CN104167828B - Design method for multi-repeater magnetic-coupling resonant wireless power transmission system - Google Patents

Abstract

Disclosed is a design method for a multi-repeater magnetic-coupling resonant wireless power transmission system. Through comparison of an MCR-WPT system provided with any number of repeaters and a multisection coupling resonator bandpass filter and use of a mature filter design theory, an internal constraint relation between transmission performance indexes (transmission efficiency, transmission power and transmission distance) and circuit parameters (inductance value, mutual induction coefficient, bandwidth, resonance frequency and tuning capacity) in the multi-repeater MCR-WPT system is proposed explicitly respectively for two conditions: a source resistance is zero Ohm and not zero Ohm. A typical design procedure obtained by a user on the basis is capable of rapidly and accurately extracting design parameters of a multi-repeater MCR-WPT system capable of meeting the transmission performance indexes, and meeting design and development demands of a long-distance-transmission MCR-WPT system with any number of repeaters. The method has no concrete constraint on the inductance value of hollow coils of repeaters so that is the design is significantly flexible.

Description

A kind of method for designing of multi-repeater magnet coupled resonant type wireless power transmission system

Technical field

The invention belongs to wireless energy transfer system design field.

Background technology

As a kind of novel wireless energy transmission technology, magnet coupled resonant type wireless charging (MCR-WPT) technology Electric energy can transmitted times over the distance of inductance necklace bore with higher efficiency, overcome vicarious wireless charging technology Can only be in the nearest distance just applicable drawback.It is applicable to the various application scenarios from milliwatt level to multikilowatt.

Traditional magnetic resonance manifold type wireless charging system has four coil forms and two coil forms two kinds.In four coil shapes In formula, power supply is coupled by a coupling coil and transmitting coil, and load is then by another coupling coil and reception Coil is coupled；And in four coil forms, coupling coil is cancelled, power supply, load directly and transmitting coil, connect Take-up circle is connected.The transmission range of magnet coupled resonant type wireless charging technique is comparatively short, its best transmission distance Depend primarily on load, coil bore and operating frequency, but generally not over 2～3 times of coil bore.When When transmission range is more than best transmission distance, the efficiency of system is along with the increase rapid decrease of distance.

Theory and practice shows, utilize superconductor technology can significantly improve on the premise of not reducing efficiency of transmission transmission away from From, but this technical price is high, realize complexity.And the simple and practical cheap method of another kind is at transmitting coil and to connect (hereinafter referred to as repeater, by the hollow electricity of high q-factor to be appropriately interposed one or more relaying resonator between take-up circle Sense coil and tuning capacity are in series), the coverage of wireless energy transfer can be significantly increased.Due to repeater originally Body also has certain loss, and efficiency of transmission and through-put power therefore can be caused to reduce to a certain extent, uses high q-factor Relaying resonator can effectively alleviate this defect.The application of repeater also contribute to people conveniently set up source coil, The geometric size of loading coil and locus, improve design flexibility.But, increasing of repeating coil number also can It is greatly increased and analyzes and the complexity of design.And abuse relaying LC resonator irrelevantly, not only can not improve effect Rate and through-put power, may cause reverse effect on the contrary.

At present, for magnetic resonance manifold type wireless charging system, traditional analysis design method mainly includes that coupled mode is managed Opinion, lumped parameter equivalent circuit are theoretical.From the point of view of mathematics, coupled mode theory can be equivalent to solve N in time domain The partial differential equations on rank；Lumped parameter equivalent circuit theory can be equivalent to solve the matrix equation on N rank on frequency domain, Here N-2 represents the number of repeating coil.When N is the biggest, either solve the partial differential equations on N rank still The non-singular matrix equation solving N rank is all considerably complicated, is difficult to obtain solution with practical value.The most also there is people Utilizing filter theory, MCR-WPT system is equivalent to wave filter, be then analyzed design, its advantage is letter Just, fast, bandwidth, the isoparametric computing formula of efficiency of transmission can be directly obtained, design WPT system for people and carry For full and accurate theoretical foundation.But at present this technology mainly for or the most non-relay tradition four coil form or two coils The MCR-WPT system of form.It is therefore desirable to for many relaying MCR-WPT systems, utilize filter theory to open It is simple to send out a set of, system, effectively analysis and method for designing.

Summary of the invention

In view of this, the technical issues that need to address of the present invention are for the MCR-WPT system with multi-repeater, Use filter theory, it is provided that a kind of convenient, fast and accurate method for designing.This method for designing utilizes arbitrary number Similarity between repeater MCR-WPT and more piece coupled resonators band filter, utilizes ripe wave filter to set Meter theory obtains the determining including parameter such as including inductance value, mutual inductance, efficiency of transmission, through-put power and transmission range Component analysis computing formula.On this basis, user can carry out distance multi-repeater MCR-WPT system rapidly and accurately The design of system.

For the many relaying MCR-WPT systems shown in Fig. 1, its circuit structure includes transmitting terminal TX, multiple relaying Device, receiving terminal RX.Transmitting terminal TX is by alternating current power supply (operating frequency f₀, voltage amplitude value V_S), transmitting terminal hollow Inductance coil L₁, transmitting terminal tuning capacity C₁Composition, R_SAnd R₁It is respectively source internal resistance and transmitting terminal line loss resistance. Repeater is by air-core inductance L_iWith tuning capacity C_iIt is in series, 1 < i < N, R_iFor loss resistance.Receiving terminal RX is by air-core inductance L_N, receiving terminal tuning capacity C_N, receiving terminal load R_LIt is in series, R_NFor loss electricity Resistance.k_i,i+1(i=1 ..., N-1) it is the mutual inductance between adjacent inductive coil i and i+1.The usual coiling of air-core inductance Circular or rectangle, it is possible to be triangle, pentagon, hexagon or other geometry.

System operating frequency f₀It it is alternating current power supply V_SFrequency, be also each LC resonator (TX, RX and repeater) Resonant frequency.Resonant frequency can be in 125KHz, 133KHz, 225KHz, 13.56MHz or other ISM (work Industry, science, medical treatment) frequency range selects.

The alternating current power supply of transmitting terminal can be full-bridge or semi-bridge inversion power supply, it is also possible to puts from high-frequency signal source through power Big device exports after amplifying, and the former can be equivalent to source internal resistance R_SThe voltage source of=0 Ω, the latter is then equivalent to source internal resistance R_SOne Fixed but be not the voltage source of 0 Ω.According to R_SWhether is 0 Ω, filter prototype corresponding for MCR-WPT can be divided into source The both-end wave filter that internal resistance is the single-ended filter of 0 Ω and source internal resistance is not 0 Ω；And according to amplitude-frequency response feature, again may be used Being divided into the types such as Butterworth, Chebyshev, ellipse, the Bart being typically selected to have maximally-flat characteristic in application irrigates This type.

Method for designing of the present invention, as follows:

Step 101: determine R_S, R_LValue；

Step 102: determine operating frequency f₀；

Step 103: the filter type of correspondence is set；

Step 201: according to efficiency of transmission and transmission range-coil relative aperture, number of repeaters N-2 is set；

Step 202: relative bandwidth w is set；

Step 203: determine filter prototype parameter g_i；

Step 204: counting circuit parameter L_i, C_i, K_i,i+1；

Step 205: design air-core inductance；

Step 206: calculating system performance index: efficiency of transmission, bearing power, transmission range；

Step 207: supply voltage amplitude is set；

Step 301: judge whether to meet design objective, be, go to step 401；Otherwise go to step 201；

Step 401: draw system detailed design parameter.

Filter prototype parameter g of step 203 of the present invention_iDetermination:

Being N (number of repeaters is N-2) for LC resonator number, relative bandwidth is w, system operating frequency f₀Multi-repeater MCR-WPT system, be single-ended or both-end according to the filter prototype of system equivalence, and width Frequently response characteristic (Butterworth type, Chebyshev type, ellipse etc.), determine N rank filter low pass prototype parameter g_i(i=0 ..., N+1).

The circuit parameter L of step 204 of the present invention_i, C_i, K_i,i+1Calculating, as follows:

(1) if R_S=0 Ω:

Transmitting terminal TX: $L_1=\frac{g_1{R}_L}{2\mathrm{\&pi;w}{f}_0},C_1=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_1}$

Receiving terminal RX: $L_N=\frac{g_N{R}_L}{2\mathrm{\&pi;w}{f}_0},C_N=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_N}$

Repeater: L_iWithout constraint, $C_i=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_i},(i=2,...,N-1)$

The mutual inductance of adjacent windings: $k_{i,i+1}=\frac{w}{\sqrt{g_i{g}_{i+1}}},(i=1,...,N-1)$

(2) if R_S(for being not equal to the pure resistance of zero non-pure resistance is loaded, impedance can be utilized to become at load end Switching network transforms it into pure resistance):

Transmitting terminal TX: $L_1=\frac{g_1{R}_S}{2\mathrm{\&pi;w}{f}_0},C_1=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_1}$

Receiving terminal RX: $C_N=\frac{1}{4{\mathrm{\&pi;}}^2{f_0}^2{L}_N}$

Repeater: L_iWithout constraint, $C_i=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_i},(i=2,...,N-1)$

The mutual inductance of adjacent windings: $k_{i,i+1}=\frac{w}{\sqrt{g_i{g}_{i+1}}},(i=1,...,N-1)$

The air-core inductance design of step 205 of the present invention: determine air-core inductance according to the requirement of design Shape and allow bore scope, then according to air-core inductance L_iThe value of calculation of inductance value determines air-core inductance The concrete bore of geometric parameter, the number of turn and line footpath, estimation coil loss resistance and Q-value.Inductance value can use Neumann Formula calculates, and other call parameter can be estimated by equation below:

Loss resistance: $R=\sqrt{\frac{{\mathrm{\&mu;}}_0{\mathrm{\&omega;}}_0}{2\mathrm{\&sigma;}}}\frac{l}{2\mathrm{\&pi;a}}$

Quality factor: $Q=\frac{{\mathrm{\&omega;}}_{0}L}{R}$

μ₀Being the pcrmeability in vacuum, σ is wire electrical conductivity.L is that conductor bus is long, and a is wire radius.

The system performance index of step 206 of the present invention can be estimated as follows:

Efficiency of transmission η: $\mathrm{\&eta;}=100\exp (-\frac{0.0691}{{\mathrm{wf}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{g_i{R}_i}{L_i}).$

Bearing power P_L: to R_SThe voltage source of ≠ 0 Ω, bearing power

To R_SThe voltage source of=0 Ω, bearing power

The relative position put with coil due to the transmission range of multi-repeater MCR-WPT system is relevant, is determining line After the geometric parameter of circle, according to mutual inductance k_i,i+1Theoretical value, the available Neumann calculating self-inductance/mutual inductance Formula determines the relative position between coil and the reasonable value of transmission range.It is close as a example by air-core inductance by circle, If the transmitting coil in system, repeating coil and receiving coil are the most coaxially placed in parallel, can according to Neumann formula Obtain distance d of its adjacent two coils_i,i+1With mutual inductance k_i,i+1Relation be:

$k_{i,i+1}=\frac{{\mathrm{\&mu;}}_0{n}_i{n}_{i+1}\sqrt{r_i{r}_{i+1}}[(2-G^2)K\left(G\right)-2E\left(G\right)]}{{\mathrm{GL}}_i{L}_{i+1}}$

Whereinn_i、n_i+1For coil turn, r_i、r_i+1For coil bore (radius), K (G) It is the first kind and complete elliptic integral of the second kind with E (G).

Transmit total distance: $D=\underset{i=1}{\overset{N-1}{\mathrm{\&Sigma;}}}{d}_{i,i+1}$

The present invention there is no concrete constraint to the inductance value of repeater air core coil, but in order to reduce the loss on circuit, should Use as far as possible low-loss, high q-factor inductance coil as repeater coil.

The effect of invention: the present invention is directed to the multi-repeater MCR-WPT system of complexity, give the meter of set of system Calculate circuit element parameter (L_i, C_i, k_i,i+1) and system design objective (efficiency of transmission, through-put power and transmission range) Quantitative analysis formula.According to the computing formula that these are detailed and perfect, user can be carried out arbitrarily rapidly and accurately The design of the MCR-WPT system of the multi-repeater longer transmission distance of number and exploitation.The present invention is to repeater tubular wire The concrete value of inductance value of circle there is no constraint, and this also to the design of many relaying MCR-WPT systems to realize bringing greatly Degree of freedom.

Accompanying drawing explanation

Fig. 1 is the system circuit diagram that the present invention is targeted.Wherein, transmitting terminal TX is by alternating current power supply V_S, launch End air-core inductance L₁, transmitting terminal tuning capacity C₁Composition, R_SAnd R₁It is respectively source internal resistance and transmitting terminal circuit damages Power consumption hinders.Repeater is by air-core inductance L_iWith tuning capacity C_iIt is in series, 1 < i < N, R_iFor loss resistance. Receiving terminal RX is by air-core inductance L_N, receiving terminal tuning capacity C_N, receiving terminal load R_LIt is in series, R_NFor Loss resistance.k_i,i+1(i=1 ..., N-1) it is the mutual inductance between adjacent inductive coil i and i+1.

Fig. 2 is the system design detail flowchart of embodiment.

Fig. 3 is in embodiment, the curve chart of frequency (kHz) efficiency of transmission (%) of multi-repeater MCR-WPT system. When frequency is 133kHz (operating frequency), efficiency of transmission η=90.3%.

Fig. 4 is in embodiment, the curve chart of frequency (kHz) bearing power (W) of multi-repeater MCR-WPT system. When frequency is 133kHz (operating frequency), bearing power P_L=10.45W.

Detailed description of the invention

Below with reference to accompanying drawing, the preferred embodiments of the present invention are described in detail: should be appreciated that and be preferable to carry out Example is only for the explanation present invention rather than in order to limit the scope of the invention.

Embodiment.Designing a operating frequency is 133kHz, and efficiency of transmission is more than 90%, loads 20 Ω, bearing power 10W, coil bore (radius) 25cm, the transmission range many relay wireless power transmission system more than 75cm, electricity Potential source uses full bridge inverse conversion power.Its detailed design flow process is as shown in Figure 2.

Step 101: determine R_S=0 Ω, R_L=20 Ω.

Step 102: determine f₀=133kHz.

Step 103: the filter type arranging correspondence is R_SThe single-ended Butterworth type of=0 Ω.

Step 201: according to efficiency of transmission and transmission range-coil relative aperture, the initial value arranging N is 4.

Step 202: w=0.05 is set.

Step 203:4 rank single-ended Butterworth filter prototype parameter is g₀=0, g₁=1.5307, g₂=1.5772, g₃=1.0824, g₄=0.3827, g₅=1.

Step 204: determine $L_1=\frac{g_i{R}_L}{2\mathrm{\&pi;w}{f}_0}=732\mathrm{\&mu;H},L_4=\frac{g_4{R}_L}{2\mathrm{\&pi;w}{f}_0}=183\mathrm{\&mu;H}.$ C₁=1.9nF, C₄=7.8nF. k₁₂=0.032, k₂₃=0.038, k₃₄=0.077.

Step 205: utilize Nuo Yiman formula to carry out comprehensively, L₄For close around 10 circles with the copper cash of copper wire diameter 1.26mm, Bore (radius) is the circular hollow inductance coil of 24.2cm, and its inductance is about 183 μ H.L₁The number of turn is 20, its Its same L₄.Estimation L₁Q-value be about 850, L₄Q-value be about 425.And in order to improve the efficiency of transmission of system, L₂And L₃Q-value should be larger.Therefore by L₂And L₃The number of turn is set to 25.Its inductance is about 1146 μ H, Q-value It is about 1055.

Step 206,207: calculate η=0.900, meet index request.When these 4 with bore air core coil When coaxial line is placed in parallel, according to k₁₂=0.032, k₂₃=0.038, k₃₄=0.077 can determine that transmission range is about 92cm, More than the 75cm required.For making bearing power P_L=η | V_S|²/(2R_L)=0.0225 | V_S|²=10W, is arranged | V_S|=21V.

Step 301,401: efficiency of transmission 90%, transmission range 92cm, bearing power 10W, therefore meet index Requirement.To sum up, system detailed design parameter is listed:

Power work frequency 133kHz, power source voltage amplitude 21V；

Load resistor value 20 Ω；

Number of repeaters 2；

Air-core inductance:

L₁Copper wire diameter 1.26mm, 20 circles, bore (radius) 24.2cm, circular；

L₂With L₃Copper wire diameter 1.26mm, 25 circles, bore (radius) 24.2cm, circular；

L₄Copper wire diameter 1.26mm, 10 circles, bore (radius) 24.2cm, circular；

Tuning capacity C₁=1.9nF, C₂=C₃=1.21nF, C₄=7.8nF；

Mutual inductance k₁₂=0.032, k₂₃=0.038, k₃₄=0.077；

Bearing power 10W, efficiency of transmission 90%, transmission range > 90cm.

Fig. 3-Fig. 4 gives frequency (kHz) efficiency of transmission (%) of embodiment and frequency (kHz) bearing power (W) Simulation curve.Compare with theoretical value, when frequency is 133kHz (operating frequency), bearing power P_L=10.45W, transmission Efficiency eta=90.3%, error is less than 5%.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, it is clear that the technology of this area Personnel can carry out various change and modification without departing from the spirit and scope of the present invention to the present invention.So, if originally These amendments of invention and modification belong within the scope of the claims in the present invention and equivalent technologies thereof, then the present invention also anticipates Figure comprises these and changes and modification.

Claims (8)

1. a method for designing for multi-repeater magnet coupled resonant type wireless power transmission system, the circuit structure bag of system Include transmitting terminal TX, multiple repeater, receiving terminal RX, and be all LC resonator；Transmitting terminal TX by alternating current power supply, Transmitting terminal air-core inductance L₁, transmitting terminal tuning capacity C₁Composition, R_SAnd R₁It is respectively source internal resistance and launches end line Road loss resistance；Repeater is by air-core inductance L_iWith tuning capacity C_iIt is in series, R_iFor loss resistance, 1 < i < N, N are resonator total numbers；Receiving terminal RX is by air-core inductance L_N, receiving terminal tuning capacity C_N, receiving terminal Load R_LIt is in series, R_NFor loss resistance；It is characterized in that as follows:

Step 101: determine R_S, R_LValue；

Step 102: determine operating frequency f₀；

Step 103: the filter type of correspondence is set；

Step 201: according to efficiency of transmission and transmission range-coil relative aperture, number of repeaters N-2 is set；

Step 202: relative bandwidth w is set；

Step 203: determine filter low pass prototype parameter g_i；

Step 204: counting circuit parameter L_i, C_i, k_i,i+1；

Step 205: design air-core inductance；

Step 206: calculating system performance index: efficiency of transmission, bearing power, transmission range；

Step 207: supply voltage amplitude V is set_S；

Step 301: judge whether to meet design objective, be, go to step 401；Otherwise go to step 201；

Step 401: draw system detailed design parameter；

Wherein, L_iAnd C_iIt is inductance value and the capacitance of i-th resonator, 1≤i≤N；k_i,i+1(i=1 ..., N-1) it is I resonator and the inductive coupling coefficient of i+1 resonator.

Method for designing the most according to claim 1, is characterized in that the filter prototype parameter of described step 203 g_iDetermination be: being N for LC resonator number, relative bandwidth is w, system operating frequency f₀Multi-repeater magnetic Coupled resonance formula wireless charging system, is single-ended or both-end according to the filter prototype of system equivalence, and amplitude-frequency response Feature, determines N rank filter low pass prototype parameter g_i(i=0 ..., N+1).

Method for designing the most according to claim 1, is characterized in that the circuit parameter L of described step 204_i, C_i, k_i,i+1Calculating, as follows:

(1) if R_S=0 Ω:

Transmitting terminal TX:

Receiving terminal RX:

Repeater: L_iWithout constraint,

The mutual inductance of adjacent windings:

(2) if R_S≠ 0:

Transmitting terminal TX:

Receiving terminal RX:

Repeater: L_iWithout constraint,

The mutual inductance of adjacent windings:

Wherein L₁And C₁It is inductance and the electric capacity of transmitting terminal resonator；L_NAnd C_NIt is inductance and the electricity of receiving terminal resonator Hold.

Method for designing the most according to claim 1, is characterized in that the air-core inductance of described step 205 sets Meter: determine the shape of air-core inductance according to the requirement of design and allow bore scope, then according to air core inductor line Circle L_iThe value of calculation of inductance value determines the concrete bore of geometric parameter, the number of turn and the line footpath of air-core inductance, estimates coil Loss resistance and Q-value；Inductance value uses Neumann formula to calculate, and other call parameter equation below is estimated:

Loss resistance:

Quality factor:

μ₀Being the pcrmeability in vacuum, σ is wire electrical conductivity, and l is that conductor bus is long, and a is wire radius, ω₀For humorous Shake angular frequency: ω₀=2 π f₀。

Method for designing the most according to claim 1, it is characterized in that the system performance index of described step 206 by Equation below is estimated:

Efficiency of transmission η:

Bearing power P_L: to R_SThe voltage source of ≠ 0 Ω, bearing power

To R_SThe voltage source of=0 Ω, bearing power

Wherein R_iBeing the loss resistance of i-th resonator, Vs is the voltage amplitude of transmitting terminal alternating-current voltage source.

Method for designing the most according to claim 1, is characterized in that described operating frequency f₀For 125KHz, 133KHz, 225KHz or 13.56MHz.

Method for designing the most according to claim 1, it is characterized in that described air-core inductance turn to circle, Rectangle, triangle, pentagon or hexagon.

Method for designing the most according to claim 1, is characterized in that described air-core inductance is low-loss, height The inductance coil of Q-value.