Dual-frequency power inverter for wireless power transfer

Abstract

According to an aspect, there is provided a dual-frequency inverter comprising: a push-pull inverter, an LCC compensation network, a first transmission coil for wireless power transfer at a first frequency when the push-pull inverter is fed by out-of-phase gate signals having the first frequency, a compensation capacitor and mutually coupled second and third transmission coils for wireless power transfer at twice the first frequency when the push-pull inverter is fed by said out-of-phase gate signals. The first transmission coil is connected to first and second output terminals of the push-pull inverter via the LCC compensation network. A first terminal of the second transmission coil and a second terminal of the third transmission coil are connected, respectively, to the first and second output terminals of the push-pull inverter. A first terminal of the compensation capacitor is grounded. A second terminal of the second transmission coil is connected to a first terminal of the third transmission coil and a second terminal of the compensation capacitor.

Description

DUAL-FREQUENCY POWER INVERTER FOR WIRELESS POWER TRANSFERTECHNICAL FIELD

[0001] Various example embodiments relate to wireless power transfer.BACKGROUND

[0002] Wireless power transfer (WPT) technology has been developed as safe andconvenient solutions for wide range of applications, e.g., wearable devices and electrical vehicles. Under the high application demands, several WPT standards have been establishedat different working frequencies, for example, AirFuel Resonant working at 6.78 MHz andNear Field Communication (NFC) Wireless Charging Standard (WLC) [2] for 13.56 MHzpower transfer. High performance multi-band WPT systems are in a great demand,especially with the abilities to simultaneously and independently charge devices designedfor different frequency bands. In particular, there have been several efforts to realize dual- frequency WPT systems that support charging of the loads tuned at two-frequencies. SUMMARY

[0003] According to an aspect, there is provided the subject matter of the independentclaims. Embodiments are defined in the dependent claims.

[0004] According to a first aspect, there is provided a dual-frequency power inverterfor wireless power transfer, comprising:a push-pull inverter; an LCC compensation network; a first transmission coil for wireless power transfer at a first frequency when the push-pull inverter is fed by out-of-phase gate signals having the first frequency, wherein the first transmission coil is connected to first and second output terminals of the push-pull inverter via the LCC compensation network; a compensation capacitor having a first terminal connected to the ground and a second terminal;second and third transmission coils for wireless power transfer at a second frequency, being equal to the first frequency times two, when the push-pull inverter is fed by the out-of-phase gate signals having the first frequency, wherein -a first terminal of the second transmission coil is connected to the first outputterminal of the push-pull inverter, -a second terminal of the second transmission coil and a first terminal of thethird transmission coil are connected together and to the second terminal of the compensation capacitor, -a second terminal of the third transmission coil is connected to the secondoutput terminal of the push-pull inverter, and -the second and third transmission coils are mutually coupled such that whena current flows into the second terminal of the second transmission coil, an induced voltage of the same polarity is generated at the first terminal of the third transmission coil.

[0005] According to a second aspect, there is provided a dual-frequency powerinverter for wireless power transfer, comprisinga push-pull inverter; an LCC compensation network; a first transmission coil for wireless power transfer at a first frequency when the push-pull inverter is fed by out-of-phase gate signals having the first frequency, wherein the first transmission coil is connected to first and second output terminals of the push-pull inverter via the LCC compensation network; first and second compensation capacitors, wherein -a first terminal of the first compensation capacitor is connected to the firstoutput terminal of the push-pull inverter, -a second terminal of the first compensation capacitor and a first terminal ofthe second compensation capacitor are connected together, and -a second terminal of the second compensation capacitor is connected to thesecond output terminal of the push-pull inverter; and a second transmission coil for wireless power transfer at a second frequency, being equal to the first frequency times two, when the push-pull inverter is fed by the out- of-phase gate signals having the first frequency, wherein -a first terminal of the second transmission coil is connected to the ground- a second terminal of the second transmission coil is connected to the secondterminal of the first compensation capacitor.

[0006] According to a third aspect, there is provided a system for wireless powertransfer, comprising: the dual-frequency power inverter according to the first aspect; aDC voltage source connected to the dual-frequency power inverter;a first wireless power transfer receiver comprising a first reception coil mutually coupled to the first transmission coil of the dual-frequency power inverter forreceiving a power signal having the first frequency, wherein the first wireless power transferreceiver comprises or is connected to a first load; and a second wireless power transfer receiver comprising a second reception coil mutually coupled to the second and third transmission coils for receiving a power signal having the second frequency, wherein the second wireless power transfer receiver comprises or is connected to a second load.

[0007] According to a fourth aspect, there is provided a system for wireless powertransfer, comprising: the dual-frequency power inverter according to the second aspect aDC voltage source connected to the dual-frequency power inverter;a first wireless power transfer receiver comprising a first reception coil mutually coupled to the first transmission coil for receiving a power signal having the first frequency, wherein the first wireless power transfer receiver comprises or is connected to a first load; and a second wireless power transfer receiver comprising a second reception coil mutually coupled to the second transmission coil for receiving a power signal having the second frequency, wherein the second wireless power transfer receiver comprises or is connected to a second load.

[0008] According to a fifth aspect, there is provided a method comprising:using the dual-frequency power inverter according to the first or second aspect for wireless power transfer to a first wireless power transfer receiver at the first frequencyand to a second wireless power transfer receiver at the second frequency simultaneously.

[0009] One or more examples of implementations are set forth in more detail in theaccompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 illustrates system for wireless power transfer according to anembodiment;

[0011] FIGs. 2A & 2B illustrate differential and common mode equivalent circuits ofa WPT transmitter 160 of FIG. 1;

[0012] FIGs. 3A, 3B & 3C illustrate equivalent circuits of a T-network of FIG. 1, itsdifferential-mode equivalence circuit, and its common-mode equivalence circuit;

[0013] FIGs. 4A & 4B illustrate measured system input power ^^^ and DC-DCefficiency for a converter of FIG. 1; and

[0014] FIG. 5 illustrates an alternative system for wireless power transfer accordingto an embodiment. DETAILED DESCRIPTION OF SOME EMBODIMENTS

[0015] In the following, the following mathematical notational conventions areemployed. Vectors are denoted using non-bold italic letters with an overlining (horizontal)arrow. Scalars are denoted using non-bold italic letters.

[0016] In the following, the following convention for naming of terminals of variouscircuit elements depicted in Figures is employed. For circuit elements arranged horizontallyin a Figure, a first terminal refers to a left terminal of a given circuit element while a secondterminal refers to a right terminal of a given circuit element. For circuit elements arrangedvertically in a Figure, a first terminal refers to a top terminal of a given circuit element whilea second terminal refers to a bottom terminal of a given circuit element.

[0017] Wireless power transfer (WPT) technology has been developed as safe andconvenient solutions for wide range of applications, e.g., wearable devices and electricalvehicles. Under the high application demands, several WPT standards have been establishedat different working frequencies, for example, AirFuel Resonant [1] working at 6.78 MHzand Near Field Communication (NFC) Wireless Charging Standard (WLC) [2] for 13.56 MHz power transfer. High performance multi-band WPT systems are in a great demand, especially with the abilities to simultaneously and independently charge devices designed for different frequency bands. In particular, there have been several efforts to realize dual frequency WPT systems that support charging of the loads tuned at two-frequencies. Tableshown below provides comparison of the realizations of several dual-frequency WPTsystems as well as their performance. In said Table, the following abbreviations are used:HF – half bridge converter, PP – push-pull converter, CE – class E converter and DF classΦ –dual frequency class Φ converter. In general, the converter configurations proposed in literature for dual-frequency WPT consisted of the combination of two separate power converters to either two individual transmitter (Tx) coils or single Tx coil with a dual- frequency compensation network. For example, using one single Tx coil, [3] designed a band-stop filter for each receiver (Rx) circuit, while in [4], a dual-frequency compensationcircuit is applied to the Tx side. However, both works use a combination of two half-bridgeinverters for two kHz power transfers, and the system suffers from high switch count that degrades the system efficiency significantly at MHz bands. Some works tried to cover both kHz and MHz standards by combining low-frequency and high-frequency converters [5], [6], where the class E topology was used for MHz-frequency power channels. However, the increased frequency gap between the two channels also brings difficulty on compensation network design, where two separate Tx coils are required. On the other hand, the Tx coils in [5], [6] are tuned to have low reflected impedance when the Rx moves far away (low mutual inductance M). Such connection to a voltage source converter has a risk of taking high power to the system at low mutual inductance, since it equivalents to a short-circuited load at the inverter output. In order to maintain safe operations of the WPT system with inherent short- circuit protection, the Tx coils should maintain constant current (CC) during Rx movements. In addition, all the above mentioned works use two converters with two gate-driving frequencies, which introduces high complexity to the design of gate drivers and control algorithms. For example, due to the use of 6 power switches and 2 driving frequencies in [6], six control variables are required in the proposed WPT system to achieve zero-voltage switching (ZVS) and independently drive two Txs of two power channels. In paper [7], adual-band output matching Tx coil [8] is proposed for both 6.78MHz and 13.56 MHz WPTwith a single class E inverter. However, in their proposal, the power transfer is limited toone receiver at a time. Above all the current works, there is no solution that provides ability to fulfill all the discussed four requirements, including simplicity of control frequency, decoupled and simultaneous WPT in two power channels, and the inherent short-circuit protection against low mutual inductance.References [3] [4] [5] [6] [7] FIG. 1Tx No. of Tx1 1 2 2 1 2side coils conf. Type and2 × (HB) 2 × (HB) 2 ^PP CE PP CE 1 × (CE) 2 × (DFHB^ 2 ^No.PP HB^of class Φ) converters Additional multi- DF compen-not needed reactancedual-band not needed circuit relays + sation steering output band-stop network network matching filter coilNo. of switches 4 4 4 6 1 2Frequency2 2 2 2 2 1components in gate drive signals Power transfer 347 kHz 20 kHz 200 kHz 100 kHz 6.78 MHz 6.78 MHz frequencies 446 kHz 85 kHz 6.78 kHz 13.56 13.56 13.56 MHz MHz MHz Simultaneousyes yes yes yes no yesWPT Inherent short-yes yes no no no yescircuit protection against low mutual inductance Maximum68.6% 95.2% 78.8% 82.5% 71% 80%efficiencyNominal power 11-12.5 W 99W:41W 7.4W:9W 15W:15W 1.5W:2W 64W:16W

[0018] Here, we propose a new inverter (or equally converter) topology with theability to simultaneously charge dual-frequency (DF) power receivers. Properties of oneexemplary implementation of the new inverter topology are summarized in the rightmostcolumn of the above Table. The main idea of the new device comes from the fact thatvoltages in inverters are pulses with a broad spectrum, while in conventional WPT devices only one (the fundamental) harmonic is used for realizing power transfer. By a proper modification of the class-Φ2 inverter [9],

[0010] , we can also utilize the second harmonic as a carrier of power to the receiver. This is an important possibility to enhance overall system efficiency and power output capability, because in usual devices all the higher-orderharmonics are not used but simply filtered out. For example, the proposed inverter may becontrolled by 6.78 MHz pulse width modulation (PWM) signals, while it can be tuned tosupply power via two power channels at both 6.78 MHz and 13.56 MHz in a simultaneousor independent fashion to the receiver devices according to load requirements. No additional compensation or matching networks are needed. The nominal powers of the power channels at two frequencies can be independently designed without affecting the soft-switchingbehavior of the inverter. Furthermore, it has the advantage of inherent protection against no-load condition (i.e., inherent short-circuit protection against low mutual inductance).

[0019] FIG. 1 shows a WPT system according to an embodiment. The WPT systemof FIG. 1 comprises a WPT transmitter 160 comprising a DC voltage (or power) source 101and a dual-frequency (power) inverter 130 as well as a first WPT receiver 140 and a secondWPT receiver 150. As used here and in the following, the dual-frequency inverter may besometimes called a dual-frequency power inverter, a dual-frequency converter or a dual-frequency power converter. The dual-frequency inverter may be called a dual-frequencyclass-Φ inverter or a dual-frequency class-Φ converter. The dual-frequency inverter may becalled a dual-frequency push-pull inverter or a dual-frequency push-pull converter.

[0020] The dual-frequency inverter 130 of the WPT transmitter 160 comprises a push-pull inverter 131 for direct current to alternating current (DC-to-AC) conversion, an LCCcompensation network 132, a first transmission coil 111 ^^^^, a compensation capacitor 112^^^^ and second and third transmission coils 113, 114 ^^^^^ & ^^^^^ (forming a mutuallycoupled pair). The dual-frequency inverter 130 is connected to (and powered by) the DCvoltage source 101 of the WPT transmitter 160.

[0021] For enabling the push-pull operation, the push-pull inverter 131 (sometimescalled a push-pull circuit or circuitry) comprises first and second switches 102,&Q^ (i.e., first and second transistors or first and second transistor-based switches) whichoperate in a complementary manner so that one switch conducts while the other is off andvice versa. Namely, the push-pull inverter 131 is configured to enable push-pull operationwhen the switches Q^ & Q^ 102, 103 are fed by out-of-phase gate signals with a firstfrequency ^^ . The push-pull inverter 131 has two symmetric legs named leg-a & leg-b. Dueto the push-pull operation, the phase shift between leg-a & leg-b is π. Leg-a & leg-b maywork with a half switching cycle shiftwhere the duration of the switching cycle isdefined as ^^ = 1 / ^^. Each leg may comprise, in addition to a switch 102, 103, a DC chokeinductor 106, 107 (for smoothing input current and reducing input voltage ripple) and / or adrain-source capacitor 104, 105 (for acting as a snubber for absorbing voltage spikesappearing due to the switching action). The push-pull inverter 131 comprises a first andsecond DC input terminals (one of which is grounded) and first and second output terminals123, 124. In FIG. 1, the first and second DC input terminals are connected to a DC voltagesource 101.

[0022] In some embodiments (such as the one shown in FIG. 1), the push-pull inverter131 comprises specifically first and second N-channel field-effect transistors (FETs) 102,103. The first and second output terminals 123, 124 of the push-pull inverter 131 correspond,in this case, to drains of the first and second N-channel FETs 102, 103, and sources of thefirst and second N-channel FETs 102, 103 are connected to the (common) ground. Gate-to-source voltages of the first and second FETs 102, 103 are denoted, respectively, as ^^^^ &^^^^. In other embodiments, first and second P-channel FETs may be employed, instead offirst and second N-channel FETs. The first and second N-channel (or P-channel) FETs 102,103 may be, for example, metal-oxide semiconductor FETs (MOSFETs), gallium nitride FETs (GaN FETs), junction field-effect FETs (JFETs) or metal-semiconductor FETs or FinFETs.

[0023] In the N-channel FET case discussed above and shown in FIG. 1, the push-pullinverter 131 may specifically further comprise:- a first drain-source capacitor 104 arranged between the drain and the sourceof the first N-channel FET 102; and- a second drain-source capacitor 105 arranged between the drain and thesource of the second N-channel FET 103;- a first direct current (DC) choke inductor 106 connected between the drain ofthe first N-channel FET 102 and a DC voltage input terminal (^^^) of the push-pull inverter131; and -a second DC choke inductor 107 connected between the drain of the secondN-channel FET 103 and the DC voltage input terminal (^^^) of the push-pull inverter 131.Voltages over the first and second drain-source capacitors 104, 105 (i.e., drain-to-sourcevoltages for the first and second transistors 102, 103) are denoted, respectively, as ^^^^& ^^^^.

[0024] The LCC compensation network 132, connected between the push-pullinverter 131 and the first transmission coil 111, may comprise an inductor 108 ^^, a firstcapacitor 109 ^^ and a second capacitor 110 ^^^^. Namely, a first terminal of the inductor108 is connected to a first output terminal 123 of the push-pull inverter 131 (or specificallyto the drain of the first transistor 102 in the N-channel FET implementation), and a secondterminal of the inductor 108 is connected to a first terminal of the first capacitor 109 and toa first terminal of the second capacitor 110. A second terminal of the first capacitor 109 isconnected to a second terminal of the first transmission coil 111 and to the second outputterminal 124 of the push-pull inverter 131 (or specifically to the drain of the second transistor103 in the N-channel FET implementation). A second terminal of the second capacitor 110is connected to a first terminal of the first transmission coil 111.

[0025] The first transmission coil 111 is usable for wireless power transfer at a firstfrequency when the push-pull inverter 131 is fed by out-of-phase gate signals having thefirst frequency= ^^. The first transmission coil 111 may be equally called a fundamentalTx coil. The first transmission coil 111 is connected to the first and second output terminals123, 124 of the push-pull inverter 131 (or specifically to the drains of the first and secondtransistors 103 in the N-channel FET implementation) via the LCC compensation network132. Namely, the first terminal of the first transmission coil 111 is connected to the second terminal of the second capacitor 110 of the LCC compensation network, and the secondterminal of the first transmission coil 111 is connected to the second terminal of the firstcapacitor 109 of the LCC compensation network.

[0026] In the WPT system of FIG. 1, the first transmission coil 111 is mutuallycoupled, at said first frequency = ^^, to a first reception coil 116 ^^^^ of the first WPTreceiver 140. The mutual inductance between the first transmission coil 111 and the firstreception coil 116 is denoted asThe first transmission coil 111 and the first receptioncoil 116 may be mutually coupled such that when a current flows into the first terminal (i.e.,the top terminal in FIG.1) of the first transmission coil 111, an induced voltage of the same polarity is generated at a first terminal (i.e., the top terminal in FIG.1) of the first reception coil 116, as indicated in FIG. 1 with the polarity dots of the first transmission coil 111 and the first reception coil 116.

[0027] The compensation capacitor 112 has a first terminal connected to the groundand a second terminal connected between the second and third transmission coils 113, 114(i.e., to the second and first terminals of the second and third transmission coils 113, 114,respectively).

[0028] The second and third transmission coils 113, 114 are usable together forwireless power transfer at a second frequency ^^, when the push-pull inverter is fed by theout-of-phase gate signals having the first frequency= ^^ . The second frequency ^^ isequal to the first frequency times two (i.e., ^^ = 2^^). In other words, the second and thirdtransmission coils 113, 114 act together as the second-harmonic Tx branch. The second and third transmission coils 113, 114 are mutually coupled such that when a current flows into a second terminal of the second transmission coil 113, an induced voltage of the same polarity is generated at a first terminal of the third transmission coil 114, as indicated in FIG.1 withthe polarity dots of the second and third transmission coils 113, 114. The mutuallyinductance between the second and third transmission coils 113, 114 is denoted as ^^^. It should be noted that, apart from acting as transmitting coils, the second and thirdtransmission coils 113, 114 also work as part of the dual-frequency (DF) class-Φ converter(or specifically the DF class- Φ inverter), forming a T-network together with theircompensation capacitor 112 and play crucial rule in the inverter operation.

[0029] In the WPT system of FIG. 1, the second and third transmission coils 113, 114are both mutually coupled, at said second frequency ^^ = 2^^ , to a second reception coil 120^^^^ of the second WPT receiver 150. Namely, both the second and third transmission coils113, 114 are mutually coupled with the second reception coil 120 such that when a currentflows into the second terminal (i.e., the bottom terminal in FIG.1) of the second transmissioncoil 113 and / or into the first terminal (i.e., the top terminal in FIG.1) of the third transmissioncoil 114, an induced voltage of the same polarity is generated at a first terminal (i.e., the top terminal in FIG.1) of the second reception coil 120, as indicated in FIG.1 with the polaritydots of the second and third transmission coils 113, 114 and the second reception coil 120.Notably, the power channels at the first and second frequencies are nearly independent from each other, thus providing a high flexibility on the design and load adjustment.

[0030] The second and third transmission coils 113, 114 are connected to the otherelements of the dual-frequency inverter 130 as follows. A first terminal of the secondtransmission coil 113 is connected to the first output terminal 123 of the push-pull inverter131 (or specifically to the drain of the first transistor 102 in the N-channel FETimplementation). A second terminal of the second transmission coil 113 and a first terminalof the third transmission coil 114 are connected together and to the second terminal of thecompensation capacitor 112. A second terminal of the third transmission coil 114 isconnected to the second output terminal 124 of the push-pull inverter 131 (or specifically tothe drain of the second transistor 103 in the N-channel FET implementation).

[0031] As mentioned above, the WPT system of FIG. 1 further comprises first andsecond WPT receivers 140, 150 comprising first and second reception coils 116, 120mutually coupled, respectively, to the first transmission coil 111 of the dual-frequency powerinverter 130 for receiving a power signal having the first frequency ^^ = ^^ and to the secondand third transmission coils 113, 114 of the dual-frequency power inverter 130 for receivinga power signal having the second frequency ^^ = 2^^ . A power signal may be equally calleda wireless power signal (WPS), an energy signal or a wireless energy signal.

[0032] The first WPT receiver 140 may further comprise a first reception capacitor115 and a first rectifier 117. The first rectifier 117 is connected between a first terminal ofthe first reception capacitor 115 and a second terminal of the first reception coil 116. Asecond terminal of the first reception capacitor 117 is connected to a first terminal of the firstreception coil 116. The first WPT receiver 140 may further comprise or be connected to afirst load 118 (corresponding, e.g., to a charging circuit such as a battery). In either case, thefirst load may be connected to the first rectifier 117 of the first WPT receiver 140.

[0033] Similarly, the second WPT receiver 140 may further comprise a secondreception capacitor 119 and a second rectifier 121. The second rectifier 121 is connectedbetween a first terminal of the second reception capacitor 119 and a second terminal of thesecond reception coil 120. A second terminal of the second reception capacitor 119 isconnected to a first terminal of the second reception coil 120. The second WPT receiver 150(or specifically the second rectifier thereof 121) may further comprise or be connected to asecond load 122 (corresponding, e.g., to a charging circuit such as a battery). In either case,the second load may be connected to the first rectifier 121 of the second WPT receiver 150.

[0034] In some embodiments, the first and second frequencies may be megahertzfrequencies (i.e., frequencies equal to or larger than 1 MHz and smaller than 1 GHz). In someembodiments, the first and second frequencies may be (megahertz) frequencies larger than or equal to 2 MHz (i.e., the dual-frequency inverter 130 may be suitable for multi-MHz dual-frequency wireless power transfer applications). For example, the first frequency may be6.78 MHz and the second frequency may be 2*6.78 MHz = 13.56 MHz.

[0035] As the push-pull inverter 131 has two symmetric legs named leg-a & leg-bworking with a half switching cycle shift ^^ / 2 , the drain-source voltages ^^^^ & ^^^^(equally called ^^^^& ^^^^in FIG. 1) as of the first and second transistors 102, 103 of the push-pull inverter 131 can be written as sum of the nth-harmonic components ^^^,^:where ^^ is angular frequency corresponding to the first frequency ^^ , ^ is time, ^^^ is DCvoltage and ^ is a summing index. Therefore, the odd components on leg-a and leg-b alwayshave 180° phase difference, while the DC and even components on two legs are always inphase. The inverter topology can be split into differential-mode and common-modeequivalent circuits for the analysis of the fundamental-frequency and second-harmonicfrequency power transfer, as shown in FIGs. 2A & 2B, respectively. In FIGs. 2A & 2B, thecircuit elements having no effect on the differential-mode or common-mode operation, respectively, have not been depicted.

[0036] First, the design of the fundamental frequency ^^ output branch Tx1 isdiscussed. The differential mode circuit, as shown in FIG.2A, describes operations of all the odd harmonic components. The differential currents are considered as circulating from oneleg to the other one due to the 180° phase shift, with the two legs equivalent to connected inseries. Due to the 180° shift in voltage (1)–(2), we define the differential voltageand use it as the output to supply power channel 1. Considering the fundamental-frequency,the differential output ^^^^^^ has intrinsically load-independent constant voltage due to thepush-pull T-network structure (PPT) [9]. With a mutual coupling ^^to Rx1, the Tx1 branchis connected to the differential output through the LCC compensation circuit 132

[0011] ,resulting in the Tx1 current and inverter side reflected impedance written aswhere ^^^^^^is the fundamental amplitude of ^^^^^^, and ^^^^^is the equivalent impedance atthe input port of rectifier 1. As seen from (5), the Tx1 current is only affected by ^^ and theconverter output voltageshowing the feature of constant current at ^^^^^ variations.The load-independent current ^^⃗^^also ensures the safe operation of WPT channel 1 againstits unloaded situation, since the transfer power ^ ^^^^ = (^^^^ / 2 ) · (^^^^)^ / ^^^^^willnaturally return to zero when the Rx1 moves away from Tx1→ 0). At thedifferential output of the converter, the load from Rx1 is equivalent to a load impedance^^^^, which can be simplified to a resistive load ^^^^ if the Rx1 equivalent load is alsoresistive (^^^^^ = ^^^^^).

[0037] Apart from the fundamental-frequency differential current, the LCCcompensation circuit 132 also brings in inductive current ^^^^ at the third-harmonicfrequency. The impedance seen at LCC network input is written as=j3^^2 ^^^^ (7)which can be equivalent to an inductor branch in parallel with the 2^^(^) branch, with value2^^^^.

[0038] In the differential-mode circuit, the ^^^,^ and ^^^,^(^) branches are connectedin parallel with the load branch ^^^^. Therefore, the total differential current flow through^^ ∥ ^^^ branch (or ^^ ∥ ^^^ branch) is represented by a combination of resistive andinductive currents ^^^^^^^^^,^=^^^^^(8)where ^^^^^,^ is the harmonic amplitude of the total inductive current in the differentialmode ^^^^^,^ = ^^^^^^ + ^^^^^^, ^^ represents the phase of the fundamental resistive branch(referring to 0-phase atswitch-off moment), and ^ is the angle between current vectors^⃗^^^,^and ^⃗^^^^, calculated as (9)where ^^^ = ^^ ∥ ^^(^) models the equivalent inductance of the total inductive current^^^^^ at the fundamental frequency ^^. On the other hand, the inductive current from LCCbranches ^^^^ can be absorbed to the total inductive current ^^^^^,^ at the third-harmonicfrequency. Therefore, the equivalent inductance at 3^^ is also modified as ^^^^ = ^^^ ∥^^^^.

[0039] In the following, the design of the second-harmonic frequency 2^^ outputbranch Tx2 is discussed. The common-mode circuit, as shown in FIG. 2B, describesoperations of the DC and even-harmonic components, where the current or voltage in thetwo legs always have the same phase, forming an equivalent parallel connection. The common output voltage of the inverter is given as

[0040] FIG. 3A shows the detailed configuration of the T-network, where Tx2 isconnected as the horizontal branches, and 2^^^^is the series compensation capacitor. Thereceiver coil LRx2 is in resonance with ^^^^ at 2^^. Due to the T-connection, both odd- andeven-harmonic currents will flow through the Tx2 branches. To create second-harmoniccurrent at the Rx2 branch, Tx2 is designed as a dot-to-dot connection of two inductors ^^^^^and ^^^^^, with mutual inductance ^^^and the same value of self-inductance ^^^^. Thecoupling coefficient is represented as ^^^ = ^^^ / ^^^^ . Each part of Tx2 has mutualinductance ^^ to the Rx2 (i.e., the second WPT receiver 150). According to the definitionsshown in Fig. 3A, the differential- and common voltages are re-written asFIGs. 3B & 3C illustrate differential-mode and common-mode equivalence circuits of theT-network of FIG. 3A. Based on the equivalent structures in FIG. 3B and 3C, the Tx2 branchequivalent inductance in the differential mode L2(d) and in the common mode ^^(^) (cf.,FIGs.2A & 2B) are found as ^^(^) = ^^^^ − ^^^ (14)^^(^) = ^^^^ + ^^^ (15)Here, ^^^^ is the reflected impedance of the inverter common output, ^^^^^ is the equivalentimpedance seen from Rectifier 2 (i.e., element 121) input port. Therefore, the common-modecurrent in FIG. 2B and FIG. 3C is written as^^^^ (^^^) = ^^^^ sin(2^^^ − ^^) . (17)Since ^^(^)and ^^^^are in resonance at 2^^, only second-harmonic current can flow through the Tx2 branch, and ^^represents the phase of the second-harmonic current, which is in- phase with the second-harmonic voltage due to a resistive load ^^^^at this branch.

[0041] Through the analysis in the wireless links, we obtained load information forboth power channels of the DF class Φ inverter 130 of FIG. 1. Considering given systemspecifications such as the load power and resistances in both channels ^^^^^^,^and ^^^^^^,^,the parameters in the converter can be calculated following the differential- and common-mode analysis provided above. A similar design guideline for the single frequency PPT classΦ^ converter

[0010] can also be developed for the proposed DF class Φ^ circuit with modifiedconditions. In the following, we provide calculation steps for parameter design neglectinglosses in the components.

[0042] Step 1: By analyzing separately in the differential- and common-modes of thedual-frequency inverter, we can represent DC and all the harmonic voltage components in^^^^^ and ^^^^^ [i.e., (12)–(13)] by given specifications, defined as^^^^^^ = j3^^2^^^^^^^^^^. (21)The current harmonic components can also be calculated in a similar way.

[0043] Step 2: On the other hand, time-domain expressions for the current and voltageat a first (power) switch102 and its parallel capacitor 104 are writtenwhere ^^ = ^ − 2^^ is the phase corresponding to the passive period when both switchesare OFF, D is the duty cycle of Q^,^ and ^^ (or ^^^) is the capacitance of the drain-sourcecapacitor 104. In the same way as in (23), an equation for the ^^^^ (^^^) can be written forthe time period [0, ^^] ∪ [^, 2^], and, accordingly, we write time-domain equations for^^^^^ and ^^^^^ following their definitions in (3) and (10).

[0044] Step 3: After expanding ^^^^^ and ^^^^^ into Fourier series, the voltages andphases of harmonics are obtained following (4) and (11), expressed as^^^,^(^^^^) = ^^^,^sin (^^^^ − ^^), (24)where ^^^^^ ^ = 2^^^,^ , ^ = 1, 3, … , and ^^^^^^ = ^^^,^ , ^, ^ = 2, 4 ,… applies.Representing the values in (18)–(21) by the amplitudes and phases of the current harmonics,we get four equations to calculate the four parameters ^^(^) ,^^^^^^^ , and ^^^ in theprevious steps. Further, to satisfy the ZVS condition, ^^^^should return to zero beforeswitch Q1 is turned on, that is, we require that^^^^(^ + ^^) = 0.The passive phase ^^ as well as the duty cycle D can be found from (25).

[0045] Step 4: Since the operation of the dual-frequency inverter is complex withparameters coupled with each other, the above 5 equations were solved numerically inMATLAB. The circuit parameters can be found through the following numerical relationswhen the transmitter current ratio for two channels ^^^^ : ^^^^ is around 2:3:^ = 1.14, (26)^^^ = 0.4^^^^^^ , (28)0.528 ^^= ^. (29)^^^^^During implementation of the WPT system, the parallel capacitor value ^^ and input DCsource may need slight adjustment due to the parasitic effects and losses in the circuits. Tolimit the input current ripple, the DC inductor is designed with a relatively large inductance,e.g., ^^ = 10^^(^). Therefore, ^^(^) = 1.1^^^, and the remaining circuit parameters arecalculated asThe above parameter design equations are valid under the given condition ^^^^ ∶ ^^^^ ≈ 2 ∶3.

[0046] To verify operation of the dual-frequency inverter 130 of FIG. 1, a dual-frequency wireless charging system of FIG. 1 with load power ^^^^^^ = 64 W for Rx1 outputand load power ^^^^^^ = 16 W for Rx2 output was designed and built as a simulation model.Due to the push-pull operation, the phase shift between leg-a and leg-b of the push-pullinverter is π. The ^^^ waveform during the switch-off period is obtained by integrating thecurrent flowing through the parallel capacitor (i.e., element 104, 105 of FIG. 1). The dual-frequency inverter was observed to provide two sinusoidal currents ^^^^ and 2^^^^ atfrequencies ^^ and 2^^, respectively. Class Φ rectifiers were used for both Rx outputs.

[0047] In the simulations, both transmitter coils Tx1 and Tx2 were observed to showload independent constant currents. Moreover, the power transfers at the two frequencieswere observed to be independent from each other. Tx1 coil was observed to provide naturallylower power to Rx1 when the coil is far away (i.e., for low ^^), while the power channel at 2^^(^^^^^^) is independent from ^^variations. Similarly, for variations of ^^, the current ^^^^and the load power ^^^^^^were observed to be almost constant regardless of Tx2-Rx2 coupling. The power transfer via the 2^^WPT link was seen to be enhanced at closer distances due to higher values of ^^.

[0048] The proposed concept of a dual-frequency inverter 130 of FIG. 1 was verifiedin an experimental WPT system corresponding to the WPT system of FIG.1 with receiversat both frequencies ^^ and 2^^. A digital signal processor (DSP) TMS320F28379 was usedto provide PWM signals with the designed duty cycle D to first and second GaN FETsGS66504B of the push-pull inverter (i.e., elements 102, 103 of FIG. 1). The WPT coils forthe 6.78 MHz power channel (Tx1-Rx1) were made from a copper tube, providing qualityfactors ^^^^ of around 400. Printed circuit board (PCB) coils were used for the 13.56MHzpower channel (Tx2-Rx2) with the quality factors ^^^^ of around 200. Class Φ2 passiverectifiers were used for both receiver outputs to obtain DC voltage for load charging. Thedetailed system specifications and parameters for the implementation of the proposed dual-frequency class Φ inverter are given in the below Table. The summary provided in theprevious Table for the dual-frequency inverter 130 of FIG. 1 is based on use of saidspecifications and parameters. System parameters Dual-frequency inverter parametersChannel 1 2 L1a,b 400 µH C1a,b 150 pFRLoadn (Ω) 7.6 50 LTx2a 1.974 µH LTx2a 1.973 µHPLoadn (W) 64 16 ML2 1.4235 µH 2CTx2 71.3 pFfn (MHz) 6.78 13.56 LTx1 4.56 µH CTx1 167 pFMn (µH) 0.95 0.166 Lf 1.31 µH Cf 405 pF

[0049] The implemented WPT system realizes simultaneous power delivery of ^^^^^^= 65.44W for 6.78 MHz and ^^^^^^= 17.04 W for 13.56 MHz at the nominal loads for both WPT channels. According to the measurements, the DC-DC efficiency of the dual-frequencyWPT system was 79.82%. The DC-DC efficiency ^^^^ was calculated aswhere ^^^ is DC system power. Based on measurements, both first and second GaN FETs(Q1 & Q2) were observed to show zero-voltage switching. The realized dual-frequencyinverter was observed to simultaneously provide currents for the Tx1 coil (i.e., coil 111) andTx2 coils (i.e., coils 113, 114) at 6.78 and 13.56 MHz, respectively.

[0050] The effects of load variation for both WPT channels were also verified in theexperiment. The results of the corresponding measurements of the input and output powers(^^^, ^^^^^^, ^^^^^^), as well as the system overall efficiency ^^^^ are shown as scatter pointsin FIGs. 4A & 4B. FIGs. 4A & 4B also show corresponding simulation results as continuouscurves. The measured power and efficiency vary in a similar trend compared to thesimulation results. It may be observer from FIG. 4A that during ^^^^^^ variation between30% and 140% of the full-load power ^^^^^^, the load power of Rx2 keeps almost constantat around 20W. Since the rectifier 1 has constant voltage output, the power of channel 1gradually reduces with increased ^^^^^^ . The overall system efficiency, including bothpower channels, keeps almost flat during the load variation, while it reduces slightly at highload resistances since a reduction in the load power makes the power loss more comparableto the useful power. Similarly for the 13.56 MHz WPT channel, the output power of channel1 ^^^^^^ maintains around 65W during ^^^^^^ variation from 40% to 140%, as depicted inFIG. 4B. Thus, independent operation at the two power transfer frequencies is achieved. Themeasured DC-DC efficiency including power transfer in both channels keeps constant ataround 79%.

[0051] Moreover, the ^^^ waveforms of the dual-frequency inverter were studiedexperimentally under variations of WPT channels 1 and 2, respectively, from 40% to 120%load power. It was observed that the two power switches& Q^ always maintain ZVSsoft-switching from the full-load to the empty-load case, while ZVS is still kept even if theload power is slightly higher than the nominal value till around 120% ^^^^^^,^.

[0052] Loss distribution of the dual-frequency class Φ inverter was also calculatedusing LTspice simulations. LTspice simulation model was built based on the components and coil measurement results. The losses of each circuit element were calculated accordingto the simulation results. The simulated loss distribution for each component in the DF classinverter is given in the below Table. We see that the losses in the inverter are mainlycontributed by Tx2 coil and the conducting loss in the power switches. These are caused by the low quality factor of Tx2 coils and the high current flowing through Tx2 as well as power switches. Efficiency optimization may be further optimized by considering different GaN FETs and proper building materials for the Tx2 coils. Circuit element Loss contributionPower switches Q1, Q2 33.9% Transmitter 1 LTX19.1% LCC inductor Lf4.7%Transmitter 2 and T-network LTx2a,b 52% DC choke inductor L1a,b0.3 %

[0053] FIG. 5 shows an alternative WPT system according to an embodiment. TheWPT system of FIG. 1 comprises a WPT transmitter 560 comprising a dual-frequencyinverter 530 (or a dual-frequency converter) according to an embodiment and a first WPT receiver 540 and a second WPT receiver 550.

[0054] The WPT system of FIG. 5 corresponds to a large extent to the WPT systemof FIG.1. Any of the features and definitions discussed above for the WPT system of FIG.1 apply, mutatis mutandis, for the system of FIG. 5, unless otherwise stated. Namely,elements 501 to 511, 515 to 522, 540, 550 of FIG. 5 may correspond fully to elements 101,to 111, 115 to 122, 140, 150 of FIG. 1. The operation of these elements is, thus, not discussedhere for brevity.

[0055] The difference between the WPT system of FIG. 5 and the WPT system ofFIG. 1 lies in how the second-harmonic Tx branch of the dual-frequency inverter 130, 530has been implemented. Namely, in FIG.5, the L-C-L type of T-network of FIG.1 (consistingof elements 112, 113, 114) has been replaced with a C-L-C type of T-network (consisting ofelements 512, 513, 514). In other words, the dual-frequency inverter 530 comprises first andsecond compensation capacitors 513, 514 (which may have equal value ^^^^) and a secondtransmission coil 512 ^^^^^for wireless power transfer at a second frequency, being equalto the first frequency times two (^^ = 2^^ = 2^^), when the push-pull inverter is fed by theout-of-phase gate signals having the first frequency (^^ = ^^).

[0056] The elements 512, 513, 514 of the C-L-C type of T-network may be connectedas follows. A first terminal of the first compensation capacitor 513 is connected to the firstoutput terminal 523 of the push-pull inverter 531 (or specifically to a drain of the first transistor 502 in the N-channel FET implementation). A second terminal of the firstcompensation capacitor 513 and a first terminal of the second compensation capacitor 514are connected together. A second terminal of the second compensation capacitor 514 isconnected to the second output terminal of the push-pull inverter 531 (or specifically to adrain of the second transistor 503 in the N-channel FET implementation). A first terminal ofthe second transmission coil 512 is connected to the ground. A second terminal of the secondtransmission coil 513 is connected to the second terminal of the first compensation capacitor513 (and to the first terminal of the second compensation capacitor 514). Moreover, thesecond transmission coil 512 of the dual-frequency inverter 530 and the second receptioncoil 520 of the second WPT receiver 550 may be mutually coupled, for example, such thatwhen a current flows into the second terminal (i.e., the right terminal in FIG. 1) of the secondtransmission coil 512, an induced voltage of the same polarity is generated at a first terminal(i.e., the top terminal in FIG. 1) of the second reception coil 520, as indicated in FIG. 1 withthe polarity dots of the second transmission coil 512 and the second reception coil 520.

[0057] In some embodiments, the first and second frequencies may be megahertzfrequencies (i.e., frequencies equal to or larger than 1 MHz and smaller than 1 GHz). In someembodiments, the first and second frequencies may be (megahertz) frequencies larger thanor equal to 2 MHz (i.e., the dual-frequency inverter 530 may be suitable for multi-MHz dual-frequency wireless power transfer applications).

[0058] In a differential-mode equivalent circuit of the dual-frequency inverter 130 or530, only the vertical branch of the T-network (i.e., the second-harmonic Tx branch) of FIG.1 or 5 appear (as shown in FIG. 2A for the dual-frequency inverter 130 of FIG. 1). In otherwords, only the second and third transmission coils 113, 114 appear in the differential-modeequivalent circuit of the dual-frequency inverter 130 of FIG. 1 (as depicted in FIG. 2A), andonly the second and third compensation capacitor 513, 514 appear in the differential-modeequivalent circuit of the dual-frequency inverter 530 of FIG. 5. Thus, this T-network canprovide either inductive or capacitive current to the power switches in these two cases. Onother hand, the T-network can be equivalent to two parallel LC branches in the common-mode equivalent circuit, where ^^^^, ^^^^^ & ^^^^^ (FIG. 1) or ^^^^ and ^^^^ (FIG. 5) aredesigned to resonate at the second frequency ^^ = 2^^ . The equivalent reflected impedancefrom the Rx2 side will always appear in series with the horizontal branch, regardless of theT-network structure, which is only valid in the common-mode equivalent circuit.

[0059] In some embodiments, the dual-frequency power inverter 130 or 530 may beconfigured to be operatable using a PWM signal without use of any additional compensationor matching circuit. Here, the configuration may involve, e.g., appropriate choice ofcapacitance and inductance values of the capacitors and inductors of the dual-frequencypower inverter 130 or 530.

[0060] The dual-frequency (class Φ) inverter (or converter) according to any of theembodiments discussed above provides at least the following benefits. ^The dual-frequency inverter can simultaneously feed two output power channels forwireless power transfer at two working frequencies up to megahertz (MHz) frequencies: at the fundamental frequency ^^and the second-harmonic frequency 2^^. Only one control frequency ^^ is required for the converter. Here, megahertzfrequencies may correspond to frequencies equal to or above 1 MHz and below 1 GHz. ^The dual-frequency inverter provides independent operations and designs for the twopower channels. The two power channels can work in either simultaneous or independent fashion to supply receiver (Rx) devices at two frequencies. The rated power of two power channels can be independently designed or adjusted. ^Both of the two power channels in the dual-frequency inverter have inherent short-circuit protection characteristics against no-load and too far transfer distance cases. Each power channel can deliver higher power when the Rx device moves closer to the transmitter, while the power delivery automatically drops when the Rx moves too far away or is removed. The system is safe from taking high power when the Rx is far away. Similarly, the power delivery automatically falls when the Rx side battery is nearly full (i.e., equivalent to a low-load or empty-load case). ^The T-network in the proposed inverter can be made of two alternative arrangements(see FIGs.1 & 5) without affecting the inverter performance. ^The dual-frequency inverter converter enables realizing a dual-frequency WPTsystem using one single inverter.

[0061] Reference throughout this specification to one embodiment or an embodimentmeans that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present solution. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment.

[0062] As used herein, a plurality of items, structural elements, compositionalelements, and / or materials may be presented in a common list for convenience. However, these lists should be construed as though each member of the list is individually identified as a separate and unique member. Thus, no individual member of such list should beconstrued as a de facto equivalent of any other member of the same list solely based on their presentation in a common group without indications to the contrary. In addition, variousembodiments and example of the present solution may be referred to herein along withalternatives for the various components thereof. It is understood that such embodiments, examples, and alternatives are not to be construed as de facto equivalents of one another, but are to be considered as separate and autonomous representations of the present solution.

[0063] Even though embodiments have been described above with reference toexamples according to the accompanying drawings, it is clear that the embodiments are notrestricted thereto but can be modified in several ways within the scope of the appendedclaims. Therefore, all words and expressions should be interpreted broadly and they are intended to illustrate, not to restrict, the embodiment. It will be obvious to a person skilledin the art that, as technology advances, the inventive concept can be implemented in variousways. Further, it is clear to a person skilled in the art that the described embodiments may, but are not required to, be combined with other embodiments in various ways. INDUSTRIAL APPLICABILITY

[0064] At least some embodiments find industrial application in wireless powertransfer. REFERENCES[1] “AirFuel Alliance Resonant Wireless Power Transfer (WPT) System Baseline SystemSpecification (BSS),” Jul. 2018, AFA TS-0010-A v2.00.[2] “NFC Forum Releases Wireless Charging Specification 2.0,” Available at https: / / nfc-forum.org / news / 2021-10-nfc-forum-releases-wirelesscharging-specification-2-0 / (2021 / 10 / 20). [3] X. Hou, Z. Wang, Y. Su, Z. Liu, and Z. Deng, “A Dual-Frequency Dual-Load Multirelay Magnetic Coupling Wireless Power Transfer System Using Shared PowerChannel,” IEEE Trans. Power Electron., vol. 37, no. 12, pp. 15717–15727, 2022.[4] X. Gao, B. Du, Y. Zhang, and S. Cui, “A Dual-Frequency Compatible Wireless PowerTransfer System With a Single Transmitter and Multiple Receivers,” IEEE Access, vol. 10,pp.102564–102574, 2022. [5] D. Ahn and P. P. Mercier, “Wireless Power Transfer With Concurrent 200-kHz and6.78-MHz Operation in a Single-Transmitter Device,” IEEE Trans. Power Electron., vol.31, no.7, pp.5018–5029, 2016. [6] M. Liu and M. Chen, “Dual-Band Wireless Power Transfer With Reactance SteeringNetwork and Reconfigurable Receivers,” IEEE Trans. Power Electron., vol. 35, no. 1, pp.496–507, 2020. [7] M.-L. Kung and K.-H. Lin, “A dual-band wireless power transfer system withefficiency-boosting converter,” IEEE Microw. Wireless Compon. Lett., vol. 30, no. 11, pp.1108–1111, 2020. [8] M. -L. Kung and K. -H. Lin, “Enhanced Analysis and Design Method of Dual-BandCoil Module for Near-Field Wireless Power Transfer Systems,” IEEE Trans. Microw.Theory Techn., vol.63, no.3, pp.821–832, 2015.[9] L. Gu, G. Zulauf, Z. Zhang, S. Chakraborty, and J. Rivas-Davila, “Push–Pull Class Φ2RF Power Amplifier,” IEEE Trans. Power Electron., vol. 35, no. 10, pp. 10515–10531,2020.

[0010] Y. Liu, P. Jayathurathnage and J. Kyyrä, “A New Simplified Method and Design Guidelines for the Optimization of Push–Pull Class Φ2 Converters for Wireless PowerTransfer Applications,” IEEE Trans. Power Electron., vol. 38, no. 8, pp. 10442–10459,2023.

[0011] Z. Pantic, S. Bai, and S. M. Lukic, “ZCS LCC-compensated resonant inverter forinductive-power-transfer application,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3500–3510, 2010.

Claims

CLAIMS 1. A dual-frequency power inverter for wireless power transfer, comprising:a push-pull inverter; an LCC compensation network; afirst transmission coil for wireless power transfer at a first frequency when thepush-pull inverter is fed by out-of-phase gate signals having the first frequency, whereinthe first transmission coil is connected to first and second output terminals of the push-pullinverter via the LCC compensation network;a compensation capacitor having a first terminal connected to the ground and a second terminal; second and third transmission coils for wireless power transfer at a secondfrequency, being equal to the first frequency times two, when the push-pull inverter is fedby the out-of-phase gate signals having the first frequency, wherein- a first terminal of the second transmission coil is connected to the first outputterminal of the push-pull inverter, -a second terminal of the second transmission coil and a first terminal of the thirdtransmission coil are connected together and to the second terminal of the compensation capacitor, -a second terminal of the third transmission coil is connected to the second outputterminal of the push-pull inverter, and -the second and third transmission coils are mutually coupled such that when acurrent flows into the second terminal of the second transmission coil, an induced voltageof the same polarity is generated at the first terminal of the third transmission coil.

2. A dual-frequency power inverter for wireless power transfer, comprising:a push-pull inverter; an LCC compensation network; afirst transmission coil for wireless power transfer at a first frequency when thepush-pull inverter is fed by out-of-phase gate signals having the first frequency, whereinthe first transmission coil is connected to first and second output terminals of the push-pullinverter via the LCC compensation network;first and second compensation capacitors, wherein- a first terminal of the first compensation capacitor is connected to the first outputterminal of the push-pull inverter, -a second terminal of the first compensation capacitor and a first terminal of thesecond compensation capacitor are connected together, and -a second terminal of the second compensation capacitor is connected to thesecond output terminal of the push-pull inverter; and a second transmission coil for wireless power transfer at a second frequency, being equal to the first frequency times two, when the push-pull inverter is fed by the out-of-phase gate signals having the first frequency, wherein- a first terminal of the second transmission coil is connected to the ground, and- a second terminal of the second transmission coil is connected to the secondterminal of the first compensation capacitor.

3. The dual-frequency power inverter of claim 1 or 2, wherein two legs of the push-pull inverter are symmetric and configured to operate using a half switching cycle shift.

4. The dual-frequency power inverter according to any preceding claim, whereinthe push-pull inverter comprises first and second switches for enabling push-pull operation.

5. The dual-frequency power inverter according to any preceding claim, whereinthe push-pull inverter comprises first and second N-channel field-effect transistors, FETs,wherein the first and second output terminals of the push-pull inverter correspond to drains of the first and second N-channel FETs, and sources of the first and second N-channel FETs are connected to the ground.

6. The dual-frequency power inverter of claim 5, wherein the push-pull inverterfurther comprises: a first drain-source capacitor arranged between the drain and the source of the first N-channel FET; and a second drain-source capacitor arranged between the drain and the source of the second N-channel FET; a first direct current, DC, choke inductor connected between the drain of the firstN-channel FET and a DC voltage input terminal of the push-pull inverter; anda second DC choke inductor connected between the drain of the second N-channelFET and the DC voltage input terminal of the push-pull inverter.

7. The dual-frequency power inverter of claim 5 or 6, wherein the first and secondN-channel FETs are GaN FETs.

8. The dual-frequency power inverter according to any preceding claim, wherein the LCC compensation network comprises: an inductor having a first terminal connected to the first output terminal of thepush-pull inverter and a second terminal,a first capacitor having a first terminal connected to the second terminal of the inductor of the LCC compensation network and a second terminal connected to the second output terminal of the push-pull inverter, and a second capacitor having a first terminal connected to the second terminal of thefirst capacitor of the LCC compensation network and a second terminal connected to a firstterminal of the first transmission coil, a second terminal of the first transmission coil being connected to the second output terminal of the push-pull inverter.

9. The dual-frequency power inverter according to any preceding claim, whereinthe first and second frequencies are megahertz frequencies.

10. The dual-frequency power inverter according to any preceding claim, wherein the dual-frequency power inverter is configured to be operatable using a pulse width modulation, PWM, signal without use of any additional compensation or matching circuit.

11. A system for wireless power transfer, comprising: a wireless power transfer receiver comprising the dual-frequency power inverter ofclaim 1 and a DC voltage source connected to the dual-frequency power inverter;a first wireless power transfer receiver comprising a first reception coil mutually coupled to the first transmission coil of the dual-frequency power inverter for receiving a power signal having the first frequency, wherein the first wireless power transfer receivercomprises or is connected to a first load; anda second wireless power transfer receiver comprising a second reception coil mutually coupled to the second and third transmission coils for receiving a power signalhaving the second frequency, wherein the second wireless power transfer receivercomprises or is connected to a second load.

12. A system for wireless power transfer, comprising: a wireless power transfer transmitter comprising the dual-frequency power inverterof claim 2 and a DC voltage source connected to the dual-frequency power inverter;a first wireless power transfer receiver comprising a first reception coil mutually coupled to the first transmission coil for receiving a power signal having the firstfrequency, wherein the first wireless power transfer receiver comprises or is connected to afirst load; and a second wireless power transfer receiver comprising a second reception coil mutually coupled to the second transmission coil for receiving a power signal having thesecond frequency, wherein the second wireless power transfer receiver comprises or isconnected to a second load.

13. The system of claim 11 or 12, wherein the first wireless power transfer receiver further comprises: a first reception capacitor having a first terminal and a second terminal, wherein the second terminal of the first reception capacitor is connected to a first terminal of the first reception coil; and a first rectifier connected between the first terminal of the first reception capacitor and a second terminal of the first reception coil, and the second wireless power transfer receiver further comprises: a second reception capacitor having a first terminal and a second terminal, wherein the second terminal of the second reception capacitor is connected to a first terminal of the second reception coil; and a second rectifier connected between the first terminal of the second reception capacitor and a second terminal of the second reception coil.

14. A method comprising: using the dual-frequency power inverter according to any of claims 1 to 10 forwireless power transfer to a first wireless power transfer receiver at the first frequency and to a second wireless power transfer receiver at the second frequency simultaneously.

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