Parameter derivation method

Abstract

A method for determining parameters of a wireless power transmission system is disclosed where the wireless power transmission system transmits power from a power transmission device to a power reception device via electric field coupling. The parameters include a coupling coefficient ke of an electric field coupling unit that is formed of active electrodes and passive electrodes of the power transmission device and the power reception device.

Claims

1. A method for determining parameters of a wireless power transmission system that transmits power from a power transmission device to a power reception device by electric field coupling, where the power transmission device includes first and second electrodes and a step-up transformer that outputs a stepped up alternating current voltage between the first and second electrodes, and the power reception device includes third and fourth electrodes and a step-down transformer that steps down a voltage induced in the third and fourth electrodes when facing the first and second electrodes, respectively, the method comprising: measuring at least one of a resonant frequencies ω.sub.1 and ω.sub.2 and anti-resonant frequencies ω.sub.00 and ω.sub.0 of an input impedance from a primary side of the step-up transformer when the third and fourth electrodes are in an open state; measuring at least one of a resonant frequency ωr and an anti-resonant frequency ωa of an input impedance from the primary side of the step-up transformer when the third and fourth electrodes are short circuited; and determining a coupling coefficient ke of an electric field coupling unit that includes the first, second, third and fourth electrodes, where the coupling coefficient ke is determined according to either Equation (A) or Equation (B), wherein Equation (A) is: $k_e=\sqrt{1-{\left(\frac{{\omega }_a{\omega }_{\mathrm{eq}}}{{\omega }_{00}{\omega }_0}\right)}^2}$ $\mathrm{where}$ $\frac{1}{{\omega }_{\mathrm{eq}}^2}=\frac{1}{{\omega }_0^2}+\frac{1}{{\omega }_{00}^2}-\frac{1}{{\omega }_a^2},$ and Equation (B) is: $k_e=\sqrt{1-{\left(\frac{{\omega }_r{\omega }_{\mathrm{eq}}}{{\omega }_1{\omega }_2}\right)}^2}$ $\mathrm{where}$ $\frac{1}{{\omega }_{\mathrm{eq}}^2}=\frac{1}{{\omega }_1^2}+\frac{1}{{\omega }_2^2}-\frac{1}{{\omega }_r^2}.$

2. The method according to claim 1, wherein the third electrode of the power reception device faces the first electrode of the power transmission device with a gap therebetween, and the fourth electrode of the power reception device faces the second electrode of the power transmission device with a gap therebetween or is in contact with the second electrode.

3. The method according to claim 2, wherein the power reception device includes a rectification smoothing circuit that rectifies and smoothes the stepped down voltage output from the step-down transformer.

4. The method according to claim 1, further comprising determining an equivalent inductance L.sub.eq of a resonance circuit that includes the step-down transformer of the power reception device.

5. The method according to claim 4, wherein the determining of the equivalent inductance L.sub.eq comprises measuring the inductance L.sub.eq of the resonance circuit.

6. The method according to claim 5, wherein the measuring of the equivalent inductance of the inductor Leq comprises measuring an inductance of a primary coil of the step-down transformer of the power reception device.

7. The method according to claim 4, further comprising determining a self-inductance L.sub.1 of the secondary coil of the step-up transformer of the power transmission device.

8. The method according to claim 7, wherein the power transmission system further includes an equivalent circuit of a capacitive coupling unit that comprises a first capacitor connected in parallel with the secondary coil of the step-up transformer, a second capacitor connected in parallel with a primary coil of the step-down transformer, a third capacitor connected between the first capacitor and the second capacitor, and wherein the method further comprising determining a capacitance C.sub.1 of the first capacitor, a capacitance C.sub.2 of the second capacitor and a capacitance C.sub.3 of the third capacitor, wherein $\begin{array}{c}{C}_G=\frac{1}{L_1{\omega }_a^2}\\ C_L=\frac{1}{L_{\mathrm{eq}}{\omega }_{\mathrm{eq}}^2}{C}_1=C_G-C_3{C}_2=C_L-C_3{C}_3=\mathrm{ke}\sqrt{C_G{C}_L}.\end{array}$

9. A method for determining parameters of a wireless power transmission system that transmits power from a power transmission device to a power reception device by electric field coupling, where the power transmission device includes first and second electrodes an a step-up transformer that outputs a stepped up alternating current voltage between the first and second electrodes, and a power reception device includes third and fourth electrodes and a step-down transformer that steps down a voltage induced in the third and fourth electrodes when facing the first and second electrodes, the method comprising: measuring at least one of a resonant frequencies ω.sub.1 and ω.sub.2 and anti-resonant frequencies ω.sub.00 and ω.sub.0 of an input impedance from a secondary side of the step-down transformer when the first and second electrodes are in an open state; measuring at least one of a resonant frequency ωr and an anti-resonant frequency ωa of an input impedance from the secondary side of the step-down transformer when the first and second electrodes are short circuited; and determining a coupling coefficient ke of an electric field coupling unit that includes the first, second, third and fourth electrodes, where the coupling coefficient ke is determined according to either Equation (A) or Equation (B), wherein Equation (A) is: $k_e=\sqrt{1-{\left(\frac{{\omega }_a{\omega }_{\mathrm{eq}}}{{\omega }_{00}{\omega }_0}\right)}^2}$ $\mathrm{where}$ $\frac{1}{{\omega }_{\mathrm{eq}}^2}=\frac{1}{{\omega }_0^2}+\frac{1}{{\omega }_{00}^2}-\frac{1}{{\omega }_a^2},$ and Equation (B) is: $k_e=\sqrt{1-{\left(\frac{{\omega }_r{\omega }_{\mathrm{eq}}}{{\omega }_1{\omega }_2}\right)}^2}$ $\mathrm{where}$ $\frac{1}{{\omega }_{\mathrm{eq}}^2}=\frac{1}{{\omega }_1^2}+\frac{1}{{\omega }_2^2}-\frac{1}{{\omega }_r^2}.$

10. The method according to claim 9, wherein the third electrode of the power reception device faces the first electrode of the power transmission device with a gap therebetween, and the fourth electrode of the power reception device faces the second electrode of the power transmission device with a gap therebetween or is in contact with the second electrode.

11. The method according to claim 10, wherein the power reception device includes a rectification smoothing circuit that rectifies and smoothes the stepped down voltage output from the step-down transformer.

12. The method according to claim 9, further comprising determining an equivalent inductance L.sub.eq of a resonance circuit that includes the step-up transformer of the power transmission device.

13. The method according to claim 12, wherein the determining of the equivalent inductance L.sub.eq comprises measuring the inductance L.sub.eq of the resonance circuit.

14. The method according to claim 13, wherein the measuring of the equivalent inductance of the inductor Leq comprises measuring an inductance of a secondary coil of the step-up transformer of the power transmission device.

15. The method according to claim 12, further comprising determining a self-inductance L.sub.2 of the primary coil of the step-down transformer of the power reception device.

16. The method according to claim 15, wherein the power transmission system further includes an equivalent circuit of a capacitive coupling unit that comprises a first capacitor connected in parallel with the secondary coil of the step-up transformer, a second capacitor connected in parallel with a primary coil of the step-down transformer, a third capacitor connected between the first capacitor and the second capacitor, and wherein the method further comprising determining a capacitance C.sub.1 of the second capacitor, a capacitance C.sub.2 of the first capacitor and a capacitance C.sub.3 of the third capacitor, wherein $\begin{array}{c}{C}_G=\frac{1}{L_1{\omega }_a^2}.\\ C_L=\frac{1}{L_{\mathrm{eq}}{\omega }_{\mathrm{eq}}^2}{C}_1=C_L-C_3{C}_2=C_G-C_3{C}_3=\mathrm{ke}\sqrt{C_G{C}_L}.\end{array}$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a circuit diagram of a wireless power transmission system according to an embodiment.

(2) FIG. 2 illustrates an equivalent circuit of a capacitive coupling unit.

(3) FIG. 3 illustrates measurement results of frequency characteristics in a case where a capacitor section is not short circuited.

(4) FIG. 4 illustrates measurement results of frequency characteristics in a case where a capacitor section is short circuited.

(5) FIG. 5 illustrates an equivalent circuit of a capacitive coupling unit.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

(6) FIG. 1 is a circuit diagram of a wireless power transmission system 300 according to an embodiment. The wireless power transmission system 300 includes a power transmission device 101 and a power reception device 201. The power reception device 201 includes a load RL. The load RL is a battery module that includes a rechargeable battery and a charging circuit. The power reception device 201 is for example a mobile electronic appliance equipped with a rechargeable battery. Examples of such a mobile electronic appliance include cellular phones, PDAs, portable music players, laptop PCs, digital cameras and so forth. The power reception device 201 is mounted on the power transmission device 101 and the power transmission device 101 charges the rechargeable battery of the power reception device 201.

(7) The power transmission device 101 includes a direct current power supply Vin that outputs DC 5V or 12V. An input capacitor Cin is connected to the direct current power supply Vin. In addition, a DC-AC inverter circuit, which converts a direct current voltage into an alternating current voltage, is connected to the direct current power supply Vin. The DC-AC inverter circuit includes switching elements Q1, Q2, Q3 and Q4 and the switch elements Q1 and Q4 and the switch elements Q2 and Q3 are alternately turned on and off.

(8) A primary coil L.sub.11 of a step-up transformer T1 is connected to a connection point between the switching elements Q1 and Q2 and a connection point between the switching elements Q3 and Q4. An active electrode 11 and a passive electrode 12 are connected to a secondary coil L.sub.12 of the step-up transformer T1. The step-up transformer T1 steps up an alternating current voltage and applies the stepped-up alternating current voltage between the active electrode 11 and the passive electrode 12. The frequency of this alternating current voltage is set to be in the range of from 100 kHz to 10 MHz.

(9) A capacitor Ca is connected in parallel with the secondary coil L.sub.12 of the step-up transformer T1. The capacitor Ca is a stray capacitance generated between the active electrode 11 and the passive electrode 12 or is a combined capacitance made up of the capacitance of a capacitor and the stray capacitance in the case where the capacitor is connected. The capacitor Ca forms a series resonance circuit with a leakage inductance (not illustrated) of the secondary coil L.sub.12 of the step-up transformer T1.

(10) The power reception device 201 includes an active electrode 21 and a passive electrode 22. When the power reception device 201 is mounted on the power transmission device 101, the active electrode 21 and the passive electrode 22 face the active electrode 11 and the passive electrode 12 of the power transmission device 101 with gaps therebetween. The passive electrodes 12 and 22 may directly contact each other. A capacitor Caa illustrated in FIG. 1 is a capacitance formed between the active electrodes 11 and 21 and a capacitor Cpp is a capacitance formed between the passive electrodes 12 and 22.

(11) A primary coil L.sub.21 of a step-down transformer T2 is connected to the active electrode 21 and the passive electrode 22. A capacitor Cb is connected to the primary coil L.sub.21. The capacitor Cb is a stray capacitance generated between the active electrode 21 and the passive electrode 22 or is a combined capacitance made up of the capacitance of a capacitor and the stray capacitance in the case where the capacitor is connected. The capacitor Cb forms a parallel resonance circuit with an excitation inductance of the primary coil L.sub.21 of the step-down transformer T2.

(12) A diode bridge DB formed of four diodes is connected to a secondary coil L.sub.22 of the step-down transformer T2. The load RL, which is a rechargeable battery, is connected to the diode bridge DB via a smoothing capacitor Cout.

(13) The power reception device 201 is mounted on the power transmission device 101 and a voltage is applied between active electrode 11 and the passive electrode 12 of the power transmission device 101, whereby the active electrodes 11 and 21 and the passive electrodes 12 and 22, which are arranged so as to face each other, become capacitively coupled with each other and an electric field is generated therebetween. Then, power is transmitted from the power transmission device 101 to the power reception device 201 via the electric field. In the power reception device 201, an alternating current voltage induced by the power transmission is stepped down by the step-down transformer T2, rectified and smoothed by the diode bridge DB and the smoothing capacitor Cout, and then applied to the load RL.

(14) A method for deriving parameters related to capacitive coupling using the active electrode 11, the passive electrode 12, the active electrode 21 and the passive electrode 22 in the thus-configured wireless power transmission system 300 will be described. By deriving the parameters related to capacitive coupling, design of the sizes and the shapes of the active electrodes 11 and 21 and the passive electrodes 12 and 22 will become easier and the time and labor involved in design and trial manufacture can be reduced compared with the case where the design of electrodes is repeatedly performed by trial and error using the so-called “cut and try” process.

(15) First, in order to derive the value of the coupling capacitance, a coupling coefficient ke of the active electrodes 11 and 12 and the passive electrodes 12 and 22 is derived. By deriving the coupling coefficient ke, the size of the capacitive coupling between the electrodes can be obtained and the magnitude of the power transmission efficiency can be determined. The coupling coefficient ke can be derived by measuring the resonant frequency and anti-resonant frequency of a capacitive coupling unit of the power transmission device 101 and the power reception device 201 and using certain equations. M1 and M2 in FIG. 1 indicate measurement locations of the resonant frequency and anti-resonant frequency. In this embodiment, a method for deriving the coupling coefficient ke by focusing on the input impedance when looking at the power reception device 201 side from the measurement locations M1 and M2 will be described. Measurement of the resonant frequency and anti-resonant frequency is not limited to being realized by measurement of impedance Z and the resonant frequency and anti-resonant frequency can be similarly measured from frequency characteristics of admittance Y or an S parameter S11.

(16) Hereafter, L.sub.1 denotes a self-inductance of the secondary coil L.sub.12 of the step-up transformer T1 and L.sub.2 denotes a self-inductance of the primary coil L.sub.21 of the step-down transformer T2. In addition, k.sub.m1 denotes a coupling coefficient of the step-up transformer T1 and k.sub.m2 denotes a coupling coefficient of the step-down transformer T2.

(17) FIG. 2 illustrates an equivalent circuit of the capacitive coupling unit. In an upper part of FIG. 2, the step-up transformer T1 and the step-down transformer T2 are represented as T-type equivalent circuits. In these T-type equivalent circuits only equivalent circuits of inductance portions of the step-up transformer T1 and the step-down transformer T2 are illustrated and illustration of an ideal transformer, which is a voltage transformation unit, is omitted. Hereafter, in the figure, C.sub.1 denotes the capacitance of a capacitor C1, C.sub.2 denotes the capacitance of a capacitor C2 and C.sub.3 denotes the capacitance of a capacitor C3. The lower part of FIG. 2 illustrates a circuit diagram for the case where the T-type equivalent circuit of the step-down transformer T2 is replaced with a single inductor Leq.

(18) Input terminals IN1 and IN2 illustrated in FIG. 2 correspond to the measurement locations M1 and M2 in FIG. 1 and the DC-AC inverter circuit of FIG. 1 is connected to the input terminals IN1 and IN2. In addition, the diode bridge DB illustrated in FIG. 1 is connected to output terminals OUT1 and OUT2.

(19) First, the resonant frequency and anti-resonant frequency are measured at the input terminals IN1 and IN2 in the case where a capacitor C2 section (that is, active electrode and passive electrode of power reception device) is not short circuited and in the case where the capacitor C2 section is short circuited. First, the frequency characteristics of the impedance of the circuit seen from the input terminals IN1 and IN2 in a state where the capacitor C2 section is not short circuited are measured. FIG. 3 illustrates measurement results of frequency characteristics in a case where capacitor C2 section is not short circuited. In the case where the capacitor C2 section is not short circuited, resonant frequencies f.sub.1 and f.sub.2 and anti-resonant frequencies f.sub.00 and f.sub.0 can be measured as illustrated in FIG. 3.

(20) At the time of measurement, coupling between the load and the resonance circuit is made weak so that a Q of the power-reception-side resonance circuit is not allowed to decrease. In the case where the measurement is performed using a minute signal, provided that the load and the resonance circuit are separated from each other using a diode bridge as in this embodiment, the coupling can be made weak even when the load is connected. Any appropriate means for making the coupling weak (not physically connecting the load, providing a switch to disconnect the load and the resonance circuit) may be applied.

(21) In addition, the frequency characteristics of the impedance of the circuit seen from the input terminals IN1 and IN2 in a state where the capacitor C2 section is short circuited are measured. FIG. 4 illustrates measurement results of frequency characteristics in the case where capacitor C2 section is short circuited. In the case where the capacitor C2 section is short circuited, a resonant frequency fr and an anti-resonant frequency fa can be measured as illustrated in FIG. 4.

(22) Hereafter, angular frequencies corresponding to the resonant frequencies f.sub.1 and f.sub.2 and the anti-resonant frequencies f.sub.00 and f.sub.0 are denoted by ω.sub.1 and ω.sub.2 (ω.sub.1≦ω.sub.2) and ω.sub.00 and ω.sub.0. In addition, angular frequencies corresponding to the resonant frequency fr and the anti-resonant frequency fa are denoted by ωr and ωa.

(23) An input impedance Zin in the case where the capacitor C2 section is not short circuited in the circuit illustrated in the lower part of FIG. 2 can be expressed by the following Equation (1).

(24) $\begin{array}{cc}\mathrm{Equation}1& \\ Z_{\mathrm{in}}=j\omega L_1\frac{\left(1-{\omega }^2{L}_{\mathrm{eq}}{C}_L\right)-{\omega }^2\left(1-k_{m1}^2\right)\left(L_1{C}_G-\left(1-k_e^2\right){\omega }^2{L}_1{L}_{\mathrm{eq}}{C}_G{C}_L\right)}{1-{\omega }^2\left(L_1{C}_G+L_{\mathrm{eq}}{C}_L-\left(1-k_e^2\right){\omega }^2{L}_1{L}_{\mathrm{eq}}{C}_G{C}_L\right)}\mathrm{where}{C}_G=C_1+C_3{C}_L=C_2+C_3{k}_e=\frac{C_3}{\sqrt{C_G{C}_L}}& \left(1\right)\end{array}$

(25) By making Leq=0 in Equation (1), the input impedance Zin in the case where the capacitor C2 section is short circuited can be derived, giving the following Equation (2).

(26) $\begin{array}{cc}\mathrm{Equation}2& \\ Z_{\mathrm{in}}=j\omega L_1\frac{1-\left(1-k_{m1}^2\right){\omega }^2{L}_1{C}_G}{1-{\omega }^2{L}_1{C}_G}& \left(2\right)\end{array}$

(27) The resonant frequency ωr in the case where the capacitor C2 section is short circuited is the frequency when Zin=0, that is, when the numerator of Equation (2) is 0 and the relational expression of Equation (3) holds true.

(28) $\mathrm{Equation}3$$\begin{array}{cc}{\omega }_r^2=\frac{1}{\left(1-k_{m1}^2\right)L_1{C}_G}=\frac{1}{L_{1S}{C}_G}& \left(3\right)\end{array}$

(29) Here, L.sub.1S is a leakage inductance of the step-up transformer T1.

(30) In addition, the anti-resonant frequency ωa in the case where the capacitor C2 section is short circuited is the frequency when Zin=∞, that is, when the denominator of Equation (2) is 0 and the relational expression of Equation (4) holds true.

(31) $\mathrm{Equation}\mathrm{Math}4$$\begin{array}{cc}{\omega }_a^2=\frac{1}{L_1{C}_G}& \left(4\right)\end{array}$

(32) Here, considering an LC resonance circuit made up of the capacitance C.sub.L=C.sub.2+C.sub.3 and the inductor Leq in the circuit illustrated in the lower part of FIG. 2, the following Equation (5) is defined.

(33) $\mathrm{Equation}\mathrm{Math}5$$\begin{array}{cc}{\omega }_{\mathrm{eq}}^2\equiv \frac{1}{L_{\mathrm{eq}}{C}_L}& \left(5\right)\end{array}$

(34) The anti-resonant frequencies ω.sub.00 and ω.sub.0 in the case where the capacitor C2 section is not short circuited are frequencies at which Zin=∞. Zin=∞ when the denominator of Equation (1) is 0 and is expressed by the following Equation (6).
Equation Math 6
1−ω.sup.2(L.sub.1C.sub.G+L.sub.eqC.sub.L−(1−k.sub.e.sup.2)ω.sup.2L.sub.1L.sub.eqC.sub.GC.sub.L)=0  (6)

(35) Substituting the anti-resonant frequencies ω.sub.00 and ω.sub.0 into Equation (6), the relational expressions of the following Equation (7) and Equation (8) hold true.
Equation Math 7
1−ω.sub.00.sup.2(L.sub.1C.sub.G+L.sub.eqC.sub.L−(1−k.sub.e.sup.2)ω.sub.00.sup.2L.sub.1L.sub.eqC.sub.GC.sub.L)=0  (7)
1−ω.sub.0.sup.2(L.sub.1C.sub.G+L.sub.eqC.sub.L−(1−k.sub.e.sup.2)ω.sub.0.sup.2L.sub.1L.sub.eqC.sub.GC.sub.L)=0  (8)

(36) Substituting Equation (4) and Equation (5) into Equation (7) and Equation (8) and rearranging, the relational expressions of the following Equation (9) and Equation (10) hold true.

(37) 0$\mathrm{Equation}\mathrm{Math}8$$\begin{array}{cc}\left(1-\frac{{\omega }_{00}^2}{{\omega }_{\mathrm{eq}}^2}\right)-\frac{{\omega }_{00}^2}{{\omega }_a^2}\left(1-\left(1-k_e^2\right)\frac{{\omega }_{00}^2}{{\omega }_{\mathrm{eq}}^2}\right)=0& \left(9\right)\\ \left(1-\frac{{\omega }_0^2}{{\omega }_{\mathrm{eq}}^2}\right)-\frac{{\omega }_0^2}{{\omega }_a^2}\left(1-\left(1-k_e^2\right)\frac{{\omega }_0^2}{{\omega }_{\mathrm{eq}}^2}\right)=0& \left(10\right)\end{array}$

(38) The resonant frequencies ω.sub.1 and ω.sub.2 in the case where the capacitor C2 section is not short circuited are frequencies at which Zin=0. Zin=0 when the numerator of Equation (1) is 0 and is expressed by the following Equation (11).
Equation 9
(1−ω.sup.2L.sub.eqC.sub.L)−ω.sup.2(1−k.sub.m1.sup.2)(L.sub.1C.sub.G−(1−k.sub.e.sup.2)ω.sup.2L.sub.1L.sub.eqC.sub.GC.sub.L)=0  (11)

(39) Substituting the resonant frequencies ω.sub.1 and ω.sub.2 into Equation (11), the relational expressions of the following Equation (12) and Equation (13) hold true.
Equation 10
(1−ω.sub.1.sup.2L.sub.eqC.sub.L)−ω.sub.1.sup.2(1−k.sub.m1.sup.2)(L.sub.1C.sub.G−(1−k.sub.e.sup.2)ω.sub.1.sup.2L.sub.1L.sub.eqC.sub.GC.sub.L)=0  (12)
(1−ω.sub.2.sup.2L.sub.eqC.sub.L)−ω.sub.2.sup.2(1−k.sub.m1.sup.2)(L.sub.1C.sub.G−(1−k.sub.e.sup.2)ω.sub.2.sup.2L.sub.1L.sub.eqC.sub.GC.sub.L)=0  (13)

(40) Substituting Equation (3) and Equation (5) into Equation (12) and Equation (13) and rearranging, the relational expressions of the following Equation (14) and Equation (15) hold true.

(41) $\mathrm{Equation}11$$\begin{array}{cc}\left(1-\frac{{\omega }_1^2}{{\omega }_{\mathrm{eq}}^2}\right)-\frac{{\omega }_1^2}{{\omega }_r^2}\left(1-\left(1-k_e^2\right)\frac{{\omega }_1^2}{{\omega }_{\mathrm{eq}}^2}\right)=0& \left(14\right)\\ \left(1-\frac{{\omega }_2^2}{{\omega }_{\mathrm{eq}}^2}\right)-\frac{{\omega }_2^2}{{\omega }_r^2}\left(1-\left(1-k_e^2\right)\frac{{\omega }_2^2}{{\omega }_{\mathrm{eq}}^2}\right)=0& \left(15\right)\end{array}$

(42) Solving for the coupling coefficient ke using the resonant frequencies ω.sub.00, ω.sub.0 and ωa obtained through measurements, the coupling coefficient ke (ke>0) can be expressed by the following Equation (16) from Equation (9) and Equation (10).

(43) $\mathrm{Equation}12$$\begin{array}{cc}{k}_e=\sqrt{1-{\left(\frac{{\omega }_a{\omega }_{\mathrm{eq}}}{{\omega }_{00}{\omega }_0}\right)}^2}& \left(16\right)\\ \mathrm{where}& \\ \frac{1}{{\omega }_{\mathrm{eq}}^2}=\frac{1}{{\omega }_0^2}+\frac{1}{{\omega }_{00}^2}-\frac{1}{{\omega }_a^2}& \end{array}$

(44) On the other hand, solving for the coupling coefficient ke from Equation (14) and Equation (15) using the resonant frequencies ω.sub.1, ω.sub.2 and ωr obtained through measurements, the coupling coefficient ke (ke>0) can be expressed by the following Equation (17).

(45) $\mathrm{Equation}13$$\begin{array}{cc}\begin{array}{c}{k}_e=\sqrt{1-{\left(\frac{{\omega }_r{\omega }_{\mathrm{eq}}}{{\omega }_1{\omega }_2}\right)}^2}\\ \mathrm{where}\\ \frac{1}{{\omega }_{\mathrm{eq}}^2}=\frac{1}{{\omega }_1^2}+\frac{1}{{\omega }_2^2}-\frac{1}{{\omega }_r^2}\end{array}& \left(17\right)\end{array}$

(46) Thus, by using the anti-resonant frequencies ω.sub.00, ω.sub.0 and ωa or the resonant frequencies ω.sub.1, ω.sub.2 and ωr, the coupling coefficient ke of the electrodes of the power transmission device 101 and the electrodes of the power reception device 201, which capacitively couple with each other, can be derived from Equation (16) or Equation (17). By deriving the coupling coefficient ke, the size of the capacitive coupling can be obtained and from that the magnitude of the power transmission efficiency can be determined. In addition, Equations (16) and (17) are not only derived from Equations (9) and (10) and Equations (14) and (15) respectively and can be derived by forming and calculating simultaneous equations using any two equations among Equations (9), (10), (14) and (15).

(47) Next, a method of deriving values of capacitances of an equivalent circuit of a capacitive coupling unit using the derived coupling coefficient ke will be described.

(48) First, the inductance L.sub.1 of the secondary coil L.sub.12 of the step-up transformer T1 and an inductance Leq of the inductor Leq are measured. As a method for measuring the inductance of the secondary coil L.sub.12, for example, a parallel resonance circuit made up of the secondary coil L.sub.12 and a parasitic capacitance possessed by the secondary coil L.sub.12 is considered, the frequency characteristics of this circuit are measured and the inductance L.sub.1 of the inductor L.sub.12 is derived from these results. In the case where the step-up transformer T1 of the power transmission device 101 has been provided with a shield, the inductance L.sub.1 is measured in a state where the shield is fitted. It is preferable that the values of the inductances of step-up and step-down transformers be measured in a state where the transformers are incorporated into the devices.

(49) The inductance of the inductor Leq can be derived by measuring the inductance L.sub.2 of the primary coil L.sub.21 of the step-down transformer T2. The method for measuring the inductance of the primary coil L.sub.21 of the step-down transformer T2 is the same as the method for measuring the inductance of the secondary coil L.sub.12 of the step-up transformer T1. In the equivalent circuit of FIG. 2, the output terminals OUT1 and OUT2 are open in the case where the capacitor C2 section is not short circuited, and the inductance Leq of the inductor Leq in this case is L.sub.2, that is, the inductance of the primary coil L.sub.21 of the step-down transformer T2. In addition, in the case where the secondary coil of the step-down transformer T2 is short circuited, Leq of the equivalent circuit of FIG. 2 is the leakage inductance of the step-down transformer T2. The inductance Leq of the inductor Leq in this case is (1−k.sub.m2.sup.2)L.sub.2. Whether the secondary coil of the step-down transformer T2 is to be short circuited or open should be appropriately selected in accordance with the circuit. (Ease of measurement of the resonant frequency (anti-resonant frequency) is an aim.) Next, the capacitances C.sub.G, C.sub.L, C.sub.1, C.sub.2 and C.sub.3 are derived using the measured inductance L.sub.2 and the derived inductance Leq. The following Equation (18) and Equation (19) are obtained by respectively modifying Equation (4) and Equation (5).

(50) $\mathrm{Equation}14$$\begin{array}{cc}{C}_G=\frac{1}{L_1{\omega }_a^2}& \left(18\right)\\ C_L=\frac{1}{L_{\mathrm{eq}}{\omega }_{\mathrm{eq}}^2}& \left(19\right)\end{array}$

(51) Since the inductances L.sub.2 and Leq and the resonant frequency ωa are known from design values set in advance or from values obtained from measurements, the capacitances C.sub.1, C.sub.2 and C.sub.3 can be derived from the relational expressions C.sub.G=C.sub.1+C.sub.3, C.sub.L=C.sub.2+C.sub.3 and ke=C.sub.3/√(C.sub.G.Math.C.sub.L) and Equation (4), Equation (18) and Equation (19) described above. As a result of deriving the capacitances C.sub.1, C.sub.2 and C.sub.3, work in which the active electrodes 11 and 21 and the passive electrodes 12 and 22 are repeatedly designed using a “cut and try” process in order to obtain optimum capacitance values is reduced.

(52) In this embodiment, a method for deriving the coupling coefficient ke and the values of the capacitances C1, C2 and C3 by focusing on the input impedance seen from the power transmission device 101 has been described, but the parameters may instead be derived by focusing on the input impedance seen from the power reception device 201.

(53) FIG. 5 illustrates an equivalent circuit of a capacitive coupling unit in the case where the input impedance seen from the power reception device 201 is focused upon. In the circuit illustrated in the lower part of FIG. 5, the T-type equivalent circuit of the step-up transformer T1 has been replaced with a single inductor Leq. The resonant frequency and the anti-resonant frequency are measured for the circuit illustrated in FIG. 5 in the case where the capacitor C1 section (that is, the active electrode and the passive electrode of the power transmission device) is short circuited and in the case where it is not short circuited and the coupling coefficient ke can be derived from Equation (16) or Equation (17).

(54) When the measurement is performed with the primary side (low voltage side) of the power transmission transformer not short circuited (case in which power transmission resonance circuit is made to operate as parallel resonance circuit), it is necessary to make the coupling between the power supply circuit and the resonance circuit weak so that a Q of the power-transmission-side resonance circuit will not be reduced. In the case where the measurement is performed using a minute signal, provided that the power supply (=Cin) and the resonance circuit are separated from each other with a bridge circuit as in FIG. 1, the coupling can be made weak even when the power supply is connected. Any appropriate means for making the coupling weak (not physically connecting the power supply, providing a switch to disconnect the power supply and the resonance circuit) may be applied. In the case where the primary side of the power transmission transformer is short circuited, no particular considerations are necessary.

(55) In addition, the capacitors C1, C2 and C3 shown in the circuit illustrated in FIG. 5 can be derived using the following Equation (20) and Equation (21). The following Equation (20) and Equation (21) can be derived similarly to as in the above-described embodiment by short circuiting the capacitor C1.

(56) $\mathrm{Equation}15$$\begin{array}{cc}{C}_G=\frac{1}{L_2{\omega }_a^2}& \left(20\right)\\ C_L=\frac{1}{L_{\mathrm{eq}}{\omega }_{\mathrm{eq}}^2}& \left(21\right)\end{array}$
where C.sub.1=C.sub.L−C.sub.3 C.sub.2=C.sub.G−C.sub.3 C.sub.3=ke√{square root over (C.sub.GC.sub.L)}

REFERENCE SIGNS LIST

(57) 11—active electrode (first electrode) 12—passive electrode (second electrode) 21—active electrode (third electrode) 22—passive electrode (fourth electrode) 101—power transmission device 201—power reception device 300—wireless power transmission system C1, C2, C3—capacitor M1, M2—measurement location IN1, IN2—input terminal OUT1, OUT2—output terminal T1—step-up transformer T2—step-down transformer L.sub.11, L.sub.21—primary coil L.sub.12, L.sub.22—secondary coil