Phase-switched impedance modulation techniques and related architectures

Abstract

A phase-switched impedance modulation (PSIM) system for use within a tunable matching network is provided herein. The system comprises a primary port configured to receive an RF signal, at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof, at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer, a switch connected to each of plurality of reactive elements, and a controller configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.

Description

Attorney Docket No. 00777-WOPHASE-SWITCHED IMPEDANCE MODULATION TECHNIQUES AND RELATED ARCHITECTURESTECHNICAL FIELD

[0001] The present disclosure relates to impedance modulation techniques for power conversion and switching circuits, and more particularly to phase-switched impedance modulation (PSIM) architectures, systems, and methods utilizing transformers, capacitors, and switching elements for controlling power flow and impedance characteristics in electronic circuits.BACKGROUND

[0002] The ability to deliver radio-frequency (RF) power into widely-varying load impedances at kilowatt power levels and beyond is crucial to a diverse range of existing and emerging applications and especially in RF plasma generation. For example, in the semiconductor manufacturing industry, the increasing demand for fabricating complex nanoscale structures has motivated the use of significantly more sophisticated plasma-based processing. This typically involves rapid and repetitive pulsing of RF power over a very wide dynamic range (several kilowatts) leading to abrupt plasma load impedance transitions over time intervals as short as few tens of microseconds. Such wide load impedance variations in many of these applications make it particularly challenging to achieve efficient RF power generation while maintaining acceptable loading of the RF amplifier or inverter and providing accurate and agile power control.

[0003] As a result, many RF power generation systems required to deliver power to a varying load impedance commonly employ a Tunable Matching Network (TMN) between the load and the RF source or generator. Through their ability to provide dynamically adjustable impedance transformation, TMNs can transform the varying load impedance to a nearly constant one (e.g., 50 Ohms) that is suitable for driving by the RF generator. Conventional TMNs for HF and VHF applications often rely on lumped-element reactive networks, where the reactance of some of the elements can be tuned dynamically. TMN performance characteristics (e.g., tuning range and resolution, speed, power handling, etc.) are determined to a great extent by the implementation of the tunable reactance elements.Attorney Docket No. 00777-WO

[0004] A common technique for implementing TMNs, especially in high-power plasma applications, involves using mechanically-adjustable vacuum / air capacitors or inductors controlled by servo motors. While these systems offer fine tuning resolution across a wide impedance range, they suffer from slow tuning times (hundreds of milliseconds) and reliability issues due to moving components. Alternatively, faster tuning responses (few milliseconds) can be achieved using electronically-tunable components like varactors or MEMS-varactors. However, operation at high power levels necessitates large dynamically- adjustable bias voltages, limiting their power handling capability and tuning bandwidth. Another approach utilizes reconfigurable arrays of passive components, with switches connecting or disconnecting discrete capacitors or inductors. While offering relatively faster tuning speeds (hundreds of microseconds) and high power handling, these implementations suffer from limited tuning range and resolution, affecting impedance matching accuracy in addition to their high-cost implementation.

[0005] One recently-proposed solid-state technique showing significant promise in implementing rapidly-tunable reactance elements is phase-switched impedance modulation (PSIM). By integrating PSIM-based variable capacitors with other components, tunable matching networks can be realized with tuning times that are orders of magnitude faster than conventional methods (few microseconds). This technique also supports operation at high power levels, offers arbitrarily fine tuning resolution, and is suitable for high frequencies. Essentially, PSIM involves switching the connection of a reactive element — such as a capacitor, inductor, or a combination of both — to modulate its impedance at the switching frequency. This enables efficient and rapid adjustments to impedance, providing substantial advantages in RF impedance matching applications.

[0006] Conceptually, phase-switched impedance modulation (PSIM) is a narrowband technique which achieves impedance modulation by introducing and controlling (through switching) the harmonic content of the voltage and current waveforms of a reactive element. To illustrate the principle of phase-switched impedance modulation, consider the simple switched capacitor network consisting of a parallel combination of a capacitor Coand an ideal switch driven with a sinusoidal current source, as shown in FIG. 1 A. The switch state is controlled by the signal q; the switch is on or off when q is high or low, respectively. When the switch is on, the voltage vcacross the capacitor is clamped to zero and all the current icflows through the switch. When the switch is in the off state, the voltage vcis determined by the current flowing through Co. If the phase of the switch control signal q is selectedAttorney Docket No. 00777-WO appropriately with respect to the current ic, one can ensure both zero-voltage switch turn-on and turn-off as shown in FIG. 1 A. (For the case of purely sinusoidal current excitation, as in FIG. 1 A, zero-voltage switching is ensured by centering the switch off-state around the positive-to-negative current transition at 6 = TT.) Soft-switching in this manner is highly desirable for efficient operation at high frequencies.

[0007] Performing a Fourier analysis on the capacitor voltage (under sinusoidal current drive and zero-voltage switching operation) reveals that its fundamental component lags the current by 90° for any switch duty cycle, suggesting that the switched capacitor network behaves effectively as a capacitor at the switching frequency. Moreover, by adjusting the duty-cycle of the switch, one can control the peak capacitor voltage and the magnitude ratio of the fundamental components of the voltage vcand current ic. This essentially allows one to effectively modulate the effective capacitance CEFFof the network (at the switching frequency) by appropriately controlling the switch duty cycle. For example, if the switch duty cycle is zero, i.e. the switch is always off, and the effective capacitance seen looking into the network of FIG. 1A is just the base capacitance Co. On the other hand, if the switch is always on, i.e. unity duty cycle, the network is shorted, and the effective capacitance CEFFapproaches infinity. Hence, by controlling the switch duty cycle from zero to unity one can theoretically achieve any effective capacitance from Coto infinity (short-circuit). In the case of an ideal switch and linear capacitor with purely sinusoidal current excitation, it can be shown that the relationship between switch duty cycle (or conduction angle a) and effective capacitance CEFFis given by (1) and shown in FIG. 3A (HWPSIM curve).

[0008] By analogy to the switched capacitor network shown in FIG. 1 A, it is also possible to construct a switched inductor network that allows continuous control of its effective inductance. Such a switched inductor network is shown in FIG. IB, and corresponds to the topological dual of the switched capacitor network of FIG. 1 A. Similarly to its switched-capacitor counterpart, it allows its effective inductance LEFFat the switching frequency to be modulated from a base value Lo(when the switch is permanently on) to infinity (when the switch is permanently off). FIG. IB shows the voltage vLand current iLwaveforms when the switched inductor network is driven with a purely sinusoidal voltage source and the switch is turned on a radians into the positive cycle of the voltage. It can beAttorney Docket No. 00777-WO seen from FIG. IB that the voltage waveform of the switched capacitor network is analogous to the current waveform of the switched inductor network and vice versa - a result that follows from the properties of topological duality. Similarly to the technique employed for calculating the effective capacitance of the switched capacitor network, by performing a frequency analysis of the inductor current and determining the relationship between the magnitude of its fundamental component (at the switching frequency) and <z, it can be shown that effective inductance LEFFis given by (1). The expression is identical to that of the effective capacitance - another not surprising result that follows from the properties of topological duality. The basic networks illustrated in FIG. 1 A and IB can be further expanded with additional reactive elements to achieve reactance modulation across both capacitive and inductive ranges.

[0009] The switched capacitor and inductor networks shown in FIGS. 1 A and IB, respectively, can be operated to produce unipolar capacitor voltage vcand inductor current iLwaveforms, in a method referred to herein as "half-wave phase-switched impedance modulation" (HWPSIM). Operation in this manner may be preferable in some RF systems due to its implementation simplicity. However, one significant drawback of this operation mode is the rapid increase in switching harmonics with higher switch duty cycle and large reactance modulation. It is often these switch-generated harmonics that preclude practical PSIM operation at large switch duty cycles, limiting the achievable reactance modulation to a factor of 4-5 compared to the theoretically infinite modulation range suggested by (1).

[0010] An alternative switching technique that significantly reduces generated harmonics involves operating the aforementioned switches as illustrated in FIGS. 2A and 2B to produce symmetrically bipolar voltage and current waveforms. This method, referred to herein as "full-wave phase-switched impedance modulation" (FWPSIM), eliminates the DC component and even harmonics in the waveforms, significantly reducing harmonic distortion compared to HWPSIM, as shown in FIG. 3B. For instance, in the switched capacitor network in FIG. 2A, FWPSIM is achieved by turning off the switch twice per RF cycle, with the off periods centered around the zero current instants. Similarly, in the switched inductor network in FIG. 2B, FWPSIM is achieved by turning on the switch twice per RF cycle, with the on periods centered around the zero voltage instants.

[0011] Although FWPSIM significantly reduces switching harmonics, implementing it as depicted in FIGS. 2 A and 2B poses challenges for high-frequency RF applications. ForAttorney Docket No. 00777-WO example, the switch must operate at twice the RF frequency and have bidirectional voltage blocking capability.

[0012] Known conventional implementations of PSIM for the design of TMNs are based on the half-wave switching scheme shown in FIGS. 1 A and IB. This approach suffers from numerous significant limitations related to power handling capability, tuning range, operating frequency, switching harmonics and design flexibility.

[0013] For example, in TMN designs based on the half-wave PSIM configuration, the peak RF power handling capability is often constrained by the breakdown voltage of the PSIM switching device (e.g., one or more GaN FETs, due the requirement for high frequency operation). For instance, the peak voltage stress on the PSIM transistors is directly related to the RF power and the target match impedance (typically 50 ohms), scaling with the square root of power.

[0014] Additionally, the technology choice for the PSIM switching device (i.e., GaN FETs) may limit the availability of high-voltage devices, creating a significant bottleneck for power scaling. Although some approaches, attempt to address these limitations by implementing impedance scaling at various levels of the matching network, these methods can be cumbersome to implement and may restrict the TMN matching range.

[0015] Although theoretically both HWPSIM and FWPSIM allow for infinite reactance modulation range, in practice the achievable reactance modulation range is severely limited by the generation of switching harmonics and device losses both of which rapidly increase with PSIM reactance modulation range.

[0016] All known PSIM implementations entail switching the PSIM device directly at the RF operating frequency. This makes PSIM an extremely challenging technique to realize at frequencies above the HF range, i.e., above 30 MHz, due to switching device limitations.

[0017] Further, both half-wave and full-wave PSIM implementations can generate significant switching harmonics, particularly at high switch duty cycles and reactance modulation ratios, which can severely limit the achievable reactance tuning range. High harmonic content in the switch voltages can significantly distort the current in the PSIM circuit, thereby altering the relationship between the effective PSIM reactance and switch duty cycle. This can severely impact overall system stability in addition to injecting undesirable harmonics into the load and RF generator.Attorney Docket No. 00777-WO

[0018] When employing PSIM for high frequency applications, it is often desirable to operate the switching device in a grounded configuration, i.e. with a ground-connected source terminal of the FET. This limits the utility of half-wave PSIM strictly to the realization of shunt-connected tunable reactance elements, with one side of the element having to be ground-connected. This severely constraints TMN design flexibility and architectures limiting their tune range and operating efficiency.

[0019] Embodiments of the present invention described in greater detail below address the problems and limitations described above. For example, embodiments of the present invention provide new techniques and architectures designed to enhance PSIM performance by enabling operation at higher power levels, expanding reactance tune range, supporting higher frequency operation into the HF and VHF range, and reducing harmonic distortions. Furthermore, embodiments of the present invention provides greater design flexibility by allowing the implementation of both ground-referenced and floating PSIM tuning elements enabling the design of efficient, wide tuning range TMNs with multiple PSIM actuators. These innovations thus aim to make PSIM more versatile and efficient for modern RF applications.SUMMARY

[0020] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0021] In one embodiment, a phase-switched impedance modulation (PSIM) system for use within a tunable matching network is provided. In this embodiment, the system comprises a primary port configured to receive an RF signal. The system comprises at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof. The system comprises at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer. The system comprises a switch connected to each of plurality of reactive elements. The system comprises a controller configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.Attorney Docket No. 00777-WO

[0022] In another embodiment, a method of controlling a phase-switched impedance modulation (PSIM) system for use within a tunable matching network is provided. In this embodiment, the system comprises a primary port configured to receive an RF signal, at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof, at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer, a switch connected to each of the plurality of reactive elements, and a controller. The method comprises generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.

[0023] In yet another embodiment, a non-transitory computer-readable medium storing instructions is provided. In this embodiment, when the instructions are executed by a processor of a controller in a phase-switched impedance modulation (PSIM) system for use within a tunable matching network, the system comprises a primary port configured to receive an RF signal, at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof, at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer, and a switch connected to each of the plurality of reactive elements. The instructions cause the processor to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.

[0024] The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure and are not restrictive.BRIEF DESCRIPTION OF FIGURES

[0025] Non-limiting and non-exhaustive examples are described with reference to the following figures.

[0026] FIGS. 1 A and IB conceptually illustrate operation of phase-switched capacitance and inductive elements, respectively, and their corresponding half-wave voltage and current waveforms.Attorney Docket No. 00777-WO

[0027] FIGS. 2A and 2B conceptually illustrate operation of phase-switched capacitance and inductive elements, respectively, and their corresponding full-wave voltage and current waveforms.

[0028] FIG. 3 A depicts a graph comparing performance of half- and full-wave phase- switched impedance modulation operations (HWPSIM and FWPSIM, respectively) as a function of switch conduction angle.

[0029] FIG. 3B depicts a graph comparing total harmonic distortion (THD) of the switched voltage and current between half- and full-wave phase-switched impedance modulation.

[0030] FIG. 4 schematically and conceptually illustrates a phase-switched impedance modulation (PSIM) system, according to various embodiments of the present invention.

[0031] FIGS. 5A-5C illustrate schematic diagrams of magnetic flux-coupled capacitive PSIM (C-PSIM) modules according to some embodiments of the present invention. Generally, FIGS. 5B and 5C can be characterized as illustrating some embodiments of PSIM coupling networks formed by electrically connecting, in series, multiple constituent PSIM reactive element submodules, such as shown in FIG. 5A, together.

[0032] FIGS. 6A-6C depict waveforms and switch control signals associated with different operation modes of the C-PSIM module shown in FIG. 5A. Specifically, FIG. 6A depicts waveforms and switch control signals associated with a half-wave operation mode, FIG. 6B depicts waveforms and switch control signals associated with a symmetric full-wave operation mode and FIG. 6C depicts waveforms and switch control signals associated with a non-symmetric full-wave operation mode.

[0033] FIG. 7 illustrates a schematic diagram of a PSIM module with additional, optional, passive components, such as capacitors, to compensate for transformer parasitics, provide harmonic filtering and introduce DC current blocking in the secondary winding, according to some embodiments of the present invention.

[0034] FIGS. 8A-8C illustrate schematic diagrams of magnetic flux-coupled inductive PSIM (L-PSIM) modules according to some embodiments of the present invention. Generally, FIGS. 8B and 8C can be characterized as illustrating some embodiments of PSIM modules formed by magnetically connecting multiple constituent PSIM reactive element submodules, such as shown in FIG. 8A, together via a series fluxAttorney Docket No. 00777-WO path. In FIGS. 8B and 8C, the secondary windings of the constituent PSIM reactive element submodules share the same flux linkage.

[0035] FIGS. 9A and 9B illustrate schematic diagrams of PSIM modules according to some embodiments of the present invention, in which primary windings of multiple constituent PSIM reactive element submodules, each having a toroidal core, are electrically connected together in series.

[0036] FIG. 10 illustrates a schematic diagram of a PSIM module according to an embodiment of the present invention, in which multiple constituent PSIM reactive element submodules are magnetically coupled to a common primary winding with a single magnetic core.

[0037] FIGS. 11 A and 1 IB illustrate schematic diagrams of PSIM modules according to some embodiments of the present invention, in which multiple constituent PSIM reactive element submodules are magnetically coupled via or more secondary windings.

[0038] FIG. 11C illustrates a schematic diagram of a PSIM module according to an embodiment of the present invention, in which multiple constituent PSIM reactive element submodules are electrically and magnetically coupled together.

[0039] FIGS. 12A-12E illustrate schematic diagrams of a transmission line-coupled PSIM modules, according to some embodiments of the present invention.

[0040] FIG. 13 illustrates a schematic diagram of a series-stacked PSIM architecture for power scaling applications, according to an embodiment of the present invention.

[0041] FIG. 14A illustrates a schematic diagram of a tunable matching network (TMN) with a simple switched capacitor network operated based on HWPSIM, according to an embodiment of the present invention.

[0042] FIG. 14B depicts voltage and current waveforms at the TMN input port of FIG. 14 A.

[0043] FIG. 14C depicts voltage and current waveforms across the switched capacitor network of FIG. 14 A.

[0044] FIG. 15A illustrates a schematic diagram of a TMN with a PSIM module, such as that shown in FIG. 5 A operated based on FWPSIM, according to an embodiment of the present invention.Attorney Docket No. 00777-WO

[0045] FIG. 15B depicts voltage waveforms across the switches in the PSIM coupling of FIG. 15 A.

[0046] FIG. 15C depicts voltage and current waveforms at the TMN input port of FIG.15 A.

[0047] FIG. 15D depicts voltage and current waveforms across the PSIM module of FIG.15 A.

[0048] FIG. 16A illustrates a schematic diagram of a TMN with a PSIM module, such as that shown in FIG. 5B operated based on FWPSIM, according to an embodiment of the present invention.

[0049] FIG. 16B depicts voltage waveforms across the FETs in the network of FIG. 16 A.

[0050] FIG. 16C depicts voltage and current waveforms at the TMN input port of FIG.16 A.

[0051] FIG. 16D depicts voltage and current waveforms across the PSIM module of FIG. 16 A.

[0052] FIG. 17 illustrates a schematic diagram of an impedance step-up TMN, according to an embodiment of the present invention, which includes a PSIM module provided in any manner as exemplarily described above.

[0053] FIGS. 18A-18C illustrate schematic diagrams of the PSIM module shown in FIG. 17, according to some embodiments of the present invention, any of which may be operated according to the HWPSIM or FWPSIM techniques described herein.

[0054] FIGS. 19A to 19C illustrate the progressive improvement in load impedance matching range achieved by PSIM modules with different coupling network configurations. Specifically, FIG. 19A depicts a chart showing load impedance matching range for the TMN shown in FIG. 17, with the PSIM module shown in FIG. 18A operated by HWPSIM. FIG. 19B depicts a chart showing load impedance matching range for the TMN shown in FIG. 17, with the PSIM module shown in FIG. 18B operated by FWPSIM. FIG. 19C depicts a chart showing load impedance matching range for the TMN shown in FIG. 17, with the PSIM module shown in FIG. 18C operated by FWPSIM.

[0055] FIG. 20A illustrates a schematic diagram of a PSIM module incorporating a plurality of PSIM reactive element submodules according to an embodiment of the present invention.Attorney Docket No. 00777-WO

[0056] FIG. 20B depicts waveforms and switch control signals associated with interleaved operation of the PSIM reactive element submodules shown in FIG. 20A.

[0057] FIG. 20C depicts conceptual waveforms and switch control signals associated with for multiplexed operation of the PSIM reactive element submodules shown in FIG. 20A.

[0058] FIG. 21 A depicts switch control signals for interleaved operation, at 27.12 MHz, of the PSIM module shown in FIG. 20A.

[0059] FIG. 2 IB depicts simulated voltage and current waveforms for interleaved operation, at 27.12 MHz, of the PSIM module shown in FIG. 20A.

[0060] FIG. 22A depicts switch control signals for multiplexed operation, at 27.12 MHz, of the PSIM module shown in FIG. 20A.

[0061] FIG. 22B depicts simulated voltage and current waveforms for multiplexed operation, at 27.12 MHz, of the PSIM module shown in FIG. 20A.

[0062] FIG. 23 A depicts switch control signals for combined interleaved and multiplexed operation, at 54.24 MHz, of the PSIM module shown in FIG. 20A.

[0063] FIG. 23B depicts simulated voltage and current waveforms for combined interleaved and multiplexed operation, at 54.24 MHz, of the PSIM module shown in FIG. 20A.

[0064] FIG. 24A illustrates a schematic diagram of a PSIM module, with an arbitrary number, N, of PSIM reactive element submodules, according to some embodiments of the present invention.

[0065] FIG. 24B depicts a control scheme diagram showing duty cycle for each submodule shown in FIG. 24A as a function of the desired effective capacitance Cx at the primary input port of the PSIM module.

[0066] FIG. 25 A depicts graphs showing the relationship between switch duty cycle and total harmonic distortion for PSIM coupling networks with different numbers (1, 2, 4 and 6) of PSIM reactive element submodules.

[0067] FIG. 25B depicts graphs showing the distribution of discrete capacitance ranges for different active PSIM reactive element submodules.

[0068] FIG. 26 illustrates a conceptual block diagram of an PSIM system with tunable matching network components according to embodiments of the present invention.Attorney Docket No. 00777-WODETAILED DESCRIPTION

[0069] The following description sets forth exemplary aspects of the present disclosure. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure. Rather, the description also encompasses combinations and modifications to those exemplary aspects described herein.

[0070] Example embodiments of the present invention are described herein with reference to the accompanying FIGS. Unless otherwise expressly stated, in the drawings the sizes, positions, etc., of components, features, elements, etc., as well as any distances therebetween, are not necessarily to scale, but are exaggerated for clarity.

[0071] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should be recognized that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Unless otherwise specified, a range of values, when recited, includes both the upper and lower limits of the range, as well as any sub-ranges therebetween. Unless indicated otherwise, terms such as "first," "second," etc., are only used to distinguish one element from another. For example, one node could be termed a "first node" and similarly, another node could be termed a "second node", or vice versa. The section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

[0072] Unless indicated otherwise, the term "about," "thereabout," "substantially," etc., means that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art.

[0073] It will be appreciated that many different forms and embodiments are possible without deviating from the spirit and teachings of this disclosure and so this disclosure should not be construed as limited to the example embodiments set forth herein. Rather, theseAttorney Docket No. 00777-WO examples and embodiments are provided so that this disclosure will be thorough and complete, and will convey the scope of the disclosure to those skilled in the art.

[0074] Generally, this written disclosure is organized into two main parts. The first part introduces embodiments of a modular, full-wave PSIM architecture, providing various implementation examples based on magnetic flux-coupled and transmission-line transformers. The second part describes example techniques and configurations for employing multiple PSIM modules, according to various embodiments of the present invention, to achieve higher power levels, wide reactance tuning range, high-frequency operation, and reduced switching harmonics.Embodiments of Modular PSIM Architectures

[0075] According to embodiments of the present invention, modular PSIM architectures can be provided for realizing a PSIM-based tuning element whose effective reactance is adjustable via an external control signal. Circuitry for synchronization, driving and protection of the internal PSIM switches can be integrated in the module to provide stand-alone operation. Furthermore, the modularity of this architecture allows for ease of connecting and interfacing multiple PSIM modules in various ground-referenced and floating configurations to enable high power handling, HF and VHF operation, wide reactance tuning range and reduced switching harmonics.

[0076] FIG. 4 generally illustrates a PSIM system according to embodiments of the present invention. The PSIM system includes a PSIM module, a PWM generation and switch driving circuitry, zero-voltage switching (ZVS) / zero-current switching (ZCS) sensing circuitry, and a local controller. The PSIM module includes a PSIM input port P[N(also referred to herein as an PSIM primary port or, more simply, as a “primary port”), a multiport coupling network (also referred to herein simply as a “coupling network” or a “PSIM coupling network”, or as a “multiport PSIM coupling network”) with an input port P[Nand N switch ports P to PN, and PSIM switches S to SN(also referred to herein simply as “switches”) connected respectively to corresponding switch ports P to PN. As will be discussed in greater detail below, the coupling network refers to the circuitry connecting the input port P[Nto the switches S to SN.

[0077] In the coupling network of FIG. 4, multiple switch ports P to PNare passively coupled to a single PSIM input port P[N(e.g., via one or more transformers and / or transformer types, as exemplarily described below). Each switch port is connected to aAttorney Docket No. 00777-WO respective one of the switches S to SN, which can be switched on or off with individually- controlled duty cycles to achieve modulation of the effective reactance seen at the PSIM input port PjN. As will be described in greater detail below, the phase and duty cycle of each switch may be independently controlled to achieve various PSIM operating modes, including half-wave and full-wave operation.

[0078] The PWM generation and driving circuitry, which may be included in the PSIM module or implemented as an external unit, synthesizes the drive signal for each of the PSIM switches with the appropriate duty cycle and phase synchronized to an external reference signal. An optional internal ZVS / ZCS monitoring circuitry may be employed to provide feedback to the PWM generation circuit via the local controller and ensure soft-switching of the PSIM switches. Generally, the local controller may be implemented as a computer, microprocessor, etc., operating in response to instructions stored on a computer-readable medium or otherwise embodied in fixed or field-programmable circuitry, or the like. In some embodiments, the computer-readable medium may include non-transitory storage such as memory chips, solid state drives, or magnetic hard drives. The instructions may cause the computer or microprocessor to perform functions such as generating or modulating switch control signals, implementing the various PSIM operational modes described in greater detail below.

[0079] The following two subsections of the disclosure explore various implementations of the multiport coupling network based on magnetic flux-coupled and transmission line- coupled structures.Magnetic Flux-Coupled PSIM Coupling Networks

[0080] This section presents the notion of multiport PSIM coupling networks based on magnetic flux-coupled transformers for realizing both capacitive and inductive tunable reactance elements and provides various practical realization examples.

[0081] Embodiments of a transformer-based coupling network passively coupling multiple switch ports to a single PSIM input port (primary port) are shown in FIGS. 5A-5C, with each switch port connected to a respective switch. Generally, according to the various embodiments described herein, a switch (e.g., SltS2, etc.) can be provided as a field-effect transistor (FET) or any other suitable switching device, each switch is connected between a respective first pair of nodes of the multiport PSIM coupling network, and such first pair ofAttorney Docket No. 00777-WO nodes constitute a corresponding switch port (e.g., PltP2, etc., as shown in FIG. 4) connected to a switch. The ground-referenced connection of the switches to the coupling network facilitates operation at high switching frequencies. By controlling the duty cycle and phase of the switches, one can modulate the effective reactance seen looking into the PSIM primary port. As exemplarily illustrated in FIGS. 5A-5C, a transformer isolates the PSIM input port (primary port) from each switch port, allowing one to realize tunable reactance elements that can be connected in both grounded and floating configurations. Furthermore, the transformer turns ratio or, more generally, the “transformation ratio”, of teach transformer offers additional degree of design freedom in selecting a balance between device current and voltage stresses and allowing for impedance scaling.

[0082] FIGS. 5A-5C thus illustrate embodiments of a multiport PSIM coupling network using a magnetic flux transformer to couple a PSIM primary port to two switch ports (as in FIG. 5 A), four switch ports (as in FIG. 5B), and an arbitrary number, N, switch ports (as in FIG. 5C). For purposes of facilitating discussion herein, the multiport coupling networks can be identified in terms of the number of switch ports that are provided. Thus, and by way of example, the coupling network illustrated in FIG. 5A forms a “two-switch port coupling network,” the coupling network illustrated in FIG. 5B) forms a “four-switch port coupling network,” and the coupling network illustrated in FIG. 5C forms an “N-switch port coupling network.” Additionally, for purposes of facilitating discussion herein, the portion of the circuitry at the secondary side of each transformer (i.e., each coupling network) can be considered to be a “PSIM reactive element submodule” (or, more simply, a “reactive element submodule” or even more simply a “submodule”) of the coupling network. Accordingly, the coupling network may include one a single submodule coupled to the primary PSIM port (e.g., as shown in FIG. 5 A) or multiple submodules coupled to the same primary PSIM port (e.g., as shown in FIGS. 5B and 5C). Lastly, the secondary of each transformer is connected between a second pair of nodes of a corresponding submodule, and such second pair of nodes constitutes an input port of the submodule.

[0083] According to embodiments of the present invention, in the coupling networks shown in FIGS. 5A, 5B and 5C, the capacitive reactance seen looking into the PSIM primary port can be modulated by adjusting the phase and duty-cycle of the switches. Further, the various switches S do not have to be operated with the same duty cycle as this allows for greater operational flexibility by simultaneously allowing for reactance modulation and controlling the harmonic profile of the switched voltage waveforms. For instance, theAttorney Docket No. 00777-WO coupling network of FIG. 5 A can be operated in half-wave mode by keeping one of the switches permanently on while modulating the other of the switches between on and off states (e.g., as shown in FIG. 6A, where a control signal q2 is permanently applied to switch S2while control signal ql is intermittently applied to switch Sx), full-wave symmetric mode by modulating operation of the switches S and S2with identical duty cycle (FIG. 6B), or full-wave non-symmetric mode by allowing different switch duty cycles (FIG. 6C, which requires DC-blocking in the secondary winding loop to prevent transformer saturation.) Employing combinations of these operating modes to expand tune range, power handling capabilities and reduce harmonics is explored in subsequent sections of this disclosure.

[0084] The coupling network of FIGS. 5A-5C can be augmented with additional passive components to absorb and compensate for transformer parasitics, implement harmonic filtering, and provide DC-blocking for non-symmetric full-wave operation. For example, as shown in FIG. 7, the coupling network shown in FIG. 5A can be augmented with series capacitors and C2to resonate the leakage inductance of the transformer thus simultaneously providing harmonic filtering and DC-blocking, while a shunt capacitor C3can be used to resonate out the transformer magnetizing inductance L^.

[0085] By series-connecting multiple two-switch port coupling networks of FIG. 5 A together, one can realize multiport PSIM coupling networks with an arbitrary number of switch ports as shown in FIG. 5B (four-switch port coupling network) and FIG. 5C (N-switch port coupling network). Although FIGS. 5A-5C schematically illustrate cascading multiple two-switch port coupling networks by series-connecting their primary windings, such cascading can also be effectively achieved by electrically connecting and / or magnetically coupling the individual coupling networks as illustrated in the example embodiments described below. Additionally, even though the switches are schematically depicted as MOSFETs in FIGS. 5A-5C, in practice they can be implemented using any other suitable switching devices.

[0086] Neglecting switch and transformer parasitics, the PSIM coupling networks in FIGS. 5A-5C allow for reactance modulation over a strictly capacitive range. Analogous to FIG. 2B, the properties of topological duality can be used to synthesize the PSIM coupling networks in FIGS. 8A-8C, allowing for inductive reactance modulation.

[0087] Similar to FIGS. 5A-5C, the inductive PSIM coupling networks in FIGS. 8A-8C rely on a flux-coupled transformer to couple multiple switch ports to a single primary PSIMAttorney Docket No. 00777-WO port. Adjusting the phase and duty cycle of the switches allows for modulation of the effective inductive reactance seen looking into the PSIM primary port. Consistent with the properties of topological duality, voltage waveforms in the capacitive PSIM (C-PSIM) networks of FIGS. 5A-5C are analogous to the current waveforms in the inductive PSIM (L- PSIM) networks of FIGS. 8A-8C, and vice-versa. Whereas switching in the C-PSIM coupling networks modulates the harmonic content of the primary PSIM port voltage vP, switching in the L-PSIM coupling networks analogously modulates the harmonic content in the primary PSIM port current iP. While the C-PSIM coupling network switch ports support bidirectional current carrying and unipolar voltage blocking capability, the L-PSIM coupling network switch ports require bidirectional voltage blocking capability and only need to be able to carry unipolar current. Hence each switch in the L-PSIM coupling networks of FIGS. 8A-8C can be implemented as a diode in series with a FET (e.g., in FIG. 8A, switch S would be implemented as diode D connected in series with FET Q and switch S2would be implemented as diode D2connected in series with FET Q2though it is appreciated that other configurations are possible in practice.

[0088] Even though the C-PSIM (FIGS. 5A-5C) and L-PSIM (FIGS. 8A-8C) coupling networks both offer analogous reactance modulation range and support half-wave, symmetric full-wave, and non-symmetric full-wave operation, the C-PSIM architectures are often a more practical choice for RF applications. This is because the C-PSIM coupling network architectures allow the absorption of the parasitic switch output capacitance into the PSIM base capacitance. Furthermore, by appropriately adjusting the phase of the C-PSIM switches, efficient and highly-desired zero-voltage switching (ZVS) can be achieved. In contrast, one can only achieve zero-current switching (ZCS) for the FETs in the L-PSIM coupling networks while still having to sustain power losses from turning the FETs on at non-zero voltage. For this reason, focus is made below on providing various implementation examples of multiport C-PSIM coupling networks. However, it will be appreciated that the techniques described herein can be also applied to the implementation of L-PSIM coupling networks.

[0089] As FIGS. 5 A-5C and 8A-8C illustrate, one can realize multiport C-PSIM and L- PSIM modules of arbitrary size and number of switches by interconnecting multiple, smaller coupling networks . These interconnections are schematically depicted in FIGS. 5A-5C by electrical series connection of smaller coupling networks all sharing the same primary port current iP, while in FIGS. 8A-8C, the coupling networks are connected via a series magnetic flux path, with all secondary windings sharing the same flux linkage. However, it is worthAttorney Docket No. 00777-WO noting that the L-PSIM and C-PSIM multiport networks can be each realized in practice by both electric current and magnetic flux interconnections. Some examples of possible realizations of C-PSIM coupling networks based on both approaches are discussed in greater detail below.

[0090] One example implementation of a four-switch C-PSIM coupling network is shown in FIG. 9A based on electrically connecting the primary windings of two two-switch port coupling networks in series. Each coupling network in FIG. 9A comprises toroidal cores T and T2and corresponding secondary windings, each with two-switch ports connected to FETs Q11 / Q12, and Q21 / Q22, respectively. Conceptually, this notion can be extended to an arbitrary number N of series-connected coupling networks, as shown in FIG. 9B. A notable advantage of this implementation approach is that it facilitates design flexibility, modularity, and ease of system scaling. For instance, by employing a toroidal core for each two-switch port coupling network, the individual coupling networks can be constructed and assembled independently from each other. At system design level, any number of these coupling networks can be interconnected in series by a common primary winding. The number of interconnected coupling networks can be adjusted to easily scale power handling capability and tune range. As will be appreciated, FETs QlltQ12, Q21, Q22in FIGS. 9A and 9B, FETs QN1and QN2in FIG. 9B, and all other FETs (whether or not designated in the FIGS, by a Q- type identifier) which are not connected in series to a diode as in FIGS. 8A-8C can be understood to constitute a “switch” as discussed above with respect to FIG. 4.

[0091] An alternative approach for synthesizing multiport PSIM coupling networks is by magnetically coupling smaller coupling networks as conceptually illustrated in FIG. 10. Here, a single magnetic core with multiple parallel branches links N two-switch port coupling networks to a primary winding. Ignoring flux leakage out of the core, flux balance maintains that the flux in the primary winding Op is the sum of the flux-wthrough all the secondary windings. Since the voltages across the secondary windings are related to the corresponding winding flux linkage, it can be shown that the primary port voltage vPis related to the sum of all the secondary voltages vsl- vSN. Effectively the design approach in FIG. 10 achieves series voltage combining of all N coupling networks similar to the series- connected implementation of FIGS. 9A and 9B while employing only a single magnetic structure.Attorney Docket No. 00777-WO

[0092] One example of employing the concept of magnetic flux-based linking to implement a four-switch PSIM coupling network is shown in FIG. 11 A and FIG. 1 IB in the context of realizing a planar magnetic design. In FIG. 1 IB, two two-switch port coupling networks are coupled through the outer legs of a planar E-core, while the primary winding is wrapped around the center leg of the core. The magnetic flux in the center leg (primary winding) distributes between the two outer legs, linking each of the secondary windings resulting in the primary port voltage vPbeing a series combination of the secondary voltages vsland vS2. Similar series combining of secondary voltages is also achieved in the example design of FIG. 11 A, although in this case, there is only a single secondary winding with four switches wrapped around the center core leg.

[0093] As shown herein, multiport PSIM coupling networks of arbitrary size can be synthesized by either electrical interconnection (see, e.g., FIGS. 9A and 9B) or magnetic coupling (see, e.g., FIGS. 11 A and 1 IB) of multiple, smaller PSIM coupling networks. It is also possible to synthesize hybrid PSIM coupling networks which employ both electric and magnetic linking, such as the example shown in FIG. 11C. This design comprises N coupling networks with their primary windings electrically connected in series. Each coupling network, in turn, employs magnetic linking to realize a four-switch PSIM coupling network. The construction exemplarily illustrated in FIG. 11C can be used to conveniently construct modular multiport PSIM architectures of arbitrary size.Transmission Line-Coupled PSIM Coupling Networks

[0094] The previous section explored the implementation of multiport PSIM coupling networks based on magnetic flux-coupled transformers. In high-frequency RF applications, conventional flux-coupled transformers are often limited by core losses such as hysteresis and eddy current losses, which become significant at higher frequencies. These transformers are also hindered by resistive losses exacerbated by the skin effect, where currents are confined to the surface of the conductor, increasing resistance. In contrast, transmission-line transformers (TLTs) eliminate or minimize the use of magnetic cores, thereby reducing core losses. They are designed with specialized conductors that mitigate the skin effect, leading to lower resistive losses. Additionally, these transformers excel in maintaining consistent impedance matching across a broad frequency range, enhancing power transfer efficiency, and reducing signal reflections. This makes transmission-line transformers particularly advantageous for high-frequency RF applications, where they deliver improved performance,Attorney Docket No. 00777-WO bandwidth, and reliability. This section explores the implementation of multiport PSIM coupling networks based on transmission-line transformers.

[0095] The simplest TLT-based two-switch PSIM coupling network is shown in FIG. 12A, which comprises a single transmission-line and two PSIM switch ports Q1and Q2. Operating the switch ports 180° degrees out of phase, while adjusting their duty cycle in the manner depicted in FIGS. 6A-6C allows for capacitive reactance modulation seen at the primary port of the transmission line. Similarly to the network architectures in FIGS. 5A-5C, the TLT-based implementation also supports half-wave, symmetric full-wave, and non- symmetric full-wave PSIM operation. Furthermore, this network can be used in TMN systems with the primary side of the transmission line either ground-connected or floating, while the PSIM switches are conveniently operated in the balanced, ground-referenced configuration. This allows multiple TLT-based two-switch coupling networks to be cascaded by series-connecting the primary side of the respective transmission lines in a manner similar to FIG. 5C. When constructing the TLT, the transmission line length is selected to be considerably shorter than the wavelength at the operating frequency. Furthermore, the common-mode impedance of the line must be high enough to limit common-mode currents between the primary and secondary line ports. This is often achieved by well-known prior art TLT construction techniques such as wrapping the transmission-line around a magnetic core. (In contrast to conventional flux-coupled transformers, the magnetic core in TLT designs only provides common-mode choking capability and does not carry considerable RF power; most of the RF power is transferred through the transmission line.)

[0096] One limitation of the simple TLT-based network in FIG. 12A is that it implements a fixed 1 : 1 primary -to-secondary voltage / current transformation ratio. However, by appropriately interconnecting multiple such coupling networks, one can theoretically achieve any rational transformation ratio. For example, FIG. 12B shows a TLT-based two- switch PSIM coupling network with 2: 1 primary-to-secondary voltage transformation ratio achieved by series-connecting the primary ports of the two transmission lines TLXand TL2, and parallel-connecting their secondary ports. This approach can be generalized to N transmission lines TL - TLNas shown in FIG. 12D to achieve an arbitrary N: 1 voltage stepdown transformation ratio. Such step-down TLT networks can be particularly advantageous when having to operate at large primary port voltages in high-power RF applications under the constraints of low voltage-rated switches. For example, PSIM at high RF frequencies often relies on switch ports having fast GaN FETs with limited voltage handling capabilities.Attorney Docket No. 00777-WO

[0097] Similarly, by swapping the interconnections of the transmission lines, one can also implement voltage step-up (current step-down) TLT networks. In FIG. 12C for instance, by parallel-connecting the primary ports of transmission lines TL and TL2, and series connecting their secondary ports, the TLT network achieves 1 :2 voltage step-up (or 2: 1 current step-down). This approach can be generalized to N transmission lines as illustrated by FIG. 12E to realize an arbitrary primary -to-secondary voltage step-up (or current step-down) ratio of N. Such current step-down networks can be particularly useful when deploying PSIM in high-power, high-current matching applications.Embodiments of Modular PSIM Configurations

[0098] The previous section of this disclosure discussed modular PSIM architectures that support both half-wave and full-wave operation, offering reactance modulation in both ground-connected and floating configurations, with various implementation examples utilizing magnetic flux-coupled transformers and transmission-line transformers. This section presents various techniques and configurations for interconnecting and controlling multiple PSIM modules to achieve higher power levels, expanded reactance tuning range, operation in the HF and VHF ranges, and reduced switching harmonics. A TMN design example is provided for each case to illustrate the improved PSIM performance.Scaling PSIM for Operation at Higher Voltage / Current / Power Levels

[0099] As discussed above, conventional half-wave PSIM architectures have a limited RF power handling capability due to the breakdown voltage constraints of the PSIM switching devices. In these configurations, the peak voltage stress on the PSIM transistors scales with the square root of the RF power. The selection of switching devices, such as GaN FETs needed for high-frequency operations, further restricts the availability of high-voltage options, creating a bottleneck for power scaling. While various impedance scaling techniques have been proposed by literature to address these issues, they often prove cumbersome to implement and limit the TMN's tuning range. One potential solution could be stacking multiple half-wave PSIM coupling networks in series to handle higher voltages. However, this approach is impractical at RF frequencies due to the complexities of providing isolated and floating gate drive for the switches and ensuring uniform voltage distribution across all the PSIM coupling networks.Attorney Docket No. 00777-WO

[0100] One notable advantage of the modular PSIM architectures presented in FIGS. SA- 50 and 8A-8C is their isolated primary port and ground-referenced switches, allowing for easy interconnection of multiple PSIM modules. FIG. 13 illustrates an example architecture, comprising a series stack of k PSIM coupling networks, each implementing a primary-to- secondary voltage transformation ratio nT, achievable with either flux-coupled transformers or transmission-line transformers (TLTs) as discussed in the previous section. The secondary side switch ports in FIG. 13 are realized as a combination of nPFETs in parallel. The ability to independently select the transformation ratio, the number of PSIM coupling networks, and the number of paralleled FETs provides significant design flexibility for scaling the architecture to meet various voltage, current, and impedance requirements.

[0101] To illustrate the voltage, current and impedance scaling capability of the architecture in FIG. 13, consider that each FET used in realizing the PSIM switches has a peak voltage rating VSW,PKand peak current rating / SW,PK- Consequently, the peak rated voltage at the primary port Vy.PK scales linearly with the number of series-connected coupling networks k and the transformation ratio nT, as given by (2). Similarly, the peak current rating at the primary port scales linearly with the number of FETs nPin parallel and inversely with the transformation ratio as expressed by (3). Finally, the impedance presented at the primary port is the sum of the impedances of each of the PSIM coupling networks appropriately scaled by the transformation ratio according to (4).VX.PK —nr sw,PK (2)Tip h,PK=w.PK (3) nTZx = n^iZt (4)

[0102] To demonstrate the versatility of this architecture, a practical design example focused on power scaling within a tunable matching network (TMN) illustrating how the modular PSIM architecture in FIG. 13 can effectively meet high-power RF system requirements is discussed with respect to FIG. 14A.

[0103] In the example TMN design, based on an impedance step-up network shown in FIG. 14A with single shunt, half-wave PSIM actuator, L2and C2form a high-Q resonant tankAttorney Docket No. 00777-WO whose reactance can be effectively tuned by narrow band frequency adjustment, i.e. dynamic frequency tuning (DFT). Further, adjusting the duty cycle of the PSIM switch port modulates the shunt reactance seen at the PSIM. Hence, by appropriately controlling both the operating frequency and the PSIM switch duty cycle, one can achieve impedance transformation of the load impedance ZLto the desired 50 £1 impedance at the input port of the TMN. The input filter implemented with L and serves to provide filtering of P SIM-generated switching harmonics. The transmission-line transformer at the input of the match provides a fixed 4: 1 impedance transformation and steps down the 50 £1 TMN input impedance to 12.5 £1 - the impedance plane to which ZLis matched by the rest of the matching network. This fixed impedance transformation can help to scale down the voltage stress on the PSIM switch. However, a significant disadvantage of this approach is that it can severely limit the matching range of the TMN. For instance, in the design example shown in FIG. 14 A, the network can theoretically only match load resistances below 12.5 , which often falls short of the requirements for typical RF plasma applications.

[0104] The PSIM switch in the example design of FIG. 14A can be implemented with a single GaN FET (e.g., a 650 V GaN FET, model GS66516T by GAN SYSTEMS). Further, L = 370 nH, = 372 pF, L2= 709 nH, C2= 330 pF, L^= luH, although other values could be selected as suitable or desired. Simulated voltage and current waveforms are shown at the TMN input port (FIG. 14B) and across the PSIM switch (FIG. 14C) when delivering 500 W to a load impedance of ZLof 2 - j 20 £1 at 13.56 MHz and PSIM switch duty cycle of 0.70. As can be seen from FIG. 14B, at this operating power level, the peak primary PSIM voltage VpsiM across the switch reaches 450 V. To allow for a reasonable voltage safety margin, this is the largest peak voltage and power level the network of FIG. 14A can safely handle in practice. To achieve operation at higher power levels with this network and the half-wave PSIM architecture, one would either have to use a higher voltage-rated switch, which may be challenging due to current GaN technology constraints, or appropriately scale the network to operate at lower voltages at the cost of even further reduced matching range. Furthermore, notice that the large duty cycle of the switch introduces appreciable harmonic content in both the primary PSIM current iPSiM(FIG. 14C) and the input current qN(FIG. 14B).

[0105] As an alternative approach, the half-wave PSIM coupling network in FIG. 14A can be replaced with a full-wave, two-switch coupling network described with respect to FIG. 5 A, as shown in FIG. 15 A. To preserve the same matching range, each of the switch ports Q1Aand Q1Bare implemented with a parallel combination of two GaN FETs (e.g., two 650 VAttorney Docket No. 00777-WOGaN FETs, model GS66516T by GAN SYSTEMS). In this simulation, the PSIM transformer has a 1 : 1 turns ratio and 1 H magnetizing inductance. (Although practical transformer implementations may have some leakage inductance, it can be conveniently absorbed in the operation of PSIM or resonated out to provide additional filtering.) In the network architecture shown in FIG. 15 A, L = 370 nH, = 372 pF, L2= 709 nH, C2= 330 pF, L^= luH, although other values could be selected as suitable or desired. The two 650 V GaN FETs are connected in parallel for each of Q1Aand Q1B.

[0106] Simulated waveforms for the full-wave PSIM-based design show the voltages across the FETs (FIG. 15B), the voltage and current at the TMN input port (FIG. 15C) and the primary PSIM voltage and current (vPSiMand iPSiM) across the PSIM module (FIG. 15D) when delivering 2000 W to the same load impedance ZLof 2 - j 20 £1 as in the case of FIG. 14A. Impedance matching to 50 £1 is achieved at 13.56 MHz with switch ports Q1Aand Q1Boperated 180° out-of-phase and with identical duty cycle of approximately 0.70. Note from FIG. 15B that the peak voltage across the FETs vQ1Band vQ1Aat 2000 W is similar to the peak voltage across the FET in FIG. 14A at 500 W. That is, the full-wave PSIM architecture in FIG. 15A has 4x the power handling capability of the half-wave PSIM implementation of FIG. 14A for the same peak voltage / current stress on the switches.

[0107] Furthermore, the complimentary operation and differential combining of the switches eliminates even harmonics in the PSIM voltage as indicated by the bipolar symmetry of the VPSIM waveform in FIG. 15D. This considerably reduces the harmonic content in both the PSIM current IPSIM (FIG. 15D) and TMN input current ijN(FIG. 15C) compared to the half-wave PSIM implementation of FIG. 14A.

[0108] The notion of modular PSIM architectures presented in the previous section can be applied to the design in FIG. 15A to further increase the power handling capability of PSIM-based TMNs. To illustrate this, in FIG. 16A the PSIM module is implemented as a series-stacked combination of two full-wave PSIM coupling networks (e.g., the four-switch coupling network described with respect to FIG. 5B). Switches Q1A, Q1B, Q2Aand Q2Bare each implemented with a parallel combination of four GaN FETs (e.g., four 650 V GaN FETs, model GS66516T by GAN SYSTEMS GS66516T) to provide the same PSIM reactance tune range as in the case of FIGS. 14A and 15 A. In the network architecture shown in FIG. 16A, L = 370 nH, = 372 pF, L2= 709 nH, C2= 330 pF, L^= luH, although other values could be selected as suitable or desired. Simulated FET voltage waveforms (FIG.Attorney Docket No. 00777-WO16B), TMN input current and voltage waveforms (FIG. 16C) and PSIM voltage and current waveforms (FIG. 16D) are shown when operating at 13.56 MHz and delivering 8 kW to a load impedance ZLof 2 - j 20 £1. The two switches in each of the PSIM coupling networks are operated 180° out-of-phase with identical duty cycle of approximately 0.70. Comparing FET voltage waveforms in FIGS. 14C and 16B demonstrates that the series-stacked PSIM design of FIG. 16A has 16x the power handling capability of the half-wave PSIM-based design in FIG. 14A for the same peak voltage / current stress on the switches.

[0109] As the examples above demonstrate, the modular PSIM architectures presented in the previous section offer significant advantages for high-power TMN design. Their ability to be easily interconnected and series-stacked facilitates the construction of robust, high-power PSIM-based TMNs while effectively reducing voltage stress on the switching devices. This modularity not only enhances the scalability of the system but also improves its overall performance and reliability, making it well-suited for demanding RF applications.Modular PSIM Configurations for Scaling Tune Range

[0110] As mentioned previously, the basic PSIM coupling network, whether operated in half-wave (FIGS. 1 A and IB) or full-wave (FIGS. 2A and 2B) switching mode, theoretically offers infinite reactance modulation range by adjusting the switch duty cycle from 0% (permanently off) to 100% (permanently on). In practice, however, the modulation range is often limited by switching harmonics and power dissipation in the PSIM switch ports. This latter issue is discussed in this subsection, describing how the proposed modular PSIM architectures can dramatically expand the achievable PSIM modulation range, thereby also enhancing the TMN matching range. The following subsection will focus on modular PSIM control techniques for mitigating switching harmonics.[OHl] Consider again the TMN design example from the previous section (FIG. 17), which is based on an impedance step-up network transforming a load impedance ZLto 50 at the input port of the match. As previously mentioned, the network utilizes a frequency- tuned series reactance, formed by the L2-C2resonant tank, and a shunt PSIM module whose reactance is adjusted by varying the duty cycle of the PSIM switches. In addition, the network in FIG. 17 incorporates a capacitor Cxin series with the PSIM module. This capacitor sets the maximum attainable capacitance of the entire shunt branch when the PSIM module is shorted, i.e., when the PSIM switches are permanently on (100% duty cycle).Including Cxin series with the PSIM module reduces the voltage stress on the switches andAttorney Docket No. 00777-WO limits the peak current stress when operating at the full modulation range, up to 100% switch duty cycle.

[0112] Example design of an impedance step-up TMN for 13.56 MHz RF plasma applications incorporating dynamic frequency tuning (DFT) tank formed by L2— C2, a tunable shunt reactance PSIM module in series with a voltage-dividing capacitor Cx, input filter formed by L — C , and 4: 1 transmission-line transformer.

[0113] Suppose that the shunt PSIM module in FIG. 17 is implemented with the halfwave switching network of FIG. 18 A. The resulting range of load impedance ZLthat can be matched to a TMN input impedance ZINof 50 fl is shown in FIG. 19A corresponding to 12.88 MHz - 14.24 MHz frequency tuning range, and 0 % (PSIM switch permanently off) to 100 % (PSIM switch permanently on) duty cycle modulation. In this example the network is implemented with L2= 650 nH, C2= 330 pF, Cx= 3 nF, and no input filter, i.e. (Lx- is shorted). In this example, Cocan be 1.5 nF to model the FET output capacitance in addition to any externally-added capacitance in parallel with the switch. As can be seen from FIG. 19A, the load impedance region spans approximately 1 fl - 6 fl in resistance and nearly 10 fl in total reactive range. As FIG. 19A suggests, for every load impedance point, there is a particular combination of PSIM switch duty cycle and frequency that is required for matching the load to 50 fl. Duty cycle modulation handles most of the resistive load range, while frequency tuning compensates for load reactance as indicated by the frequency (dashed, curved) and duty cycle (solid, generally vertical though slightly inclined) contour lines. The matching range in FIG. 19A may not be wide enough, particularly in resistive range; many RF plasma processes would require operation over at least 1 fl - 10 fl resistive range. (The reactive range, on the other hand, can be easily shifted or extended by changing the tank resonant frequency or characteristic impedance.)

[0114] The duty cycle contours in FIG. 19A show that the required switch duty cycle to match a specific load impedance to 50 £1 is inversely related to the load's resistive component. The minimum resistance bound of the load region corresponds to the maximum switch duty cycle (100% in this example) and thus the maximum shunt branch capacitance. The shunt branch capacitance in FIG. 17 consists of the series combination of Cxand the effective PSIM capacitance, where at a 100% duty cycle (PSIM module shorted), the shunt branch capacitance equals Cx. Conversely, the maximum resistance bound is determined by the minimum switch duty cycle, corresponding to the minimum PSIM branch capacitance.Attorney Docket No. 00777-WO

[0115] Thus, to extend the load range to higher resistances, one has to reduce the Cobase capacitance in the half-wave PSIM module of FIG. 18A by either decreasing the number of FETs in parallel, or by using transistors with less output capacitance. However, both of these approaches result in increased switching device stress and power loss which may not be an option given practical thermal management constraints. In the former case, less devices in parallel implies higher current stress per device for a given load impedance and output power, while in the latter case, devices with smaller output capacitance implies higher FET on- resistance (for a given device technology) and higher power losses.

[0116] One possible approach for extending tune range without increasing device stresses is by employing the modular PSIM architectures presented in the previous section. For example, consider implementing the PSIM module in FIG. 17 with the full-wave, two- switch port PSIM coupling network of FIG. 18B. The switch ports Q1Aand Q1Bare implemented identically to Q in FIG. 20A with same base capacitance Coof 1.5 nF and are operated 180° out-of-phase with the same duty cycle. The transformer coupling the primary PSIM port to the switches has 1 : 1 turns ratio in this example, although other turns ratios may be implemented.

[0117] Now consider device stresses: for the same PSIM port voltage and current, the peak voltage and current stress on switch ports Q (FIG. 18 A) and Q1A, Q1B(FIG. 18B) are identical since all FETs block the same peak voltage and conduct the same peak current. However, the minimum equivalent capacitance seen at the PSIM port of the full-wave module (FIG. 18B) when switch duty cycle is 0 % (both FETs are off) is the series combination of their output capacitances, i.e. C 12. This is half the minimum capacitance of the half-wave PSIM coupling network in FIG. 18 A. Consequently, the TMN with the fullwave PSIM module of FIG. 18B has a significantly expanded load impedance matching range as shown by FIG. 19B, with a resistance range more than 50% greater than the halfwave PSIM implementation.

[0118] This approach can be generalized by series-combining multiple full-wave PSIM coupling networks to further reduce the minimum PSIM capacitance and expand the tuning range for given switching device stresses. For instance, FIG. 18C shows a PSIM implementation based on series-combining two of the networks from FIG. 18B. For the same switch implementation as in FIGS. 18A and 18B, the four-switch port coupling network in FIG. 18C exhibits identical switch stresses while achieving Co / 4 minimum PSIM capacitance. The dramatically expanded load impedance matching range corresponding toAttorney Docket No. 00777-WO this PSIM module implementation is shown in FIG. 19C, offering more than twice the resistance range compared to its half-wave PSIM counterpart.

[0119] Note that due to the 4: 1 transmission-line transformer (TLT) at the input of the TMN example design in FIG. 17 and its impedance step-up architecture, the load impedance matching range of the TMN is theoretically limited to a maximum resistance of 12.5 fl. As previously mentioned, impedance scaling stages, such as the TLT in this case, are often employed to reduce voltage stress on the switching devices at the expense of limiting matching range. However, by employing the proposed modular multiport PSIM architectures, one can simultaneously reduce device stresses and expand the tuning range, eliminating the need for impedance scaling TLTs.PSIM Interleaving and Multiplexing for Operation at Higher Frequencies

[0120] As mentioned above, previously-proposed and demonstrated PSIM implementations rely on switching the transistors at the RF operating frequency, limiting PSIM use beyond the HF range due to transistor driving and switching speed constraints. However, many RF plasma applications would greatly benefit from fast PSIM-based TMN systems capable of operating at VHF frequencies. This section introduces the techniques of interleaving and multiplexing of submodules, enabling the implementation of the reactance elements for HF and VHF operation while switching the switches at a subharmonic of the operating frequency. The section details these techniques, and design examples demonstrate their utility in implementing PSIM modules in, for example, 27 MHz and 60 MHz applications.

[0121] To illustrate these techniques, consider the multiport PSIM coupling network in FIG. 20A comprising a series-connected stack of two PSIM submodules A and B with switches Q1A- Q4Aand Q1B- Q4B, respectively. In this example embodiment, the submodules are coupled to the primary port with 1 : 1 turns ratio transformers, though in general, transformers with any desired or suitable turns ratios may be employed. Shown explicitly for the purpose of this discussion, however, the transistors in each of the FET pairs Q1A / Q2A, QZA / QAA, QIB / Q2B, and Q3B / Q4B are connected in parallel. (In general, a design may comprise more devices in parallel.) As described below, both techniques of interleaving and multiplexing rely on operating each PSIM switch for only some of the RF cycles. Essentially, different RF cycles are handled by different switches or PSIM coupling networks, thereby effectively scaling down the switching frequency. In essence, multiplexingAttorney Docket No. 00777-WO relates to the time-domain distribution of RF cycles among switches connected in parallel, while interleaving relates to the time-domain distribution of RF cycles among different PSIM submodules.Interleaving of PSIM Modules

[0122] To illustrate the notion of interleaving, consider FIG. 20B showing conceptual voltage and current waveforms and switch control signals when interleaving PSIM submodules A and B in FIG. 20A. As shown by the switch control signals, switches in a given parallel combination are operated identically. However, each of the PSIM submodules is only actively switched every other RF cycle, and it is shorted when inactive. That is, during one RF cycle, submodule A is operated in a full-wave mode and submodule B is shorted Q1B- Q4Bare kept on), and vice-versa during the next RF cycle, as illustrated by the drain voltage waveforms vswlp, vswlnfor submodule A and vsw2p, vsw2nfor submodule B. This mode of interleaved operation achieves modulation of the effective reactance seen at the PSIM input port directly at the RF carrier frequency by adjusting the duty cycle of the PSIM switches and switching them at the second subharmonic. In other words, each of the FETs in FIG. 20A turns on and off only once every two RF cycles, effectively reducing the switching frequency by a factor of two.

[0123] FIGS. 21A and 21B illustrate the interleaved operation of PSIM submodules A and B from FIG. 20A at 27.12 MHz, showing two RF cycles of simulated voltage and current waveforms (FIG. 2 IB) and PSIM switch control signals (FIG. ). In this example, each PSIM switch in submodules A and B is modeled as a GaN FET (e.g., aforementioned model GS66516T), though any other desired or suitable FET may be used. In this simulation, the PSIM primary port is driven by a sinusoidal current source at 27.12 MHz, while the switches operate at 13.56 MHz. As shown by the FET drain voltage waveforms in FIG. 2 IB, submodule A is full -wave- switched during the first RF cycle and shorted during the second, while submodule B is shorted during the first cycle and full-wave-switched during the second. The resulting primary port RF voltage vRFhas a fundamental frequency of 27.12 MHz and lags the current iRFby 90 degrees, as would be expected from a capacitive PSIM reactance element.

[0124] The example discussed above demonstrates interleaving two PSIM submodules, allowing switch operation at half the RF frequency. The concept of interleaving can beAttorney Docket No. 00777-WO extended to more than two PSIM submodules, enabling an even greater reduction in switching frequency. However, a drawback of this approach is the increased voltage stress of the switches. Since only one submodule is active at a time (with the others shorted), the switches in the active submodule must be able to withstand the peak RF voltage at the primary port.Multiplexing of Switching Devices

[0125] In contrast to interleaving, the technique of multiplexing allows for switching at a subharmonic of the RF operating frequency by distributing RF cycles among different parallel-connected switches, i.e. time-domain multiplexing of switches in a given parallel- connected group. Voltage and current waveforms and switch control signals in FIG. 20C illustrate conceptually the switch multiplexed operation for the example design of FIG. 20 A. As can be seen from the switch control signals q1A- q4Aand the drain voltage waveforms vswlp,vswin, switches Q1Aand Q3Aare full-wave switched during the first RF cycle while keeping Q2Aand Q4Aoff. During the next RF cycle, Q1Aand Q3Aare kept off, while fullwave switching Q2Aand Q4A. The switches in submodule B are operated in a similar manner in phase with the respective switches in submodule A. Analogous to interleaving, switch multiplexing also enables modulation of the effective reactance seen into the PSIM input port at the RF frequency while operating the switches at half that frequency.

[0126] Multiplexed operation of the network in FIG. 20A is simulated at 27.12 MHz, with FIG. 21 A showing the PSIM switch control signals and FIG. 2 IB showing the voltage and current waveforms at the primary port and across the switches for two RF cycles. Each PSIM switch in submodules A and B is modeled as a GaN FET (e.g., aforementioned model GS66516T). As can be seen from the switch control signals, each switch is turned on and off only once every two RF cycles, effectively operating at half the RF frequency. Also notice that corresponding switches in submodules A and B are operated identically, resulting in the respective drain voltages vswlp, vsw2pand vswln, vsw2nbeing in phase. Notice that even though the switch control signals in the multiplexed mode of operation (FIG. 22A) look very different from those in interleaved operation (FIG. 21 A) in terms of duty cycle, both operating schemes achieve identical primary port voltage waveforms for the same RF current excitation while switching devices at half the RF frequency. This demonstrates that both interleaving and multiplexing can achieve the same effective reactance modulation at theAttorney Docket No. 00777-WOPSIM primary port at a subharmonic switching frequency, despite the differing switch control duty cycles. This variation in duty cycles arises because interleaving disables a network by turning all its switches on, whereas multiplexing disables switches by turning them off.

[0127] This example demonstrates time-domain multiplexing of two parallel-connected switches, allowing switch operation at half the RF frequency. The concept of multiplexing can be extended to multiple switches in parallel, enabling an even greater reduction in switching frequency. However, a drawback of this approach is the increased current stress on each switch. Since only one switch conducts at a time in a given parallel-connected group, the current stress per switch is higher, requiring the switches to be rated for the peak RF current.Interleaving of PSIM Modules with Switch Multiplexing

[0128] The examples in FIGS. 21 A, 21B, 22A and 22B demonstrate that both interleaving of PSIM submodules and multiplexing of parallel-connected switches can be employed to reduce switching frequency. Multiplexing increases system complexity, as multiple PSIM submodules must be series-stacked, and it leads to increased switch voltage stress proportional to the frequency scaling (or interleaving) factor. On the other hand, switch multiplexing may be simpler to implement but comes with increased switch current stress proportional to the multiplexing factor. A balanced approach to achieve larger switching frequency reduction while alleviating overall system complexity and switch stresses is to employ both interleaving and switch multiplexing simultaneously.

[0129] Simulation waveforms using both interleaving and switch multiplexing for VHF operation are shown in FIG. 23 A (showing PSIM switch control signals) and FIG. 23B (showing simulated voltage and current waveforms). This simulation is based on the example PSIM coupling network design of FIG. 20A, with all switches modeled as 650 V GaN FETs (GS66516T, GaN Systems) driven by a sinusoidal current source at 54.24 MHz. As indicated by the 90° phase shift between the RF voltage vRFand current iRFwaveforms at the primary port, the network behaves as a capacitive reactance at the 54.24 MHz operating frequency while switches are operated at 13.56 MHz — a quarter reduction in switching frequency. A factor of two reduction in frequency is achieved by interleaving PSIM submodules A and B, and an additional factor of two reduction comes from multiplexing the two parallel-connected switches in each submodule. The effective capacitance can be modulated by appropriatelyAttorney Docket No. 00777-WO adjusting the duty cycle and phase of the switches. This example demonstrates that PSIM- based reactance modulation in HF and VHF applications can be achieved by employing interleaving and multiplexing techniques to allow switching at a much lower, practically- feasible frequency.Control Techniques for Reducing PSIM-generated Switching Harmonics

[0130] Both half-wave PSIM (FIGS. 1 A and IB) and full-wave PSIM (FIGS. 2A and 2B) operating modes can generate significant switching harmonics, especially when operating at large switch duty cycles and high reactance modulation ratios. Although fullwave PSIM eliminates even harmonics and results in significantly less harmonic content compared to half-wave PSIM at small duty cycles, the content of odd harmonics increases rapidly for reactance modulation ratios beyond 4-5x. High switching harmonics severely restrict the achievable PSIM reactance modulation range and pose significant challenges to the performance of PSIM-based TMN systems. These challenges include higher voltage and current stresses on the switches, increased switching losses, control loop instabilities, and the leakage of undesired harmonics into the RF generator and load (e.g., a plasma processing chamber). This section presents a control technique based on the series-stacked modular PSIM architecture discussed above, which dramatically reduces PSIM switching harmonics over a very wide reactance modulation range.

[0131] Consider the series-stacked PSIM architecture in FIG. 24A, which combines N full-wave PSIM modules with their primary ports connected in series. Each module includes two switches, Qkland Qk2, operated with a duty cycle Dkand coupled to the primary side of the network via a transformer with nkprimary-to-secondary turn ratio, where subscript k refers to the fcth module. The switches have a base capacitance wfcC0, where wkis some weighting factor. The base capacitance refers to the total output capacitance of a switch, including any additional external capacitance in parallel. The effective PSIM capacitance Cxseen looking into the primary port of the network is then given by the series combination of the effective PSIM capacitances of all N modules according to (2), where (Dk) is the PSIM modulation factor and is a function of the switch duty cycle Dkfor a given module k.Attorney Docket No. 00777-WO

[0132] The PSIM modulation factor (£)) is defined as the ratio of the PSIM effective capacitance at some switch duty cycle D to the base capacitance (that is the PSIM effective capacitance with 0 % duty cycle) seen looking into the ideal PSIM switched networks of FIGS. 1 A and IB (half-wave) and FIGS. 2A and 2B (full-wave). For example, under the ideal conditions of sinusoidal current excitation and linear capacitance Co, the modulation factor is given by equation (1). As discussed previously and as illustrated in Fig. 3, is unity when duty cycle is zero, and approaches infinity as duty cycle approaches unity, that is Um M(D) = 1 and Hm J f(D) -> oo. PSIM switching harmonics generally increase with increasing modulation factor as FIG. 3B illustrates.

[0133] As discussed above in the sections on power and impedance scaling, one control approach for the architecture in FIG. 24A is to operate the switches in all modules with the same duty cycle, that is D = D2= ••• = DN= D. This results in uniform distribution of voltage stresses among all the switching devices and the same modulation factor for all modules. Consequently, the expression for the effective PSIM capacitance Cxcan be simplified to equation (6), suggesting that Cxcan only be controlled by adjusting the modulation factor . Large capacitance modulation would imply the need for large switch duty cycle, and hence high switching harmonics. Although this control approach may be simpler to realize in practice, high PSIM switching harmonics can severely limit the achievable capacitance modulation range.

[0134] Here, an alternative control approach that combines both continuous and discrete capacitance modulation to significantly reduce switching harmonics over a very wide reactance modulation range. Continuous modulation is achieved by operating multiple PSIM submodules but at least two PSIM submodules are operated at different switch duty cycles,Attorney Docket No. 00777-WO while discrete modulation is implemented by enabling or disabling the operation of particular PSIM submodules. To illustrate this approach, consider the modular PSIM architecture of FIG. 24A, where each submodule k (where k is an integer from 1 to N) operates with a switch duty cycle Dk. FIG. 24B illustrates the proposed control scheme for the duty cycle of the switches in each PSIM module as a function of the desired total effective capacitance Cxseen at the PSIM primary port of the network. To achieve a desired Cxcapacitance, the network is configured to operate in one of the N discrete capacitance ranges by disabling some of the PSIM modules (discrete modulation) and simultaneously employing a small amount of PSIM modulation (continuous modulation) by adjusting switch duty cycle.

[0135] As FIG. 24B illustrates in more detail, one can think of the entire capacitance Cxmodulation range comprising N discrete ranges R — RN. A given capacitance range RKcorresponds to the first K modules being active with their switches operated with the same duty cycle, while the rest of the modules, that is module K + 1 through module N, being inactive. (When a module is inactive, its switches are permanently turned on shorting its secondary winding.) Each range RKstarts at minimum effective capacitance of CKcorresponding to operating all active modules with 0 % zero duty cycle, i.e., PSIM modulation factor of unity. One can think of CKas the base capacitance corresponding to range RKwhich can be modulated by adjusting the duty cycle of the active PSIM switches. CKcan be expressed as the series equivalent capacitance of all the active module base capacitances as given by (7), where Cois some normalizing capacitance, nkis the primary -to- secondary transformer turns ratio, and wkis some weighting factor to be discussed in greater detail below.

[0136] For example, the architecture in FIG. 24A comprises N PSIM modules, and hence has N discrete capacitance ranges as shown in FIG. 24B, with range N starting at a minimum capacitance of CN, range N — 1 starting atetc., with CN< CN-< ••• < C2< . Note that the starting capacitance of each range increases as the number of disabled (shorted) modules increases since there are effectively less capacitance elements in series.Attorney Docket No. 00777-WO

[0137] In FIG. 24B, starting at the minimum boundary of the Cxdynamic range, CNrepresents the base capacitance corresponding to the lowest range 7?w; increasing the duty cycle of the active PSIM switches in this range modulates CNand raises the effective capacitance Cxat the network’s input port. When the duty cycle reaches a maximum threshold dmax, the input capacitance Cxequals the starting capacitance CN-of the next range RN-, that is CN-=. At this point, the network switches to the next discrete range RN- by disabling module N, and resetting the active switches’ duty cycle to zero. Increasing the duty cycle again cause Cxto increase beyond CN-until it reaches Cw-2, the start of the next discrete capacitance range. The network is then reconfigured into the RN-2 range, and so on. Thus, one can traverse through the entire dynamic range of Cxby employing both discrete and continuous capacitance modulation.

[0138] This control strategy minimizes the required PSIM modulation factor and switch duty cycle in any given range, thereby reducing PSIM switching harmonics. To maintain the same maximum duty cycle threshold dmaxacross all ranges, the base capacitances - CNmust be distributed in a geometric series along the Cxdynamic range, according to (8), where and C.MINarethe maximum and minimum bounds of the desired Cxdynamic range.This geometric distribution can be achieved by appropriately selecting the weighting factor wkfor each PSIM module in FIG. 24A according to (9), where the geometric series step y is defined in (8).

[0139] From equation (8), as the number N of series-stacked PSIM modules increases, the ratio y of base capacitances between two consecutive discrete ranges decreases, reducing the maximum PSIM switch duty cycle dmaxrequired in any given range. This means that dividing the desired dynamic capacitance range Cxinto more discrete ranges lessens the PSIM modulation needed in each range, thus lowering switching harmonics. Therefore, by increasing the number N of series-stacked PSIM modules, as shown in FIG. 24A, the PSIM-Attorney Docket No. 00777-WO generated switching harmonics can be reduced to an arbitrary level for a given capacitance dynamic range, albeit at the cost of increased architectural complexity.

[0140] To demonstrate the feasibility of the proposed control approach, consider an example design based on the series-stacked modular PSIM architecture of FIG. 24A, which operates over a 100: 1 capacitance modulation range. We explore the performance of four implementations with varying numbers of series-stacked modules. The base capacitances for each module are selected according to equations (8) and (9). FIG. 25A displays the PSIM switch duty cycle and the resulting total harmonic distortion (THD) of the switch voltage waveforms across the normalized PSIM capacitance Cxat the network's input port for designs using 1, 2, 4, and 6 series-stacked PSIM modules. FIG. 25B shows the corresponding distribution of discrete capacitance ranges for each of the four designs and highlights the active PSIM modules (shaded ) within each range.

[0141] With a single PSIM module, the entire capacitance dynamic range is handled by varying the switch duty cycle over a 0% to 90% range, causing significant harmonic distortion and a peak THD of approximately 80%. In contrast, using two PSIM modules introduces two discrete capacitance ranges, each providing a factor of 10 modulation. Consequently, the peak switch duty cycle required drops below 80%, reducing the peak THD to around 50% in each range. Increasing to four and six series-stacked PSIM modules further reduces the necessary duty cycle modulation range and harmonic distortion. With six modules, for example, the PSIM modulation requires no more than 50% switch duty cycle, resulting in a peak THD of less than 10%. Comparatively, a 10% THD in a single-module design would achieve less than a 3 : 1 capacitance modulation range. Thus, the six-module design offers over a 3 Ox wider capacitance modulation range than the single-module design for the same peak THD.

[0142] The modular PSIM architectures and control techniques described above may be integrated into complete tunable matching network (TMN) for practical RF applications. FIG. 26 illustrates a block diagram of such a TMN, showing how the PSIM modules interface with control circuitry, sensing components, and external systems to achieve dynamic impedance matching between a power source and a load. Referring to FIG. 26, the tunable matching network (TMN) may incorporate a PSIM system according to various embodiments of the present invention, exemplarily described above. The TMN can be electrically connected between the power source and the load in the same manner as illustrated in and described with respect to FIGS. 15A, 16A and 17 (i.e., via a shunt connection between the powerAttorney Docket No. 00777-WO source and the load). However, the TMN can be electrically connected in parallel between the power source and the load.

[0143] The PSIM system includes a PSIM module having a PSIM input port and X number of PSIM submodules, where X may be an integer greater than or equal to 1. Each PSIM submodule includes N number of input ports and M number of switch ports, where N may be an integer greater than or equal to 1 and M may be an integer greater than or equal to 2. Each PSIM submodule is coupled to the PSIM input port through a transformer, which may be implemented as a magnetic flux-coupled transformer or a transmission line transformer as described herein. It should be appreciated that each PSIM submodule can be provided as exemplarily described with respect to any of the embodiments above.

[0144] The system further comprises a local controller operatively connected to the PSIM module. The local controller may include a processing unit configured to execute instructions stored in a memory module to perform control functions for the PSIM system. The processing unit may comprise one or more microprocessors, microcontrollers, digital signal processors, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), or other suitable processing devices. The memory module may comprise volatile memory such as random access memory (RAM), non-volatile memory such as readonly memory (ROM), flash memory, solid-state drives, magnetic hard drives, or other computer-readable storage media. The instructions stored in the memory module, when executed by the processing unit, cause the local controller to generate control signals for switches coupled to each PSIM submodule to modulate an effective reactance seen at the PSIM input port by controlling at least one of a duty cycle and a phase of each switch and effectuate any of the control techniques discussed above.

[0145] The system includes PWM generation and driving circuitry operatively connected to the switches within the PSIM submodules. The PWM generation and driving circuitry may be configured to synthesize drive signals for each switch with appropriate duty cycle and phase synchronized to an external reference signal. The PWM generation and driving circuitry receives control commands from the local controller and generates corresponding gate drive signals suitable for operating the switches, which may be implemented as fieldeffect transistors (FETs), insulated-gate bipolar transistors (IGBTs), or other suitable switching devices. The drive signals may be isolated and level-shifted as necessary to provide proper voltage levels for controlling the switches in ground-referenced or floating configurations.Attorney Docket No. 00777-WO

[0146] A ZVS / ZCS sensing and monitoring block is operatively connected to each PSIM submodule to monitor switching conditions therein. The sensing and monitoring block may include voltage sensing circuits, current sensing circuits, or both, configured to detect zerovoltage switching (ZVS) or zero-current switching (ZCS) conditions at the switches. The sensing and monitoring block provides feedback signals to the local controller indicating the switching conditions, enabling the local controller to adjust the control signals to maintain soft-switching operation. The local controller may implement control algorithms that process the feedback signals and adjust at least one of the duty cycle, phase, and timing of the switch control signals to optimize switching performance and minimize switching losses.

[0147] An external controller may be operatively connected to the local controller to provide higher-level control functions. The external controller may communicate with the local controller through wired or wireless communication interfaces supporting various communication protocols. The external controller may receive information from the local controller regarding the operating state of the PSIM system, including effective reactance values, switching conditions, and performance metrics. The external controller may also send commands to the local controller to adjust the operation of the PSIM system based on system-level requirements, such as impedance matching targets, power delivery requirements, or load conditions. The external controller may interface with one or more external systems associated with the power source or load, such as an RF generator or a plasma processing chamber, to coordinate the operation of the TMN system with other system components and achieve desired impedance matching and power delivery performance.

[0148] The foregoing is illustrative of embodiments and examples of the invention and is not to be construed as limiting thereof. Although a few specific embodiments and examples have been described with reference to the drawings, those skilled in the art will readily appreciate that many modifications to the disclosed embodiments and examples, as well as other embodiments, are possible without materially departing from the novel teachings and advantages of the invention. Accordingly, all such modifications are intended to be included within the scope of the invention as defined in the claims. For example, skilled persons will appreciate that the subject matter of any sentence, paragraph, example or embodiment can be combined with subject matter of some or all of the other sentences, paragraphs, examples or embodiments, except where such combinations are mutually exclusive. The scope of theAttorney Docket No. 00777-WO present invention should, therefore, be determined by the following claims, with equivalents of the claims to be included therein.

Claims

Attorney Docket No. 00777-WOCLAIMS1. A phase-switched impedance modulation (PSIM) system for use within a tunable matching network, the system comprising: a primary port configured to receive an RF signal; at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof; at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer; a switch connected to each of plurality of reactive elements; and a controller configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.

2. The system of claim 1, wherein the at least one transformer is a magnetic flux- coupled transformer.

3. The system of claim 1, wherein the at least one transformer is a transmission line transformer.

4. The system of claim 1, wherein the at least one transformer comprises a plurality of transformers.

5. The system of claim 4, wherein transformation ratios of at least two of the plurality of transformers are different from one another.

6. The system of claim 4, wherein transformation ratios of at least two of the plurality of transformers are the same.

7. The system of claim 1, wherein at least one of the plurality of reactive elements includes a capacitor.

8. The system of claim 1, wherein at least one of the plurality of reactive elements includes an inductor.Attorney Docket No. 00777-WO9. The system of claim 1, wherein the controller is configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing at least two of the plurality of switches to be operated at different duty cycles.

10. The system of claim 1, wherein the controller is configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing only one switch of the plurality of switches of the at least one submodule to be operated during an RF cycle of the RF signal.

11. The system of claim 1, wherein the at least one submodule includes a plurality of submodules.

12. The system of claim 11, wherein at least two of the plurality of submodules are electrically coupled to one another.

13. The system of claim 11, wherein at least two of the plurality of submodules are magnetically coupled to one another.

14. The system of claim 11, wherein the controller is configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing at least one of the plurality of switches of only one of the plurality of submodules to be operated during an RF cycle of the RF signal.

15. The system of claim 11, wherein the controller is configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing switches of different submodules of the plurality of submodules to be operated at different duty cycles.

16. The system of claim 11, wherein the controller is configured to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing switches of less than all of the plurality of submodules to be operated during a period of time.Attorney Docket No. 00777-WO17. A method of controlling a phase-switched impedance modulation (PSIM) system for use within a tunable matching network, the system comprising a primary port configured to receive an RF signal, at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof, at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer, a switch connected to each of the plurality of reactive elements, and a controller, the method comprising: generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.

18. The method of claim 17, wherein generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port comprises causing at least two of the plurality of switches to be operated at different duty cycles.

19. The method of claim 17, wherein generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port comprises causing only one switch of the plurality of switches of the at least one submodule to be operated during an RF cycle of the RF signal.

20. The method of claim 17, wherein the at least one submodule includes a plurality of submodules; and generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port comprises causing at least one of the plurality of switches of only one of the plurality of submodules to be operated during an RF cycle of the RF signal.

21. The method of claim 17, wherein the at least one submodule includes a plurality of submodules; andAttorney Docket No. 00777-WO generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port comprises causing switches of different submodules of the plurality of submodules to be operated at different duty cycles.

22. The method of claim 17, wherein the at least one submodule includes a plurality of submodules; and generating control signals for the plurality of switches to modulate an effective reactance seen at the primary port comprises causing switches of less than all of the plurality of submodules to be operated during a period of time.

23. A non-transitory computer-readable medium storing instructions that, when executed by a processor of a controller in a phase-switched impedance modulation (PSIM) system for use within a tunable matching network, the system comprising a primary port configured to receive an RF signal, at least one transformer having a primary side and a secondary side, wherein the primary port is connected to the at least one transformer at the primary side thereof, at least one submodule comprising a plurality of reactive elements coupled to the at least one transformer, and a switch connected to each of the plurality of reactive elements, cause the processor to: generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by controlling at least one selected from the group consisting of a duty cycle and a phase of each of the plurality of switches.

24. The non-transitory computer-readable medium of claim 23, wherein the instructions cause the processor to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing at least two of the plurality of switches to be operated at different duty cycles.

25. The non-transitory computer-readable medium of claim 23, wherein the instructions cause the processor to generate control signals for the plurality of switches to modulate anAttorney Docket No. 00777-WO effective reactance seen at the primary port by causing only one switch of the plurality of switches of the at least one submodule to be operated during an RF cycle of the RF signal.

26. The non-transitory computer-readable medium of claim 23, wherein the at least one submodule includes a plurality of submodules; and the instructions cause the processor to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing at least one of the plurality of switches of only one of the plurality of submodules to be operated during an RF cycle of the RF signal.

27. The non-transitory computer-readable medium of claim 23, wherein the at least one submodule includes a plurality of submodules; and the instructions cause the processor to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing switches of different submodules of the plurality of submodules to be operated at different duty cycles.

28. The non-transitory computer-readable medium of claim 23, wherein the at least one submodule includes a plurality of submodules; and the instructions cause the processor to generate control signals for the plurality of switches to modulate an effective reactance seen at the primary port by causing switches of less than all of the plurality of submodules to be operated during a period of time.

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