阅读说明：本技术 变压器谐振转换器 (Transformer resonance converter ) 是由 肯尼斯·E·米勒 詹姆斯·R·普拉格 迪麦西·M·津巴 约翰·G·卡斯凯德 艾丽亚·斯劳伯道 于 2018-02-06 设计创作，主要内容包括：一些实施例可包括纳秒脉冲器,该纳秒脉冲器包括：多个固态开关；变压器,具有杂散电感L<Sub>s</Sub>、杂散电容C<Sub>s</Sub>和匝数比n；以及具有电阻R的电阻器,所述电阻器串联设置在所述变压器和所述开关之间。在一些实施例中,谐振电路根据以下公式产生Q因子：<Image he="116" wi="209" file="DDA0002225575130000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>以及纳秒脉冲器根据以下公式、从输入电压V<Sub>in</Sub>产生输出电压V<Sub>out</Sub>：V<Sub>out</Sub>＝QnV<Sub>in</Sub>。(Some embodiments may include a nanosecond pulser, comprising: a plurality of solid state switches; transformer with stray inductance L s And a stray capacitor C s And a turns ratio n; and a resistor having a resistance R, the resistor being arranged in series between the transformer and the switch. In some embodiments, the resonant circuit generates the Q factor according to the following equation： And a nanosecond pulser from the input voltage V according to the following formula in Generating an output voltage V out ：V out ＝QnV in 。)

1. A resonant converter, comprising:

providing an input voltage V_inA DC input of (1);

a plurality of solid state switches electrically coupled to the DC input;

transformer with stray inductance L_sAnd a stray capacitor C_sAnd a turns ratio n, the transformer electrically coupled with the plurality of solid state switches;

a resistor having a resistance R, the resistor being arranged in series between the transformer and the switch; and

a plurality of rectifier diodes;

wherein the resonant circuit produces a Q factor according to the following equation:

wherein the resonant converter is based on the following formula according to an input voltage V_inGenerating a voltage having an output voltage V_outOutput pulse of (2):

V_out＝QnV_in。

2. the resonant converter circuit of claim 1, wherein the output pulse has a voltage greater than about 10 kV.

3. The resonant converter circuit of claim 1, wherein the output pulses have a frequency greater than 25 kHz.

4. The resonant converter circuit of claim 1, wherein the resonant frequency is greater than 100 kHz.

5. The resonant converter circuit of claim 1, wherein the output pulse has an output power greater than 5 kW.

6. The resonant converter circuit of claim 1, wherein the output pulse has an output power greater than 50 kW.

7. The resonant converter circuit of claim 1, wherein the resonant converter has a switching transition time of less than 40 ns.

8. The resonant converter circuit of claim 1, wherein the resonant converter circuit has a total circuit inductance measured on the primary side of the transformer of less than about 300 nH.

9. The resonant converter circuit of claim 1, wherein the resonant converter circuit operates with a total circuit capacitance of less than about 100pF, the total circuit capacitance measured on the secondary side of the transformer.

10. The resonant converter circuit of claim 1, wherein the output pulse has a rise time and a voltage slew rate greater than 10⁹V/s。

11. The resonant converter circuit of claim 1, wherein the resonant converter has a capacitance greater than 1W/cm³Of (2) isDensity.

12. The resonant converter circuit of claim 1, wherein the stray capacitance C_sIncluding over 50% of the total circuit resonant capacitance C.

13. A resonant converter circuit, comprising:

with stray inductance L_sThe transformer of (1), wherein the stray inductance L_sNot from the inductor;

stray capacitance C_sWherein the stray capacitance C_sNot from the capacitor; and

a resistor having a resistance R, the resistor being in series with the transformer;

wherein the resonant circuit produces a Q factor according to the formula:

14. the resonant converter circuit of claim 13, wherein the transformer has a turns ratio n, and the resonant converter is based on an input voltage V, according to the following equation_inGenerating a voltage having an output voltage V_outOutput pulse of (2):

V_out＝QnV_in.。

15. the resonant converter circuit of claim 13, wherein the resonant converter circuit generates pulses having a voltage greater than about 10 kV.

16. The resonant converter circuit of claim 13, wherein the resonant converter operates at a resonant frequency greater than 0.1 MHz.

17. The resonant converter circuit of claim 13, wherein the resonant converter circuit generates a pulse with a switching transition time of less than 40 ns.

18. The resonant converter circuit of claim 13, wherein the resonant converter circuit has a total circuit inductance measured on the primary side of the transformer of less than about 300 nH.

19. The resonant converter circuit of claim 13, wherein the resonant converter circuit operates with a total circuit capacitance of less than about 100pF, the total circuit capacitance measured on the secondary side of the transformer.

20. The resonant converter circuit of claim 13, wherein the output pulse has a rise time and a voltage slew rate greater than 10⁹V/s。

21. The resonant converter circuit of claim 13, wherein the resonant converter circuit generates a power density greater than 1W/cm³The output pulse of (1).

22. The resonant converter circuit of claim 13, wherein the resonant converter does not include an inductor.

23. The resonant converter circuit of claim 13, wherein the resonant converter does not include a capacitor.

24. The resonant converter circuit of claim 13, wherein a ratio between peak output power and average output power is greater than a factor of 10.

25. The resonant converter circuit of claim 13, wherein the stray inductance L_sIncluding over 50% of the total circuit resonant inductance.

26. The resonant converter circuit of claim 13, wherein the output pulse has a rise time and a voltage slew rate greater than10⁹V/s。

Background

Generating high voltage pulses with fast rise times is challenging. For example, to achieve a fast rise time (e.g., less than about 50ns) for a high voltage pulse (e.g., greater than about 10kV), the slope of the pulse rise must be very steep. Such steep rise times are difficult to produce. This is particularly difficult for using standard electrical components in a compact manner. It is also difficult to generate such high voltage pulses with variable pulse width and/or variable high pulse repetition rate and with fast rise time.

Disclosure of Invention

A system and method for generating high voltage, high frequency pulses using a switched voltage source and a transformer including a resonant converter, such as a series resonant converter, is disclosed.

Some embodiments may include a resonant converter including a DC input; a plurality of solid state switches (which for us may comprise SPA, switching power amplifiers based on full bridge topology); transformer with stray inductance L_sAnd a stray capacitor C_sAnd a primary to secondary turns ratio n; total series resistance R, from stray series circuit resistance R_sAnd any additional series resistance R_aComposition of the additional series resistance R_aIntentionally added to control Q; a diode rectifier located on the secondary side of the transformer; and an output waveform filter. In some embodiments, the resonant circuit has a Q factor in accordance with

Obtaining; and the resonant converter is based on the following formula, according to the input voltage V_inGenerating an output voltage V_out：V_out＝QnV_in.. In some embodiments, the stray inductance is measured from the primary side of the transformer, and the stray capacitance is measured from the secondary side. In some embodiments, an additional capacitor C may be included_aAnd/or inductance L_aTo produce a desired resonant frequency and/or to change the circuit Q.

Some embodiments may include a resonant converter circuit having: a transformer having a stray inductance L_sAnd a stray capacitance C_s(ii) a And a stray resistor connected in series with the transformer and having a resistance R_s. In some embodiments, the resonant circuit is produced according to the following equationQ factor, where R is the series stray resistance R_sAnd any additional added resistance R_aAnd an equivalent series load resistance R_LSum, C is stray capacitance C_sAnd any added capacitance C_aAnd any other stray capacitance C_soSum, L is stray series inductance L_sAnd any additional added inductance L_aAnd any other stray series inductance L_soAnd (4) summing.

In some embodiments, the output may have a voltage greater than 5kV, 15kV, and/or 50 kV.

In some embodiments, the resonant converter may operate at a frequency greater than about 25kHz or 100 kHz.

In some embodiments, the ratio between the peak output power and the average output power is greater than a factor of 10.

In some embodiments, stray inductance L_sIncluding over 50% of the total circuit inductance.

In some embodiments, the output pulse has a rise time and the voltage slew rate is greater than 10⁹V/s。

In some embodiments, the resonant converter includes an output galvanically isolated from its input (e.g., a floating output).

In some embodiments, the pulse output voltage may be adjusted to a new voltage output level on a time scale of less than 10 μ s for the duration of the pulse.

In some embodiments, stray capacitance C_sIncluding over 50% of the total circuit resonant capacitance.

In some embodiments, the peak output power is greater than 5kW or greater than 50 kW.

References to embodiments described in this document (whether in this section or elsewhere) are not intended to limit or define the disclosure, but rather examples are provided to assist in understanding the disclosure. Additional embodiments are discussed in the detailed description section and further description is provided. Advantages provided by one or more of the various embodiments may be further understood by examining this specification or by practicing one or more embodiments presented.

Drawings

Fig. 1 is an example transformer resonant converter according to some embodiments.

Fig. 2 is a circuit diagram of an example transformer resonant converter coupled with a switching circuit and a load, in accordance with some embodiments.

Fig. 3 is a photograph of an example resonant converter.

Fig. 4 is an example waveform created from a transformer resonant converter according to some embodiments.

Fig. 5 is an example waveform created from a transformer resonant converter according to some embodiments.

Fig. 6 is an idealized example of a series resonant circuit according to some embodiments.

Fig. 7 is a circuit diagram of an example transformer resonant converter, in accordance with some embodiments.

Detailed Description

A system and method for generating high voltage, high frequency pulses using a switched voltage source and transformer arranged, among other components, as a series resonant converter or a transformer resonant converter is disclosed. For example, the switched voltage source may comprise a full-bridge or half-bridge topology. For example, the switched voltage source may comprise a full-bridge or half-bridge switching topology. As another example, the switched voltage source may have an additional output filter element. For example, the switched voltage source may comprise a full-bridge topology or a half-bridge topology. In some embodiments, the switching voltage source may include a switching power amplifier.

For example, the transformer resonant converter may not include any physical capacitors and/or inductors. In contrast, in some embodiments, the transformer resonant converter may include a resistor in series with at least a stray capacitance and/or a stray inductance of the transformer. Stray inductances L of other circuit elements_soAnd/or stray capacitance C_soMay also be used as part of a resonant converter. In some embodiments, the total stray inductance and/or stray capacitance may be small. For example, the stray inductance measured at the primary side of the transformer may be less than about 3000nH, 300nH, 30nH, 3nH, etc. As anotherAs an example, the stray capacitance measured on the secondary side of the transformer may be less than about 300pF or less than about 30 pF. Additional capacitance C may be added in combination with (e.g., in parallel and/or series with) stray capacitance and stray inductance_aAnd an inductance L_a。

Resonant converters typically utilize the resonance of a circuit when the circuit is driven at a resonant frequency (an exemplary series resonant circuit is shown in fig. 6). The resonant frequency may be determined from the total inductance and capacitance of the circuit elements, for example, according to the following equation:

in this example, L and C represent the total effective and/or equivalent series circuit inductance and capacitance, respectively, and as defined above, L ═ L_s+L_so+L_aAnd C ═ Cs + C_so+C_a. Fig. 6 shows an idealized series resonant circuit 600 with an inductor 620, a capacitor 610 and a power supply 605 without any resistance. The resistance may be present in various forms throughout the circuit.

When the resonant circuit is driven at its resonant frequency, the effective reactance of each circuit element is equal in magnitude but opposite in sign. They therefore cancel each other out, leaving behind the actual resistance of the circuit, whether it consists of stray resistances and/or resistive elements (including the load). In some cases, the actual resistance may be the resistance of the copper trace and/or the resistance of any other circuit component in series with the resonant LC component. The ratio of the reactive component to the actual resistance is defined as the Q factor, which is a dimensionless parameter that is a good estimate of the multiplier that the drive voltage will reach when measured across L or C. The resonant frequency and the Q factor may be calculated according to the following equations:

r is the total equivalent series/dissipation resistance and may include any series stray resistance R_sAnd any additionalAdded resistance R_aAnd an additional equivalent series load resistance R_LAnd any other dielectric or other dissipative losses from switches or other components. Typical resonant converters use discrete physical circuit components as inductors, capacitors, and/or resistors to produce the desired Q factor and resonant frequency f. In some embodiments, additional resistors may be omitted to improve circuit efficiency. In some embodiments, some form of feedback and control may be used to regulate the output voltage to a value lower than the value that circuit Q naturally sets. For example, one such form of feedback and control may rely on pulse width modulation of the switching voltage source.

Fig. 1 is a circuit diagram of an example transformer resonant converter 100, in accordance with some embodiments. On the primary side 160 of the transformer, the resonant converter 100 may comprise a DC input 105 coupled to a switch 110, for example. In some embodiments, the switch may comprise a freewheeling diode or a body diode. The switch 110 may be opened and closed at a high frequency, for example at the resonant frequency of the transformer resonant converter 100.

For example, the switch 110 may be any type of solid state switch. The primary side 160 of the resonant converter may also include a resonant series inductance 115 and a resonant series resistance 120. For example, the switch 110 may generate high frequency pulses at frequencies greater than 50KHz, 500kHz, 5000KHz, for example.

In some embodiments, the switch 110 may operate with a switching time of less than, for example, about 40ns, 10ns, or 1 ns.

In some embodiments, the switch 110 may comprise a solid state switch. The switch 100 may comprise, for example, an IGBT switch, a MOSFET switch, a FET switch, a GaN switch, or the like. In some embodiments, the switch 110 may be a high efficiency switch. In some embodiments, the switch 110 may be a fast switch (e.g., switching at a frequency greater than 100 kHz), which may allow an output with low ripple. In some embodiments, Pulse Width Modulation (PWM) techniques may be used to rapidly control the output voltage to allow control of beam characteristics, for example, with a resolution of tens of μ s, for example, when driving a neutral beam.

The resonant series inductance 115 may include, for example, stray inductance of the transformer, stray inductance of the primary side 160 circuitry, and/or physical inductors. The resonant series inductance 115 may be small, for example, less than about 3000nH, 300nH, 30nH, 3nH, etc.

The resonant series resistance 120 may include a stray resistance and/or a physical resistor. In some embodiments, the physical resistor may reduce circuit efficiency, however, the physical resistor may allow for faster circuit response times and/or may reduce the need for feedback and control loops for controlling/regulating the output voltage.

The transformer 125 may comprise any type of transformer, such as a toroidal transformer having one or more primary side windings and a plurality of secondary side windings. As another example, the transformer 125 may be a coaxial transformer having one or more primary side windings and a plurality of secondary side windings. In some embodiments, one or more primary side windings may comprise a conductive sheet. In some embodiments, the one or more secondary windings may comprise conductive strips.

The circuit on the secondary side of the transformer 125 may include a resonant series capacitance 130. The resonant series capacitance 125 may comprise, for example, a stray capacitance of a transformer, and/or a stray capacitance of a secondary side circuit and/or a capacitor. The resonant series capacitance 125 may be small, for example, less than about 1000pF, 100pF, 10pF, and so on. A resonant series capacitance 125 may be connected in parallel with the transformer output. The secondary side 165 of the circuit may include a rectifier 135 and/or an output filter 140.

In some embodiments, the primary winding and/or the secondary winding may comprise a single conductive sheet wound around at least a portion of the transformer core. The conductive sheets may be wound around the outer, top and inner surfaces of the transformer core. Conductive traces and/or planes on and/or within the circuit board may complete the primary turns and/or connect the primary turns to other circuit elements. In some embodiments, the conductive sheet may comprise a metal sheet. In some embodiments, the conductive sheet may comprise portions of tubes, pipes, and/or other thin-walled metal objects having a particular geometry.

In some embodiments, the conductive strips may terminate on one or more pads on the circuit board. In some embodiments, the conductive strips may be terminated with two or more wires.

In some embodiments, the primary winding may include a conductive paint that has been coated on one or more outer surfaces of the transformer core. In some embodiments, the conductive sheet may comprise a metal layer that has been deposited on the transformer core using deposition techniques such as thermal spray, vapor deposition, chemical vapor deposition, ion beam deposition, plasma, and thermal spray deposition. In some embodiments, the conductive sheet may comprise a conductive tape material wound around the core of the transformer. In some embodiments, the conductive sheets may include conductors that have been plated onto the transformer core. In some embodiments, multiple parallel wires may be used instead of conductive strips.

In some embodiments, an insulator may be disposed or deposited between the transformer core and the conductive sheet. For example, the insulator may comprise a polymer, polyimide, epoxy, or the like.

The rectifier 135 may include any type of rectifier, such as a diode-based rectifier, a full-bridge rectifier (e.g., as shown in fig. 7), a half-bridge rectifier, a three-phase rectifier, a voltage-doubler rectifier, and so forth. Any other type of rectifier may be used.

The output filter 140 may include any type of filter. For example, the output filter 140 may include a high pass filter, a low pass filter, a band pass filter, and the like.

Some embodiments may include a transformer resonant converter 100 with low stray inductance measured from the primary side 160. The low stray inductance may include an inductance of less than, for example, about 3000nH, 300nH, 30nH, 3nH, etc.

Some embodiments may include a transformer resonant converter 100 with low stray capacitance measured from the primary side 160. The low stray capacitance may include a capacitance of less than, for example, about 1000pF, 100pF, 10pF, etc.

Some embodiments may include a transformer resonant converter 100 that may produce a high average output power, e.g., greater than about 3kW, 100kW, 3 MW. For short bursts, the peak power output may exceed 30kW, 300kW, 3MW, for example. Some embodiments may comprise a transformer resonant converter 100 generating pulses with a high voltage, e.g. greater than e.g. 5kV, 25kV, 250kV, 2500 kV. Some embodiments may include a transformer resonant converter 100 that produces high power burst operation (high power burst operation) with peak power greater than 5 times the average operating power of the converter. In some embodiments, the peak power output may exceed the average output power by, for example, a factor of 5, 50, 500.

In some embodiments, the transformer resonant converter 100 may generate high voltage pulses with fast rise times (e.g., less than about 10 μ s, 1 μ s, 100ns, 10ns, etc.) for voltages greater than, for example, 5kV, 30kV, 100kV, 500kV, etc.

In some embodiments, the transformer resonant converter 100 may produce output pulses with low voltage ripple (e.g., less than about 5%). Typical output voltage ripples may be less than, for example, 15% or 0.5%.

In some embodiments, the transformer resonant converter 100 may operate with pulse width modulation, which may allow for better control of the output waveform and/or allow for high efficiency power output. In some embodiments, the transformer resonant converter may include real-time feedback and control of high voltage and/or power output. In some embodiments, low stray inductance and/or low stray capacitance, and/or high frequency operation may allow the feedback loop to be fast.

In some embodiments, the transformer resonant converter 100 can significantly increase the overall power density of the system. For example, the transformer resonant converter 100 may be used with a tube driver for a high power radar system and/or an RF system. In some embodiments, the transformer resonant converter 100 may increase the overall power density of a high power radar system and/or RF system. The power density may exceed, for example, 0.5W/cm³、5W/cm³、50W/cm³Or 500W/cm³。

In some embodiments, the transformer resonant converter 100 may include switching components at low voltage in a standard H-bridge power supply configuration with a hard ground reference. This may eliminate the need to float each module to a high voltage, as seen in pulse step modulators, for example.

In some embodiments, the transformer resonant converter may include high voltage components including a high voltage transformer and rectifier diodes, among other high voltage components. For example, the components may be encapsulated using oil, potting, or other methods to achieve a safe high voltage. In some embodiments, some components may have appropriate spacing in air to eliminate corona generation, arcing, and/or tracking (tracking).

In some embodiments of the transformer resonant converter, the output is transformer isolated, so the same system may provide a floating or ground reference output and/or may be configured to provide a positive or negative polarity. This may, for example, allow the same design to be used for any of a variety of high voltage grids with specific neutral beam implantation designs, including, for example, positive or negative ion extraction and acceleration and ion and electron suppression grids.

In some embodiments, the resonant converter can produce the same power level while the overall system size and/or control complexity is significantly reduced compared to pulse step modulators currently used for smaller neutral beam injector systems.

In some embodiments, the resonant converter may be safe for arc faults due to the inherent series resonant behavior of the power supply. The series resonant behavior of the resonant converter may have a supply impedance (fundamental) matched to the load. For example, when an arc occurs, this mismatch can reduce the power flowing in the primary side 160 of the circuit, and the voltage on the secondary can drop, whereby the current in the arc cannot continue to increase to the point of damage to the grid.

In some embodiments, the transformer resonant converter may store very little energy in its output filter components. For example, the stored energy may be less than, for example, about 10J, 1.0J, or 0.1J. High frequency operation allows this stored energy to be minimized. In some embodiments, it may be important to minimize this stored energy. For example, such energy can damage load components in the event of an arc.

In some embodiments, the transformer resonant converter may be modular. In some embodiments, the transformer resonant converter can be easily scaled to higher output power levels, making it a possible choice for large neutral beam injector systems (e.g., such as those used in NSTX, DIII-D, or ITER). For example, a power supply with a transformer resonant converter may be added with the output arranged in series to easily increase the output voltage. Similarly, the output current can be increased by adding cells in parallel on the primary side, as long as the high side is scaled to account for the increased current level.

Fig. 2 is a circuit diagram of a transformer resonant converter 200 coupled to a load 250 according to some embodiments. For example, the transformer 225 may have any number of turns. For example, the transformer may have a turn ratio of n-1, n-30, n-50, n-100, or the like. The total series inductance is represented by the inductor circuit element 205 on the primary side 260 (e.g., having an inductance of less than about 3000nH, 300nH, 30nH, 3 nH), which may be primarily by the stray inductance L of the transformer_sAnd (4) forming. The total series capacitance is represented by capacitor circuit element 210 on secondary side 265 (e.g., having a capacitance of less than about 1000pF, 100pF, 10pF, etc.), which may be primarily by stray capacitance C of the transformer_sAnd (4) forming. Stray inductance 205 and/or stray capacitance 210 may be any value based on the size, type, material, etc. of the transformer and/or the number of turns of the transformer. In this circuit, a primary resistor 215 may be included in the circuit in series with the inductor 205 and/or the capacitor 210. In some embodiments, the main resistor 215 may have small values, e.g., less than 3000m Ω, 300m Ω, 30m Ω, 3m Ω.

In this example, the transformer resonant converter 200 includes a switching circuit having four switching circuits 230. However, any number of switching circuits may be used. Each switching circuit 230 may include a solid state switch 235 having any number of circuit elements. The solid state switches may include, for example, IGBT switches, MOSFET switches, FET switches, GaN switches, and the like. Each switching circuit 230 may also include a stray inductance represented by circuit element 240 and/or a stray resistance represented by circuit element 245. Each switching circuit 230 may also include a diode 255.

In this example, the secondary side of the transformer may also include a full bridge rectifier 260, an output filter 270, a load element 250 (e.g., including a 86k ohm resistor in the particular example), and/or a filter resistor 280 (e.g., including a 10k ohm resistor in the particular example) that acts in conjunction with an external user load capacitor 285 (e.g., including a 30pF capacitor in the particular example). For example, in the illustrated circuit, feedback and control adjustments may not be required.

Any number of circuit elements combined in any configuration may follow the rectifier. These other elements may include, for example, capacitive components, inductive components and/or resistive filter components, and/or external loads.

In some embodiments, a transformer resonant converter (e.g., transformer resonant converter 100, transformer resonant converter 200, transformer resonant converter 700, etc.) may generate pulses having various characteristics. For example, a transformer resonant converter may generate pulses with voltages greater than about 30 kV. For example, a transformer resonant converter may generate pulses with voltages greater than about 5kV, 25kV, 250kV, or 2500 kV. For example, a transformer resonant converter may generate pulses having rise or fall times starting at voltages greater than about 25kV and less than about 300, 30, 3 μ s. For example, a transformer resonant converter may generate pulses with variable pulse widths. For example, a transformer resonant converter may generate pulses with a variable frequency. For example, a transformer resonant converter may generate pulses with a variable voltage. For example, a transformer resonant converter may generate pulses for a dielectric barrier discharge and/or neutral beam injection device. For example, a transformer resonant converter may produce pulses having a pulse width of any duration, for example ranging from about 1 μ s to DC.

For example, a transformer resonant converter may generate pulses with a pulse repetition rate greater than about 1kHz for continuous operation at average power levels in excess of several kilowatts. For example, a transformer resonant converter may produce pulses with a pulse repetition frequency greater than about 1kHz, 30kHz, or 1000 kHz. For example, a transformer resonant converter may produce pulses with a power greater than about 3kW, 100kW, or 3 MW.

In some embodiments, the transformer resonant converter may be housed in a housing mountable in a rack (e.g., a standard 6U housing having dimensions of approximately 10 "x 17" x 28 "). In some embodiments, the transformer resonant converter may have a high power density, for example, the power density may exceed 0.5W/cm³、5W/cm³、50W/cm³Or 500W/cm³。

In some embodiments, the transformer resonant converter may include any type of solid state switch, such as an IGBT, FET, MOSFET, SiC junction transistor, GaN switch, or the like.

Fig. 3 is a photograph of an example transformer resonant converter including a transformer having a winding 310 and a plurality of resistors 305. The cumulative resistance value of the plurality of resistors 305 may be determined by equation 2 for a given Q factor. The transformer resonant converter further includes a plurality of solid state switches 315 coupled to the heat sink. For example, in this case, the solid state switches may be arranged in a full bridge topology. The transformer resonant converter also includes a plurality of full bridge rectifier diodes 320. Many other circuit elements may also be included.

Fig. 4 is an example waveform created from a transformer resonant converter according to some embodiments. In this example, the output voltage is greater than 30kV, the rise time is about 4s, and the plateau width is about 12 μ s.

Fig. 5 is another example waveform created from a transformer resonant converter according to some embodiments. This waveform is generated by the switched resonant converter shown in fig. 2. In this example, the input voltage of the transformer resonant converter is 600V and the output pulse is 30 kV. In this example, the rise time is about 5 μ s and the plateau width is about 20 μ s. These waveforms may have additional rises, plateaus and falls depending on the modulation of the resonant converter. The waveform shows a typical output pulse; various other output pulses are also possible. In some embodiments, the high power density, power, frequency, rise time, and/or voltage of the output of the transformer resonant converter may be unique. For example, these properties may be achieved by using a transformer (and/or circuit) with low stray capacitance and/or low stray inductance that allows operation at high frequencies and allows the use of solid state switches that operate at high power, very fast switching times.

Fig. 7 is a circuit diagram of an example transformer resonant converter 700 according to some embodiments. In this example, transformer 705 is coupled to and/or is part of a resonant converter topology, where transformer 705 has a step voltage of n, which represents the ratio of the number of turns of the primary winding to the number of turns of the secondary winding of transformer 705. In this transformer, stray inductance L_sRepresented by inductor 715, and/or stray capacitance C_sRepresented by capacitor 720 of the transformer. These stray elements are used as part of the resonant converter 700. Stray inductances L of other circuit elements may also be used_soAnd stray capacitance C_soAnd stray inductance L_s715 and the capacitance Cs720 are used in combination to achieve the desired resonant frequencies f and Q. Resistor 710 represents an additional resistance R that may be included on the primary side of the transformer_a. Once the stray inductance L of the transformer is known_sAnd stray capacitance C_sAnd knowing the total inductance and capacitance, the resistance (e.g. R) can be chosen even if they consist of only stray elements_pri) To produce a given Q factor using, for example, equation (2). In this example, the voltage on the transformer secondary can be calculated by the following equation:

V_out＝QnV_c(3).

thus, the voltage on the transformer secondary can be accelerated by the transformer by multiplying n times by Q times through the resonant converter.

In some transformer resonant converters, the total stray inductance and total stray capacitance of the transformer and/or other circuit elements is kept low, for example, to produce a high frequency resonant oscillating voltage, and an output voltage with a fast rise time and/or a fast fall rise time. For example, the circuit may switch at a high frequency, for example, at a frequency greater than 50kHz, 500kHz, 5 MHz. For example, the low total stray inductance and low total stray capacitance of the transformer and/or other circuit elements may also be kept low to produce fast commutation rise times, e.g., faster than 100 μ s, 10 μ s, 1 μ s.

In some embodiments, stray capacitance may be measured from the secondary side of the transformer. Alternatively, the stray capacitance may be measured from the primary side of the transformer, which is equal to the capacitance on the secondary side of the transformer multiplied by the square of the turns ratio n.

In some embodiments, the stray inductance may be measured from the primary side of the transformer. Alternatively, the stray inductance may be measured from the secondary side of the transformer, which is equal to the inductance of the primary side of the transformer multiplied by the square of the turns ratio n.

In some embodiments, the total equivalent series capacitance may be measured from the secondary side of the transformer. Alternatively, the total equivalent series capacitance may be measured from the primary side of the transformer, which is equal to the total equivalent series capacitance on the secondary side of the transformer multiplied by the square of the turns ratio n.

In some embodiments, the total equivalent series inductance may be measured from the primary side of the transformer. Alternatively, the total equivalent series inductance may be measured from the secondary side of the transformer, which is equal to the total equivalent series inductance on the primary side of the transformer multiplied by the square of the turns ratio n.

The term "substantially" is within 5% to 15% of the stated value, or within manufacturing tolerances.

Numerous specific details are set forth herein to provide a thorough understanding of claimed subject matter. However, it will be understood by those skilled in the art that claimed subject matter may be practiced without these specific details. In other instances, methods, devices, or systems known to those of ordinary skill in the art have not been described in detail so as not to obscure claimed subject matter.

The use of "adapted to" or "configured to" herein is meant to be an open and inclusive language that does not exclude devices adapted to or configured to perform additional tasks or steps. Additionally, the use of "based on" is meant to be open and inclusive in that a process, step, calculation, or other action that is "based on" one or more stated conditions or values may, in practice, be based on additional conditions or values beyond those stated. The headings, lists, and numbers included herein are for convenience of explanation only and are not limiting.

While the subject matter of the present invention has been described in detail with respect to specific embodiments thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. It is therefore to be understood that the present disclosure has been presented for purposes of illustration and not limitation, and does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.