes, the scope according to needed for application, calculate respectively
ε (n, r/a) corresponding to different n and different r/a, result corresponding to every kind of coil is arranged into the self-induction correction factor ε of this kind of coil
(n, r/a) zoom table.
4. the method as described in claim 1, it is characterised in that mutual inductance function f (x/a, d/a) zoom table in the step 1),
Obtaining step is as follows：
Coil geometric parameter 1-3-1) is inputted into MathCAD documents：
The coil of any shape is chosen, by wire radius r=2 × 10-3M, coil dimension a=1m, coil turn n=1, primary line
Circle and fore-and-aft distance d between secondary coil, unit m, lateral shift x between two coils, unit m, are input to MathCAD documents
In, respectively obtain x/a and d/a value；If primary coil and secondary coil are regular polygon coils, into step 1-3-2)；
If primary coil and secondary coil are circular coils, into step 1-3-3)；
1-3-2) establish unified straight wire section magnetic field function；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B (x2,
y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate；Remember that tested point P is to conductor spacing
dP,：Work as dPDuring ＜ r, then magnetic induction intensity is 0；Work as dPDuring ＞ r, then Biot-Savart law calculated magnetic induction intensity is utilized：
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<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>d</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>&CenterDot;</mo>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&CenterDot;</mo>
<mo>(</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&CenterDot;</mo>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mfrac>
</mrow>
<mo>)</mo>
<mo>)</mo>
<msub>
<mi>dl</mi>
<mn>0</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein：l0It is integration variable；lABIt is the length of straight wire section；D=2r, i.e. diameter of wire；I.e.
On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2, it is space permeability；
1-3-3) establish primary coil magnetic field function；
For regular polygon coil, primary coil magnetic field function Bz(x, y, z) is by multiple end to end straight wire section magnetic field functions
Bz(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil,
<mrow>
<msub>
<mi>B</mi>
<mi>z</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>&mu;</mi>
<mn>0</mn>
</msub>
<mrow>
<mn>4</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>I</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>-</mo>
<mi>R</mi>
<mi>cos</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>-</mo>
<mi>sin</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>&CenterDot;</mo>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mi>cos</mi>
<mi>&theta;</mi>
<mo>+</mo>
<mi>y</mi>
<mi>sin</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>&theta;</mi>
<mo>,</mo>
</mrow>
Wherein, θ is integration variable；R is the radius of whole coil, and I is the empty electric current that size is 1 ampere；
1-3-4) mutual inductance M between calculating coil；
Primary coil magnetic field function B in secondary coil plane to vertical directionz(x, y, z) is integrated and is added, and obtains primary
Magnetic flux of the coil magnetic field in secondary coil plane, then divided by 1 ampere of empty electric current, obtain mutual inductance M between coil；M is
For step 1-3-1) in x/a, the value of the mutual inductance function f (x/a, d/a) corresponding to d/a；
1-3-5) repeat step 1-3-1) to 1-3-4), for coil of different shapes, the scope according to needed for application, calculate respectively
F (x/a, d/a) corresponding to different x/a and different d/a, result corresponding to every kind of coil is arranged into the mutual inductance function f of this kind of coil
(x/a, d/a) zoom table.
5. the method as described in claim 1, it is characterised in that mutual inductance correction factor τ (n, r/a in the step 1)）Quick checking
Table, obtaining step are as follows：
Coil geometric parameter 1-4-1) is inputted into MathCAD documents；
The coil of any shape is chosen, by wire radius r, unit m, coil dimension a=1m, coil turn n, n ＞ 1, two lines
Lateral shift x=0m between circle, fore-and-aft distance d=0.2m is input in MathCAD documents between two coils, and obtains r/a value；If
Primary coil and secondary coil are regular polygon coils, then into step 1-4-2)；If primary coil and secondary coil are circular
Coil, then into step 1-4-3)；
1-4-2) establish uniform magnetic field function；
Establish unified straight wire section magnetic field function Bz(x1, y1, z1, x2, y2, z2, x, y, z), wherein A (x1, y1, z1) and B (x2,
y2, z2) be respectively straight wire two-end-point coordinate, P (x, y, z) be tested point coordinate；Remember tested point P to conductor spacing be dP：
Work as dPDuring ＜ r, then magnetic induction intensity is 0；Work as dPDuring ＞ r, then Biot-Savart law calculated magnetic induction intensity is utilized：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>B</mi>
<mi>z</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<msub>
<mi>z</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>&mu;</mi>
<mn>0</mn>
</msub>
<mrow>
<mn>4</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<munderover>
<mo>&Integral;</mo>
<mn>0</mn>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</munderover>
<mrow>
<mo>(</mo>
<mfrac>
<mi>I</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>d</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>&CenterDot;</mo>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&CenterDot;</mo>
<mo>(</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&CenterDot;</mo>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mfrac>
</mrow>
<mo>)</mo>
<mo>)</mo>
<msub>
<mi>dl</mi>
<mn>0</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein：l0It is integration variable；lABIt is the length of straight wire section；D=2r, i.e. diameter of wire；I.e.
On projected size；I is that size is 1 ampere of empty electric current, μ0=4 π × 10-7Newton/ampere2, it is space permeability；
1-4-3) establish primary coil magnetic field function；
For regular polygon coil, primary coil magnetic field function Bz(x, y, z) is by multiple end to end straight wire section magnetic field functions
Bz(x1, y1, z1, x2, y2, z2, x, y, z) be added obtain；
For circular coil,
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>B</mi>
<mi>z</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>&mu;</mi>
<mn>0</mn>
</msub>
<mrow>
<mn>4</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>I</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>-</mo>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mi>cos</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>-</mo>
<mi>sin</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>&CenterDot;</mo>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mo>(</mo>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>(</mo>
<mi>x</mi>
<mi>cos</mi>
<mi>&theta;</mi>
<mo>+</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mi>sin</mi>
<mi>&theta;</mi>
<mo>)</mo>
<mo>)</mo>
<mi>d</mi>
<mi>&theta;</mi>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, θ is integration variable；R (n)=R-2 (n-1) r, it is the radius of each circle coil circle；R is the radius of whole coil, I
It is the empty electric current that size is 1 ampere；
1-4-4) mutual inductance M between calculating coil；
Primary coil magnetic field function B in secondary coil plane to each circle coil vertical directionz(x, y, z) integrate and phase
Add, obtain total magnetic flux of the primary coil magnetic field in secondary coil plane, then divided by 1 ampere of empty electric current, obtain between coil
Mutual inductance M；Resulting M is step 1-4-1) in n, the value of the τ (n, r/a) corresponding to r/a；
1-4-5) repeat step 1-4-1) to 1-4-4), for coil of different shapes, the scope according to needed for application, calculate respectively
τ (n, r/a) corresponding to different r/a and different n, result corresponding to every kind of coil is arranged into the mutual inductance correction factor τ of this kind of coil
(n, r/a) zoom table.
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| CN111007342A (en) * | 2019-12-20 | 2020-04-14 | 上海创远仪器技术股份有限公司 | Method for realizing measurement processing of wireless power charging transmission efficiency for handheld instrument based on computer software |
| CN111523256A (en) * | 2020-07-06 | 2020-08-11 | 南京航空航天大学 | Mutual inductance calculation method of coaxial multi-coil related to non-ferromagnetic metal medium |
| CN111969730A (en) * | 2020-07-07 | 2020-11-20 | 宁波大学 | Method for extracting coupling inductance of wireless power transmission link |
| CN111985136A (en) * | 2020-08-10 | 2020-11-24 | 中国矿业大学 | Parameter design method for fillet square coupler of IPT system |
| CN112069660A (en) * | 2020-08-17 | 2020-12-11 | 南京航空航天大学 | Mutual inductance calculation method between coaxial multi-coil with moving coil |
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| CN112290689A (en) * | 2020-09-16 | 2021-01-29 | 复旦大学 | Optimal design method for mutual inductance coefficient in wireless energy transmission system of medical implant device |
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| CN111523256B (en) * | 2020-07-06 | 2020-10-20 | 南京航空航天大学 | Mutual inductance calculation method of coaxial multi-coil related to non-ferromagnetic metal medium |
| CN111523256A (en) * | 2020-07-06 | 2020-08-11 | 南京航空航天大学 | Mutual inductance calculation method of coaxial multi-coil related to non-ferromagnetic metal medium |
| CN111969730A (en) * | 2020-07-07 | 2020-11-20 | 宁波大学 | Method for extracting coupling inductance of wireless power transmission link |
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| CN112069660A (en) * | 2020-08-17 | 2020-12-11 | 南京航空航天大学 | Mutual inductance calculation method between coaxial multi-coil with moving coil |
| CN112069753A (en) * | 2020-08-28 | 2020-12-11 | 中国能源建设集团湖南省电力设计院有限公司 | Magnetic field calculation method of regular polygon plane spiral coil |
| CN112069753B (en) * | 2020-08-28 | 2023-11-10 | 中国能源建设集团湖南省电力设计院有限公司 | Magnetic field calculation method for regular polygon plane spiral coil |
| CN112290689A (en) * | 2020-09-16 | 2021-01-29 | 复旦大学 | Optimal design method for mutual inductance coefficient in wireless energy transmission system of medical implant device |
| CN112290689B (en) * | 2020-09-16 | 2022-06-21 | 复旦大学 | Optimal design method for mutual inductance coefficient in wireless energy transmission system of medical implant device |
| CN115730427A (en) * | 2022-10-31 | 2023-03-03 | 国网江苏省电力有限公司苏州供电分公司 | Line electrical parameter estimation method and system based on electromagnetic field domain calculation |
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