This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics Tunable Matching Networks based on Phase- Switched Impedance Modulation1 Alexander S. Jurkov Aaron Radomski David J. Perreault MKS Instruments, Inc. MKS Instruments, Inc. Massachusetts Institute of Rochester, NY Rochester, NY Technology Cambridge, MA Abstract—The ability to provide accurate, rapid and controlled externally to dynamically match the load impedance dynamically-controlled impedance matching offers significant to a desired input impedance. Based on the technology advantages to a wide range of present and emerging radio- employed for realizing the variable reactance elements, frequency (RF) power applications. This work develops a new type conventional TMNs can be classified as either analog of tunable matching network (TMN) that enables a combination (continuously adjustable) or digital (adjustable among a set of of much faster and more accurate impedance matching than is discrete values). (Here we characterize the tuning mechanism available with conventional techniques, and is suitable for use at itself, neglecting the fine-scale discretization that may be high power levels. This implementation is based on a narrow-band imposed by the control system.) The former group of TMNs technique, termed here phase-switched impedance modulation relies on variable reactance elements whose impedance can be (PSIM), which entails the switching of passive elements at the RF tuned in an (ideally) continuous manner. For instance, operating frequency, effectively modulating their impedances. The conventional high-power RF plasma drives often employ TMNs proposed approach provides absorption of device parasitics and zero-voltage switching (ZVS) of the active devices, and we based on mechanically adjusting physical passive components, introduce control techniques that enable ZVS operation to be such as by using stepper-motor-adjusted variable-vacuum maintained across operating conditions. A prototype PSIM-based capacitors [18]. While widespread, this technique is TMN is developed that provides a 50 Ohm match over a load extraordinarily slow. Faster response can be obtained by impedance range suitable for inductively-coupled plasma appropriately adjusting bias conditions of electronic processes. The prototype TMN operates at frequencies centered components such as varactors [8] or MEMS-varactors [9]. around 13.56 MHz at input RF power levels of up to 200 W. Nevertheless, power handling with such components is Keywords—tunable matching network, antenna tuning unit, somewhat limited by the relatively high bias voltages required impedance matching, switched capacitor, impedance modulation, when operating at high power levels [10]. phase-switching. In digital TMNs, on the other hand, tunability is achieved by I. INTRODUCTION implementing the variable reactive elements as digitally- switched arrays, thus allowing adjustment of the impedance of Dynamic component tuning and impedance matching have the variable reactances in discrete steps. The realization of application to a diverse range of radio-frequency (RF) power digital TMNs is typically based on CMOS switches [13], MEMS applications, including software-defined radios [1], frequency- switches [11], PIN diodes [12] or discrete power transistors. agile and adaptive RF transmitters and receivers [2], [3], new MEMS switches are characterized with very low on-state types of highly-efficient RF power amplifiers [4], plasma drivers resistance and can operate at rf frequencies up to tens of GHz [17], generators [5], [6], wireless power transfer [7, 19, 20], with negligible power consumption. The reliability of MEMS power converters [14] and many other industrial processes. switch-based TMNs, however, is still an issue due to the large Electronically-controlled tunable impedance matching networks control voltages required by MEMS switches. On the other (TMNs) in particular can be valuable in many RF applications. hand, PIN diode and CMOS switch-based TMN realizations Such TMNs (e.g., [15]) – also known as “Antenna Tuning offer the capability to handle very high power levels at the Units”, or ATUs – typically match a variable load impedance to expense of some power loss in the switches due to their on-state a desired input impedance (e.g., 50 Ohms) at an RF operating resistance. Such TMN realizations are particularly favorable for frequency, though other functions are possible. on-die integration and find wide applicability in software- For high-frequency (HF) and very-high-frequency (VHF) defined radio (SDR) IC modules and other on-chip TMNs. The applications (e.g., 3-300 MHz), a TMN is typically implemented main drawback of digital TMNs, however, is their limited tuning as an ideally-lossless, lumped-element reactive network, where resolution, and hence, the accuracy with which impedance some of its reactive elements are realized as variable (tunable) matching can be achieved with an acceptable number of components. That is, the impedance of the tunable components switched components. In some high power applications where at a particular frequency, or over a range of frequencies, can be accurate impedance matching is required over a very wide 1 This paper is an extension to the authors’ conference paper entitled “Tunable impedance matching networks based on phase- switched impedance modulation”, IEEE Energy Conversion Congress and Exposition, 2017. It offers in-depth discussion of the operation and design of PSIM-based TMN networks, presents additional implementation details and provides extensive prototype performance results. 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics impedance range, such as RF plasma drivers, for example, the one ought to be able to control the effective capacitance CEFF of use of digital TMNs may be impractical due to the large number the switched capacitor anywhere from C0 to infinity by of digital switches needed to achieve the required fine tuning controlling the conduction angle of the switch from 0 to 2π with resolution. For instance, conventional high-power RF plasma proper phase. drivers often still employ TMNs based on stepper-motor- adjusted continuously-variable capacitors as a result of the requirements for accurate impedance matching and operation over very wide impedance ranges. The limitations of existing techniques motivates improvement of the capabilities of TMNs to provide more accurate and faster impedance matching (higher tuning bandwidth) over wider impedance ranges while simultaneously allowing operation at high power levels with minimum insertion loss. This is the goal of the new approach developed here, which expands upon the authors’ conference paper [21]. Section II introduces the concept of phase-switched impedance modulation. Sections III, IV and V describe implementation and control techniques for a PSIM-based tunable matching network and present the design of a prototype system operating at frequencies centered at 13.56 MHz. Section VI examines the Fig. 1: Schematic illustrating the implementation of a phase-switched variable performance of the prototype PSIM-based matching system, and capacitance and its current and voltage waveforms. The effective capacitance CEFF at the switching frequency can be modulated by controlling the conduction Section VII concludes the paper. angle of the switch which is related to . II. PHASE-SWITCHED IMPEDANCE MODULATION Suppose that the switch is turned off every cycle of the A. The Concept current waveform  radians after the current transitions from negative to positive, and it is turned back on after the capacitor Phase-switched TMNs are a class of tunable matching voltage rings down to zero. The source current iC, capacitor network which achieve tunability by incorporating one or more voltage vC and switch control signal q for this scenario are shown phase-switched variable reactances. A phase-switched variable in Fig. 1 as a function of the cycle angle . Thus, the switch is reactances modulates the effective impedance of a switched turned off α radians after the current through it becomes positive, reactive element (capacitor, inductor, or some combination of and is turned back on when the net charge delivered into the both) by switching the connection of the element at the RF capacitor returns to zero. Note that turning the switch on after frequency. In essence, it is a narrow-band technique for the capacitor voltage rings down to zero ensures zero-voltage- controlling the effective impedance seen looking into the switching (ZVS) turn on of the switch. Likewise, the switch terminals of a reactive element at the frequency at which this turns off under ZVS owing to the capacitor C0 in parallel with element is switched (e.g., with a shunt or a series switch) by the switch, and C0 naturally absorbs the parasitic switch appropriately adjusting the phase and/or duty-cycle of the capacitance. Each of these traits is valuable for efficient switch. The use of switched reactive elements was exploited in operation at high frequencies. [14] in the different context of controlling resonant dc-dc converters by modulating their effective tank network resonant As can be inferred from Fig. 1, by adjusting , i.e. setting frequency, in [16] to tune the resonant frequency of a wireless how far into the cycle the switch turns off, one can control the power transfer receiver to a fixed transmitter frequency, and in conduction angle of the switch and the peak capacitor voltage. [20] to tune the tank network resonant frequency of a wireless It is clear from Fig. 1 that for a purely sinusoidal current source power transmitter. However, it has not previously been applied the conduction angle of the switch is given by 2. Performing to the notion of tunable matching networks for dynamic a Fourier analysis on the capacitor voltage (under sinusoidal impedance matching. current drive) reveals that its fundamental component lags the current by 90° for any switch conduction angle, suggesting that To illustrate the notion of a phase-switched variable the switched capacitor network does indeed behave effectively reactance, consider the parallel combination of a capacitor C0 as a variable capacitor at the switching frequency. and an ideal switch being driven with a purely sinusoidal current Consequently, by analyzing the relationship between the switch source (see Fig. 1). conduction angle and the magnitude of the fundamental The switch state is controlled by the signal q; the switch is on or component of vC(), it can be shown that the effective off when q is high or low respectively. If q is zero all the time, capacitance of the switched capacitor as a function of  is given i.e. the switch is permanently turned off, then the effective by (1) [14]. capacitance CEFF seen looking into the network is equivalent to 𝜋 the physical capacitance C0. On the other hand, if the switch is CEFF = C0 (1) always on, then the capacitor C is effectively shorted, and the 𝜋 − 𝛼 + sin(𝛼) cos(𝛼)0 network behaves as an infinite capacitor in the sense that the Indeed (1) is consistent with the intuitive expectation for voltage across it remains zero irrespective of its terminal current infinite effective capacitance when the switch is always on ( (at the drive frequency). Thus it makes sense to conclude that = ) and predicts the equivalence between CEFF and C0 when 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics the switch is permanently off ( = 0). Fig. 2 plots the fundamental and all of its harmonics tend to zero at a normalized effective capacitance CEFF/C0 of the switched- comparable rate. This is also illustrated in Fig. 4 showing the capacitor network of Fig. 1 at the switching frequency. (Here magnitude of the first five harmonics of 𝑣𝐶 relative to that of the we refer to C /C fundamental as 𝛼 increases to 180°. EFF 0 as the effective modulation factor.) As can be seen, CEFF does indeed increase rapidly with α and approaches infinity with α approaching π (corresponding to a switch conduction angle of 2π). The precision with which effective capacitance can be adjusted depends upon the resolution with which the switch conduction angle can be controlled. Although theoretically one can conclude that the effective capacitance can be modulated continuously over an infinite range, from a practical perspective, the range over which CEFF can be modulated depends on the amount of harmonic distortion one is able to tolerate in the network. Fig. 4: Magnitude of the harmonic components relative to that of the fundamental of the voltage waveform 𝑣𝐶 for the ideal PSIM element of Fig. 1 versus the switch conduction angle 𝛼. The amount of harmonic distortion one can tolerate is highly dependent on the limit of harmonic content that is allowed into the source and/or load. It is, however, important to distinguish between the harmonic distortion of the capacitor voltage of the switched network of Fig. 1 and the harmonic content that is actually injected into the source/load of the RF system. The switched network of Fig. 1 serves as a fundamental building block in the design of PSIM TMNs for RF systems. TMN designs often naturally provide a degree of harmonic filtering; if Fig. 2: Normalized effective capacitance C of the switched capacitor network necessary, additional filtering can be incorporated into these EFF at the switching frequency versus  for a purely sinusoidal current excitation. systems to further reduce injected harmonic content into the source and/or load. It is important to note that the derivation of (1) and the PSIM analysis presented in this section assume a purely sinusoidal current excitation of the switched capacitor network of Fig. 1. In reality, this may not be the case; harmonic content in 𝑖𝐶 can cause the relationship between CEFF, C0 and 𝛼 to differ from the one expressed by (1). Nevertheless, if this relationship remains monotonic with 𝛼 , an external feedback controller can be employed to appropriately adjust 𝛼 based on some overall system performance metric (e.g. impedance measurements as we demonstrate in section VI). In the TMN design presented Fig. 3: Total harmonic distortion of the voltage waveform 𝑣𝐶 for the ideal PSIM here, we aim to maintain the harmonic content of 𝑖𝐶 to be less element of Fig. 1 versus the switch conduction angle 𝛼. than -10 dBc. (For the system implementation described in section III, this roughly corresponds to a 0° - 110° range for 𝛼, As  increases towards  the conduction angle (given by 2 or 4x in effective capacitance modulation.) for a purely-sinusoidal current excitation) of the switch increases, and hence the ringing of the capacitor voltage 𝑣𝐶 (see B. Practical Implications Fig. 1) is limited to a shorter period. As Fig. 3 depicts, this results One possible realization of the PSIM element of Fig. 1 in significant harmonic content of the capacitor voltage for large comprising an N-channel device in parallel with some external CEFF/C0 ratios. The total harmonic distortion THD plotted in Fig. capacitance C0 is shown in Fig. 5A. Such an implementation is 3 is defined here as the ratio of the rms of all harmonics of 𝑣𝐶 to particularly suitable for RF applications as it allows one to the total rms of the waveform2. Note that as Fig. 3 suggests, the absorb the parasitic capacitance of the device into C0 while THD of 𝑣𝐶 saturates at approximately 90% as the conduction maintaining zero-voltage switching (ZVS) of the device and angle increases. Indeed, this can be shown to be the case and can thus minimizing voltage-current overlap losses. be understood by considering Fig. 1: taking the limit of  as it approaches 180°, the peak of 𝑣 , the magnitude of its Furthermore, the unipolar voltage-blocking characteristic of 𝐶 device due to the intrinsic body-diode (or the ability of the 2 In this work, total harmonic distortion (THD) of a voltage waveform is possible THD that can be attained is 100 % and corresponds the case when ∑∞ 2 ∑∞ 2 the entire energy of the waveform is contained in its harmonics, i.e. V1 = 0. defined as 𝑇𝐻𝐷 = √ 𝑛=2 𝑉𝑛 ⁄√ 𝑛=1 𝑉𝑛 , where Vn is the magnitude of the nth harmonic of the waveform. According to this definition, the maximum 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics device to turn-on in reverse in the case of GaN devices) engages for a portion of the reverse conduction period of the somewhat simplifies the control and synchronization of the switch. It is the power losses due to the conduction of the body- device by providing a certain safety margin in achieving ZVS. diode that renders quasi-ZVS as a more lossy alternative to ideal ZVS. Note that (1) can also be used in the case of Fig. 6B as a reasonable approximation to the effective PSIM capacitance, provided that the peak of 𝑣𝐶 is much larger than the forward voltage drop of the body-diode, which is often the case in practical applications. For both Fig. 6A and Fig. 6B the forward conduction angle 𝛼 in (1) is equivalent to 𝑤𝐹 . Finally, Fig. 6C illustrates the case of 𝑤𝑅 > 𝑤𝐹 resulting in hard switching of the device and large switching losses; hence (A) (B) this operating mode is typically avoided. It is interesting to note Fig. 5: Implementation of a PSIM element with an N-channel FET (A), and from Fig. 6 that all three cases achieve the same total device equivalent circuit model (B), where 𝑟0 is the ESR of the total base capacitance conduction angle, although in each case, the total pulse width C0, 𝑟𝑜𝑛 is the on-resistance of the FET, and 𝑟𝐷 and 𝑉𝐷 are the on-resistance and forward voltage drop of the body diode, respectively. 𝑤𝑅 + 𝑤𝐹 and phase of 𝑞 are different. In fact, there are infinite many combinations of pulse width and phase of 𝑞 that will To better understand this, consider Fig. 6 illustrating the achieve a given switch conduction angle and the desired three possible operating modes of the PSIM element from Fig. effective capacitance. Nevertheless, to minimize losses in the 5A depending on the synchronization of the device gate-drive PSIM element, it is best to operate as close to ideal ZVS as signal 𝑞 with respect to the PSIM current 𝑖𝐶 . Here we assume possible while avoiding hard switching of the device. sinusoidal current excitation, i.e. 𝑖𝐶 = 𝐼0sin (𝜔𝑡), and we denote the intervals of forward and reverse device conduction during There are many other practical design considerations to be which the device is commanded on (𝑞 is high) with 𝑤 and 𝑤 addressed in realizing a PSIM capacitor. Among these are the 𝐹 𝑅 respectively. In the case of Fig. 6A, the device is commanded on power loss in the PSIM switch (e.g., owing to conduction loss in for equal intervals of forward and reverse conduction (𝑤 = the device), the peak off-state of the device voltage vs. operating 𝐹 𝑤𝑅) thus achieving ideal ZVS operation without engaging the condition, the average voltage appearing across the device body-diode. This operating mode is also depicted in Fig. 1 and during operation, and the impact of device capacitance is the basis for the derivation of the PSIM effective capacitance nonlinearity. We discuss each of these considerations in the relation (1). Appendix, with detail provided in [24]. C. Alternative PSIM Implementations For the discussion above we have assumed that the switched capacitor network of Fig. 2 is half-wave switched, i.e. the switch is operated in such a way so that the capacitor voltage waveform is unipolar (see Fig. 1). This may often be preferable in RF systems based on the PSIM element implementation of Fig. 5A since typical power transistors can only block a unipolar voltage. However, it is interesting to note that other switching schemes such as full-wave switching [14] are also possible. In the case of full-wave switching, the switch is turned off twice every cycle, with the off periods being centered around the instants when the current iC() is zero. For a purely sinusoidal excitation of the network, this results in a bipolar capacitor voltage waveform with zero dc average. Full-wave switched networks inherently result in reduced harmonic content of the capacitor voltage compared to half-wave switched networks for the same α. On the other hand, implementing full-wave switching may be Fig. 6: Switching waveforms for the PSIM element of Fig. 5 under a sinusoidal practically harder to realize and less beneficial for high current excitation 𝑖𝐶 for (A) ideal zero-voltage switching, (B) partial body-diode frequency RF applications, since in that case the switch has to conduction (or reverse device turn-on), and (C) operation with loss of zero- operate at twice the operating frequency and bidirectional voltage switching, i.e. hard-switching. 𝑤𝑅 and 𝑤𝐹 denote the width of the forward and reverse conduction intervals, respectively, during which the device blocking switches are required. is commanded on, i.e. 𝑞 is high. PSIM implementation based on the switched capacitor Even though ideal ZVS is the most efficient and often network of Fig. 1 is particularly well suited for RF applications desired PSIM operating mode, as we later show in Section III.B, as the parasitic switch device capacitance can be absorbed into this mode may be challenging to achieve under all conditions as the shunt capacitor C0. Nevertheless, there exist other it requires very accurate synchronization between 𝑞 and 𝑖𝐶 . An possibilities for implementing phase-switched impedance alternative practically-viable operating mode for the PSIM is modulation. For instance, by analogy to the switched capacitor shown in Fig. 6B in which 𝑤𝐹 > 𝑤𝑅; we refer to this mode as network, it is also possible to construct a switched inductor quasi-ZVS in the sense that the capacitor voltage 𝑣𝐶 rings down network (comprising a series combination of a switch and an to near zero volts, although in this case, the intrinsic body-diode inductor) that allows continuous control of its effective 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics inductance (at the switching frequency). Such a switched independently. In the case of the TMN of Fig. 7, one of the inductor network corresponds to the topological dual of the variable reactances is the shunt capacitance realized with the switched capacitor network of Fig. 1 with the current through phase-switched capacitor C0. While we could implement the the inductor being analogous to the voltage across the switched second variable reactance using another phase-switched capacitor (see Fig. 1) – a result that follows from the properties capacitor, here we utilize a different technique. The second of topological duality. Of course, in the case of the switched variable reactance is implemented using the series-resonant inductor network, care must be taken to turn the switch off only output tank formed by C2 and L2: its reactance X is controlled when the current through the inductor drops to zero; this by adjusting the operating frequency over a narrow band about necessitates accurate switch control which may be hard to the nominal operating frequency. For instance, when operating achieve in RF applications. Moreover, one does not realize zero- at the resonant frequency 𝑓0 of the L2C2 tank, the reactance X is voltage switching in this case, but zero current switching. effectively zero. Increasing the operating frequency 𝑓 above 𝑓0 results in an increasing inductive reactance X (X>0), while The switched capacitor and inductor networks serve as decreasing 𝑓 below 𝑓 causes X to increase capacitively (X<0). fundamental building blocks for implementing phase-switched 0 impedance modulation. These two basic networks are only able to provide strictly capacitive or inductive variable reactances (but not both). Nevertheless, some applications could benefit substantially from variable reactances whose value can be controlled over a range spanning both capacitive and inductive reactances, and/or by modulating the effective reactance over a more limited range. For instance, in the design of tunable impedance matching networks, it is sometimes required for the tunable reactive elements to be able to achieve both capacitive and inductive values. In such cases, one can further augment the two basic capacitor and inductor switched networks with additional reactive components to allow impedance modulation over a range that includes both capacitive and inductive Fig. 7: Network topology of an L-TMN with dynamic-frequency tuning impedances. Several such networks are described in [24] and comprising a phase-switched capacitor C0 and frequency-controlled reactance X. [25], although many other network variants are also possible. In The input filter reactance does not vary considerably with frequency modulation. this work, however, we focus on the switched-capacitor implementation of Fig. 1; in-depth exploration of the advantages Thus the TMN design demonstrated here utilizes frequency and disadvantages of alternative PSIM element implementations modulation as a second control handle for load impedance is the subject of future work. transformation. Here we refer to this technique as dynamic frequency tuning (DFT). The impedance jX of the output tank is III. TUNABLE IMPEDANCE MATCHING NETWORK determined by the characteristic impedance of the tank Z0 and DESIGN the deviation of the operating frequency f from the tank's resonant frequency f0 and is given by (2), where 2𝜋𝑓 = To demonstrate the effectiveness of phase-switched 0 impedance modulation for implementing tunable impedance 1⁄√𝐿2𝐶2 and 𝑍0 = √𝐿2/𝐶2. matching, we have developed a TMN design based on an 𝑓2 − 𝑓20 impedance step-up L-section matching network with 𝑋 = 𝑍0 (2) electronically-variable effective impedances. Such a network 𝑓0𝑓 configuration is suitable for plasma drive applications where the As (2) suggests, the range over which the output reactance X driving-point impedance of an RF plasma-excitation coil must is adjustable can be expanded by either choosing L2 and C2 to often be stepped-up and matched to the output impedance of a obtain higher tank characteristic impedance, or by allowing for power amplifier PA (e.g., see [17] for a plasma matching system larger amounts of frequency modulation (or both). It can be at similar power levels). A power amplifier is thus connected at shown that to achieve a reactance range of [𝑋𝑚𝑖𝑛; 𝑋𝑚𝑎𝑥] for an the IN terminal, and the plasma load is connected at the OUT operating frequency range of [𝑓𝑚𝑖𝑛; 𝑓𝑚𝑎𝑥], one must select the terminal, with the TMN serving to match the variable plasma resonant frequency and characteristic impedance of the tank load impedance to the 50 Ω load desired for the PA. As Fig. 7 according to (3) and (4) which can then be easily solved to obtain shows, this network comprises input and output series resonant 𝐿2 and 𝐶2. tanks along with a single phase-switched capacitor element. The ground-referenced phase-switched capacitor for this design has (𝑋𝑚𝑎𝑥𝑓𝑚𝑖𝑛 − 𝑋𝑚𝑖𝑛𝑓𝑚𝑎𝑥)𝑓𝑚𝑎𝑥𝑓𝑚𝑖𝑛 the advantages described above for high frequency operation, 𝑓 = √ (3) 0 including zero-voltage switching, absorption of device parasitics 𝑋𝑚𝑎𝑥𝑓𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛𝑓𝑚𝑖𝑛 and simple transistor drive. 𝑓0(𝑋𝑚𝑎𝑥𝑓𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛𝑓𝑚𝑖𝑛) It's important to recognize that in order for any TMN to be 𝑍0 = (4) 𝑓2𝑚𝑎𝑥 − 𝑓 2 𝑚𝑖𝑛 able to match load impedances that vary independently both in resistance and reactance (i.e. provide an impedance match over The amount of frequency modulation allowed is highly a two-dimensional region in the Smith chart), the TMN must dependent on the particular application and may be constrained comprise at least two reactances that can be tuned quasi- by radio-frequency emission regulations for the particular 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics frequency band of operation. For instance, in the current system the TMN with the L2/C2 tank alone may be sufficient. The TMN design 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 are selected to be 12.20 MHz and 14.92 design presented here is tailored towards driving plasma loads, MHz, respectively which corresponds to a ± 5 % variation and for the particular application it is desirable to keep the centered around a 13.56 MHz nominal frequency. This choice harmonic content injected in the output to less than -20 dBc. of frequency operating range is consistent with the one adopted The L-TMN prototype described here is designed to operate by many plasma systems in the semiconductor fabrication at a nominal frequency of 13.56 MHz in the ISM band with up industry. On the other hand, the choice of 𝑍0 (or 𝑋𝑚𝑖𝑛 and to ±10% frequency modulation (L = 1.17 H, C , = 117pF, L 𝑋𝑚𝑎𝑥) depends on the matching network topology and the load 1 1 2 impedance range that one desires to be able to match. As we = 2.97 H, C2 = 47.5 pF, C0 = 270 pF, 50 Ω quarter-wavelength demonstrate below, to achieve a load impedance matching range line impedance). The yellow-shaded and the dotted red-line similar to the one exhibited by some industrial-grade TMN regions in the Smith chart of Fig. 8 illustrate the range of load impedances that this TMN design can successfully match to a systems for plasma applications, we select 𝑍0 = 250 Ω. (This corresponds to 𝑋𝑚𝑖𝑛 = -19.7 Ω and 𝑋 = 30.4 Ω.) In addition 50  source impedance for 5% and 10% frequency modulation 𝑚𝑎𝑥 to serving as a frequency-variable tunable reactance, the L /C respectively. (The frequency modulation percentage is defined 2 2 tank also provides filtering, limiting the injection of high- here as the ratio of the peak frequency deviation to the nominal frequency harmonic currents into the output. operating frequency.) As can be seen from Fig. 8, the range of reactive loads that the TMN can match to 50  increases with Similarly, the input filter comprising L1 and C1 is designed the amount of frequency modulation. Such dynamic-frequency to limit the injection of high-frequency harmonic content by the tuning techniques are commonly employed in plasma-related TMN back into the PA. Furthermore, note from Fig. 7 that the applications. Hence, for every particular value of load current 𝑖𝐶 flowing through the phase-switched capacitor is the impedance within the tunable range, there is a unique difference of the input and output filter currents; reducing their combination of operating frequency and switch conduction harmonic content in turn leads to a PSIM excitation current 𝑖𝐶 angle α that is required to provide an impedance match between that is closer to the ideal sinusoid of Fig. 1. Thus, on one hand it the load and the PA. is desirable to choose a large input filter characteristic impedance to reduce harmonics, while on the other hand, this also leads to larger variations of its reactance with frequency modulation. (As we demonstrate in the next section, the latter effect may not desirable as it could complicate the synchronization and control of the PSIM switch.) In this design, we select L1 and C1 so that the filter is series-resonant at the nominal operating frequency of 13.56 MHz with a characteristic impedance of 100 Ω (smaller than that of the output tank). Based on spice simulation of the design, this corresponds to less than −10 dBc harmonic content in the input filter and phase-switched capacitor currents, and approximately less than ±10 Ω variation in the reactance of the input filter (for up to ±5% frequency modulation). Note that C1 and C2 in the system of Fig. 7 also serve as dc blocking capacitors to provide dc isolation between the drain of the switch and the PA and load respectively. This is an important requirement for this TMN implementation since modulating the Fig. 8: Typical load impedance range that can be matched to a 50  source with conduction angle of the switch imposes a variable dc bias at the 5 % (yellow) and 10 % (red) frequency modulation for the TMN design of Fig. transistor drain which could interfere with the internal biasing of 7 with L1 = 1.17 H, C1, = 117pF, L2 = 2.97 H, C2 = 47.5 pF, C0 = 270 pF. the PA and, in some applications, the load characteristics. The The load impedance ranges shown in Fig. 8 correspond to shorted quarter-wavelength stub in parallel with the output of modulating the effective capacitance of the RF-switched the TMN in Fig. 7 serves to provide additional filtering of even capacitor by up to 4X the value of the base capacitance C0. (This harmonic components. It reduces harmonic content injected in amount of capacitance modulation roughly corresponds to the load by presenting a shunt impedance at the TMN’s output varying  in Fig. 1 from 0° to 110°.) Further capacitance that is high at odd harmonics and low at even harmonics of the modulation expands the TMN matching range (at the expense of operating frequency. For the design presented here, the injecting higher harmonic content into the load and the PA) to impedance of the stub (at the fundamental frequency) is much include load impedances with lower resistive components. On larger than the load impedance over the entire load and the other hand, decreasing the base capacitance C0 (while frequency operating range of the TMN. Hence, besides the allowing the same amount of capacitance modulation) results in additional filtering it provides, the quarter-wavelength stub does shifting the TMN matching range towards load impedances with not impact the control of the TMN, i.e. the choice of frequency higher resistive components. Note that with the network and switch conduction angle for matching a load to the PA. Of topology shown in Fig 1, one can conveniently use C0 to absorb course, depending on the particular application, one may adopt the drain-to-source capacitance of the switch (and in high- different output filter designs. For instances, in applications with frequency implementations, C0 may comprise only switch less stringent output harmonic content requirements, operating capacitance). A TMN with the load impedance matching range 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics shown in Fig. 8 is particularly suitable for inductively-coupled PL1. This is because both the rms current through L2 and its plasma (ICP) applications where TMNs are employed to match inductance are larger than those of L1. the drive-point impedance of an RF excitation coil to the output To ensure an impedance match between the load and the impedance of an RF power amplifier (typically 50 ). source impedance, the conduction angle and operating Table I lists the switch conduction angle, operating frequency must be selected appropriately. Note that the frequency, peak voltage across the switching device and power conduction angle listed in Table I is the total conduction angle loss distribution for matching various capacitive and inductive of the switch and it includes both forward and reverse loads to 50  based on a simulation of the TMN design of Fig. conduction of the device. (The total switch conduction angle and 7 with L1 = 1.17 H, C = 117pF, L = 2.97 H, C = 47.5 pF, α in Fig. 1 are related, however, they are not equivalent. The 1 2 2 at approximately 150 W of input power. The quality factors for total switch conduction angle includes both forward and reverse inductors L1 and L2 are assumed to be 900 and 800 respectively, device conduction, while 𝛼 corresponds only to forward consistent with the actual quality factors achieved in the conduction.) One can see from Table I that loads with smaller implementation of the TMN design. The switching device used resistive components require larger conduction angles of the in the simulation is a 650V GaN transistor (GS66504B, GaN switch. On the other hand, the required operating frequency Systems) with its spice model provided by the manufacturer. roughly decreases for an increasing inductive load reactance and Note that the base capacitance C0 (see Fig. 7) in the simulation increases for an increasing capacitive load reactance. comprises the drain-to-source capacitance of the switch and 100 For the TMN of Fig. 7 it can be shown that the effective input pF of external capacitance. impedance 𝑍𝐼𝑁 seen looking into the IN port (at the operating frequency) is given by (5), where 𝑋1 and 𝑋2 are the net TABLE I. SWITCH CONDUCTION ANGLE, OPERATING FREQUENCY AND POWER LOSS DISTRIBUTION FOR A SIMULATED TMN DESIGN EXAMPLE reactances of the input and output filters, respectively, 𝐵𝑝𝑠𝑖𝑚 is MATCHING VARIOUS LOAD IMPEDANCES TO A 50  SOURCE IMPEDANCE AT the effective susceptance of the shunt PSIM element, and 𝑍𝐿 is APPROXIMATELY 150 W OF INPUT POWER. the load impedance. However, when analyzing the operation of matching networks, it is often more convenient and insightful to do so by referring to a Smith chart. 𝑍 = ((𝑍 + 𝑗𝑋 )−1 −1 𝐼𝑁 𝐿 2 + 𝑗𝐵𝑝𝑠𝑖𝑚) + 𝑗𝑋1 (5) To illustrate the operation and control of the TMN design of Fig. 7 in more detail, consider the Smith chart of Fig. 9 with some inductive and capacitive loads Z1 and Z2 respectively that one wishes to match to 50  (the center of the Smith chart). The dashed circle corresponds to a conductance of 0.2 S, i.e. the When selecting the transistor, it is preferable to realize most equivalent load of a 50  resistance in parallel with some of the PSIM base capacitance using the drain-to-source reactance. capacitance of the device. This allows one to use the largest possible device, thus minimizing device on-resistance and conduction losses. Furthermore, the device must be rated to withstand the peak voltage imposed by the PSIM network. Based on the detailed evaluation in the Appendix, for typical modulation ranges, one can estimate the peak voltage on the device to be approximately 2.5x the magnitude of its fundamental component. In this work, the TMN is designed to provide a 50 Ω impedance matching and operate at up to 200 W of input power which corresponds to an input RF voltage magnitude of 140 V. This is roughly the magnitude of the fundamental component of the voltage across the transistor since the input L1-C1 tank in Fig. 7 is series-resonant at the operating frequency. Hence, at 200 W of input power, one would expect the peak voltage across the device to be approximately 350 V. In this design, we chose to use the GS66504B transistor since its Fig. 9: Impedance matching of an inductive load Z1 and capacitive load Z2 using drain-to-source capacitance is comparable to the required PSIM the TMN of Fig. 7 by first performing frequency control and then phase-switched base capacitance C0 while offering a sufficient voltage margin capacitance modulation. for up to 200 W of TMN input power. For the L-section matching network design of Fig. 7, One can see from Table I that the simulated TMN design is frequency modulation causes the TMN’s input impedance to able to match both capacitive and inductive loads to 50 Ω with move along a circle of constant resistance in the Smith chart most of the power losses in the TMN being distributed evenly (e.g., red and blue curves in Fig. 9). On the other hand, phase- between the output inductor and the switching device. It is switched impedance modulation of the shunt capacitor results in interesting to note that although L1 and L2 have comparable the TMN’s input impedance traversing a circle of constant quality factor, the power PL2 dissipated in L2 is much larger than conductance in the Smith chart (green curve in Fig. 9). (Here we 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics ignore the small effect of the input filter on the TMN’s input voltage vD are in phase at this frequency. Furthermore, since the impedance with frequency modulation.) Thus, in the context of phase-switched capacitor network behaves effectively as a the TMN design presented here, one can visualize the capacitor, the fundamental frequency component of the mechanism of impedance matching as a two-step process switched capacitor current iC leads that of vD by 90º. Of course, consisting of frequency control followed by phase-switched this is exactly true only at the nominal operating frequency – the impedance modulation. For example, in the case of matching frequency at which the TMN’s input filter is series-resonant. load Z1 in Fig. 9, one can first begin by decreasing the operating However, in the prototype design considered here, the frequency below the resonant frequency f0 of the output tank so characteristic impedance of the input filter is selected to be as capacitively offset the load and thus bring the TMN’s input relatively low compared to 50 , and as a result, the filter impedance to the point Z *1 on the 0.2 S dashed conductance remains nearly-resonant over the entire frequency modulation circle (blue line). At this point, one can proceed by increasing range. It can be shown that for this TMN design, the phase shift the conduction angle of the switch, forcing the TMN’s input between the fundamental components of vIN and iC is impedance to traverse along the dashed conductance circle until approximately 90º ± 5º over a ±5% frequency modulation range it reaches 50 (green line). This essentially corresponds to and the corresponding load impedance range shown in Fig. 8. adjusting the effective shunt capacitance to resonate out the (Of course, the actual deviation of the phase shift from 90° susceptive component of Z *1 . On the other hand, when matching depends on the operating frequency, the resonant frequency of a capacitive load such as Z2, one may begin by first increasing the input filter L1C1 and its characteristic impedance. This phase the frequency above f0 to inductively offset the load to point Z *2 shift is 90° only when operating at the resonant frequency of the on the 0.2 S conductance circle (orange line) and then input filter. The ±5° variation claimed here is based on a spice appropriately increase switch conduction angle until the TMN’s simulation of the presented TMN design.) Hence, by input impedance reaches 50 (green line). As Fig. 9 suggests, synchronizing the gate drive signal directly to the TMN’s input loads with larger resistive components require less shunt voltage (and by appropriately phase-shifting it), one is able to capacitance, and hence, a smaller switch conduction angle. In effectively synchronize the switching of the capacitor to the terms of frequency control, inductive loads require smaller current iC. This is the underlying principle of the proposed gate- operating frequency than capacitive loads. Note that one can drive synchronization approach. reactively offset the entire TMN matching range shown in Fig. 8 by simply changing the resonant frequency of the output tank. Although in the above matching example frequency control is performed prior to switched-capacitance modulation, in practice, one ought not to do it in this fashion. In fact, a controller optimized for fast dynamic response and agile impedance matching may require simultaneous adjustment of frequency and switch conduction angle. IV. GATE-DRIVE CONTROL AND SYNCHRONIZATION The ability to synthesize the appropriate gate waveform for driving the switch is of crucial importance to the TMN operation. As Fig. 1 suggests, the gate drive signal q should be synchronized to the current iC flowing through the switched- capacitor network over the entire TMN frequency modulation range. Furthermore, one must be able to accurately control the conduction angle of the switch. In essence, this requires one to generate a gate waveform with a variable duty cycle synchronized to the switched capacitor current iC. The resolution with which one can vary the duty cycle determines the resolution Fig. 10: Current and voltage waveforms for the TMN of Fig. 7. The switch gate with which the effective capacitance can be modulated and waveform q is phase-locked with respect to the TMN input voltage vIN, which is hence sets the limit on the overall TMN impedance matching lagging the current through the switched-capacitor network iC by approximately 90°. The phase shift Φ between 𝑣 and 𝑞 is defined with respect to the resolution. Synchronizing the gate drive signal directly to the 𝐼𝑁 negative-to-positive transition of 𝑣𝐼𝑁 and the rising edge of 𝑞. By controlling the switched-capacitor current waveform, however, can be switch conduction angle one can adjust the effective capacitance of the switched problematic as this requires one to measure the current iC; capacitor. measurement of RF current waveforms is often a challenge. As Fig. 10 illustrates in more detail, the gate-drive signal q Instead, for the TMN design presented here, we offer an having variable pulse width w is phase-locked to the TMN’s alternative approach based on synchronizing the gate drive input voltage vIN, i.e. a phase shift  is maintained between the signal q with the TMN’s input voltage vIN. rising edge of q and the negative-to-positive vIN transition. As To illustrate this approach, consider the TMN design we discuss shortly, the gate drive signal generation circuit is presented in Fig. 7 with L1 = 1.17 H, C1, = 117pF, L2 = 2.97 capable of independently controlling both  and w over the H, C2 = 47.5 pF, C0 = 270 pF. Since the TMN’s input filter is entire frequency modulation range. Since iC leads vIN by series-resonant at the 13.56 MHz nominal operating frequency, approximately 90º, one can choose w and  appropriately so that the fundamental frequency components of vIN and the drain the switch is turned on for a duration α (0 ≤ α ≤ π) after the 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics negative-to-positive transition in iC. Note that if the switch is not turned on immediately after the drain voltage vD rings back down to zero, the switch goes into reverse conduction mode and the body diode clamps the drain voltage near zero (since at this instant the current iC is negative). Assuming the switched capacitor current iC in Fig. 10 is purely sinusoidal, it can be shown that the duration of the reverse conduction mode is also α. To ensure zero-voltage switching (ZVS), the switch must be turned on either exactly at the positive-to-negative transition of Fig. 11: Block diagram of the phase-locked PWM generator and gate driver circuit employed for generating a variable duty-cycle waveform with pulse width 𝑣𝐷 , or while the body-diode is conducting. Of course, in the w and phase shift . The time delay element  in the feedback path of PLL1 is latter case, the phase shift  between q and vIN must be selected to match the gate driver delay and thus eliminate the dependence of  appropriately selected with the pulse width w chosen greater on frequency modulation. than α. This allows one to use the body-diode conduction mode The gate-waveform generation module of Fig. 11 is capable effectively as a ZVS safety margin by alleviating the of generating a variable duty-cycle gate drive which can be requirement for precise switch turn-on; ZVS operation is adjusted from 0 % to 100 % with 0.1 % resolution while guaranteed, provided that the switch is turned on anytime during synchronizing it to the switched-capacitor current waveform the body-diode conduction interval. over the entire frequency modulation range. As mentioned, this Here we introduce a PLL-based approach for generating a resolution in duty-cycle control is a result of the particular variable duty cycle gate waveform that allows one to control its implementation and can be easily increased if necessary. angular pulse width w and phase  (relative to an input voltage) It is important to clarify that although the PWM circuit is independently from frequency, i.e. frequency modulation affects capable of generating a signal q with arbitrary pulse width w and neither w or . This greatly simplifies the overall system phase shift  that are unaffected by frequency modulation, this control. (The ability to dynamically control  is not necessary is not the case for the forward conduction angle α. That is, a for the operation of the TMN design presented here; it is constant pulse-width and phase of q does not imply a constant α incorporated in the design of this phase-locked PWM generator as the TMN’s operating frequency is modulated. This is because and gate driver only for additional versatility.) The phase-locked the gate drive signal q is phase-locked with respect to vIN, and PWM circuit comprises a cascade of two PLL modules (see Fig. hence, any small variation in the phase shift between the 11). Each PLL module is designed to generate an output signal fundamental components of iC and vIN translates directly into at its OUT terminal such that the signal fed back to its IN modulation of forward conduction angle α of the switch. terminal is frequency-locked to the reference signal at its REF Similarly, this also affects the duration of the reverse conduction terminal and is phase-shifted from it by a certain amount. This interval. For instance, if the phase shift between vC and iC phase shift is digitally controlled by a microcontroller and can changes by Δ from the nominal 90º (e.g., due to modulation of be adjusted from -180º to 180º with a 10-bit resolution. The the operating frequency), the switch will stay in forward resolution is a result of the particular implementation of the PLL conduction mode for a duration of α + Δ assuming phase  and and can be easily increased. pulse width w of the gate drive signal q are kept constant. Consider Fig. 11 and assume for a moment that the time Control of the switch forward conduction α and the TMN’s delay element in the feedback path of PLL1 is zero. This causes operating frequency is the responsibility of an external feedback PLL1’s output signal A to be frequency-locked to the RF input loop. For example, such a feedback loop could be based on and phase-shifted from it by . For the particular monitoring the quality of impedance matching between the implementation of PLL1, a phase shift of  between the power amplifier and the TMN by measuring the reflected power reference and the output signals implies that the rising edge of or the impedance at the TMN’s input port, much as in the output signal pulse lags the negative-to-positive transition in conventional TMN designs. (The design of a feedback control the reference signal by . In turn, the output of PLL1 serves as loop that can fully utilize the available bandwidth offered by the the input of PLL2, whose output signal B is phase-shifted by w PSIM TMN is the subject of future work. In Section IV, from signal A. Signals A and B are combined through gate drive however, we demonstrate the closed-loop operation of the PSIM logic to produce the signal q with variable angular pulse width TMN with a lower bandwidth controller that was originally w and phase shift  between its rising edge and the negative-to- intended for the control of TMNs based on mechanically-tuned positive transition of the RF signal. Note that by selecting the capacitors.) time delay  in the feedback path of PLL1 to match the delay of the gate driver, one can eliminate the dependence on frequency As we described in Section II.B, to minimize losses in the of the phase shift between q and the RF signal. (In reality, it is switching device, it is desired to operate it in the ideal ZVS mode difficult to know the exact delay of the gate-driver. Hence, as we as shown in Fig. 6A, corresponding to 𝑤𝐹 = 𝑤𝑅 . Of course, to demonstrate in the next section, the delay element is achieve this, one must simultaneously control both the phase Φ implemented as an adjustable RC low-pass filter that can be and pulse width 𝑤 of 𝑞 as one modulates 𝛼. For the sake of manually tuned until its delay matches that of the gate driver.) simplicity, here we employ an alternative, simpler control In the TMN design presented here, the RF reference signal fed strategy in which Φ is kept constant, and control of α is achieved to PLL1 is obtained directly from the TMN’s input voltage v through pulse-width-modulation of q alone. This corresponds to IN (see Fig. 7) through capacitive voltage division. operating the device in quasi-ZVS mode as shown in Fig. 6B, 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics i.e. the body-diode of the device is allowed to engage for a The input filter inductor L1 comprises 3.75 turns with portion of the reverse conduction period. approximately 0.55” turn-to-turn spacing plus interconnect. Its inductance is measured to be approximately 1.2 H with a Of course, to guarantee zero voltage switching over the quality factor greater than 900 at 13.56 MHz. The output filter entire TMN operation range,  must be chosen appropriately to inductor is wound with 8 turns with approximately 0.51” turn- allow for variation in the phase shift between vIN and iC as to-turn spacing plus interconnect and has a measured inductance frequency is modulated. (The phase shift Φ between 𝑣𝐼𝑁 and 𝑞 of 3.2 H and a quality factor of approximately 800 at 13.56 is defined with respect to the negative-to-positive transition of MHz. Machined delrin spacers are fitted between the turns of 𝑣𝐼𝑁 and the rising edge of 𝑞 – see Fig. 10.) To do so, one can the inductors for a more rigid construction. The resonant begin by first estimating the expected variation Δ in the 90º frequencies of the input and output filters are tuned to be 13.56 nominal phase shift between iC and vIN for a given TMN MHz and 13.40 MHz respectively by adjusting the values of the frequency operating range. (A nominal phase shift of 90° input and output filter capacitors C1 and C2. C1 has a total corresponds to operation at the resonant frequency of the input capacitance of approximately 115 pF and is formed by the L1C1 tank.) One possible selection of Φ that ensures quasi-ZVS parallel combination of 1.5 kV NP0 ceramic capacitors operation over most of the range of 𝛼 is Φ = 3𝜋⁄2 − Δ. At the (HIFREQ series, Vishay), while C2 consists of a series-parallel nominal operating frequency, this corresponds to 𝑤𝑅 = Δ in combination of 2.5 kV NP0 ceramic capacitors (HiQ series, Fig. 10; however, as one modulates frequency, the phase shift AVX) with a total capacitance of approximately 44 pF . between 𝑖𝐶 and 𝑣𝐼𝑁 changes by a small amount and causes 𝑤𝑅 to vary from 0 to 2Δ . Thus, the device is always turned-on during conduction of the body-diode. Furthermore, recall from Fig. 6B that in quasi-ZVS mode, 𝑤𝑅 must be less than 𝑤𝐹 . Since the maximum expected value of 𝑤𝑅 is 2Δ , one must also maintain a minimum 𝑤𝐹 of 2Δ, resulting in a minimum total pulse width 𝑤 = 4Δ. For example, in the TMN design presented here the maximum variation Δ in the phase shift between iC and vIN is approximately 5º. Thus, we can choose  = 265º and a minimum allowed gate signal pulse width of 20º. Note from Fig. 2 that operating the phase-switched capacitor network with α less than 20º does not contribute significant additional dynamic range in effective capacitance. Of course, one can also chose Φ to be less than 265° thus reducing the time during which the body-diode is engaged. This, however, requires one also to increase the Fig. 12: Overall TMN system implementation showing the input and output filter minimum limit on the pulse width of 𝑞, which can eventually inductors, the power stage and the quarter-wavelength stub. lead to reducing the dynamic range of the PSIM capacitance. V. SYSTEM IMPLEMENTATION One can think of the TMN system proposed here as comprising a power stage and a gate-waveform generation module. The power stage consists of the RF phase-switched capacitor and the input and output filters as shown in Fig. 7, and it is responsible for providing the load-to-source impedance match. A 650 V GaN FET (GS66504B, GaN Systems) is used for a switch due to its fast turn-on and turn-off times and relatively low output device capacitance (40 pF at 300 V drain- to-source voltage). For 200 W of TMN input power, this device offers approximately 300 V of drain-to-source voltage margin, and it comes in a leadless, easy-to-work-with, low-inductance package with excellent thermal characteristics. Although in the simulated TMN design an additional 100 pF of external capacitance is added in parallel with the device, in the actual Fig. 13: Closer view of the power stage along with the gate waveform generation module. Control of the switch conduction angle is achieved through a UART TMN implementation of Fig. 12 no additional shunt capacitance serial interface. is required to achieve the same load impedance matching range as the simulated design. The device capacitance forms the entire The quarter-wavelength stub at the TMN’s output is made of phase-switched capacitor C0. This discrepancy is mainly approximately 3.65 m of 50  coax cable (RG58) coiled and attributed to underestimation of the device capacitance by the shorted at one end. The TMN implementation presented here is employed simulation model. rated up to 200 W of RF input power (with operation up to ~400 W expected to be possible with improved device heatsinking). Both inductors are coreless solenoids with a 3” inside The power stage electronics and the gate-waveform generation diameter and are wound with 0.25” copper tube (see Fig. 12). 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics module are integrated onto a single 4-layer FR4 PCB (see Fig. The delay in the feedback path of the PLL1 block in Fig. 11 13). is realized with a simple low-pass RC filter. It is empirically adjusted to provide approximately 20 ns of delay to compensate A schematic of the PLL blocks used in the gate waveform the time delay in the gate driver. One way to achieve this is to generation module is shown in Fig. 14. The design is based on a perform a frequency sweep (over the TMN operating frequency PLL chip (ADF4001, Analog Devices Inc.) and a 5-20 MHz range) of the reference input signal RF to the PWM generator in VCO (SN54LS624, Texas Instruments). The ADF4001 in Fig. 11 while simultaneously measuring RF and the output conveniently integrates a digital phase-frequency detector, pulse 𝑞 on an oscilloscope. The delay of the RC filter is then charge pump and programmable frequency dividers for the REF adjusted until a constant phase shift is observed between 𝑞 and and IN input signals. For this application, both dividers are RF as frequency is swept. programmed with unity gain (no division). The frequency of the REF and IN signals is determined by the dynamic frequency The gate driver used in this design (UCC27511, Texas tuning control and varies by ±5% around 13.56 MHz. Instruments Inc.) provides both inverting and non-inverting inputs and conveniently implements the logic AND operation of the two PLL outputs A and B in Fig. 11. As an example, Fig. 15 illustrates the generation of approximately 50 % duty-cycle gate-drive waveform 𝑞 at 13.56 MHz with its rising edge aligned in phase with the positive-to-negative transition of the RF input signal (see Fig. 11). (Additional waveforms along with more detailed exploration of the performance of the PWM generator are provided in [24], Chapter 4.) Fig. 14: Implementation of the PLL blocks of Fig. 11 based on the ADF4001 PLL chip (Analog Devices Inc.). Phase shift between the REF and OUT signals can be adjusted by controlling the current injected into the charge pump output node. The dc average of the charge pump output current into the CP node is proportional to the phase shift between the REF and IN signals. When the REF and IN signals are in phase, the charge pump output current is on average zero. On the other hand, when the phase shift between REF and IN approaches 360°, the average output current of the charge pump approaches a pre- programmed full-scale current (5 mA for the PLL design presented here). An adjustable phase shift between REF and IN can be introduced by injecting a current into the CP node. In this design, this is achieved by an external voltage-controlled dc Fig. 15: Example generation of a 50 % duty-cycle gate-drive waveform 𝑞 (ch 4, current source controlled by a 12-bit DAC (AD5620, Analog green) at 13.56 MHz based on the design of Fig. 11. In this case, the rising edge Devices Inc.). The DAC communicates to a local of the PWM waveform is aligned in phase with the positive-to-negative transition of the reference RF signal (ch 1, blue). microcontroller (PIC18F26K22, Microchip Inc.) via a serial SPI interface. The injected current into the CP node can be adjusted VI. EXPERIMENTAL PERFORMANCE over a ± 2.5 mA range and is roughly sufficient to achieve up to ±180° of phase shift between REF and IN. Note that it is the A. Measurement Setup resolution with which one can adjust this injected current that To evaluate the performance of the matching system ultimately determines the resolution with which the PSIM presented here, the TMN is powered from a 150 W RF power switch conduction angle can be modulated and hence, its amplifier (150A100B, Amplifier Research) having a 50  effective capacitance resolution. The voltage-controlled current output impedance as shown in Fig. 16. It is sinusoidally excited source in Fig. 14 is implemented with a pair of temperature- by a function generator (DG2041A, Rigol) whose frequency can compensated NPN and PNP transistor-based current mirrors be externally adjusted. The power amplifier is connected to the (BCV61 and BCV62, Infineon Technologies) that are biased TMN through an I-V probe (Model#: 000-1106-117, MKS against each other. Detailed schematics and bill-of-materials are Instruments) which directly measures the input impedance provided in [24], Appendix D. looking into the TMN. This I-V probe is also capable of directly The loop filter essentially converts the current injected into measuring the input power to the TMN at the fundamental the CP node to a voltage that drives the VCO. For this design, operating frequency. The impedance measurements derived the loop filter is realized with a lead compensator while the from this probe are used directly by the TMN controller to location of its pole and zero are selected to achieve a 1 MHz loop indicate when impedance matching is achieved and provide bandwidth and 45° phase margin. The lock time of the PLL is feedback information for adjusting the switch conduction angle measured to be less than 3 μs. and operating frequency. (Consequently, the accuracy and bandwidth with which impedance can be measured has a direct 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics impact on the overall system performance. The I-V probes suggested by Fig. 8. Consistent with the expected operation of employed in this work provide a 100 kHz sampling rate and are the L-section-based TMN design, matching of loads with small specified to have an accuracy of ±1 % in impedance magnitude resistive components requires larger switch conduction angles. and ±0.4° in impedance phase.) As the resistive component of the load increases, the required conduction angle decreases. In terms of frequency control, the The TMN controller shown in Fig. 16 is designed and larger the inductive component of the load, the smaller the fabricated by MKS Instruments Inc., and it is originally intended frequency required to provide impedance matching, while loads for controlling TMN systems based on variable vacuum with larger capacitive components demand higher operating capacitors. To evaluate the steady-state performance of the frequency, as expected. system (see section VI-B), the controller is operated in open- loop, i.e. external commands are manually provided to the Comparing the conduction angle listed in Tables I and II one controller to adjust 𝑓 and 𝛼 until proper impedance matching is can see that the simulated design does require larger shunt achieved. On the other hand, when evaluating the transient capacitance than the actual TMN implementation for every load performance (see sections VI-C and -D), we allow the controller impedance, especially in test cases A and B. Note further, that to operate in feedback mode thus automatically adjusting 𝑓 and the simulation results in Table I are based on the GS66504B 𝛼 based on input impedance measurements. The actual control device with an additional external capacitance of 100 pF, while algorithm employed is proprietary to MKS Instruments Inc. in the actual TMN implementation, no additional capacitance was added in parallel with the same device. Although there is a In this work, the criteria for achieving impedance matching small parasitic capacitance between the drain pad and ground of is to limit reflected power to less than 1%, corresponding to a the TMN’s power stage pcb (less than 10 pF), it is not enough to VSWR of less than 1.22. An identical I-V probe is connected at account for such discrepancy in conduction angle. The necessity the output of the TMN to measure its output power. The TMN’s for larger switch conduction angle for a given load impedance output port is terminated with a resistive/reactive load in the simulated TMN design is attributed to underestimation of impedance located within the 10 % frequency-modulation the device capacitance and its voltage dependence by the matching range shown in Fig. 8. employed simulation model of the device. The small difference in the required operating frequency between the TMN implementation (Table II) and the simulated design (Table I) for a given load impedance is due to fact that the resonant frequency of the output tanks of the simulated and implemented TMN designs are not identical. The power efficiency measurements in Table II reflect the Fig. 16: Experimental setup for measuring the performance of the TMN. The efficiency of the TMN at the fundamental operating frequency switch conduction angle α and the operating frequency f are adjusted until the and exclude any power loss owing to the gate driver and the gate load is matched to 50 . The TMN’s input impedance and input / output powers waveform generation circuit. As mentioned, TMN’s input and are measured directly by IV probes. output power are measured directly with a pair of I-V probes To test the TMN, we utilize a home-built adjustable RF load. connected at the input and output of the TMN. The lower power To facilitate ease of adjustment of the load over the targeted efficiency measurements in Table II compared to the simulated impedance range, the load is implemented with a variable length efficiency in Table I are attributed to additional device losses. transmission line (50  RG214 coax cable) terminated with the Note further that the difference between the measured and simulated power efficiency increases as the resistive component parallel combination of a 50 RF power resistor (CTN-250-2, of the load impedance decreases. Load impedances with lower Meca Electronics Inc.) and a variable vacuum capacitor resistive components result in a significant increase of drain (CVMN-1000A, Comet). By adjusting the length of the line current. Hence, the additional device losses measured in Table from 0 to 3 m and varying the capacitance over a 50 pF – 1000 II can be either due to a larger device channel on-resistance, i.e. pF range, one can generate all the inductive loads and most of dynamic on-resistance, or losses in the device capacitance [23]. the capacitive loads in Fig. 8 corresponding to the 5 % frequency Neither of these effects are accounted for in the spice model of modulation load range. the device. Nonetheless, the efficiency of the prototype TMN is B. Steady-State PSIM-TMN Performance adequate for the type of system considered, and achievable To demonstrate the steady-state performance of the TMN, efficiency can significantly improve as available switch device the switch conduction angle and the operating frequency are performance improves. Note that in this measurement setup we adjusted until the I-V probe measures 50  input impedance, i.e. use a linear class-A power amplifier. This class of amplifiers are the load is matched to the power amplifier. Table II shows characterized with a maximum theoretical efficiency of 50 %, example of load impedances (along with the required switch but exhibit even lower efficiencies in reality. In general, conduction angle and operating frequency) at which the TMN however, one can utilize a switched-mode DC-AC resonant inverter as the source of the rf power, provided that it is capable matches the load to 50 atW power output from the PA of operating over the frequency bandwidth required by DFT. with less than 1 % of reflected power at the input port of the TMN. Note that the conduction angle in Table II reflects the total An example oscilloscope snapshot of the TMN voltage switch conduction angle, i.e. it is the combination of forward and waveforms at the input port vIN, output port vOUT, switch drain reverse device conduction. As can be seen, the TMN is able to vD, and the gate-drive vG for a 5.00 + j15.6  inductive load (test match a wide range of capacitive and inductive loads as 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics case G, Table II) at 150 W of input power (into the TMN) is characteristic and the amount of harmonic content injected in the shown in Fig. 17. load that one is willing to tolerate. TABLE II. SWITCH CONDUCTION ANGLE AND TMN OPERATION FREQUENCY REQUIRED TO MATCH VARIOUS LOAD IMPEDANCES TO A 50  SOURCE IMPEDANCE AT 150W OF INPUT POWER. C. Transient PSIM-TMN Performance To demonstrate the transient behavior of the TMN, the Fig. 17: TMN input port voltage vIN, output port voltage vOUT, gate-drive voltage vG and switch drain-to-source voltage v for test case G (Table I) at 150 W of RF system of Fig. 16 is equipped with a controller identical to the D input power into the TMN. ones used by MKS Instruments to control some of their own TMNs based on mechanically tunable vacuum capacitors. The It can be clearly seen that the switch exhibits zero-voltage controller samples the TMN input impedance seen by the PA via turn on which is a highly desired feature for reducing switching the input I-V probe at a sampling rate of 100 kHz and losses. Note that for the test case illustrated in Fig. 17, the drain correspondingly adjusts the desired PA operating frequency and voltage rings down to zero and stays near 0 V (due to reverse TMN shunt capacitance. The detailed implementation of the switch conduction) even before the switch is commanded to turn controller and its control law is proprietary to MKS Instruments. on. (There are no body-diodes in the GaN FETs utilized; instead, they turn on in reverse, providing an “effective” body diode.) In As we mentioned previously, the experimental setup in Fig. 16 addition, Fig. 17 shows a nearly-pure sinusoidal TMN output uses a 150 W linear class A amplifier (150A100B, Amplifier voltage (the voltage across the load) suggesting a relatively Research) with a 50 Ω output impedance. The drive signal for small harmonic content injected into the load (measured to be the PA is generated directly by the controller at the desired less than -20 dBc). Similar output harmonic content is found for operating frequency and amplitude level to achieve a the rest of the test cases in Table II. On the other hand, one can commanded PA output power level. The desired TMN shunt easily notice that the input TMN voltage has significant capacitance is communicated to the TMN over a serial interface harmonic content for the test case in Fig. 17. A small portion of in the form of a digital capacitor code in the 0 – 1000 range. In it is due to relatively weak input filtering of the drain voltage. the case of TMNs based on mechanically tunable capacitors, this However, most of the harmonic content observed in TMN input digital code typically maps linearly to the actual capacitance voltage is attributed to near-saturation of the power amplifier value. However, in the case of the PSIM-based implementation, used to drive the TMN; it is notable that the phase lock gate drive the digital capacitance code is instead mapped linearly to the generation system performs extremely well even in the face of commanded switch conduction angle α (see Fig. 10); code value this distortion from the power amplifier. of 0 corresponds to a permanently-off switch (α = 0), while a code value of 1000 is roughly equivalent to a permanently-on The noticeable rise and fall time of the gate-drive signal are switch (α ≈ 180°). Hence, there is a non-linear, but monotonic a result of the driving capability of the gate driver and the gate- relationship between the digital capacitor codes issued by the to-source capacitance of the transistor (approximately 130 pF). controller and the actual effective capacitance realized by the Note that in this case, the relatively slow device turn-on does not PSIM TMN. We find that this nonlinearity is not problematic for significantly impact losses in the device since the turn-on occurs the control loop used here and results in stable system behavior while the device is in reverse conduction. for all transient experiments performed in this work. Similar voltage waveforms are measured for the rest of the For example, Fig. 18 shows the transient response of the PSIM- test cases in Table I, suggesting that the PSIM-based TMN based TMN when powering into a fixed 2 + j20 Ω inductive implementation proposed here is effective at accurately load. Initially, the power amplifier is off, and the PSIM matching a wide range of load impedances. It is important to controller is initialized with a frequency of 14.20 MHz and a note that harmonic content in the output depends on both the capacitor code of 100, corresponding nearly to a permanently- TMN’s output filter and the frequency profile of the load off switch. (Digital capacitor codes less than 200 corresponding impedance. For instance, an inductive load generated with the roughly to α ≤ 36° have negligible effect on the effective PSIM variable-length transmission line implementation discussed capacitance – see Fig. 2.) At the 10 ms mark, the PA is above has a very different frequency characteristic from that of commanded to an output power of 50 W. an equivalent inductive load formed by the series combination of a resistor and an inductor. Hence, the design of the TMN’s As Fig. 18 shows, the TMN undergoes approximately a 15 output filter must be carefully tailored to the particular load ms transient with the forward power settling to the commanded 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics power level of 50 W. Note that the TMN is able to provide a measure impedances rapidly and accurately at radio frequencies. good impedance match to 50 Ω with minimal reflected power The exploration of these and other topics towards further within a tuning time that is already at least on order of magnitude improving the dynamic performance of PSIM-based TMNs is faster than typical response times of conventional TMNs based the subject of future work. on mechanically-tuned capacitors. D. PSIM-TMN Performance with Inductively-Coupled Plasma Loads The generation and control of inductively-coupled plasma (ICP) is of importance to the semiconductor manufacturing industry among others. To be able to perform the sophisticated semiconductor wafer processing demanded by industry, plasma has to be generated and maintained over a wide range of process parameters such as gas composition, pressure, flow rate, excitation power, etc. A typical ICP chamber, as shown in Fig. 19, consists of a plasma excitation cavity through which a known gas flows at a precisely controlled rate and pressure. The plasma is generated by RF electric and magnetic fields produced by exciting a coil wrapped around this cavity at a particular frequency and power level. A secondary cavity located below the main one houses the chuck – a special platform which holds the wafer to be processed. The chuck is itself typically driven with a separate RF “bias” source producing electric fields that serve to increase the directivity of plasma ions bombarding the wafer [22]. The generation of plasma in such systems is particularly challenging since the driving-point impedances for both the coil and the chuck vary widely with process parameters and the state of the plasma. Since most conventional RF power amplifiers are designed to operate into a fixed or a very narrow range of load impedances, TMNs are used to match the widely varying impedances presented by the excitation coil and chuck to their respective PAs. Due to the requirements for accurate impedance matching over a wide load range and operation at high power Fig. 18: Forward and reflected power versus time at the input port of the PSIM levels, such systems usually rely on mechanically tunable TMNs TMN for a 0 W to 50 W step in commanded PA output power (top) and the and suffer from extraordinarily slow tuning speeds [18]. Here corresponding capacitance (middle) and frequency (bottom) controls necessary to achieve impedance matching between the 50 Ω PA output impedance and a 2 we demonstrate the ability of the PSIM TMN to match + j20 Ω load. dynamically varying plasma loads to a 50 Ω source impedance with at least two orders of magnitude reduction in tuning time As previously mentioned, the controller used in this setup compared to most mechanically-tuned TMNs. was originally designed for the control of mechanically-tuned capacitors which are typically driven by stepper or servo motors. Fig. 19 shows the experimental setup of an 800 W ICP test To minimize the jitter in the motors and the wear and tear of all chamber at an MKS Instruments testing facility. A high-power moving parts, the controller is typically designed to wait a PA driving the main plasma excitation coil is used to generate certain time period after every capacitor command before and sustain the plasma with a number of gases at various issuing the next one. This explains the stepwise nature of the pressures and flow rates and at power levels ranging from 100W control signal in Fig. 18 with approximately 2.5 ms of wait – 800 W. A second power amplifier operating at tens of W is period between successive capacitor commands. To further used to drive the wafer chuck with an rf bias. Based on the power reduce capacitance control effort, the controller used in this levels of the TMN prototype developed here, we demonstrate work attempts to tune the capacitance only if the reflected power the PSIM TMN for matching the widely-varying wafer chuck exceeds approximately 5% of the forward power. Of course, the driving-point impedance to the 50 Ω output impedance of a PSIM-based TMN implementation presented here alleviates the linear class A amplifier (A500, ENI) for the rf bias, while a mechanical limitations associated with controlling stepper conventional TMN based on mechanically-tunable vacuum motor-driven variable capacitors. capacitors is used to match the excitation coil impedance to a high-power PA. An identical controller to the one described in With an appropriately designed controller, one ought to be the previous section adjusts the PSIM switch conduction angle able to achieve still much faster response times and more and frequency of the wafer chuck rf bias drive based on an I-V accurate impedance matching than demonstrated here. An probe (Model#: 000-1106-117, MKS Instruments) measurement important step towards the design of such a custom controller is of the load impedance seen by the PA. Modulation of the wafer the development of a full dynamic model of the PSIM-TMN chuck drive frequency is constrained within a ±5% band around system. Furthermore, to fully utilize the inherent high bandwidth 13.56 MHz. capability of PSIM-based systems, one must also be able to 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics It is observed that rf bias and plasma excitation power have 600 W pulse with less than 5% of reflected power. Even faster considerably larger impacts on the chuck driving-point tuning times of less than 3 ms are demonstrated in Fig. 21 for a impedance compared to the effect of gas composition, flow rate 10 W – 40 W step in the chuck bias power with a constant and pressure. Nevertheless, the PSIM-based TMN is capable of plasma excitation of 600 W. (For the results shown in Fig. 20 providing fast and accurate impedance matching over a wide and 18, the plasma is generated in an argon gas at 20 mT range of process parameters including changes in excitation and pressure and 125 sccm flow rate.) Note that for the experiments bias power. discussed in this section, the internal controller gains were adjusted to allow for faster tuning and higher utilization of the available bandwidth of the PSIM TMN. This is the reason why the tuning transients in Fig 17 and Fig. 21 are considerably faster than the one demonstrated in Fig. 18. Fig. 19: Experimental setup for testing the performance of the PSIM-TMN with plasma loads. The PSIM-TMN matches the wafer chuck to a low power PA. A conventional TMN based on mechanically-tunable capacitors is used to match a high-power PA to the plasma excitation coil. Fig. 21: Forward and reflected power versus time at the input of the PSIM TMN for a 10W – 40 W step in the chuck rf bias power with 600 W in the plasma excitation coil. It appears from Fig. 20 that the capacitance code issued by the controller settles in a single control step. Note however that the controller will only attempt to adjust the PSIM capacitance if the reflected power measured by the I-V probe exceeds 5% of the forward power. As mentioned previously, this dead-band in capacitance control is implemented to eliminate jitter in the servo motors when the controller is used as originally intended with TMNs based on mechanically-tuned capacitors. Although in Fig. 20 a capacitance code of 566 and 619 corresponding respectively to 175 W and 600 W of plasma excitation power may not result in a perfect impedance match between the bias PA and the chuck, the measured reflected power falls within the controller dead-band. As a result, the controller issues no further adjustment to the PSIM capacitance. It is important to note that the sampling rate of the I-V probe and the data rate of the serial communication link between the controller and the PSIM match considerably limits the tuning speed with which impedance matching can be performed in our prototype setup. The PSIM technique inherently allows much faster capacitance modulation; its response speed is mainly Fig. 20: Forward and reflected power versus time at the input of the PSIM TMN (top) and the corresponding shunt capacitance (middle) and frequency (bottom) determined by how fast one can control the conduction angle of controls for a 175 W - 600 W pulse on the plasma excitation coil. the switch. If one is able to synthesize the required gate-drive signals for the PSIM transistor with high enough bandwidth, one For example, Fig. 20 shows the forward and reflected power can theoretically modulated the effective PSIM capacitance on at the input of the PSIM TMN for a 10 W commanded bias a rf cycle-per-cycle basis. By using PSIM along with a higher power during a 175 W – 600 W pulse in the plasma excitation bandwidth controller with no dead-band and faster impedance power. It can be seen that the tuning transient lasts sampling, one ought to be able to achieve even faster and more approximately 5 ms for both the falling and rising edges of the accurate impedance matching with tuning time in the range of a 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics few µs – this is nearly six orders of magnitude reduction in the values of 𝑘 . In the current prototype, we limit capacitance tuning time compared to most conventional vacuum capacitor- modulation up to approximately a factor of 4x. Implementation based TMNs! details of the switch driving and synchronization scheme employed are further presented in Section III.B. VII. CONCLUSION Another important practical aspect of PSIM to consider is This work proposes a tunable matching network based on the voltage stress imposed on the device. It can be shown (see phase-switched impedance modulation (PSIM), a technique for Appendix B, [24]) that in the case of Fig. 6A and Fig. 6B the implementing variable impedances based on switching of peak voltage 𝑉 across the device (normalized to |𝑉 | , the passive elements at the RF operating frequency. PSIM is a 𝑃𝐾 1 magnitude of the fundamental component of 𝑣 ) is given by (9), narrow-band technique in that it allows effective modulation of 𝐶 where 𝛼 is the forward conduction angle of the switch. the effective impedance only at the switching frequency. We introduce a PSIM impedance and matching network 𝑉𝑃𝐾 𝜋(1 + cos (𝛼)) implementation that enables zero-voltage-switching of the = (9) |𝑉1| 𝜋 − 𝛼 + sin (𝛼)cos (𝛼) active device with simple timing. Moreover, we introduce a PLL-based modulation control system that provides the This relationship is plotted in Fig. 22 versus 𝛼. As can be seen, necessary sensing and drive of the PSIM circuit. To demonstrate the peak of the voltage across the device is approximately twice the effectiveness of the proposed approach we present a PSIM- the magnitude of its fundamental component for less than 3x based TMN design capable of matching a wide load impedance modulation of the PSIM effective capacitance. In fact, this ratio range associated with inductively-coupled plasma processes to is slightly below 2 for up to 90° of switch forward conduction a 50  power amplifier. The TMN’s performance is angle, corresponding to 2x modulation of the PSIM capacitance. demonstrated in a narrow frequency band centered around 13.56 However, modulating the PSIM effective capacitance by more MHz at an input RF power of up to 150 W. The matching than a factor of 3x cause the peak-to-fundamental magnitude network presented here provides accurate impedance matching ratio to rapidly increase. (to < 1% reflected power) while injecting less than -20 dBc of harmonic content in the load and maintaining zero-voltage- switching over the entire load range. We also demonstrate the use of this system (with a conventional closed-loop controller) on both known loads and driving a plasma chamber. It is shown that such a PSIM-based TMN opens the door to a combination of much faster and more accurate impedance matching than is available with conventional techniques. VIII. APPENDIX One can calculate the power losses in a PSIM element by first computing an equivalent series resistance 𝑅𝐸𝑆𝑅 (in series with the effective PSIM capacitance) as given by (6). It can be shown (see Appendix B, [24]) that the equivalent series Fig. 22: Ratio of the peak capacitor voltage 𝑉𝑃𝐾 to the magnitude of the resistance for the case of Fig. 6A (𝑤𝐹 = 𝑤𝑅) and Fig. 6B (with fundamental component 𝑉1 of the capacitor voltage waveform 𝑣𝐶 for the PSIM 𝑤 = 0) is given by (7) and (8) respectively, where 𝑘 is the element of Fig. 5A versus switch forward conduction angle α. The ratio is plotted 𝑅 𝐶 /𝐶 for an ideal, linear base capacitance (red) and an actual 650V GaN FET effective capacitance modulation factor defined by 𝐸𝐹𝐹 0. (GS66516T, GaN Systems) with no additionally added external capacitance in 1 parallel with the transistor (blue). 𝑃 = 𝐼2𝐷 𝑅 (6) 2 0 𝐸𝑆𝑅 Note that for the TMN system of Fig. 7, the magnitude of the 𝑟 1 fundamental component 𝑉1 of the voltage across the PSIM 0 𝑅𝐸𝑆𝑅 = + 𝑟𝑜𝑛 (1 − ) (7) element is roughly determined by the input power level and 𝑘 𝑘 impedance of the TMN seen into the IN port. This is because the 𝑟0 𝑟𝑜𝑛 𝑟𝐷 1 𝑉𝐷 input filter is nearly resonant over most of the operating 𝑅𝐸𝑆𝑅 = + ( + ) (1 − ) + (1 − cos (𝛼)) (8) 𝑘 2 2 𝑘 𝜋𝐼 frequency range, and hence the magnitude of the fundamental 0 component 𝑉𝐼𝑁,1 of the input voltage is roughly equal to 𝑉1. Here we model the PSIM element as shown in Fig. 5B, where 𝑟𝐷 and 𝑟𝑜𝑛 are the on-resistance of the diode and the switch In practice, the device capacitance can be combined in respectively, 𝑉 is the diode forward voltage drop, and 𝑟 is the parallel with an additionally-added external capacitance, or can 𝐷 0 effective ESR of the total base capacitance C0. For typical power be used on its own to form the PSIM base capacitance C0. In devices, 𝑟 is comparable or larger than 𝑟 , and so, as (7) and general, however, due to the non-linear characteristic of the 𝐷 𝑜𝑛 (8) suggest, operating a PSIM element under quasi-ZVS, i.e. device capacitance, C0 tends to decrease with increasing device allowing the body-diode to engage, is lossier compared to voltage, altering the shape of the ideal PSIM voltage waveform operation with ideal ZVS for any given capacitance modulation illustrated in Fig. 6A. More specifically, larger C0 at low factor 𝑘. Furthermore, as can be seen from (7) and (8), losses voltages causes slower slew rates of 𝑣𝐶 near the base of the increase with larger capacitance modulation – this is another voltage pulse, while smaller C0 at higher voltages results in reason why one should avoid operation of the PSIM at large faster 𝑣𝐶 slew rate near the peak of the pulse. Consequently, this somewhat alters the ratio between the peak of the voltage 𝑉𝑃𝐾 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: University of Wollongong. Downloaded on May 30,2020 at 14:28:50 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2020.2980214, IEEE Transactions on Power Electronics and the magnitude of its fundamental component 𝑉1 . For [2] Nemati, et. al., “Design of Varactor-based tunable matching networks for example, Fig. 22 plots this ratio versus the switch forward dynamic load modulation of high power amplifiers,” IEEE Transactions on Microwave Theory and Techniques, Vol. 57, No. 5, pp. 1110-1118, conduction angle for a 650 V GaN FET device (GS66516, GaN May 2009. Systems) without any additional external capacitance in parallel [3] R. Malmqvist, et. al., “RF MEMS based impedance matching networks with it. The plot is based on a spice simulation of the for tunable multi-band microwave low noise amplifiers,” in Proc. 2009 manufacturer-provided device model. In this case, the device is International Semiconductor Conference, Vol. 1, pp. 303-306. excited with a purely-sinusoidal current 𝑖𝐶 just as in Fig. 6A, [4] S. Nagarkatti, et. al., “Radio frequency power delivery system,” U. S. where the current magnitude is appropriately adjusted to Patent 8 633 782, Jan. 21, 2014. maintain the peak of the device voltage 𝑣𝐶 at approximately 600 [5] G. J. J. Winands, et. al., “Matching a pulsed power modulator to a corona V as the conduction angle of the switch is varied. plasma reactor,” 2007 IEEE International Pulsed Power Conference, pp. 587-590, June 2007. Note from Fig. 22 that even though the peak-to-fundamental [6] D. Goodman, et. al., “RF power supply with integrated matching ratio 𝑉𝑃𝐾⁄|𝑉1| for the GS66516 device is higher than that for the network,” U.S. Patent 6 887 339, May 3, 2005. ideal case with the linear base capacitance, the two are still [7] Y. Lim, et. al., “An adaptive impedance-matching network based on a relatively close to each other. For example in the case of the novel capacitor matrix for wireless power transfer,” IEEE Transactions on Power Electronics, Vol. 29, No. 8, pp. 4403-4413, Aug. 2014. GS66516 device, the peak voltage stress on the device remains less than 2.5x the magnitude of its fundamental component for [8] W. C. E. Neo, et. al., “Adaptive multi-band multi-mode power amplifier using integrated Varactor-based tunable matching networks,” IEEE up to 3x modulation of the PSIM effective capacitance. Journal of Solid-State Circuits, Vol. 41, No. 9, pp. 2166-2176, Sep. 2006. Furthermore, the peak-to-fundamental ratio plot for the [9] Q. Shen and N. S. Barker, “Distributed MEMS tunable matching network GS66516 device in Fig. 22 corresponds to realizing the entire using minimal-contact RF-MEMS varactors,” IEEE Transactions on PSIM base capacitance only with intrinsic output device Microwave Theory and Technology, Vol. 54, No. 6, pp. 2646-2658, Jun. capacitance; by adding some external, linear capacitance in 2006. parallel with the device, one can increase the PSIM base [10] M. T. Arnous, Z. Zhang, S. E. Barbin and G. Boeck, "Characterization of capacitance C while effectively swamping some of the non- high voltage varactors for load modulation of GaN-HEMT power 0 amplifier," 2015 17th International Conference on Transparent Optical linearity in the device capacitance and thus resulting in a peak- Networks (ICTON), Budapest, 2015, pp. 1-4. to-fundamental ratio that is closer to the ideal one. As a practical [11] A. van Bezooijen, et. al., “A GSM/EDGE/WCDMA adaptive series-LC rule-of-thumb, one can assume that the peak voltage stress on matching network using RF-MEMS switches,” IEEE Journal of Soli- the PSIM switching device is roughly 2-2.5x the magnitude of State Circuits, Vol. 43, No. 10, pp. 2259-2268, Oct. 2008. its fundamental voltage component for small PSIM effective [12] C. Sanchez-Perez, et. al., “Design and applications of a 300-800 MHz capacitance modulation factors of up to 3x. tunable matching network,” IEEE Journal on Emerging and Selected Topics in Circuits and Systems, Vol. 3, No. 4, Dec. 2013. When designing PSIM elements, it is also important to [13] P. Sjoblom and H. Sjoland, “Measured CMOS switched high-quality consider the current stress imposed on the switch. It can be capacitors in a reconfigurable matching network,” IEEE Transactions on shown (see Appendix B, [24]) that for the PSIM implementation Circuits and Systems II, Vol. 54, No. 10, pp. 858-862, Oct. 2007. of Fig. 5, the rms current 𝐼𝑠𝑤,𝑟𝑚𝑠 flowing through the switch [14] W. Gu, and K. Harada, "A new method to regulate resonant converters," when it is on (through 𝑟 ) depends on the effective capacitance IEEE Transactions on Power Electronics, Vol. 3, No. 4, Oct. 1988. 𝑜𝑛 modulation factor 𝑘 according to (10), where 𝐶 is the PSIM [15] F. C. W. Po, E. de Foucald, D. Morche, P. Vincent, and E. Kherherve, “A 0 novel method for synthesizing an automatic matching network and its base capacitance, and 𝜔 is the operating frequency (in rad/s). control unit,” IEEE Transactions on Circuits and Systems – I, Vol. 58, No. 9, pp. 2225-2236, Sept. 2011. 𝐼𝑆𝑊,𝑟𝑚𝑠 = 0.5𝑉1𝜔𝐶0√2𝑘(𝑘 − 1) (10) [16] E. 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