FIELD OF THE INVENTION

The present invention relates to the field of voltage conversion and generation. Particularly, the present invention relates to a resonant converter for high voltage generation and a method for controlling a resonant converter.

BACKGROUND OF THE INVENTION

Resonant power converters are regularly used, in combination with a transformer, to produce isolated DC, direct current, voltages. In a particular application, such a converter is used in combination with a Cockroft- Walton multiplier to produce the high DC voltages which are necessary to drive an X-Ray tube. Due to the presence of the transformer, AC, alternating current, voltage waveforms are required. Furthermore, in order to mitigate switching losses and electromagnetic interference (EMI), smooth voltage and current waveforms are preferred.

When using super-resonant operation, which is the preferred mode when non reverse-blocking semiconductor switching devices such as MOSFETs, metal-oxide- semiconductor field-effect transistors, or IGBTs, insulated-gate bipolar transistors, are used, the voltage swing across the resonant capacitor can range from a maximum corresponding to the natural resonant frequency of the resonant tank, down to very small values - theoretically down to zero, corresponding to very (infinitely) high switching frequencies.

In practice, this range cannot be used to its full extent, because at high frequencies the switching losses in various circuit elements would increase so much that a useful design is not feasible.

Therefore, a span of capacitor voltages over somewhat more than a decade is seen as a sensible rule of thumb for design. The corresponding range in current to be delivered to the load is even smaller, because the increase in frequency at light loads counteracts the reduction in capacitor voltage swing.

In order to remedy this situation and obtain a useful range of current control (preferably down to zero) with a limited range of capacitor voltages and frequencies, a shunting capacitor is connected across the AC terminals of the diode rectifier and/or the primary terminals of the transformer. This capacitor effectively shunts some of the current flowing in the resonant tank away from the output, thereby facilitating zero output current while a nonzero current flows in the resonant tank. The resulting topology is denoted as LCC.

It is also proven practice to place relatively large capacitances in parallel to the switching devices, and have the devices operate under zero-voltage switching conditions. The resulting topology is denoted as CLC.

By combining both aforementioned changes to the original (LC) circuit, a so- called CLCC resonant topology is obtained.

Various methods exist to control resonant converters. For example frequency control, which is a well-known method, allows a very simple implementation. However, as is well-known in the art, frequency control suffers from ill-defined dynamic response, without guarantees to have sustained resonance in the circuit, or to avoid hard-switching events and voltage or current overshoots if challenging dynamic behavior is desired. Other, more developed control methods suffer from these anomalies to a lesser extent, but still the control of resonant converters, especially under dynamically challenging conditions, is considered to be a difficult problem.

The control method called optimal trajectory control (OTC) is known to produce near-instantaneous response to variations in the demanded value, which basically solves the problems cited in the previous section. In OTC, one or more system variables are controlled by means of prediction of the circuit behavior over one or more switching cycles by means of a mathematical model which describes the circuit operation. OTC has already been developed and applied to LC resonant converters, and allows precise and fast control of the swing of the voltage across the resonant capacitor in such a circuit.

For the LCC, CLC and CLCC topologies, due to the presence of the shunting capacitor and the capacitors in parallel to the switching devices, the behavior of the circuit is changed, making the response of the circuit to the OTC as developed for the LC converter no longer optimal. The non-optimality shows up in the voltage swing across the resonant capacitor, which becomes larger than commanded. Ultimately, at extreme load situations or severe dynamical conditions, control of the CLCC circuit cannot be maintained as the voltage swing across the resonant capacitor no longer follows its commanded value.

Until now, an optimal trajectory control law has not been derived for the so- called LCC, CLC, and CLCC variants of resonant power converters.

US 6,178,099 Bl describes a phase-shifted control for a series resonant converter involving instantaneous monitoring of state variables, e.g. resonant capacitor voltage, resonant inductor current and output voltage, and the implementation of a control law for providing a quasi-square-wave-with-maximum-coasting mode of operation. The control law uses the instantaneous resonant inductor current, the instantaneous resonant capacitor voltage and the output voltage to determine the optimal time to perform switching events in order to operate on a desired control trajectory. The quasi- square- wave- with- maximum-coasting converter operates at a minimized frequency in a super-resonant mode with zero-voltage switching, minimized electrical stresses, and reduced electromagnetic interference due to nearly sinusoidal resonant tank currents. SUMMARY OF THE INVENTION

There may be a need to improve resonant converters for high voltage generation.

These needs are met by the subject-matter of the independent claims. Further exemplary embodiments are evident from the dependent claims and the following description.

An aspect of the invention relates to a resonant converter for high voltage generation, the resonant converter comprising: at least one switch; a measuring unit, which is adapted to measure at least two variables, a first variable and a second variable, of the resonant converter on at least one state transition per cycle of the resonant converter; a processing unit, which is adapted to evaluate a control model of a circuit operation of the resonant converter using at least the measured first variable and at least one circuit parameter of the resonant converter generating an evaluated value; and to compare the evaluated value to at least the second variable, determining an instant at which the evaluated value and the measured at least the second variable cross; and a switching unit, which is adapted to control the at least one switch based on the determined instant and on the comparison of the evaluated value with the at least the second variable.

Each of the measured at least two variables may be any voltage or current of the circuit of the resonant converter, e.g. a measured quantity measured at different instants, defining a function over time, representing a time-dependency. The same applies to the evaluated value; this might be any kind of characteristic voltage or current of the circuit of the resonant converter, e.g. an evaluated quantity evaluated at different instants, defining a function over time, representing a time-dependency.

In other words, the determining of the instant at which the evaluated value and the measured second variable cross implies a determining of the instant at which a first or evaluated function over time of the evaluated value and a second or measured function over time of the measured second variable cross.

A further, second aspect of the invention relates to a high voltage generator for X-ray generation comprising at least one resonant converter according to any implementation form of the first aspect.

A further, third aspect of the present invention relates to an X-ray generator comprising a high voltage generator according to the second aspect.

A further aspect of the invention relates to a method for controlling a resonant converter, the method comprising the steps of: measuring at least two variables, a first variable and a second variable, of the resonant converter on at least one state transition per cycle of the resonant converter; evaluating a control model of a circuit operation of the resonant converter using the measured at least the first variable and at least one circuit parameter of the resonant converter generating an evaluated value and comparing the evaluated value to at least the second variable, determining an instant at which the evaluated value and the measured second variable cross; and controlling the at least one switch based on the determined instant and the comparison of the evaluated value with the second variable.

The present invention provides a non-linear control law which can be used to control LC, LCC, CLC, and CLCC series-resonant converters. The control law is derived using first principles from circuit theory. Without loss of generality, only the case for the CLCC converter at positive current flow in the resonant circuit will be addressed.

The present invention advantageously provides a method which can be used to precisely control so-called LCC, CLC, and CLCC variants of resonant power converters. The present invention advantageously makes use of parameters of the resonant tank circuit, the shunt capacitor (if present), and the device capacitances (if present), and measured voltages to predict the instant of switching such that a predefined peak voltage across the resonant capacitor is reached at the end of a resonant (half)cycle.

The present invention advantageously allows precisely reaching a predefined system state at the next relevant state transition. Relevant state transitions could be, for example, the instants where the current in the resonant tank crosses zero, i.e. the instants at which the voltage in the resonant tank reaches a local maximum or minimum over time. In the time interval between these zero crossings, the operation can be described as a sequence of linear circuits, the configuration of which depends on the semiconductor switches which are conducting. The present invention advantageously provides an optimal trajectory control law which can be used to precisely control the LCC, CLC and CLCC types of series-resonant converters. By using this control law, the peak voltage across the resonant capacitor can be accurately controlled to a desired value. As a result, the external behavior of the resonant converter changes to a controlled current source, which is advantageous to allow control of the output voltage of the system. In other words, the present invention advantageously proposes considering a resonant inverter, which in steady state operation cyclically traverses through a limited number of system states. Circuit variables are measured at one state transition or more state transitions per cycle, for example at the zero crossings of the inductor current. Using these measured variables, the desired system state at the next relevant state transition, and a mathematical model of the circuit operation, a control value is evaluated directly after this measurement and stored. Next a comparing of a measured circuit variable, defined as the measured variable, in time to the evaluated value is performed; a switching instant is derived implicitly and, correspondingly, an activating or deactivating of the at least one switch at this very instant leads to reaching exactly the desired system state at the next relevant state transition.

The method can be used for controlling resonant converters. The term "switch" used within the description of the present invention may relate to a three-terminal power semiconductor device power transistor as a switch, in a single device. The switch may be any power semiconductor switch, such as a GTO - gate turn-off thyristor -, a JFET - junction gate field-effect transistor-, a Bipolar transistor, an IGCT - Integrated Gate-Commutated Thyristor -, an IGBT - insulated-gate bipolar transistor -, or a MOSFET - metal oxide semiconductor field-effect transistor. The switches may be used for resonant power conversion using CLC, LCC or CLCC type converters, for which accurate control of the power flow is needed, in particular for high voltage generators in the fields of interventional X-Ray and diagnostic X-Ray.

The term "instant" used within the description of the present invention may relate to a very short period of time, e.g. between 1 ns and 500 ns, or between 1 ns and 1000 ns, or between 1 ns and several hundreds of or several hundreds of ms. The term "instant" may relate to a single, usually precise, point in time, relating to a switching event.

According to an exemplary embodiment of the present invention, the processing unit is adapted to evaluate the control model by means of an analogue circuit.

This advantageously provides an improved evaluation of the optimal switching time, e.g. optimal turn off and optimal turn on time. According to an exemplary embodiment of the present invention, the processing unit is adapted to evaluate the control model by means of a digital signal processor.

This advantageously provides an improved evaluating of the optimal switching time, providing optimized digital signal processing.

According to an exemplary embodiment of the present invention, the processing unit is adapted to evaluate the control model by means of a field-programmable gate array (FPGA).

According to an exemplary embodiment of the present invention, the processing unit may be adapted to store a control value based on the comparison of the evaluated value with the measured variable.

According to an exemplary embodiment of the present invention, the switching unit may be adapted to activate or to deactivate the at least one switch.

According to an exemplary embodiment of the present invention, the processing unit is adapted to compare the evaluated value and the second variable at the instant where the evaluated value and the second variable cross.

According to an exemplary embodiment of the present invention, the control device is adapted to control an LC resonant converter, an LCC resonant converter, a CLC resonant converter, or a CLCC series-resonant converter, or any other resonant converter.

A computer program performing the method of the present invention may be stored on a computer-readable medium. A computer-readable medium may be a floppy disk, a hard disk, a CD, a DVD, an USB (Universal Serial Bus) storage device, a RAM (Random Access Memory), a ROM (Read Only Memory) and an EPROM (Erasable Programmable Read Only Memory). A computer-readable medium may also be a data communication network, for example the Internet, which allows downloading a program code.

The methods, systems and devices described herein may be implemented as software in a Digital Signal Processor, DSP, in a micro-controller or in any other side- processor or as hardware circuit within an application specific integrated circuit, ASIC, CPLD or FPGA.

The present invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof, e.g. in available hardware of conventional mobile devices or in new hardware dedicated for processing the methods described herein. A more complete appreciation of the invention and the attendant advantages thereof will be more clearly understood by reference to the following schematic drawings, which are not to scale, wherein:

Figure 1 shows a schematic diagram of a circuit of an LC resonant converter for explaining the invention;

Figure 2 shows a schematic diagram of a simplified circuit of an LC resonant converter for explaining the invention;

Figure 3 shows a schematic diagram of a control circuit for explaining the invention;

Figure 4 shows a schematic diagram of a circuit of an LCC resonant converter for explaining the invention;

Figure 5 shows a schematic diagram of frequency vs. rectifier current for an LC converter and a schematic diagram of frequency vs. rectifier current for an LCC converter for explaining the invention;

Figure 6 shows schematic diagrams of circuits of CLC and CLCC resonant converters according to an exemplary embodiment of the invention;

Figure 7 shows a schematic diagram of a simplified circuit of a CLCC resonant converter according to an exemplary embodiment of the invention;

Figure 8 shows a schematic diagram of a circuit of a resonant converter according to an exemplary embodiment of the invention;

Figure 9 shows a state plane plot and a signal versus time diagram for explaining the invention;

Figure 10 shows a schematic diagram of impressed load voltage, a set point for the peak capacitor voltage and the actual capacitor voltage and the capacitor current for explaining the invention;

Figure 11 shows a schematic flowchart diagram of a method for a resonant converter according to an exemplary embodiment of the invention;

Figure 12 shows a schematic diagram of a resonant converter according to an exemplary embodiment of the invention; and

Figure 13 shows a schematic diagram of an X-ray generator according to an exemplary embodiment of the invention. DETAILED DESCRIPTION OF EMBODIMENTS

The illustration in the drawings is purely schematical and does not intend to provide scaling relations or size information. In different drawings, similar or identical elements are provided with the same reference numerals. Generally, identical parts, units, entities or steps are provided with the same reference symbols in the description.

Figure 1 shows a schematic diagram of a circuit of a resonant converter for explaining the invention.

Figure 1 shows a circuit of a resonant converter. Also other circuits for resonant converters may be used. In particular, other switching devices, such as MOSFETs, can be used instead of the IGBT devices in form of the switches 40 shown here, a half-bridge inverter circuit can be used, and other configurations of the voltage multiplier are possible.

Instead of addressing the Cockro ft- Walton voltage multiplier as depicted on the right of Figure 1, in the sequel a simplified version of the circuit, later shown in Figure 2, will be used to explain the context of the invention. In particular, the step-up transformer is removed, and the voltage multiplier replaced by a full- wave diode rectifier.

Figure 2 shows a schematic diagram of a circuit of a resonant converter for explaining the invention.

As the dose and spectrum of the X-Ray radiation applied to a patient are determining for the quality of the image and the damage to the patient's tissues, accurate control of the high DC voltage applied to the tube is of prime importance. This high DC voltage is defined by the difference in charges delivered to, and taken out of, the output capacitance, i.e. Cload in the circuit shown in Figure 2, of the high voltage generating circuit. The current delivered to the load circuit, i.e. the rectifier current Irect as indicated in Figure 2, can be used to control this voltage to a desired value. Control of this current is therefore a prerequisite to control of the high DC voltage at the output.

Figure 3 shows a schematic diagram of a control circuit for explaining the invention.

If "Irect", the rectifier current, is well-defined, control of the load voltage can be established in a relatively simple way by means of a standard feedback control loop. An example of such a control loop is shown in Figure 3. In the example of Figure 3, the actual load voltage is measured by an instrument denoted as "Vload", and compared to the desired value of this voltage (i.e. the set point) "s Vload" by means of a subtracter "Sub".

The resulting control error is further processed by a controller to generate a set point value for the rectifier current "Irect". This current serves to charge the load circuit consisting of "Cload" and "Rload" to the desired load voltage. This control loop will, where necessary, be denoted as the outer or voltage control loop. Note that the controlled current source "Irect" here represents the averaged operation of the resonant converter, including the output rectifier, as depicted in Figure 2.

In the control setup as depicted in Figure 3, it is of key importance that the controlled source "Irect" shows quick and deterministic response to its input signal. To obtain such behavior from a resonant converter, a special control method for the inner loop, i.e. the mechanism which determines and commands the actual value of Irect, is necessary.

When using Optimal Trajectory Control (OTC), the swing of the voltage across the capacitor in the resonant tank is precisely controlled for every individual half-cycle of the resonant current. Thereby, also the charge which is displaced in the resonant tank is precisely defined for such a half cycle. Due to the series connection of resonant tank and rectifier, the charge per (half) cycle which the rectifier delivers to the load is also defined. In fact, assuming a linear capacitance Cres, the relation between the voltage swing across this capacitor and the charge delivered to the load is linear.

Even though the charge per (half) cycle is properly defined and has a linear relation to the swing of the voltage across the capacitor in the resonant tank, this is not the case for the average current Irect. The reason for this difference is that the time which is needed for a (half) cycle of current varies depending on operating conditions (such as supply voltage, current level and output voltage).

As a result, the relation between the swing in voltage across the resonant capacitor and the average rectifier current shows a varying gain. This can be catered to by appropriate design of the outer control loop; due to the closed loop set-up as shown in Figure 3 the desired voltage can eventually be reached.

Figure 4 shows a schematic diagram of a circuit of a resonant converter for explaining the invention. Typically, X-Ray tube loads are driven under a wide variety of conditions. Limiting cases are restricted time spans (in the order of tens of milliseconds) at maximum current and high voltage (power pulse mode), and extended time spans (many seconds) over a range of output voltages and at very small current (less than 1% of the maximum).

This latter requirement poses a problem for a "classic" LC series resonant power converter because, as discussed above, it suffers from the fact that the rectifier current in continuous mode cannot be reduced to zero for a finite range of operating frequencies. This problem can be circumvented by using a so-called LCC converter, which is shown in Figure 4.

As shown in Figure 4, in the circuit of the LCC converter an extra capacitance Cmain is connected across the AC terminals of the output rectifier. This capacitor allows some of the current in the resonant tank to be shunted away from the output. Note that for a given load voltage Vload, in every halfcycle of operation a fixed amount of charge

(2*Cmain*Vload) is consumed by the shunt capacitor, and the remaining charge is delivered to the load. This implies that the linear relation between the swing of Vc and the charge which is delivered to the load is maintained.

Figure 5 shows a schematic diagram of frequency vs. rectifier current for an

LC converter on the left panel and a schematic diagram of frequency vs. rectifier current for an LCC converter on the right panel for explaining the invention.

In Figure 5, on the left panel, a stylized version of the shape of the control characteristic (i.e. the relation between operating frequency and rectifier current) of the LC converter is shown. Note that this curve is not the actual characteristic of any practical LC converter, it is only used to illustrate the difference between the LC and the LCC converter.

As has already been explained above, the current in the resonant circuit and the rectifier current of the LC converter decrease with increasing frequency, but do not reach zero for finite frequencies. If now a part (shown schematically with the dotted line in Figure 5, upper panel, of the current in the resonant circuit is shunted away through capacitor Cmain, the rectifier current is reduced with respect to the current in the resonant circuit and the control characteristic of the LCC converter is obtained as sketched in Figure 5 on the lower panel.

Note that a constant current has been drawn here to explain the operation, but in fact the part of the current which is shunted away does not need to be constant over frequency, as long as a well-defined crossing between the two curves as shown in the upper panel of Figure 5 is obtained.

As is shown in this example, the rectifier current in the LCC now indeed reaches zero for a finite value of the operating frequency.

Therefore, in the LCC converter, the output current can be zero while the resonant operation is sustained, i.e. while a nonzero current is still flowing in the resonant tank. The frequency span needed to cover the range of necessary output currents (from close to zero to ca. 10 A in the example given here) can be greatly reduced. Figure 6 shows a schematic diagram of a circuit of a resonant converter 200 according to an exemplary embodiment of the invention. The circuit as shown in the left panel of Figure 6 will in the following be referred to as CLC converter, and for its counterpart in Figure 6 in the right panel, the label CLCC will be used.

The extra capacitances across the switching devices have been denoted as

CrAl, CrA2, CrBl and CrB2. For ease of explanation, in the following, they will be assumed to be equal in value, but this is not a necessity. Their purpose is to limit the slopes of the voltages on the switching nodes, which are known to be a main cause for EMI. Due to the presence of these capacitances, the voltage commutation takes significant time, and as a result the accuracy of the control is hampered. In particular, when using "standard" optimal trajectory control as developed for the LC converter, controlling the output current down to zero becomes near impossible.

Until now, optimal trajectory control has not been applied to the so-called LCC, CLCC, and CLC variants of resonant power converters. (C)LCC converters are especially interesting in the context of generation of high DC voltages, such as used in X-Ray equipment.

Due to the high voltage, the transformer used in such apparatus typically has a very large winding ratio, and thereby unavoidably features a relatively large parasitic input capacitance. In the (C)LCC converter, this capacitance can be incorporated as a functional element of the power converter.

The invention allows controlling such an (C)LCC converter with a similar level of accuracy as in the already established case of the LC converter.

Figure 7 shows a schematic diagram of a circuit of a resonant converter 200 according to an exemplary embodiment of the invention. Figure 7 shows a full bridge circuit with resonant tank and load rectifier. The circuit as shown in Figure 7 represents a resonant converter 200 for high voltage generation, the resonant converter 200 comprising: at least one switch 40, a measuring unit 10, a processing unit 20, and a switching unit 30.

Note that the load circuit has been redrawn here as a voltage source, as it is assumed that the change in output voltage in one half cycle of resonant current is small enough to be neglected. If this would not be the case, the circuit would feature relatively high ripple at the output, which is in general not desired.

When neglecting the influence of the node capacitances (CrAl, CrA2, CrBl, CrB2), in case of bipolar switching, switches QAl and QB2 are opened and closed synchronously, as are switches QA2 and QBl . Furthermore, the top switches (QAl and QBl) are opened and closed in perfect counter phase to their bottom companions (QA2 and QB2 respectively). As a result, either Vdc or -Vdc is applied to the left-side terminals of the resonant tank consisting of Lres and Cres. In other words, only two different voltages are produced by the full bridge.

In another method called unipolar switching, a third voltage which can be generated by the full bridge is also used. This voltage, ideally equal to zero (hence called a zero vector), can be produced by enabling either the top switches (QAl, QBl) or the bottom switches (QA2, QB2) at the same time. Using unipolar switching has slight advantages with respect to the current stress applied to the power semiconductors, but shows distinct disadvantages in view of the EMI behavior of the circuit. Using unipolar switching introduces a common-mode voltage across the load circuit, leading to significant currents flowing through various parasitic capacitances.

The only variable which can be directly influenced by the controller for the inner (current) loop is the instant when the voltage commutation is initiated, i.e. when the power semiconductors in the full bridge as shown in Figure 7 are turned off.

The switching unit 30 is adapted to control the at least one switch 40 based on the determined instant and on the comparison of the evaluated value with the second variable. In other words, the switching unit 30, due to the input received from the measuring unit 10 and from the processing unit 20, provides optimum switching control for operating the resonant converter at the resonant frequency. Advantageously, the switching unit 30 can control power delivered to a load by varying its switching frequency to an optimum resonant frequency of the resonant converter, providing the optimum control of at least one switch 40 switch transitions will be more efficient. This fact allows operation at very high frequency without an appreciable loss of converter efficiency, and, consequently, yields a converter with very high power density.

The task of the switching unit 30 is to attain a desired value for the voltage swing across the resonant capacitor (i.e. the net charge displaced during a half cycle of the operation). In the following, the voltage across the resonant capacitor (Cres) will be denoted as Vc.

The control law can be defined as a mathematical algorithm using the initial value of the resonant capacitor voltage (Vcinit), its desired final value (Vcend), and various circuit variables and parameters to define this very instant. One method comprises calculating Vccomm, i.e. the value of the voltage across the resonant capacitor at the desired start of voltage commutation. The parameters used may include the extra shunt and device capacitances. A summation of Vcend, doubled VDC, and doubled Vload is multiplied with Vcend, a summation of negative Vcinit, doubled VDC, and doubled negative Vload is multiplied with Vcinit, both sums are added together and then divided by the fourfold of VDC, subtracted from this value is Cr multiplied with VDC and divided by doubled Cres, further subtracted from this value is Cmain multiplied with the square of Vload and divided by Cres multiplied with VDC:

V _Cend (V _Cend + 2V _DC + 2V _load ) + V _cinit {— V init + 2VD 2V _IOAD ) C _r CmaivYloa _d

Vccomm = — —— V _dc —

dc ^res ^res * dc

This value can be calculated either at the beginning of the resonant half cycle only, or continuously during the current flow. By comparing the actual voltage across the resonant capacitor, which is by definition a continuous and monotonously rising function of time, to this value the commutation instant can be found in real time.

Figure 8 shows a schematic diagram of a circuit of a resonant converter according to an exemplary embodiment of the invention. On the left panel, Figure 8 shows, an active part of circuit during voltage commutation. On the right panel, Figure 8 shows also once again, the same active part of circuit during voltage commutation, however, with node capacitances combined.

For the case of bipolar switching, the circuit during voltage commutation where none of the power switches or their antiparallel diodes conduct current can be redrawn as shown in Figure 8 on the left panel. As shown there, the node capacitances for nodes A and B (CrAl, CrA2 and CrBl, CrB2 respectively) end up in a parallel configuration, be replaced with advantage by single capacitors CrA and CrB, respectively. This situation is illustrated in Figure 8 on the right panel

Figure 9 shows a schematic diagram of a state plane plot and a signal versus time diagram for explaining the invention. An example of the operation of the control law is shown in Figure 9. This example has been produced by simulation.

In Figure 9, instants where a new circuit configuration starts are marked with a small circle. The big panel on the top of Figure 9 shows a state plane plot, on the two smaller lower panels, diagrams depicting signals versus time are shown.

Here, Vcinit equals -100 V. The target for Vcend is set to 100 V. In this example, a short time after the current flow is initiated, the output diodes start conducting. When Vc reaches Vccomm, all power semiconductors are turned off, and the voltage commutation starts. After the voltage commutation, the current decreases, and the capacitor voltage exactly reaches its intended value at the instant where Ic equals zero.

Unipolar switching implies that the voltage commutations of both phase legs do not coincide in time. An extra degree of freedom exists in this the duration of the interval where a zero vector is produced can be chosen freely, bounded to the extreme cases where the first voltage commutation starts immediately at the beginning of the positive half cycle, or where the second voltage commutation finishes at the end of the half cycle.

The result is a summation of VccommA and VccommB divided by 2 resulting in Vccomm. VccommA and VccommB indicate the voltages across Cres at the start of commutation of phase legs A and B, respectively.

Application of the control law defined above can be performed in various ways. The entries of the control model partly consist of circuit variables which need to be measured (the various voltages), and partly on circuit parameters (i.e. the capacitor values).

In principle, the control model can be evaluated in real time using an analogue circuit consisting of multipliers and operational amplifiers. Another method could be to sample the necessary signals at a high rate and convert them to the digital domain, and subsequently evaluate the control model digitally by means of a Digital Signal Processor (DSP), Field Programmable Gate Array (FPGA), or similar device.

Yet another method would be to calculate the control model at the beginning of the current flow only, and store the thus calculated value for Vccomm for continuous comparison to the actual measured capacitor voltage. An interesting variation on this method would be to convert the calculated value for Vccomm back to the analogue domain by means of a D/A converter, and perform the comparison needed to find the commutation instant in the analogue domain. Such a setup would avoid the need for very fast sampling and converting of analogue signals, and could be used at relatively low cost up to high frequencies.

In addition to the control law as defined above, the usual measures as known in the state of the art to operate a power converter are needed. In actual implementations, often a state machine architecture is used to govern the switching of the power

semiconductors.

Note that states 1 up to 3 correspond to positive values of Ic, and states 4 up to 6 to negative values. Only the conditions which are valid in normal operation are listed in the following. In a first state, QAl and QB2 are on, the condition for changing to a second state then is Vc >= Vccomm. In a second state, all switches are off, the condition for changing to a third state then is that the voltage commutation is finished. In a third state, DA2 and are DB1 on, the condition for changing to a fourth state then is that lc<0. In a fourth state, QA2 and QB1 are on, the condition for changing to a fifth state then is that Vc <= -Vccomm. In a fifth state, all switches are off, the condition for changing to a sixth state then is that the voltage commutation is finished. In a sixth state, DAI and DB2 are on, the condition for changing to a first state then is that lc>0.

Some additional conditions, which are not mentioned here, can apply at circuit startup.

Figure 10 shows a schematic diagram of impressed load voltages, a set point for the peak capacitor voltage and actual capacitor voltage and the capacitor current for explaining the invention.

In the simulation, the set point value for the peak capacitor voltage and the output voltage can be changed step-wise in order to illustrate the operation of the control algorithm. Note that changing the output voltage step-wise is not possible in most practical circuits, this particular feature is only used here to show the robustness of the control law to such harsh environments. The results are shown in Figure 10.

Figure 10 shows in the top trace: impressed load voltage, in the middle traces: set point for the peak capacitor voltage (both positive and negative) and actual capacitor voltage, in the lower trace: capacitor current. As depicted in Figure 10, the peak capacitor voltage indeed closely follows its set point. Exceptions are visible in the cases where either the impressed load voltage or the set point changes in a time interval where corrective action is not immediately possible, i.e. shortly after a voltage commutation.

In the cases observed here, the deviations in the exception cases are rather small, in the order of 10% of the maximum peak capacitor voltage, and last only for a single half cycle of the resonant current. The operation under more realistic conditions, where the output voltage by the nature of for example an R/C load as depicted in Figure 2 will have a smoother appearance, shows even better behavior.

Figure 11 shows a schematic flowchart diagram of a method for a resonant converter according to an exemplary embodiment of the invention.

The method for controlling a resonant converter may comprise the following steps of: As a first step of the method, measuring SI at least two variables, a first variable and a second variable, of the resonant converter 200 on at least one state transition per cycle of the resonant converter 200 is conducted.

As a second step of the method, evaluating S2 a control model of a circuit operation of the resonant converter 200 using the measured first variable and at least one circuit parameter of the resonant converter generating an evaluated value and comparing the evaluated value to the second variable, determining an instant at which the evaluated value and the measured second variable cross and is performed.

As the at least one circuit parameter of the resonant converter, a parameter of an extra shunt or any kind of device capacitances, for instance, may be used.

As a third step of the method, controlling S3 the at least one switch 40 based on the determined instant and the comparison of the evaluated value with the second variable is conducted.

According to an exemplary embodiment of the invention, these steps may be carried out simultaneously, divided into multiple operations or tasks or iteratively repeated. The iteration of the steps may be implemented recursively, by count-controlled loops or by condition-controlled loops.

The control model of the circuit operation of the resonant converter may be defined for every other sub-interval of the circuit operation, by using the following connecting equations:

a) Continuity of the state variables Vc and Ic at the transitions from one sub circuit to the other

b) The initial value of Vcmain is equal to -Vload, and the final value to Vload c) The initial value of V(CrA2) and V(CrBl) is equal to Vdc, and the final value to zero

d) The initial value of V(CrAl) and V(CrB2) is equal to zero, and the final value to Vdc.

e) Capacitors when connected in series process the same charge and the change in their voltage is therefore inversely proportional to their capacitance value.

Figure 12 shows a schematic diagram of a resonant converter 200 according to an exemplary embodiment of the invention.

The resonant converter 200 may comprise: at least one switch 40, a measuring unit 10, a processing unit 20, and a switching unit 30. In another exemplary embodiment of the present invention, a computer program or a computer program element is provided that is characterized by being adapted to execute the method steps of the method according to one of the preceding embodiments, on an appropriate system.

Figure 13 shows a schematic diagram of an X-ray generator according to an exemplary embodiment of the invention.

A high voltage generator 300 for X-ray generation may comprise at least one resonant converter 200. An X-ray generator 400 may comprise a high voltage generator 300.

According to a further exemplary embodiment of the present invention, the computer program element might therefore be stored on a computer unit, which might also be part of an embodiment of the present invention. This computing unit may be adapted to perform or induce a performing of the steps of the method described above.

Moreover, it may be adapted to operate the components of the above described apparatus. The computing unit can be adapted to operate automatically and/or to execute the orders of a user. A computer program may be loaded into a working memory of a data processor. The data processor may thus be equipped to carry out the method of the invention.

This exemplary embodiment of the invention covers both, a computer program that right from the beginning uses the invention and a computer program that by means of an up-date turns an existing program into a program that uses the invention.

Further on, the computer program element might be able to provide all necessary steps to fulfill the procedure of an exemplary embodiment of the method as described above.

According to a further exemplary embodiment of the present invention, a computer readable medium, such as a CD-ROM, is presented wherein the computer readable medium has a computer program element stored on it, which computer program element is described by the preceding section.

A computer program may be stored and/or distributed on a suitable medium, such as an optical storage medium or a solid state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the internet or other wired or wireless telecommunication systems.

However, the computer program may also be presented over a network like the World Wide Web and can be downloaded into the working memory of a data processor from such a network.

According to a further exemplary embodiment of the present invention, a medium for making a computer program element available for downloading is provided, which computer program element is arranged to perform a method according to one of the previously described embodiments of the invention.

It has to be noted that embodiments of the invention are described with reference to different subject matters. In particular, some embodiments are described with reference to method type claims whereas other embodiments are described with reference to the device type claims.

However, a person skilled in the art will gather from the above and the following description that, unless otherwise notified, in addition to any combination of features belonging to one type of subject matter also any combination between features relating to different subject matters is considered to be disclosed with this application.

However, all features can be combined providing synergetic effects that are more than the simple summation of the features.

While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or controller or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.