Load tolerant resonant converter

Abstract

A resonant converter (100) comprises a DC input (111), an AC output (161, 162), a switching section (120) and a resonator section (130). The switching section comprises a pair of switch devices (M1, M2) configured to alternatingly connect a first voltage node (112) and a second voltage node (113) to a shared node (114) at a switching frequency. The resonator section comprises a first resonator network (140) coupled to a second resonator network (150), both comprising a LC tank circuit. The second resonator network comprises an inductor (L3) and a capacitor (C3). A terminal of the inductor is connected to the first or second voltage node and the capacitor (C3) is connected such that in an equivalent electric circuit of an odd mode impedance seen by the switch devices the capacitor shunts the AC output. The first resonator network (140) and the second resonator network (150) are tuned to define odd frequency components of a voltage waveform across the pair of switch devices at the switching frequency and at a third harmonic frequency of the switching frequency, and to short an even mode impedance seen by the pair of switch devices at a second harmonic frequency of the switching frequency.

Description

LOAD TOLERANT RESONANT CONVERTERTechnical field

[0001] The present disclosure is related to switched-mode resonant converters, in particular to switched-mode resonant inverters, and to power amplifiers or generators, in particular radio frequency (RF) power amplifiers or generators, comprising such converters.Background art

[0002] Plasma applications, common in semi-conductor technologies, require narrow control of the ion energy density and ion flux. RF sources are used to excite a plasma in a plasma chamber. The power excited in the plasma by an RF source needs to be precisely controlled. Currently, plasma RF sources use a classical set-up consisting of a 50Q RF source, a 50Q transmission line and an impedance matching box connected to a coil of a plasma chamber (in case of inductively coupled plasma). The impedance presented by the load (in this example the coil coupled to the plasma) is highly variable and the matching box is required to enable operation at high efficiency and non-destructive voltages and currents. The matching box closely tracks the impedance seen by the RF source, commonly 50Q. If the coil is kept unmatched, standing waves will be present on the transmission line, manifesting as reflections which may severely limit the classical RF source efficiency and power. Since the plasma inside the chamber changes over time, power and process conditions, the matching box continuously needs to be adjusted to minimize standing waves. The aforementioned setup hence introduces system complexity, limiting speed and inhibits high-efficiency RF generation.

[0003] Such a classical set-up is applicable to many other high-power RF applications, such as, but not limited to RF magnetic resonance imaging (MRI), RF heating / defrosting, RF welding and RF laser excitation. All these applications have operating frequencies from 2 MHz up to 2.4 GHz.

[0004] At frequencies below 300 MHz, switched-mode power amplifiers offer high-efficiency operation. Switched-mode amplifier topologies utilize zero-voltage switching to reduce losses due to energy stored in parasitic capacitances. Ideally, during zero-voltage switching the voltage across the transistor is 0 V at time of switching. As an example, the Class E amplifier topology uses the intrinsic device output capacitance as part of its circuit. Zero-voltage switching and zero-voltage derivative switching (the rate of change is also zero at the time of switching) is achieved by waveform shaping.Switched-mode amplifiers typically use resonant waveform shaping circuits to achieve this. An example of a topology using a waveform shaping circuit which may be used as a switched-mode amplifier is the Class F amplifier. Class F uses fundamental and harmonic impedance optimization to achieve the desired waveforms. This is achieved by using harmonic short and open circuit resonators to control the voltages and current waveforms at the transistor output.

[0005] Switched-mode amplifiers are however sensitive to load impedance variations and cannot maintain high efficiency operation when the impedance is highly variable. Loss of zero-voltage switching greatly lowers the efficiency of the amplifier, requiring large heatsinks. Many topologies other than switched-mode power amplifiers suffer from similar sensitivity to varying impedance, and these problems are thus not limited to switched-mode power amplifiers alone.

[0006] Attempts have been made to reduce the sensitivity of the amplifier to varying impedance. Many attempt to reduce the sensitivity by optimization (best-effort) of the resonant networks belonging to the amplifier class or by combining multiple amplifiers with varying phases. An exemplary prior art solution employs impedance modulation techniques, by utilizing impedance inversion networks which combine the output waveforms of multiple amplifiers.

[0007] US 7924580 discloses a switching inverter having two single-endedEF2 inverter sections coupled together with a shared ground and a shared resonant network which allows for tuning the impedance seen by the transistors. The resonant network comprises center-tapped DC feed inductors, a T-network of reactances coupled between ground and the two voltage nodes of the transistors, and series LC resonators coupled to the load. This resonant network allows to decouple the effect of the network on even and odd harmonics of the switching frequency, and the odd and even frequency components can be tuned independently by appropriate selection of the respective reactances of the resonant network. Particularly, the impedance at the second harmonic frequency is shorted, while the relative relationship between the values at the fundamental and the third harmonic are optimized for waveform shaping and zerovoltage switching. However, the switching inverter of US 7924580 still shows limited tolerance for load impedance variations.Summary

[0008] It is therefore an aim of the present disclosure to overcome the shortcomings of the prior art and provide switched-mode converters having improved tolerance to load impedance variations and which do not require any adjustableimpedance matching mechanisms. It is an aim to provide such converters which have limited complexity and hardware count and which are economical.

[0009] According to a first aspect of the disclosure, there is therefore provided a resonant converter as set out in the appended claims. A resonant converter, particularly a resonant inverter, according to the present disclosure comprises an input section comprising one or more input terminals for a DC supply voltage possibly coupled to a DC biasing network, an output section comprising one or a pair of AC output terminals configured to provide a single-ended or a differential output, a switching section and a resonator section.

[0010] The switching section comprises a pair of switch devices configured to alternatingly connect a first voltage node and a second voltage node to a shared node at a switching frequency, which is advantageously a fixed, non-variable frequency. Advantageously, the switch devices are arranged in a push-pull configuration between the first voltage node, the second voltage node and the shared node. The shared node is possibly a shared ground. These switch devices are advantageously configured to be operated at the switching frequency and with 180° phase difference.

[0011] The resonator section comprises a first resonator network and a second resonator network. Although the first and second resonator networks may be tuned individually, the two are advantageously coupled. The first resonator network comprises at least one first inductor and at least one first capacitor, e.g. forming a first LC tank circuit. The first resonator network is advantageously connected between the first and second voltage nodes. The second resonator network comprises at least one second inductor, advantageously a pair of second inductors, and a second capacitor, e.g. forming a second LC tank circuit. The second resonator network can be connected between the first and second voltage nodes. A first terminal of the at least one second inductor is connected to one of the first voltage node and the second voltage node, advantageously in an equipotential manner. Advantageously the at least one second inductor comprises a pair of second inductors having respective first terminals connected to a respective one of the first voltage node and the second voltage node. The second capacitor is connected such that in an equivalent electric circuit of an odd mode impedance seen by the switch devices, the second capacitor shunts the AC output. In some examples, the second capacitor is connected parallel to the output terminals. In addition or alternatively, a first terminal of the second capacitor is connected to a second terminal of the at least one second inductor. Advantageously, terminals of the second capacitor are connected to respective second terminals of the pair of second inductors. Yet additionally or alternatively, the resonant converter comprises a transformer. Thesecond capacitor can be connected parallel to a primary winding or a secondary winding of the transformer.

[0012] Advantageously, the resonator section is tuned such that the first and second resonator networks, particularly the first resonator network, is configured to substantially suppress even frequency components of a voltage waveform applied across the pair of switch devices, particularly at a second harmonic frequency of the switching frequency. This is achieved by shorting an even mode impedance seen by the pair of switch devices at the second harmonic frequency. Hence, the magnitude of the even mode impedance is significantly reduced (e.g., at least by a factor 10) at the second harmonic frequency compared to the magnitude at the first harmonic frequency. In addition, the first and second resonator networks, particularly the second resonator network, is tuned for a predefined (range of) load impedance, to define odd frequency components of a voltage waveform applied across the pair of switch devices, particularly at the switching frequency and at a third harmonic frequency of the switching frequency. This is achieved by defining an odd mode impedance seen by the pair of switch devices at odd frequency components of the switching frequency, particularly at the fundamental and the third harmonic frequency. As a result, the voltage waveform across the switch devices can be better defined and zero-voltage switching operation can be ensured over a large load impedance range, for both resistive and reactive loads.

[0013] One advantage of the resonant converter of the above type is that it enables to tune the resonator section, particularly the first and second resonator networks to achieve zero-voltage switching capability for a large operating range of a load impedance. As is shown in greater detail in the experimental section below, this operating range is significantly improved compared to prior art resonant converters. Without wishing to be bound by theory, it is believed that this is due to the particular topology of the second resonator network. As a result, an improved tolerance for loads showing an impedance that is variable, e.g. as a function of power, is obtained. The resonant converter according to the present disclosure can advantageously be tuned for such loads to maintain zero-voltage switching capability of the switch devices over the entire impedance trajectory, resulting in improved performance and efficiency, and avoiding the need to provide expensive matching networks.

[0014] A further benefit of resonant converters according to the present disclosure is that no variable (mechanical, electromechanical or electrical) load matching is required, leading to simplified construction, reduced component count and cost. Furthermore, component dimensioning can easily be adapted to a specific impedance range. Due to the high load tolerance of resonant converters according to the presentdisclosure, no variable tuning of duty cycles or frequency is required. Advantageously, the switching frequency is maintained fixed. This simplifies converter control and enables to obtain high efficiency performance of the converter over varying loads.

[0015] Advantageously, the at least one first inductor and the at least one first capacitor of the first resonator network are arranged in a T-network connecting the first and second voltage nodes and the shared node. Benefits of a T-network are reduced component count and capability of de-coupled tuning between the even and odd modes of the impedance seen by the pair of switch devices.

[0016] According to a second aspect of the disclosure, there is provided a power generator as set out in the appended claims. The power generator comprises one or more of the resonant converter according to the first aspect.

[0017] According to a third aspect of the present disclosure, there is provided a method of tuning a resonant converter, as set out in the appended claims, and a tuned resonant converter as obtained by the method.Brief description of the drawings

[0018] Aspects of the present disclosure will now be described in more detail with reference to the appended drawings, wherein same reference numerals illustrate same features and wherein:

[0019] Figure 1 represents a diagram of an inductively coupled plasma system according to the prior art;

[0020] Figure 2 represents a diagram of a complex impedance trajectory of an induction coil of an inductively coupled plasma (ICP) chamber;

[0021] Figure 3 represents a diagram of a resonant converter according to the present disclosure;

[0022] Figure 4 represents a diagram of a topology of a first embodiment of the resonant converter according to the present disclosure;

[0023] Figure 5 represents plots of the voltage waveforms of the drainsource voltages of the switch devices of the switching section, the corresponding drainsource currents and the gate control signals applied to the switch devices;

[0024] Figure 6A represents a graph of drain-source voltage waveforms for an operating range of various real and complex impedances of the load and a proper tuning of the resonant section of the converter in which ZVS operation is ensured; Figure 6B represents a graph of drain-source voltage waveforms over the same operating range of impedances of the load with an improper tuning of the resonant section that does not ensure ZVS conditions for some load impedance values;

[0025] Figure 7 represents a diagram of a topology of a second embodiment of the resonant converter according to the present disclosure;

[0026] Figure 8 represents a diagram of a topology of a third embodiment of the resonant converter according to the present disclosure;

[0027] Figure 9 represents a diagram of a topology of a fourth embodiment of the resonant converter according to the present disclosure;

[0028] Figure 10 represents a diagram of a topology of a fifth embodiment of the resonant converter according to the present disclosure;

[0029] Figure 11 represents a diagram of a topology of a sixth embodiment of the resonant converter according to the present disclosure;

[0030] Figure 12 represents a diagram of a topology of a seventh embodiment of the resonant converter according to the present disclosure;

[0031] Figure 13 represents a diagram of a topology of an eighth embodiment of the resonant converter according to the present disclosure, in which the first resonator network does not include a T-network of reactances;

[0032] Figure 14A represents a diagram of a comparative push-pull classEF2 resonant inverter, with a T-network resonator circuit and a series LC resonator circuit;

[0033] Figure 14B represents the equivalent electric circuit of the inverter of Fig. 14A seen by the odd frequency components of the drain-source voltage waveform; Figure 14C represents the equivalent electric circuit of the inverter of Fig. 14A seen by the even frequency components of the drain-source voltage waveform;

[0034] Figure 15 represents a simulation plot of the magnitude of the evenmode impedance of a tuned resonant inverter according to the topology of Fig. 14A;

[0035] Figure 16 represents a simulation plot of phase angle and magnitude of the odd-mode impedance of a tuned resonant inverter of Fig 13 for two different resistive loads;

[0036] Figure 17 represents a simulation plot of phase angle and magnitude of the odd-mode impedance of the same tuned resonant inverter as in Fig 16 for two different reactive loads;

[0037] Figure 18 represents a surface plot of the phase angle of the complex odd-mode impedance evaluated at the fundamental harmonic frequency (phase condition), as a function of real part (x axis) and imaginary part (y-axis) of the load impedance (Zioad) for the tuned resonant inverter as in Fig. 17;

[0038] Figure 19 represents a surface plot of the ratio of the magnitude of the complex odd-mode impedance at the third harmonic frequency to the magnitude ofthe complex odd-mode impedance at the fundamental frequency (magnitude condition) as a function of real part (x axis) and imaginary part (y-axis) of the load impedance for the same tuned resonant inverter as in Fig. 18;

[0039] Figure 20 graphically represents values of real part (x axis) and imaginary part (y-axis) of the load impedance for which both the phase condition (Fig. 18) and the magnitude condition (Fig. 19) are met;

[0040] Figure 21 A represents the equivalent electric circuit seen by the odd frequency components of the drain-source voltage waveform for the topology of Fig. 7; Figure 21 B represents the equivalent electric circuit seen by the even frequency components of the drain-source voltage waveform for the topology of Fig. 7;

[0041] Figure 22 represents a simulation plot of the magnitude of the evenmode impedance of a tuned resonant inverter of Example 2;

[0042] Figure 23 represents a simulation plot of phase angle and magnitude of the odd-mode impedance as a function of frequency of the tuned resonant inverter of Example 2 for a purely resistive load of 10 Q and 20 Q;

[0043] Figure 24 represents a simulation plot of phase angle and magnitude of the odd-mode impedance for the tuned resonant inverter of Example 2 for two different reactive loads (capacitive and inductive);

[0044] Figure 25 represents a surface plot of the phase angle of the complex odd-mode impedance evaluated at the fundamental harmonic frequency (phase condition), as a function of real part (x axis) and imaginary part (y-axis) of the load impedance for the tuned resonant inverter of Example 2;

[0045] Figure 26 represents a surface plot of the ratio of the magnitude of the complex odd-mode impedance at the third harmonic frequency to the magnitude of the complex odd-mode impedance at the fundamental frequency (magnitude condition) as a function of real part (x axis) and imaginary part (y-axis) of the load impedance for the tuned resonant inverter of Example 2;

[0046] Figure 27 graphically represents values of real part (x axis) and imaginary part (y-axis) of the load impedance for which both the phase condition (Fig. 25) and the magnitude condition (Fig. 26) are met;

[0047] Figure 28 represents a diagram of a resonant converter according to the present disclosure built into a radio frequency drive generator.Detailed description

[0048] Referring to Fig. 1 , an exemplary plasma set-up 10 with inductively coupled plasma according to the prior art is shown. The set-up comprises a plasma chamber 11 . The plasma is excited using a coil 12 which electromagnetically couples to the plasma 16 inside the chamber 11 . The coil 12 is inductive and has to be matched to the RF source 14 using a matching box 13. Prior art matching boxes typically comprise a network of variable electrical matching elements. This may become redundant in systems as described in the present disclosure, as will be detailed below.

[0049] The power from the RF source 14 is transferred via a transmission line 15 to the matching box 13. The plasma 16 inside the chamber 11 can be manipulated in view of controlling the ion energy density and ion flux. Typically a pulsed DC or AC biasing source 17 is coupled to a bottom electrode 18 which supports the substrate 19 to be processed, e.g. a silicon wafer, on which various plasma-assisted chemical processes such as low-temperature etching and deposition can be performed.

[0050] When the matching box 13 and the transmission line 15 are removed, the RF source 14 directly sees the impedance of the coil 12 while inducing the plasma 16. The RF source 14 may be optimized for the impedances presented by the coil 12 when the RF source 14 no longer needs to be 50Q matched. An optimization of the RF source 14 for the varying impedance range requires knowledge of the expected impedance trajectory as presented by the coil 12. Such an impedance trajectory can be measured, and one exemplary impedance trajectory is shown in Fig. 2. Such an impedance trajectory shows the change of impedance across the complex impedance plane over time and excitation power. The impedance has an “OFF-state” value 201. During power increase, the real and complex impedance will vary along a trajectory 202, until an ultimate impedance value 203 is reached at peak power, from which the impedance will revert back to the OFF-state value along a possibly different trajectory 204. The impedance can further be dependent on process conditions (plasma chamber pressure, process gas, gas flow rate, temperature, etc...) and chamber configuration.

[0051] The variability of the plasma impedance requires a constant change of the matching circuit, typically effected in matching box 13. This is typically achieved using a closed-loop system. However, such an adjustable matching circuit is source of inefficiency, added costs and complexity. The design of dedicated matching circuits furthermore poses challenges in transient behaviour (such as in the transient start-up behaviour of a plasma), instability (regressive power transfer) and drift / power tracking.

[0052] Switched-mode RF sources can obtain very high efficiency if zerovoltage switching (ZVS) is maintained, i.e. , the equivalent capacitance at the drain nodeof the switching transistor is fully discharged before turning the transistor on. If the transistor is turned on too early, the charge inside the transistor is discharged and energy is lost in every switching cycle. At RF frequencies there are many cycles per second (typically above 1 MHz) meaning loss of zero-voltage switching causes losses to unbearably increase. Conventional topologies only maintain zero-voltage switching at small ideal load ranges. If the load evolves outside the ideal load range (due to both reactive and resistive miss-matches), no zero-voltage switching can be maintained. The prior art matching boxes therefore are configured to enable zero-voltage switching by keeping the load presented to the RF source fixed to the optimal load (impedance) point.

[0053] According to the present disclosure, a load-tolerant converter topology is provided which enables to maintain ZVS capability over a large impedance range. As a result, the need of variable matching is avoided. Hence, a matching box with variable reactances as in the prior art can be dispensed with.

[0054] Referring to Fig. 3, a resonant converter 100 according to the present disclosure comprises an input section 110, a switching section 120, a resonator section 130 and an output section 160. Resonant converter 100 is configured to convert a DC input, particularly a DC supply voltage Vsprovided at input 111 , to an AC output, particularly an AC voltage and / or current (AC power) which advantageously is of radio frequency, and is applied at the output terminals 161 and 162. The resonant converter 100 is advantageously configured to operate as an inverter for outputting AC power Pioad to a load 104 connected to the output terminals 161 , 162. The load 104 has an impedance Zioad, which can be complex and can be variable, e.g. as a function of Pioad. Resonant converter 100 is advantageously a power amplifier, particularly a radio frequency (RF) power amplifier. Advantageously, the resonant converter 100, particularly each of the input section 110, switching section 120, resonator section 130 and output section 160 has a topology which is symmetrical with respect to a symmetry plane 101.

[0055] The input section 110 comprises an input 111 configured to receive a DC supply voltage Vs. The DC supply voltage Vsmay be supplied by a suitable voltage source (not shown). The input section 110 is configured to couple the input 111 to voltage nodes 112 and 113 which are symmetrically arranged with respect to the symmetry plane 101. The input section 110 advantageously comprises a DC biasing network, particularly a reactive network, more particularly an inductive network that couples the input 111 to the voltage nodes 112, 113. The inductive network can comprise or consist of choke inductors LChoke.

[0056] The switching section 120 is configured to alternatingly connect the voltage nodes 112, 113 to a shared node 114 at a switching frequency fs, which is advantageously a fixed, non-variable frequency. As a result, voltage waveforms Vdsi and Vds2 occur at the voltage nodes 112 and 113 respectively. In some examples, the switching section 120 can comprise a pair of switch devices, such as transistor devices, each one switchingly connecting a respective voltage node 112, 113 to the shared node 114. The shared node 114 can be a shared ground, or a negative voltage node of the voltage source supplying Vs. The switching frequency is advantageously in the radio frequency range, such as between 2 MHz and 2.4 GHz, particularly between 2 MHz and 300 MHz.

[0057] The resonator section 130 is connected between the voltage nodes112, 113 and the output section 160, which comprises, or consists of, the output terminals 161 and 162. The resonator section 130 comprises, or consists of, a first resonator network 140 and a second resonator network 150. Each of the first and second resonator networks is tuned to define at least one characteristic of a complex impedance seen by the (switch devices of the) input section 120. Particularly, as will be shown in greater detail below, the first resonator network 140 is configured to short, or at least reduce, an even mode impedance at a second harmonic frequency of the switching frequency, i.e., twice the switching frequency fs. The second resonator network 150 is configured to define a phase and magnitude of an odd mode impedance at the switching frequency fsand at a third harmonic of the switching frequency, i.e., three times the switching frequency fs. In some examples, the first resonator network 140 is connected between the voltage nodes 112, 113 and the shared node 141. The second resonator network 150 is advantageously connected between the voltage nodes 112, 113 and the output section 160. It will be appreciated that the reactive network of the input section 110 can be shared with the resonator section 130.

[0058] The output section 160 can comprise suitable signal conditioning circuitry, e.g. for converting a single-ended signal to a differential signal. In some examples, the output section can comprise a transformer. A primary side of the transformer can be connected to the resonator section 130 and a secondary side of the transformer can be connected to the output terminals 161 , 162.

[0059] Resonant converter 100 can further comprise a control unit 170.Control unit 170 is configured to control operation of the switching section 120, specifically to control operation of the switching devices, such as in terms of duty cycle and / or switching frequency. The control unit 170 can be configured to control operation of the switching section 120 in response to measurements of voltage and / or current (e.g.,power) received from the resonant converter 100, such as from the output section 160. Possibly, control unit 170 can comprise an input configured to receive a set point value of an output voltage and / or output current (e.g., output power Pioad).

[0060] Referring to Fig. 4, in a first exemplary embodiment of resonant converter 100, switching section 120 comprises a pair of switch devices Mi, M2, which can be semiconductor switch devices, such as transistors, which can be based on SiC, GaN or silicon semiconductor technology, e.g. metal oxide semiconductor field effect transistors (MOSFETs). The switch devices Mi, M2 are connected with first switch terminals (e.g., the source terminals) to shared node 114 and with second switch terminals (e.g., the drain terminals) to respective voltage nodes 112 and 113 having respective voltages Vdsi and VdS2. The shared node 114 is connected to ground 141 in some examples. The switch devices Mi, M2 are configured to open and close a conduction path between the respective first and second switch terminals upon application of a control signal, such as gate voltages vgiand vg2, occurring at a switching frequency fsand a duty cycle D. The control signal is generated by control unit 170, possibly based on a set point of Pioad and possibly based on measurement of one or more voltages and / or currents occurring in the converter 100. The duty cycle D can be fixed or variable, e.g. based on conduction angle. The switch devices Mi and M2 operate 180° out of phase (and so are the gate voltages vgiand vg2) to create a push-pull configuration. A possibly fixed duty cycle offset between the switch devices Mi and M2 can be implemented.

[0061] The first resonator network 140 comprises a series circuit 142 of shunt capacitors Cshunt connected between the voltage nodes 112 and 113. Series circuit 142 has a centre or midpoint node 143 which is advantageously capacitively stabilized, advantageously of sufficiently low impedance, and which can be connected to ground 141. The first resonator network 140 further comprises a T-network 144 provided as a CLC network. T-network 144 comprises two capacitors C2, each having a first terminal connected to a respective voltage node 112 and 113 and the second terminals of the capacitors C2 are connected to each other to from a centre or midpoint node 145. T-network 144 further comprises an inductor L2 having a first terminal connected to midpoint node 145 and a second terminal connected to the shared node 114 and / or ground 141 , e.g. via centre node 143.

[0062] The second resonator network 150 comprises an LC tank circuit, with a pair of inductors L3, each having first terminals connected to a respective voltage node 112 and 113. The second terminals of the inductors L3 are connected to output nodes 151 and 152 respectively. An output capacitor C3 is connected between the outputnodes 151 and 152. Inductors L3 advantageously have equal inductance. It will be appreciated that, unlike the prior art, the second resonator network does not comprise series LC resonator circuits, rather the output capacitor C3 is placed in parallel with the load 104. As will be shown further below, the present configuration of the second resonator network surprisingly allows to broaden the load impedance range that is tolerated by the resonant converter while operating under ZVS conditions.

[0063] The output section 160 comprises a transformer 167, configured to transform the differential voltage at the output nodes 151 , 152. The terminals of the primary winding 165 of transformer 167 are connected to the output nodes 151 and 152 of the second resonator network 150, respectively, i.e. parallel to output capacitor C3. The terminals of the secondary winding 166 of the transformer 167 are connected to the output terminals 161 , 162 respectively and the lower terminal 162 can be connected to ground 168. The primary winding 165 of transformer 167 comprises a centre-tap 163, which provides the supply voltage Vsto the voltage nodes 112, 113. The transformer can be configured to transform the load impedance to align converter specifications (e.g., transistor voltage rating) with the load.

[0064] Referring to Fig. 5, in operation, the transistor gate voltages vgi, vg2 are driven 180° out-of-phase with a given duty cycle D which determines the transistor on-time as a fraction of the switching period Ts. The proper functioning is defined by the quasi steady-state drain-source voltages Vdsi and VdS2 and drain current ldi, Id2 of transistors Mi and M2. The resonant converter 100 is operated to ensure zero-voltage switching (ZVS) of the transistors Mi and M2. Particularly, as shown in Fig. 5, the drainsource voltage Vdsi,2 should be zero at turn-on of the respective transistor. To optimize the performance, the duty cycle D may be varied such that ZVS is maintained over varying load or circuit conditions.

[0065] The drain-voltage waveform Vdsi,2(t) includes multiple frequency components, therefore the drain-source impedance is of importance to properly control the waveform and ensure ZVS operation over the impedance trajectory range of the load. The transistors’ load impedance Zds is affected by the varying impedance of the load. One benefit of the resonant converter 100 is its ability to minimize the impact of a variation of Zioad on ZdS, as will be shown in the following.

[0066] It is considered that Zds can be expanded into two components: a first one in which the transistors are driven in common-mode, referred to as the evenmode impedance Zds, even and a second one in which the transistors are driven in differential mode, referred to as the odd-mode impedance Zds, odd. Due to the nature of the push-pull operation, the effect of the Zioad on the Zds, even is negligible. By properlytuning the values of L3 and C3, and possibly Cshunt, it is possible to achieve a loadinsensitive Zds.odd over the first and third harmonic magnitude and phase. Figs. 6A-B show a comparison between correct and poor component dimensioning over an exemplary complex impedance range. Referring to Fig. 6A, in case of correct dimensioning of the resonator section 130, the zero-voltage switching operation can be maintained, since the drain-source voltage Vdsi,2 waveforms 210 for different impedance values will all return to zero within a narrow time frame 212. Referring to Fig. 6B, in case of poor tuning, the Vds voltage waveforms 211 can change significantly and the zero-voltage switching operation is lost for some values of the load impedance, rendering the converter inoperable at this point.

[0067] Referring to Figs. 7-11 , various modifications can be made to the resonant converter 100, without however departing from the benefits imparted by the present disclosure. Firstly, referring to Fig. 8, the T-network 144 can be provided as an LCL network with a pair of inductors L2 between voltage nodes 112, 113 and a capacitor C2 between centre point 145 and ground 141 , instead of a CLC network as shown in Fig. 4.

[0068] Referring to Fig. 7, in addition, or alternatively, the input 111 can be connected to the centre point 145 of the first resonator network 140 (i.e. , the centre point of the T-network 144) through a choke inductor LChoke. Referring to Fig. 10, the input 111 can alternatively be connected to the voltage nodes 112 and 113 through respective choke inductors LChoke.

[0069] Referring to Fig. 9, the output capacitor C3 can alternatively be placed parallel with the load 104 at the secondary side of transformer 167. Specifically, output capacitor C3 is connected parallel to the secondary winding 166 of transformer 167, instead of being parallel connected to the primary winding 165. The inductors L3 are connected between the voltage nodes 112, 113 respectively, and the primary winding of transformer 167.

[0070] Referring to Fig. 11 , a transformer 167 with centre-tapped primary winding 164 is provided at the output section. It is possible to integrate the inductors L3 of the second resonator network 150 in the centre-tapped primary winding 164, i.e. utilizing the leakage inductance of the centre-tapped primary winding 164 in combination with the parallel output capacitor C3 as the second resonator network. The capacitor C3 is connected between the output nodes 151 , 152, which are connected to the terminals of the secondary winding 166 of transformer 167. In the variant of Fig. 11 , the T-network 144 can be of LCL-type or of CLC-type (LCL is shown).

[0071] Referring to Fig. 8, the secondary side of the transformer 167 can have differential output (i.e., output terminals 161 , 162 are differential instead of single- ended and terminal 162 is not connected to ground. Alternatively, referring to Fig. 10, the secondary winding 166 of the transformer 167 can be center-tapped and the centertap connected to ground 168. The latter configuration has the benefit that the voltage potential of the output nodes 161 , 162 relative to ground is smaller compared to the single-ended configuration of Fig. 9.

[0072] Referring to Fig. 12, in another variant of the resonant converter100, the output section does not need a transformer. In some examples of this variant, the input is provided by DC voltage source 115 connected to the centre tap of a centretapped choke inductor 116. Opposite terminals of choke inductor 116 are connected to the voltage nodes 112, 113 respectively. The negative terminal of DC voltage source 115 is connected to the shared node 114 of the switching section 120. In this variant as well, the T-network 144 can be of LCL-type or of CLC-type (CLC is shown).

[0073] Referring to Fig. 13, another variant 300 of the resonant converter according to the present disclosure differs from the previous variants in that the first resonator network 340 does not comprise a T-network. Instead, two series LC circuits L2, C2 are connected in series between the first and second voltage nodes 112, 113. A midpoint 345 of the series LC circuits is advantageously connected to the midpoint 143 of the series shunt capacitors Cshunt and / or the shared node 114, and possibly connected to ground 141. The second resonator network 150 can be any one of the second resonator networks as described in relation to the previous variants, and comprises an output capacitor C3 which is parallel connected to the output terminals 161 , 162, either at the primary side or the secondary side of transformer 167, if present. The input section and the switching section can be provided like in any one of the variants described above.

[0074] It will be appreciated that any suitable combination can be made of the features described above in relation to Figs. 4 and 7-13. Particularly, variants of the input section 110, the switching section 120, the first and second resonator networks 140, 150 and the output section 160 can be combined as desired.

[0075] Yet alternative variants are possible. Particularly, non-explicit capacitive and / or inductive components can be utilized to replace any one of Cshunt, C2 and C3. In some examples, plane and transistor capacitances can replace Cshunt at least in part. In other examples, leakage inductance (e.g., of the primary winding of transformer 167), or mutual inductances can be utilized to replace the explicit inductive components.

[0076] It will be appreciated that, depending on the drain current ld-1,2 that the transistors Mi, M2 need to switch, use can be made of multiple transistor switches inparallel and / or multiple transistor stages Mi I M2 in parallel. Alternatively, or in addition, multiple resonant converters 100 can be arranged in parallel and / or in series, with shared or individual input 111 , to provide increased output power and / or voltage levels.

[0077] Referring to Fig. 28, resonant converters 100, 300 according to the present disclosure can be integrated in a power generator 600, e.g. for driving an antenna (coil 12) of a plasma system coupled to the output 602 of power generator 600. The resonant converter is configured to deliver the required RF power at the plasma excitation frequency, which can be in the range between 2 MHz and 300 MHz, preferably between 2 MHz and 150 MHz, such as 2 MHz, 13.56 MHz, or 27 MHz. The DC supply voltage Vsis supplied by an input converter stage 610 to a DC biasing network 621 . The input converter stage 610 can comprise an AC / DC converter coupled to a DC / DC converter. The AC / DC converter is configured to convert the input signal at input 601 , such as a single-phase or a three-phase mains supply to a stable DC bus voltage on a DC rail. The DC / DC converter is configured to transform the stable DC bus voltage to the supply voltage Vsof the resonant converter. Such a DC / DC converter can have an isolated or a non-isolated topology and is advantageously a buck converter to step down Vsfrom the DC bus voltage. Suitable examples are a half-bridge (buck) converter with or without interleaving.

[0078] The control unit 640 generates a pair of synchronized drive signals641 , such as a pulse-train of possibly rectangular pulses having the same frequency and possibly same or offset duty-cycle. The second drive signal is 180 degrees shifted compared to the first signal, resulting in switching of the switch devices Mi, M2 alternatingly. The drive signals 641 are fed to the control unit 170, which implements a gate driver which buffers and translates the drive signals to the required signal levels vgi, Vg2 of the pair of switch devices Mi, M2. It will be appreciated that control unit 170 can be integrated into control unit 640. Alternatively, drive signals 641 can be generated by control unit 170 on command issued by control unit 640.

[0079] The DC biasing network 621 is configured to supply the DC supply voltage to the switching section 120 and advantageously behaves as a short at DC. The DC biasing network can have various suitable topologies for injecting the supply voltage Vs. One suitable example is through an individual choke inductor LChoke for each of the two switch devices Mi and M2, or through a shared choke inductor.

[0080] As described previously, the output section 160 of the resonant converter 100 can comprise a transformer 167 coupled to the resonator section 130. Transformer 167 can be a balun transformer, configured to convert a differential signal to a single-ended signal. In most common plasma applications, the antenna 12 of theplasma chamber accepts a single-ended RF signal at one terminal of the antenna, while the other terminal is connected to ground. One terminal of the secondary coil of transformer 167 can be connected to ground, whereas the other terminal of the secondary coil forms the output 161 of the resonant converter 320.

[0081] In other examples, the antenna 12 is a differential antenna. A full differential path can thus be utilized from transformer 167 to the antenna 12. One advantage of such implementations is that the effective voltage from antenna terminal to ground can be twice as low compared to a single-ended implementation.

[0082] The transformer 167 can be implemented with coupled resonant coils, or alternatively with coils coupled by ferrite.

[0083] The power generator can further comprise a reactive network 630 coupled between the resonant converter output 161 and the power generator output 602. Reactive network 630 comprises or consists of one or a combination of reactive components, such as one or more inductors and / or capacitors, resulting in a reactive network of advantageously fixed reactance. The reactive network is advantageously directly connected to the antenna 12 of the plasma chamber 11 , e.g. without a transmission line 15 or matching box 13 like the prior art. The reactive components of the reactive network are selected such that the impedance operating region with and without plasma ignition is within the desired operating range of the resonant converter. The reactive component(s) should produce a high-quality factor (Q) in combination with the antenna 12 at the plasma excitation frequency. A high Q makes the ignition of the plasma substantially easier due to the high voltage across, and therewith electromagnetic field of, the antenna 12. In some examples, the plasma system is an Inductive Coupled Plasma (ICP), and the antenna 110 is a large coil with a significant reactance. In such case, the reactive network 630 is advantageously configured as a series capacitor to nullify the majority of the reactive impedance. Directly connecting the reactive network 630 to the antenna 12 can greatly reduce the size and costs of the interconnection between the power generator and the plasma chamber since most reactive current is cancelled locally.

[0084] The measurement unit 650 can be a current and voltage (IV) probe arranged at the output 161 of the resonant converter, e.g. between the output 161 (transformer 167) and the reactive network 630. The IV probe is configured to measure the complex voltage and current waveforms and therewith also the true and reactive power and complex load impedance. Alternatively, the IV probe can be arranged between the reactive network 630 and the output 602. The latter can be beneficial when the reactive network comprises multiple reactive components, of which some areconnected to ground. The measurement unit 650 is connected to the control unit 640 which uses the measured complex parameters (current and voltage) to adapt the operation of the input converter stage (e.g., DC / DC converter) and / or the resonant converter 100, 300.Simulation experiments

[0085] Advantages of the resonant converter according to the present disclosure over prior art resonant converters will be apparent from the following comparative simulation experiments.

[0086] In switched-mode RF converters, proper shaping of the voltage waveform across the transistor terminals is important to maintain ZVS operation. The complex impedance (both magnitude and phase) seen by the transistor plays a key role to obtain a well-defined voltage waveform shape. Specifically, the resonator section is designed and tuned based on the complex impedance seen by the transistor at the first, second and following harmonics. However, mainly the first three harmonics are of main interest. The above principles were already acknowledged and described in US 7924580. Referring to the graphs of Fig. 5, it can be seen that the waveform of Vdsi,2(t) is obtained by superimposing the third harmonic waveform onto the fundamental waveform, thereby obtaining a waveform shape which is closer to a block waveform. To this end, the second harmonic waveform needs to be largely suppressed.

[0087] It can further be shown by theoretical considerations that to obtain robust ZVS conditions, the phase of the impedance seen by each of the transistors at the fundamental frequency (switching frequency) fi = fsshould be between 10° and 90°, preferably between 20° and 80°, preferably between 30° and 60°. Further, it is highly advantageous that the ratio of magnitude of the impedance seen by each of the transistors at fi to the magnitude of the same impedance at the third harmonic frequency fa = 3 . fi is between 1 .5 and 5 in absolute values, preferably between 2 and 4. These considerations allow to design and tune the components of the resonator section.Example 1 : Simulation of a comparative EF2 converter

[0088] The performance of a comparative EF2 converter, analogous to the converter disclosed in US 7924580, with a series LC resonator network as second resonator network is analysed first. The converter topology is shown in Fig. 14A and comprises a push-pull stage 401 and a T-network 402, which in this exemplary case is of LCL-type. Due to the nature of a push-pull converter, with differential driving and thus opposing drain-source voltages Vdsi and dS2, the analysis of the impedance ZDS seen bytransistors Mi and M2 can be split in two parts: an odd-mode impedance Zos.odd with equivalent electric circuit shown in Fig. 14A, which refers to the impedance seen by the odd frequency (harmonic) components of the transistor voltages Vdsi,2, and an evenmode impedance Zos.even with equivalent electric circuit shown in Fig. 14C, which refers to the impedance seen by the even frequency (harmonic) components.

[0089] While both equivalent impedances are of importance, mainly theZodd-mode is of interest because it is dependent on the load impedance Zioad. Because of the push-pull nature of the transistor stage, the Zeven-mode impedance is ideally independent of the load impedance Zioad and hence of minor importance for tuning considerations. Referring to Fig. 14B, the odd-mode impedance can be written out as:The circuit of Fig. 14A may be tuned such that the following boundary conditions are met for the odd-mode impedance:1. the phase angle of ZDSodd_modeat the fundamental harmonic frequency fi is between 10° and 90°: 10°2. the ratio of absolute values of the magnitude of ZDSodd_modeat the third harmonic frequency fa to the magnitude of ZDSodd_modeat the fundamental harmonicI z I frequency fi is between 1.5 and 5: 1.5 <d, < 5 , \zds,fi \ in which ZdSrefers to Zos.odd. These conditions ensure that the circuit operates in zerovoltage switching conditions and that the third harmonic component of the transistor voltage waveform, responsible for dampening the voltage waveform on the transistor becomes significant. The phase angle and magnitude diagrams of ZDSodd_modefor an example tuned circuit are shown in Fig. 16 for a 10 Q and 20 Q real, resistive load Zioad, a switching frequency fs= fi = 13.56 MHz and an output power of 1 kW at 150 V Vsfor a circuit as in Fig. 4 with Cshunt = 312 pF, LF2 = 199 nH, CF2 = 346 pF, Ls= 330 nH, Cs= 420 pF. In addition, Fig. 15 shows the magnitude diagram of Zos.even for the same example tuned circuit, in which it can be observed that Zos.even is shorted at the second harmonic frequency f2.

[0090] Looking at Fig. 16, it can be observed that the magnitude curve of the impedance \ZDS| comprises inflection points 410 indicated by the star points, in which the following condition applies:and which are located in the region where the first condition of 10° < z zdS)fl) < 90° is maintained. It is observed that the inflection point 410 has moved only a little when theresistive load is varied from 20 Q to 10 Q, and because it is offset from the fundamental harmonic frequency fi, little difference in the phase angle at the first harmonic frequency (condition 1) is observed.

[0091] Referring to Fig. 17, however, when the same node impedance is evaluated with a reactive (capacitive and inductive) load (Zioad = 20-20j Q and 20+20j Q), it is observed that the inflection point 411 moves significantly and the phase variation is significant and zero-voltage switching conditions are not met for the capacitive loads, leading to excessive transistor losses. It is furthermore observed that for varying reactive loads, the magnitude of the impedance at the fundamental harmonic frequency fi becomes larger than the magnitude at the third harmonic frequency, causing the resonant converter to lose its characteristic waveform.

[0092] Referring to Figs. 18 and 19, the complex impedance ZDSodd modecan be swept across the x (real) and y (imaginary) axes to visualize the effect of the above phase condition (condition 1) and magnitude condition (condition 2), respectively. Referring to Fig. 20, the plots of Fig. 18 and 19 are merged to reveal the window 415 of real and imaginary values of the complex impedance ZDSodd modein which both conditions are met and the converter is assumed to be operating in ZVS.Example 2: Simulation of resonant converter according to the present disclosure

[0093] The performance of the resonant converter as shown in Fig. 7 of the present disclosure is analyzed in the following. This resonant converter shares various features with the class-EF2 converter analyzed in Example 1 , except for the second resonator network 150, which in the present case does not comprise a series LC resonator circuit, but instead comprises a capacitor connected parallel to the load 104 (Zioad). The equivalent electric circuit of the odd-mode impedance and even mode impedance seen by the transistors Mi, M2 of the circuit of Fig. 7 is shown in Figs. 21A and 21 B respectively. Comparing Fig. 21 A with Fig. 14B (equivalent circuit for the class- EF2 inverter), it can readily be seen that the capacitor C3 is connected parallel to the load and not in series with inductor L3, whereas in Fig. 14B the capacitor Csis in series with inductor Ls. It will further be appreciated that the first and second resonator networks 140, 150 in the resonant converters 100 according to the present disclosure are coupled resonator circuits, and should not be seen as separate resonators for the present analysis.

[0094] Specifically, in the equivalent circuit of Fig. 21A, the (equivalent) inductor 2L3 of the second resonator network has one terminal having an equipotential connection with the drain terminal of the switches Mi, M2. The opposite terminal of theinductor 2L3 is connected to a terminal of the capacitor C3 of the second resonator network. Referring to Fig. 21 B showing the equivalent electric circuit of the even mode impedance seen by the switch devices Mi, M2, it can be seen that the second resonator network advantageously does not contribute in this electric circuit. The resonator properties of the equivalent electric circuit of the even mode impedance seen by the switch devices Mi, M2 is advantageously defined exclusively by the first resonator network.

[0095] Due to the parallel capacitor C3 the odd-mode impedance seen by the (odd-mode frequency components of the) circuit can be derived from the equivalent circuit of Fig. 21A as follows:The circuit presents the same conditions (phase condition and magnitude condition) that have to be met to consider the switches Mi, M2 to be operating in zero-voltage switching.

[0096] Tuning of the resonant converter according to the present disclosure can be obtained by considering a design problem which relies on obtaining the largest output power Pioad into a predetermined load 104 (Zioad) and considering predetermined transistor characteristics, such as the transistor drain-source breakdown voltage Vmax, maximum transistor current Imaxand transistor drain-source (output) capacitance which dominates Cshunt. This problem can be expanded into two main simplified equations which determine the maximum operating power in terms of voltage and current (Eq. 2):The first equation is more or less fixed because of the voltage specification of the transistor, which is dependent on the supply voltage (Vsor VDD) which in simplified terms can be written as:To optimally use the transistor, based on the waveforms shown in Fig. 5, having roughly a drain voltage which is 2.2 times the supply voltage, it follows:Vs= 0A5Vmax. It will be appreciated that safety margins can be applied to Vmaxand Imax.

[0097] An optimization problem is now solved which maximizes the real value (magnitude) of the impedance seen by the transistor at the first harmonic frequency (i.e. , the switching frequency), taking the outer boundary conditions into account: Max{Real ZDS^)) (Eq. 3), wherein similar boundary conditions for the waveform shape apply (Eq. 4):10° < ZDV1< 90° DS, f 2, even * Short .Specifically for the resonant converters according to the present disclosure, comprising a second resonator network with a shunted output capacitance, the above optimization (maximization) problem allows to reduce the current stress in the transistor and therefore allows for a larger impedance range to be possible. It will be appreciated that the above maximization problem does not hold for the EF2 resonant converter of Example 1.

[0098] The set of tuning values obtained from the above optimization problem will yield the largest operating range, for a predetermined topology of resonator section, a predetermined load and predetermined characteristics of the switch devices (transistors). In some examples, the optimization may not have an explicit solution due to the practical non-zero Cshunt and may be further complicated by added reactive load range dimensions.

[0099] Hence, in practical terms, the optimization or tuning can be carried out as follows. In a first step, a real resistive operating load point and a reactive load range are determined based on the desired output power and transistor characteristics. The real resistive operating load point is advantageously a lowest real resistive operating load point, particularly the point where the drain voltage is largest. Subsequently, the shunt capacitance Cshunt is determined, set by the selected transistors. Cshunt is advantageously selected to be as small as possible. In a next step, the reactance values which maximises Real ZDS fl) while satisfying the other given boundary conditions (Eq. 4) over the entire reactive load range are determined. In the example of Eq. 1 , these reactance values are: L3, C3 and L2. It will however be appreciated that the reactance values can be different, such as L3, C3 and C2 for other variants of the resonant converter. Finally, the remaining reactances of the converter are computed, based on the reactance values obtained in the previous step. By way of example, C2 is computed based on L2 (or vice versa). In addition, the finite choke inductance LChoke can be computed as well. It will be appreciated that practical values of the load Zioad are one or more of: Real(Zioad) between 5 Ohm and 50 Ohm and lmag(Zioad) between -50 Ohm and 50 Ohm.

[0100] In the topology of Fig. 7, fora given transistor and a target reactanceImag(Zload) with a given Cshunt of 300 pF theobtained for L3 = 165 nH, 2C3 = 840 pF, C2 = 444 pF, L2 = 155 nH. For these tuned values, Fig. 22 represents a magnitude diagram of the even mode impedance Zos.even. This can be compared with Fig. 15 showing the magnitude diagram of for the comparative circuit of Fig. 14A. It canbe seen that in both cases the impedance is shorted at the second harmonic frequency f2. Fig. 23 represents magnitude and phase angle plots of the odd-mode impedance for the tuned circuit and a resistive load of 20 Q. It is observed that the inflection point 520 is at a much lower frequency compared to Fig. 16. Fig. 24 represents the same node impedance but with two different reactive loads, capacitive and inductive, of 20-20j Q and 20+20j Q, respectively. Comparing Fig. 24 with Fig. 17, it is observed that for a same variation of Zioad, the inflection point 520 always remains below the fundamental harmonic frequency fi . I n addition, it is observed that the peak of the magnitude is not very sensitive to the reactive load, and thus the sensitivity towards the magnitude condition for maintaining ZVS is further reduced. This reduced sensitivity is shown more clearly by looking at the swept load impedance plots shown in Figs. 25 and 26. The operating window 525 in which both the magnitude condition and the phase condition for the oddmode impedance are met, and hence ZVS is ensured, is shown in Fig. 27 as a function of the real part and imaginary part of Zioad. Comparing Fig. 27 with Fig. 20, it can be seen that surprisingly, the operating window 525 is much larger for the resonant converters according to the present disclosure, and therefore it can be concluded that resonant converters according to the present disclosure are much more load tolerant as compared to the resonant converters of the prior art.

[0101] Although the topology intrinsically provides a wide operable impedance range, the operable range may be tailored to a specific application. In plasma applications, the operable range can be tailored to a specific plasma chamber configuration. This can be achieved with non-variable (i.e., having a fixed reactance) resonant components at the output of the converter, such as in a matching network.

[0102] Another benefit of the topology according to the present disclosure is that it enables the choice of power trajectory tuning, particularly for plasma applications. With a constant supply voltage Vsand a varying impedance Zioad, the converter load power may be proportional to the plasma load conductance or resistance, depending on the used configuration. The tuning of the trajectory of the load power with respect to load resistance can be used to guarantee amplifier stability with non-linear loads.

[0103] Aspects of the present disclosure are set out in the following alphanumerically ordered clauses.A1 . A resonant converter (100, 300), comprising: a DC supply voltage input (111) coupled to a first voltage node (112) and a second voltage node (113), an AC output (161 , 162),a switching section (120) comprising a pair of switch devices (Mi, M2) configured to alternatingly connect the first voltage node (112) and the second voltage node (113) to a shared node (114), a resonator section (130), comprising: a first resonator network (140, 340) connected between the first voltage node (112) and the second voltage node (113) and comprising at least one first inductor (L2) and at least one first capacitor (C2), and a second resonator network (150) comprising at least one second inductor (L3) and a second capacitor (C3), wherein a terminal of one of the at least one second inductor is connected to one of the first voltage node (112) and the second voltage node (113) and wherein the second capacitor (C3) is connected such that in an equivalent electric circuit of an odd mode impedance (Zos.odd) seen by the switch devices the second capacitor (C3) shunts the AC output.A2. Resonant converter of clause A1 , wherein the first resonator network (140) and the second resonator network (150) are tuned to define odd frequency components of a voltage waveform (Vdsi, VdS2) configured to be applied across the pair of switch devices, particularly at a switching frequency (fi) of the pair of switch devices and at a third harmonic frequency (fs) of the switching frequency, and to short an even mode impedance seen by the pair of switch devices at a second harmonic frequency (f2) of the switching frequencyA3. Resonant converter of clause A1 or A2, wherein the at least one first inductor (L2) and the at least one first capacitor (C2) are arranged in a T-network (144) connected between the first and second voltage nodes and a midpoint node (143), preferably the midpoint node being a stabilized voltage node and / or connected to ground and / or to the shared node (114).A4. Resonant converter of clause A3, wherein the T-network (144) is ofCLC type with the first inductor (L2) connected between a centre node (145) of the T- network and the midpoint node (143) and a pair of the first capacitor (C2) connected between a respective one of the first and second voltage nodes (112, 113) and the centre node (145).A5. Resonant converter of clause A3, wherein the T-network (144) is ofLCL type with the first capacitor (C2) connected between a centre node (145) of the T- network and the midpoint node (143) and a pair of the first inductor (L2) connected between a respective one of the first and second voltage nodes (112, 113) and the centre node.A6. Resonant converter of any one of the clauses A3 to A5, wherein theDC supply voltage input (111) is connected to a centre node (145) of the T-network (144), preferably through a DC biasing network, preferably the DC biasing network comprising a third inductor (LChoke).A7. Resonant converter of any one of the clauses A1 to A5, wherein theDC supply voltage input (111) is connected to the first and second voltage nodes, preferably through a DC biasing network, preferably the DC biasing network comprising respective third inductors (LChoke).A8. Resonant converter of any one of the clauses A1 to A7, wherein the pair of switch devices (Mi, M2) is arranged in a push-pull configuration and is configured to be operated at the switching frequency with 180° phase difference.A9. Resonant converter of any one of the clauses A1 to A8, wherein the shared node (114) is a shared ground (141).A10. Resonant converter of any one of the clauses A1 to A9, wherein the second resonator network (150) is free of LC series reactances connected between the first and second voltage nodes and the AC output.A11. Resonant converter of any one of the clauses A1 to A10, wherein the second resonator network (150) comprises a pair of the second inductors (L3), wherein a first terminal of each of the second inductors of the pair is connected to a respective one of the first and second voltage nodes (112, 113), preferably wherein a second terminal of each of the second inductors of the pair is connected to a respective terminal of the second capacitor (C3).A12. Resonant converter of clause A11 , wherein the pair of second inductors (L3) is arranged as a center-tapped inductor (164) forming a primary winding (164) of a transformer (167), preferably wherein a secondary winding of the transformer is coupled to the AC output.A13. Resonant converter of any one of the clauses A1 to A11 , further comprising a transformer (167) having a primary winding (165) and a secondary winding (166), the secondary winding being coupled to the AC output (161 , 162).A14. Resonant converter of clause A13, wherein the primary winding is a center-tapped inductor connected to the DC supply voltage input (111).A15. Resonant converter of clause A13 or A14, wherein the second capacitor (C3) is connected across terminals of the secondary winding (166).A16. Resonant converter of clause A13 or A14, wherein the second capacitor (C3) is connected across terminals of the primary winding (165).A17. Resonant converter of any one of clauses A1 to A16, having a topology comprising a symmetry plane (101), wherein the pair of switch devices (Mi, M2) are arranged symmetrically with respect to the symmetry plane, and wherein the symmetry plane comprises the shared node (114).A18. Resonant converter of clause A17, wherein the symmetry plane comprises the DC supply voltage input (111).A19. Resonant converter of any one of the clauses A1 to A18, further comprising a shunt capacitor (Cshunt) connected parallel to each of the pair of switch devices (Mi, M2).A20. Resonant converter of any one of the clauses A1 to A19, wherein the pair of switch devices are configured to be operated at a constant switching frequency to generate the voltage waveform, preferably with an adjustable duty cycle.A21. Resonant converter of any one of the clauses A1 to A20, wherein the switching frequency is between 2 MHz and 2.4 GHz, preferably between 2 MHz and 300 MHz.A22. Resonant converter of any one of the clauses A1 to A21 , wherein the AC output is a differential output or a single-ended output.A23. Resonant converter of any one of the clauses A1 to A22, being configured as a class EF2-type converter.B1. Method of tuning a resonant converter (100, 300), wherein the resonant converter is as recited in any one of the clauses A1 to A23, wherein the method comprises: determining a switching frequency, a resistive operating point and a reactive range of a load connected to the resonant converter, determining reactance values of reactive elements (L2, C2, L3, C3) of the first and second resonator networks based on solving an optimization problem in which a real value of an impedance seen by the switch devices at the switching frequency is maximized based on one or more boundary conditions selected from: a ratio between magnitudes of an odd mode impedance (Zos.odd), as seen by the switch devices, at three times the switching frequency (fs) and at the switching frequency (fi) is between 1.5 and 5 in absolute value; the odd mode impedance has a phase at the switching frequency (fi) between 10° and 90°, preferably between 20° and 80°; an even mode impedance (Zos.even), as seen by the switch devices, is shorted at a second harmonic frequency of the switching frequency.B2. Method of clause B1 , wherein the reactive range of the load is at least 25 Ohm, preferably at least 50 Ohm, preferably at least 100 Ohm.B3. Method of clause B1 or B2, wherein the reactive range is at least from -25 Ohm to 25 Ohm, preferably at least from -50 Ohm to 50 Ohm. B4. Method of any one of clauses B1 to B3, wherein the resistive operating point is between 5 Ohm and 25 Ohm, preferably between 5 Ohm and 50 Ohm. C1 . Resonant converter according to any one of the clauses A1 to A23, wherein reactance values of reactive elements (l_2, C2, L3, C3) of the first and second resonator networks are determined according to the method of any one of the clauses B1 to B4.C2. Power generator (600), comprising at least one resonant converter(100, 300) according to any one of the clauses A1 to A23 or C1 .C3. Power generator of clause C2, comprising a plurality of the resonant converters, wherein the plurality of resonant converters are connected with the AC output in parallel or in series.

Claims

CLAIMS1. A resonant converter (100, 300), comprising: a DC supply voltage input (111) coupled to a first voltage node (112) and a second voltage node (113), an AC output (161 , 162), a switching section (120) comprising a pair of switch devices (Mi, M2) configured to alternatingly connect the first voltage node (112) and the second voltage node (113) to a shared node (114) at a switching frequency (fi), a resonator section (130), comprising: a first resonator network (140, 340) connected between the first voltage node (112) and the second voltage node (113) and comprising at least one first inductor (L2) and at least one first capacitor (C2), and a second resonator network (150) comprising at least one second inductor (L3) and a second capacitor (C3), wherein a terminal of one of the at least one second inductor is connected to one of the first voltage node (112) and the second voltage node (113) and wherein the second capacitor (C3) is connected such that in an equivalent electric circuit of an odd mode impedance (Zos.odd) seen by the switch devices the second capacitor (C3) shunts the AC output, wherein the first resonator network (140) and the second resonator network (150) are tuned to define odd frequency components of a voltage waveform (Vdsi, Vds2) configured to be applied across the pair of switch devices at the switching frequency (fi) and at a third harmonic frequency (fs) of the switching frequency, and to short an even mode impedance seen by the pair of switch devices at a second harmonic frequency (f2) of the switching frequency.

2. Resonant converter of claim 1 , wherein reactance values of reactive elements (L2, C2, L3, C3) of the first and second resonator networks are such that: a ratio between magnitudes of the odd mode impedance (Zos.odd), at three times the switching frequency (fs) and at the switching frequency (fi) is between 1.5 and 5 in absolute value, and the odd mode impedance has a phase at the switching frequency (fi) between 10° and 90°, preferably between 20° and 80°.

3. Resonant converter of claim 1 or 2, wherein the at least one first inductor (L2) and the at least one first capacitor (C2) are arranged in a T-network (144) connected between the first and second voltage nodes and a midpoint node (143),preferably the midpoint node being a stabilized voltage node and / or connected to ground and / or to the shared node (114).

4. Resonant converter of the preceding claim, wherein the T- network (144) is of CLC type with the first inductor (L2) connected between a centre node (145) of the T-network and the midpoint node (143) and a pair of the first capacitor (C2) connected between a respective one of the first and second voltage nodes (112, 113) and the centre node (145).

5. Resonant converter of claim 3, wherein the T-network (144) is of LCL type with the first capacitor (C2) connected between a centre node (145) of the T- network and the midpoint node (143) and a pair of the first inductor (L2) connected between a respective one of the first and second voltage nodes (112, 113) and the centre node.

6. Resonant converter of any one of the claims 3 to 5, wherein the DC supply voltage input (111) is connected to a centre node (145) of the T-network (144), preferably through a DC biasing network, preferably the DC biasing network comprising a third inductor (LChoke).

7. Resonant converter of any one of the claims 1 to 5, wherein the DC supply voltage input (111) is connected to the first and second voltage nodes, preferably through a DC biasing network, preferably the DC biasing network comprising respective third inductors (LChoke).

8. Resonant converter of any one of the preceding claims, wherein the pair of switch devices (Mi, M2) is arranged in a push-pull configuration and is configured to be operated at the switching frequency with 180° phase difference.

9. Resonant converter of any one of the preceding claims, wherein the shared node (114) is a shared ground (141).

10. Resonant converter of any one of the preceding claims, wherein the second resonator network (150) is free of LC series reactances connected between the first and second voltage nodes and the AC output.

11. Resonant converter of any one of the preceding claims, wherein the second resonator network (150) comprises a pair of the second inductors (L3), wherein a first terminal of each of the second inductors of the pair is connected to a respective one of the first and second voltage nodes (112,113), preferably wherein a second terminal of each of the second inductors of the pair is connected to a respective terminal of the second capacitor (C3).

12. Resonant converter of any one of the claims 1 to 11 , further comprising a transformer (167) having a primary winding (165) and a secondary winding (166), the secondary winding being coupled to the AC output (161 , 162).

13. Resonant converter of the preceding claim, wherein the primary winding is a center-tapped inductor connected to the DC supply voltage input (111).

14. Resonant converter of claim 12 or 13, wherein the at least one second inductor (L3) is formed by a leakage inductance of the primary winding (164, 165), or by a mutual inductance of the transformer.

15. Resonant converter of any one of the claims 12 to 14, wherein the second capacitor (C3) is connected across terminals of the secondary winding (166).

16. Resonant converter of any one of the claims 12 to 14, wherein the second capacitor (C3) is connected across terminals of the primary winding (165).

17. Resonant converter of any one of the preceding claims, further comprising a shunt capacitor (Cshunt) connected parallel to each of the pair of switch devices (Mi, M2).

18. Resonant converter of any one of the preceding claims, wherein the pair of switch devices are configured to be operated at a constant switching frequency to generate the voltage waveform, preferably with an adjustable duty cycle.

19. Resonant converter of any one of the preceding claims, wherein the switching frequency is between 2 MHz and 2.4 GHz, preferably between 2 MHz and 300 MHz.

20. Resonant converter of any one of the preceding claims, being configured as a class EF2-type converter.

21. Power generator (600), comprising at least one resonant converter (100, 300) according to any one of the claims 1 to 20.

22. Power generator of the preceding claim, comprising a plurality of the resonant converters, wherein the plurality of resonant converters are connected with the AC output in parallel or in series.

Images