CN109193964A - A kind of radio energy high-efficiency transmission method based on PCB coil - Google Patents
A kind of radio energy high-efficiency transmission method based on PCB coil Download PDFInfo
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- CN109193964A CN109193964A CN201811128189.7A CN201811128189A CN109193964A CN 109193964 A CN109193964 A CN 109193964A CN 201811128189 A CN201811128189 A CN 201811128189A CN 109193964 A CN109193964 A CN 109193964A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
- H02J50/10—Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling
- H02J50/12—Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling of the resonant type
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
- H01F27/00—Details of transformers or inductances, in general
- H01F27/28—Coils; Windings; Conductive connections
- H01F27/2804—Printed windings
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
- H01F38/00—Adaptations of transformers or inductances for specific applications or functions
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Abstract
The invention discloses a kind of radio energy high-efficiency transmission method based on PCB coil.The transmission range of PCB coil wireless power transmission also receives the limitation of efficiency of transmission.The present invention is as follows: Step 1: calculating the inductance value L of transmit coil and receiving coil；Two, the parasitic resistance values R of transmit coil and receiving coil is calculated；Three, the parasitic capacitance value C of transmit coil and receiving coil is calculated；Step 4: establishing efficiency of transmission η and inputting the relationship of frequency f, and determine corresponding maximum input efficiency ηmaxInput frequency fa.It is that step 4 acquires f to transmit coil input frequencyaAlternating current；Transmit coil and receiving coil mutual inductance, receiving coil export alternating current.The present invention improves the efficiency of wireless power transmission by the frequency of input AC electricity when optimization PCB coil wireless power transmission.
Description
Technical field
The invention belongs to electronic technology fields, and in particular to a kind of radio energy high efficiency of transmission side based on PCB coil
Method.
Background technique
Non-contacting electric energy transmission may be implemented in wireless power transmission technology, it is possible to reduce traditional wire transmits bring
Trouble.The transmission of magnet coupled resonant type wireless electric energy is one of common technological means.Currently, magnet coupled resonant type is limited
The widely applied critical issue of wireless power transmission technology is lower electric energy efficiency of transmission.The geometry of efficiency of transmission and coil
The correlations such as size, transmission range, load and working frequency.PCB coil can make coil manufacturer's standard, PCB coil category
In rigid substrate coil can effective protection coil deformation occurs, be mainly used for easily colliding, the occasions such as deformation it is wireless
Electric energy transmission, PCB coil is widely used in field of consumer electronics at present.In consumer electronics wireless power field, PCB line
The shape of circle is often depending on the shell shape and concrete application scene of wireless charger, and coil shape is restricted also directly
Cause not optimizing efficiency of transmission by optimizing coil dimension at present.The transmission distance of PCB coil wireless power transmission simultaneously
From also receiving the limitation of efficiency of transmission.Therefore it is badly in need of one kind under the premise of not changing existing PCB coil structure, spacing, mentions
The method of high two PCB coils wireless power transmission efficiency.
Summary of the invention
The purpose of the present invention is to provide a kind of radio energy high-efficiency transmission method based on PCB coil.
The specific steps of the present invention are as follows:
Step 1: calculating transmit coil inductance value L1With the inductance value L of receiving coil2；Inductance value L1、L2Expression formula such as
Shown in formula (1),
Li=0.635 μ0davg(i)Ni 2[ln(2.07/ρi)+0.18ρi+0.13ρi 2], i=1,2 (1)
In formula (1), davg(i)Expression formula be davg(i)=(dout(i)+din(i))/2；ρiExpression formula be ρi=(dout(i)-
din(i))/(dout(i)+din(i))；dout(1)、dout(2)The respectively outer diameter of transmit coil, receiving coil； din(1)、din(2)Respectively
The internal diameter of transmit coil, receiving coil；N1、N2Respectively the number of turns of transmit coil, receiving coil；ln(2.07/ρi) it is to be with e
Bottom, 2.07/ ρiLogarithm；μ0For magnetic conductivity in vacuum.
Step 2: calculating the parasitic resistance values R of transmit coil1With the parasitic resistance values R of receiving coil2；Parasitic resistance values
R1、R2Expression formula such as formula (2) shown in,
Ri=RSK(i)+RPR(i), i=1,2 (2)
In formula (2), RSK(1)、RSK(2)The respectively skin effect resistance of transmit coil and receiving coil, RSK(1)、 RSK(2)'s
Shown in expression formula such as formula (3)；RPR(1)、RPR(2)The respectively kindred effect resistance of transmit coil, receiving coil, RPR(1)、RPR(2)
Expression formula such as formula (4) shown in.
Skin effect resistance RSK(i)Expression formula are as follows:
RSK(i)=RDC(i)[1+(f/f1(i))2+(f/f0(i))5]0.1, i=1,2 (3)
In formula (3), RDC(1)、RDC(2)It is the DC impedance of transmit coil, receiving coil respectively；f1(i)Expression formula be
f1(i)=π/(2 μ0σ(i)w′(i)t′(i))；f0(i)Expression formula be
w′(i)=w(i)/(π)0.5；t′(i)=t(i)/(π)0.5；w(1)、w(2)Respectively transmit coil, on receiving coil track width
Degree；t(1)、t(2)Respectively transmit coil, on receiving coil track thickness；σ(1)、σ(2)Respectively transmit coil, reception line
The conductivity of circle.For withFor the complete elliptic integral of the first kind of variable.
Kindred effect resistance RPR(i)Expression formula are as follows:
In formula (4), lj(1)、lj(2)The respectively length of transmit coil, receiving coil jth circle from outside to inside； N(1)、N(2)Point
Not Wei transmitting coil, receiving coil the number of turns；Φ(i)Expression formula such as formula (5) shown in； Hj(i)Expression formula such as formula (6) shown in.
Φ(i)Expression formula it is as follows:
In formula (5), δ(1)、δ(2)The respectively skin depth of transmitting coil, receiving coil, δ(i)Expression formula be δ(i)=
(0.5μ0σ(i)ω)-0.5。
In formula (6), s(1)、s(2)It is divided into the spacing of two adjacent rings track on transmit coil and receiving coil.
Step 3: calculating the parasitic capacitance value C of transmit coil1With the parasitic capacitance value C of receiving coil2；Parasitic resistance values
C1、C2Expression formula such as formula (7) shown in,
In formula (7), εr,eff(1)For the dielectric constant of the PCB substrate of transmitting coil；εr,eff(2)It is served as a contrast for the PCB of receiving coil
The dielectric constant at bottom；C is the spread speed of electromagnetic wave in a vacuum；l(1)、l(2)Respectively transmit coil, receiving coil it is total
Length.
Step 4: the expression formula for establishing the efficiency of transmission η of transmitting coil and receiving coil is as follows::
In formula (8), Q1It is the quality factor of transmit coil, shown in expression formula such as formula (9)；Q2LIt is under bringing onto load state
The quality factor of receiving coil, shown in expression formula such as formula (10)；K is the coefficient of coup, shown in expression formula such as formula (11).
The quality factor Q of transmit coil1, under bringing onto load state receiving coil quality factor Q2LExpression formula it is as follows:
Q1=(1- ω2L1C1)ωL1/R1-R1ωC1 (9)
Q2L=(1- ω2L2C2)ωL2/(R2+RL)-(R2+RL)ωC1 (10)
In formula (9) and (10), the expression formula of ω is the π of ω=2 f；F is input frequency；RLFor the equivalent impedance of load.
The k expression formula of the coefficient of coup is as follows:
In formula (11), M is mutual inductance, shown in expression formula such as formula (11).
In formula (12),Expression formula such as formula (13) shown in.
In formula (13),Expression formula be Expression formula beSpacing of the z between transmitting coil and receiving coil；
Be withFor the atanh function of variable.Be withFor the atanh function of variable.
It finds out η and is maximized ηmaxWhen, corresponding input frequency fa。
Step 5: acquiring f to transmit coil input frequency for step 4aAlternating current；Transmit coil is mutual with receiving coil
Sense, receiving coil export alternating current.
The invention has the advantages that:
1, the equivalent model of the invention by establishing PCB coil wireless energy transfer, passes through equivalent model and derives acquisition
PCB coil efficiency of transmission expression formula, using efficiency of transmission as final optimization pass target, optimize PCB coil wireless power transmission when it is defeated
Enter frequency, to improve the efficiency of wireless power transmission.
2, the present invention establishes PCB line according to the geometry, track conductivity, substrate dielectric constant of PCB coil
Circle wireless power transmission efficiency is contacted with input frequency, and the peak position of calculated efficiency of transmission and real transmission are imitated
The peak position of rate is very close, therefore the input frequency that the present invention chooses can greatly improve PCB coil wireless power transmission effect
Rate.
3, the present invention need to only change transmission line without carrying out any transformation to existing PCB coil radio energy transmission system
The efficiency of electric energy transmission can be improved in the input frequency of circle.
Detailed description of the invention
Fig. 1 is the magnetic coupling equivalent circuit diagram of transmit coil and receiving coil in the present invention；
Fig. 2 is the schematic diagram of transmit coil or receiving coil in the present invention；
Fig. 3 is the schematic diagram of transmit coil or receiving coil in an example of the present invention；
Fig. 4 is the schematic diagram that transmit coil or receiving coil test quality factor in an example of the present invention；
Fig. 5 is the calculated result and test of the quality factor of transmit coil or receiving coil in an example of the present invention
Result schematic diagram；
Fig. 6 is the schematic diagram that transmit coil and receiving coil efficiency of transmission are tested in an example of the present invention；
Fig. 7 is the calculated result and test of the efficiency of transmission of transmit coil and receiving coil in an example of the present invention
Result schematic diagram.
Specific embodiment
Below in conjunction with attached drawing, the invention will be further described.
As illustrated in fig. 1 and 2, a kind of radio energy high-efficiency transmission method based on PCB coil of the present invention is specific by inputting
The mode of the alternating current of frequency, to improve two power transmission efficiencies for carrying out the PCB coil of wireless power transmission.Two progress nothings
The PCB coil of line electric energy is respectively transmit coil, receiving coil.
Concrete scene are as follows: transmit coil, signal projector, the first series compensation capacitance are sequentially connected in series into loop；Hair receives
Coil, load, the second series compensation capacitance are sequentially connected in series into loop.The equivalent impedance of load is known quantity；Transmit coil with connect
Take-up circle is square spiral coil.The printing line width w of transmit coil(1), track thickness t(1), two adjacent rings track
Distance s(1), outside diameter dout(1), internal diameter din(1)With the number of turns N1And the printing line width w of receiving coil(2), track thickness
t(2), two adjacent rings track distance s(2), outside diameter dout(2), internal diameter din(2)With the number of turns N2It is known to determine.Transmitting coil with
The spacing of receiving coil is z.
Transmit coil and receiving coil are equivalent to parasitic capacitance, parasitic inductance, dead resistance series connection cyclization by the present invention
The form of shape.It is in parallel after signal source, singal source resistance, the first series compensation capacitance are sequentially connected in series for transmit coil
At the both ends of parasitic capacitance.For receiving coil, after load, the second series compensation capacitance are sequentially connected in series, it is connected in parallel on parasitism
The both ends of capacitor.
Specific step is as follows for a kind of radio energy high-efficiency transmission method based on PCB coil:
Step 1: calculating transmit coil inductance value L1With the inductance value L of receiving coil2；Inductance value L1、L2Expression formula such as
Shown in formula (1),
Li=0.635 μ0davg(i)Ni 2[ln(2.07/ρi)+0.18ρi+0.13ρi 2], i=1,2 (1)
In formula (1), davg(1)For the internal-and external diameter mean value of transmit coil, davg(1)For the internal-and external diameter mean value with receiving coil；
davg(i)Expression formula be davg(i)=(dout(i)+din(i))/2；ρiExpression formula be ρi=(dout(i)-din(i))/(dout(i)+
din(i))；dout(1)、dout(2)The respectively outer diameter of transmit coil, receiving coil； din(1)、din(2)Respectively transmit coil, reception
The internal diameter of coil；ln(2.07/ρi) it is 2.07/ ρ using e the bottom of asiLogarithm；μ0For magnetic conductivity in vacuum, value is 4 π × 10-7N/
A2。
Step 2: calculating the parasitic resistance values R of transmit coil1With the parasitic resistance values R of receiving coil2；Parasitic resistance values
R1、R2Expression formula such as formula (2) shown in,
Ri=RSK(i)+RPR(i), i=1,2 (2)
In formula (2), RSK(1)、RSK(2)The respectively skin effect resistance of transmit coil, receiving coil, RSK(1)、 RSK(2)'s
Shown in expression formula such as formula (3)；RPR(1)、RPR(2)The respectively kindred effect resistance of transmit coil, receiving coil, RPR(1)、RPR(2)
Expression formula such as formula (4) shown in.Its reason is: parasitic resistance values mainly consist of two parts, and a part is by skin effect
Caused, another part is as caused by kindred effect.
Skin effect resistance RSKExpression formula are as follows:
RSK(i)=RDC(i)[1+(f/f1(i))2+(f/f0(i))5]0.1, i=1,2 (3)
In formula (3), RDC(1)、RDC(2)Respectively DC impedance (the i.e. transmit coil, reception of transmit coil, receiving coil
Coil leads to resistance value when direct current)；f1(i)Expression formula be f1(i)=π/(2 μ0σ(i)w′(i)t′(i))； f0(i)Expression formula bew′(i)=w(i)/(π)0.5； t′(i)=t(i)/(π)0.5；w(1)、w(2)
Respectively transmit coil, on receiving coil track width；t(1)、t(2)Respectively transmit coil, track on receiving coil
Thickness；σ(1)、σ(2)Respectively transmit coil, receiving coil conductivity (conductivity is by transmit coil, the material of receiving coil
Matter determines).For withFor the complete elliptic integral of the first kind of variable.
Kindred effect resistance RPR(i)Expression formula are as follows:
In formula (4), lj(1)、lj(2)The respectively length of transmit coil, receiving coil jth circle from outside to inside； N(1)、N(2)Point
Not Wei transmitting coil, receiving coil the number of turns；Φ(i)Expression formula such as formula (5) shown in； Hj(1)It is additional 1 ampere of transmit coil
Exciting current when, by except transmit coil from outside to inside i-th circle in addition to other tracks generate, i-th circle track on
Magnetic field size, Hj(2)When 1 ampere of exciting current additional for receiving coil, by addition to receiving coil from outside to inside the i-th circle
Other tracks generate, i-th circle track on magnetic field size, Hj(i)Expression formula such as formula (6) shown in.
Φ(i)Expression formula it is as follows:
Formula (5) be by the case of 10000 kinds (line width w from 0.1mm to 10mm, input frequency f from 0.1MHz to
1.6GHz variation range) Φ value carry out curve fitting.In formula (5), δ(1)、δ(2)Respectively transmitting coil, reception line
The skin depth of circle, δ(i)Expression formula be δ(i)=(0.5 μ0σ(i)ω)-0.5。
The dimensionless that is calculated as of formula (6) calculates, and the value of line width w and distance s is the size for being as unit of rice.Formula (6)
In, s(1)、s(2)It is divided into the spacing of two adjacent rings track on transmit coil and receiving coil, i.e.,Gained Hj(i)Unit be 10-6A/m。
Step 3: calculating the parasitic capacitance value C of transmit coil1With the parasitic capacitance value C of receiving coil2；Parasitic resistance values
C1、C2Expression formula such as formula (7) shown in,
In formula (7), εr,eff(1)For the PCB substrate of transmitting coil dielectric constant (in the present embodiment, PCB substrate use
FR-4 epoxy glass cloth laminated board is substrate, 4.4) dielectric constant value is；εr,eff(2)For Jie of the PCB substrate of receiving coil
Electric constant；C is the spread speed (i.e. 3.0 × 10 of electromagnetic wave in a vacuum8m/s)；l(1)、l(2)Respectively transmit coil, reception
The total length of coil.
Step 4: series compensation network is established, so that transmitting coil of the present invention and receiving coil work in condition of resonance
Under, transmitting coil and reception selection series resonance compensating electric capacity are respectively CC1And CC2, efficiency of transmission η under series resonance model
Expression formula it is as follows:
In formula (8), Q1It is transmit coil quality factor, shown in expression formula such as formula (9)；Q2LIt is to be connect under bringing onto load state
The quality factor of take-up circle, shown in expression formula such as formula (10)；K is the coefficient of coup, shown in expression formula such as formula (11)；The table of D
It is up to formulaRLEquivalent impedance for the load being connected with receiving coil.Usual RLMuch larger than R2, therefore D is usual
In the case of can be considered value be equal to 1.
The quality factor Q of transmit coil1, under bringing onto load state receiving coil quality factor Q2LExpression formula it is as follows:
Q1=(1- ω2L1C1)ωL1/R1-R1ωC1 (9)
Q2L=(1- ω2L2C2)ωL2/(R2+RL)-(R2+RL)ωC1 (10)
In formula (9) and (10), the expression formula of ω is the π of ω=2 f；F is input frequency.
The k expression formula of the coefficient of coup is as follows:
In formula (11), M is mutual inductance, shown in expression formula such as formula (12).
In formula (12),Expression formula such as formula (13) shown in.
In formula (13),Expression formula be Expression formula bej1、j2For the cumulative number used that adds up；Spacing of the z between transmitting coil and receiving coil；Be withFor the atanh function of variable.
Be withFor the atanh function of variable.
As can be seen that the efficiency of transmission η in formula (8) is only related to input frequency f；The expression formula of efficiency of transmission η is imported
Matlab software finds out η and is maximized ηmaxWhen, corresponding input frequency fa(abscissa).
Step 5: acquiring f to transmit coil input frequency for step 4aAlternating current；Transmit coil is mutual with receiving coil
Sense, receiving coil output frequency are faAlternating current.The wireless power transmission efficiency of transmit coil and receiving coil is higher than at this time
Wireless power transmission efficiency when being inputted with other frequency alternating currents.
As shown in figure 3, being 11 circles with coil turn, printing line width w is 2.1mm, and track thickness t is 35 μm, adjacent
The distance s of two circle tracks are 0.4mm, outside diameter doutFor 74.2mm, internal diameter dinIt is 19.2mm as example.
As shown in figure 4, using vector network analyzer to the transmit coil or receiving coil progress quality factor as example
Situation varying with frequency, as a result as shown in Figure 5.In Fig. 5, solid line is that the present invention is calculated as a result, dotted line is that test obtains
Results, it can be seen that being counted although calculated quality factor value and the quality factor tested out have certain error
Corresponding to the quality factor maximum value that abscissa (frequency values) corresponding to obtained quality factor maximum value and test obtain
Abscissa (frequency values) it is very close.It can be seen that the frequency of the quality factor maximum selection rule calculated through the invention
Rate value can accurately correspond to actual transmit coil or receiving coil quality factor maximum value.
As shown in fig. 6, using vector network analyzer to the transmit coil and receiving coil progress efficiency of transmission as example
Situation varying with frequency, as a result as shown in Figure 7.In Fig. 7, solid line is that the present invention is calculated as a result, four solid stains point
Wei the efficiency value that measures of frequency values 5MHz, 10MHz, 15MHz, 20MHz, it can be seen that although calculated efficiency of transmission with
The efficiency of transmission tested out has certain error, but abscissa (frequency corresponding to the efficiency of transmission maximum value being calculated
Value) and test abscissa (frequency values) corresponding to obtained efficiency of transmission maximum value closely.It can be seen that this
Invent frequency values base corresponding to frequency values corresponding to the efficiency of transmission maximum value calculated and actual efficiency of transmission maximum value
This is equal.It can thus be seen that the input frequency that the present invention is calculated can be by the improved efficiency of PCB wireless power transmission to most
Greatly.
Claims (1)
1. a kind of radio energy high-efficiency transmission method based on PCB coil, it is characterised in that: Step 1: calculating transmit coil electricity
Inductance value L1With the inductance value L of receiving coil2；Inductance value L1、L2Expression formula such as formula (1) shown in,
Li=0.635 μ0davg(i)Ni 2[ln(2.07/ρi)+0.18ρi+0.13ρi 2], i=1,2 (1)
In formula (1), davg(i)Expression formula be davg(i)=(dout(i)+din(i))/2；ρiExpression formula be ρi=(dout(i)-
din(i))/(dout(i)+din(i))；dout(1)、dout(2)The respectively outer diameter of transmit coil, receiving coil；din(1)、din(2)Respectively
The internal diameter of transmit coil, receiving coil；N1、N2Respectively the number of turns of transmit coil, receiving coil；ln(2.07/ρi) it is to be with e
Bottom, 2.07/ ρiLogarithm；μ0For magnetic conductivity in vacuum；
Step 2: calculating the parasitic resistance values R of transmit coil1With the parasitic resistance values R of receiving coil2；Parasitic resistance values R1、R2's
Shown in expression formula such as formula (2),
Ri=RSK(i)+RPR(i), i=1,2 (2)
In formula (2), RSK(1)、RSK(2)The respectively skin effect resistance of transmit coil and receiving coil, RSK(1)、RSK(2)Expression
Shown in formula such as formula (3)；RPR(1)、RPR(2)The respectively kindred effect resistance of transmit coil, receiving coil, RPR(1)、RPR(2)Expression
Shown in formula such as formula (4)；
Skin effect resistance RSK(i)Expression formula are as follows:
RSK(i)=RDC(i)[1+(f/f1(i))2+(f/f0(i))5]0.1, i=1,2 (3)
In formula (3), RDC(1)、RDC(2)It is the DC impedance of transmit coil, receiving coil respectively；f1(i)Expression formula be f1(i)=π/
(2μ0σ(i)w′(i)t′(i))；f0(i)Expression formula bew′(i)=w(i)/(π)0.5；
t′(i)=t(i)/(π)0.5；w(1)、w(2)Respectively transmit coil, on receiving coil track width；t(1)、t(2)Respectively send out
The thickness of track on sending coil, receiving coil；σ(1)、σ(2)The respectively conductivity of transmit coil, receiving coil；For withFor the complete elliptic integral of the first kind of variable；
Kindred effect resistance RPR(i)Expression formula are as follows:
In formula (4), lj(1)、lj(2)The respectively length of transmit coil, receiving coil jth circle from outside to inside；N(1)、N(2)Respectively
The number of turns of transmitting coil, receiving coil；Φ(i)Expression formula such as formula (5) shown in；Hj(i)Expression formula such as formula (6) shown in；
Φ(i)Expression formula it is as follows:
In formula (5), δ(i)Expression formula be δ(i)=(0.5 μ0σ(i)ω)-0.5；
In formula (6), s(1)、s(2)It is divided into the spacing of two adjacent rings track on transmit coil and receiving coil；
Step 3: calculating the parasitic capacitance value C of transmit coil1With the parasitic capacitance value C of receiving coil2；Parasitic resistance values C1、C2's
Shown in expression formula such as formula (7),
In formula (7), εr,eff(1)For the dielectric constant of the PCB substrate of transmitting coil；εr,eff(2)For Jie of the PCB substrate of receiving coil
Electric constant；C is the spread speed of electromagnetic wave in a vacuum；l(1)、l(2)The respectively total length of transmit coil, receiving coil；
Step 4: the expression formula for establishing the efficiency of transmission η of transmitting coil and receiving coil is as follows::
In formula (8), Q1It is the quality factor of transmit coil, shown in expression formula such as formula (9)；Q2LIt is receiving coil bringing onto load state
Under quality factor, shown in expression formula such as formula (10)；K is the coefficient of coup, shown in expression formula such as formula (11)；
The quality factor Q of transmit coil1, under bringing onto load state receiving coil quality factor Q2LExpression formula it is as follows:
Q1=(1- ω2L1C1)ωL1/R1-R1ωC1 (9)
Q2L=(1- ω2L2C2)ωL2/(R2+RL)-(R2+RL)ωC1 (10)
In formula (9) and (10), the expression formula of ω is the π of ω=2 f；F is input frequency；RLFor the equivalent impedance of load；
The k expression formula of the coefficient of coup is as follows:
In formula (11), M is mutual inductance, shown in expression formula such as formula (11)；
In formula (12),Expression formula such as formula (13) shown in；
In formula (13),Expression formula be Expression formula beSpacing of the z between transmitting coil and receiving coil；It is
WithFor the atanh function of variable；Be withFor the atanh function of variable；
It finds out η and is maximized ηmaxWhen, corresponding input frequency fa；
Step 5: acquiring f to transmit coil input frequency for step 4aAlternating current；Transmit coil and receiving coil mutual inductance, connect
Take-up circle exports alternating current.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811128189.7A CN109193964B (en) | 2018-09-27 | 2018-09-27 | Wireless power efficient transmission method based on PCB coil |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811128189.7A CN109193964B (en) | 2018-09-27 | 2018-09-27 | Wireless power efficient transmission method based on PCB coil |
Publications (2)
| Publication Number | Publication Date |
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| CN109193964A true CN109193964A (en) | 2019-01-11 |
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