Apparatuses and methods involving power modulation of amplifier circuitry

Abstract

In certain examples, the apparatus includes an amplifier (e g., a switched-mode power amplifier) and an impedance-regulation network. The amplifier and an impedance-regulation network are cooperatively configured to: drive a load, and control power delivered from the amplifier to the load by adjusting one or more frequencies of a signal coupled to drive the amplifier. In more-specific examples, the network has a first port (driven by the amplifier), terminated with an associated first image impedance, and the network has a second port (driven from the amplifier) with an associated second image impedance that matches the first image impedance associated with the first port. By adjusting one or more frequencies, the impedance-regulation network and the amplifier are to cause the impedance-regulation network to modulate an equivalent load resistance as seen by the amplifier.

Description

STFD.470PCT (S25-020) 1APPARATUSES AND METHODS INVOLVING POWER MODULATION OF AMPLIFIER CIRCUITRYBACKGROUND

[0001] Aspects of the present disclosure are related generally to the field of power conversion and as may be exemplified using switching devices that are turned on and off at high frequencies for delivering power to loads as in a variety of applications.[00021 Efficient amplifiers (e.g., power amplifiers such as radio-frequency (RF) power amplifiers (PA)) are important aspects in a variety of applications including, but not limited to, industrial applications such as plasma generation for semiconductor etching, induction heating, communication systems, and magnetic-resonance imaging. Many of these applications also demand fast and precise RF power modulation to enhance performance and meet operational requirements. For instance, ELF (extremely low frequency, e.g., 3 Hz -3000 Hz) wave generation may require narrow RF power pulse widths as short as tens of microseconds to minimize conductivity losses. Similarly, plasma-based semiconductor etching often demands a dynamic range greater than 20 dB to ensure precision and control during the etching process.

[0003] To achieve the desired large dynamic range and short power pulse widths, various power modulation techniques are often combined to scale up power levels while balancing fast transients with efficient steady-state performance. Existing methods for achieving fast RF power modulation often involve variations of rail voltage regulation and out-phasing control, each with its own set of advantages and limitations. A common form of rail voltage regulation adjusts the DC supply voltage to modulate the output power of amplifiers. While this approach enables efficient transitions without compromising zerovoltage-switching (ZVS) of switched-mode amplifiers (with ZVS to mitigate overlap between the voltage and current is mitigated to reduce frequency -dependent switching losses), the slew rate limitation due to the large DC bus capacitors slows down the system dynamics, limiting modulation speed.

[0004] There have been various efforts to address the issue of slow transitions. For example, one such attempt incorporated multiple DC (direct current) power supplies in a switched-rail architecture. This solution, although offering certain advantages, sacrifices continuous tunability and involves the implementation of reliable power-supply switches at RF, which is a significant challenge. As another approach, out-phasing amplifiers allow much faster power modulation by adjusting timing or even shutting down amplifiers or operatingSTFD.470PCT (S25-020) 2them in rectifier modes. However, multi-phase systems require added complexity both in the physical component count and in the control. Moreover, even when utilizing an ideally “lossless"’ combiner network, the out-phasing converter’s efficiency still tends to degrade when large phase shifts are applied.

[0005] Accordingly, aspects of the present disclosure are directed to addressing the above and other attributes of such amplifiers.SUMMARY OF VARIOUS ASPECTS AND EXAMPLES

[0006] Various examples / embodiments presented by the present disclosure are directed to issues such as those addressed above and others which may become apparent from the following disclosure. For example, some of these disclosed aspects are directed to methods and devices that use or leverage from switched-mode amplifier technology and an impedance (e.g., resistance) regulation network to effect efficient delivery of power to a load.

[0007] In one specific example according to the present disclosure, a method effects delivery of power to a load. The method includes: using an impedance-regulation network with an amplifier to drive the load; and controlling power delivered from the amplifier to the load by adjusting a frequency of a signal coupled to drive the amplifier.

[0008] In further examples, the above-exemplary method can further comprise one of more of the following aspects: (i) using the impedance-regulation network, to facilitate said controlling pow er delivered to the load, to modulate the equivalent load resistance seen by the amplifier; (ii) shaping, via the impedance-regulation network and the amplifier, a frequency profile of an image impedance specific to a port, of the impedance-regulation network, that is to be driven by the amplifier; and / or (iii) increasing the power delivered from the amplifier, in response to adjusting one or more frequencies, at least by a factor of two, while the amplifier is operating at a frequency on the order of 10 MHz, within 1 microsecond.

[0009] Another specific example is related to the above-characterized exemplary method in the form of an apparatus (e g., circuit or system). The apparatus includes an amplifier and an impedance regulation netw ork, which are cooperatively configured to: drive a load, and to control pow er delivered from the amplifier to the load by adjusting one or more frequencies of a signal coupled to drive the amplifier.

[0010] In other specific examples, the above exemplary apparatus can further comprise one of more further specific aspects. The following are examples: the impedance-regulation network has a first port, to be driven by the amplifier, terminated with an image impedance associated with the first port and has a second port, to be driven from the amplifier, with anSTFD.470PCT (S25-020) 3image impedance associated with the second port that matches the image impedance associated with the first port; the power delivered from the amplifier is modulated with frequency variations by shaping, via the impedance-regulation network and the amplifier, a frequency profile of an image impedance specific to a port, of the impedance-regulation network, that is to be driven by the amplifier; the amplifier is a switched-mode broadband power amplifier operable within a frequency range having a lower limit on the order of one-half MHz and an upper limit on the order of tens of GHz; and the impedance-regulation network has an image impedance specific to a first port of the impedance-regulation network that is to be driven by the amplifier and has an image impedance specific to a second port of the impedance-regulation network that is coupled to the load, each of the image impedances being frequency dependent and at least primarily defined by a manner in which the impedance-regulation network is designed; the first image impedance associated with a frequency profile that dictates a driving point impedance value that is to load the amplifier at any specific frequency and thereby determines output power of the amplifier.[001 I ] In yet further examples, the above exemplary apparatus can further comprise one of more of the following aspects: the amplifier is single-phase power amplifier; the amplifier uses one or more other power modulation techniques; the impedance-regulation netw ork is configured with a first port and a second port respectively connecting between the amplifier and the load and respectively having port-specific first and second purely-resistive image impedances; and / or the amplifier is to maintain zero-voltage-switching (ZVS) during switching transitions of the amplifier, and over different frequencies, from among the one or more frequencies, of the signal coupled to drive the power amplifier.

[0012] In yet further specific examples: the amplifier is a broadband class-Φ2 power amplifier, the impedance-regulation network has a first port, to be driven by the amplifier, and the impedance-regulation network has second port that is coupled to the load and that is associated with a positively-sloped image impedance; and / or the power delivered from the amplifier is to be increased, in response to adjusting one or more frequencies, at least by a factor of two, while the amplifier is operating at a frequency on the order of 10 MHz, within 1 microsecond and in more specific examples within approximately (i.e., plus or minus 20%) 500 nanoseconds.

[0013] In yet other specific examples which relate to and / or build on the abovecharacterized examples, the network may be implemented so that it consists of only passive components, ensuring efficient and fast adjustable power delivery from a broadband power amplifier to the load.STFD.470PCT (S25-020) 4

[0014] The above discussion is not intended to describe each aspect, embodiment or every implementation of the present disclosure. The following figures and detailed description of various embodiments are also intended for exemplification purposes.BRIEF DESCRIPTION OF FIGURES

[0015] Various example embodiments, including experimental examples, may be more completely understood in consideration of the following detailed description in connection with the accompanying drawings, each in accordance with the present disclosure, in which:FIG. 1 is a generalized schematic of a pulsed RF power system showing (combined) methods for power modulation: voltage rail regulation, outphasing, and frequency modulation, according and representing various examples of the present disclosure;FIGs. 2A and 2B are respectively, a generalized schematic of an impedance regulation network (RRN) and a related graph, according to an example of the present disclosure;FIGs. 3A and 3B are respectively, a generalized schematic of an inductively-coupled double tuned network (ICDT) configured as an impedance regulation network and a related graph, according to an example of the present disclosure;FIGs. 4A and 4B are respective image-impedance graphs related to the ICDT of FIG.3A, according to an example of the present disclosure;FIGs. 5A-5D are respective graphs related to the ICDT of FIG. 3 A, according to an example of the present disclosure, with FIGs. 5A and 5B being graphs of image-impedance plots for different values of coupling coefficients (k), and FIGs. 5C and 5D being graphs to show figure of merit (FoM) based on the influence of k on the nominal bandwidth (BW);FIGs. 6A-6D are respective graphs also related to the ICDT of FIG. 3A with ICDT RRN performance curves with varying load port’s image impedance slope p and a fixed coupling coefficient, of which FIGs. 6A-6B show normalized impedance versus normalized frequency for different values of the normalized slope "p. and FIGs. 6C-6D being FoM plots showing the influence of "p on parameters of the amplifier;FIG. 7 is a generalized schematic of a broadband class-Φ2 power amplifier driving a load resistance of R1, according to an example of the present disclosure;FIG. 8 is a graph showing plots of duty cycle values for the designed class-Φ2 switched network to achieve ZVS at different frequencies, according to an example of the present disclosure;STFD.470PCT (S25-020) 5FIG. 9 is a graph showing plots of normalized driving point impedance (DPI) curves showing the RRN’s loading effect on the filter, according to an example of the present disclosure;FIGs. 10A and 10B are respectively: a generalized schematic of a broadband class-Φ2 power amplifier driving a load resistance of R1 (FIG. 10A), and the equivalent circuit (FIG. 10B), according to an example of the present disclosure;FIG. 11 is a prototype semiconductor device, according to an example of the present disclosure;FIG. 12 is a graph showing plots of experimental and simulated output power of the prototype of FIG. 11 at different frequencies and DC voltages, according to an example of the present disclosure; andFIG. 13 is a graph showing plots (also for the prototype of FIG. 11) of normalized power-frequency profiles comparing the theoretical analysis, simulation, and experiment, according to an example of the present disclosure.

[0016] While various embodiments discussed herein are amenable to modifications and alternative forms, aspects thereof have been shown by way of example in the drawings and will be described in greater detail. It should be understood, however, that the intention is not to limit the disclosure to the particular embodiments described. On the contrary’, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the disclosure including aspects defined in the claims. In addition, the term “example” as used throughout this application is only by way of illustration, and not limitation.DETAILED DESCRIPTION

[0017] Certain exemplary aspects of the present disclosure are believed to be applicable to a variety of different types of apparatuses, systems and methods involving devices characterized at least in part by power amplification techniques manifesting high efficiencies and high performance attributes in terms of speed and operating over a wide range of frequencies. In certain examples of the present disclosure, it is recognized that with an approoriately-configured impedance-regulation network in place with the amplifier, a frequency of a signal driving the amplifier is adjusted so that the netw ork modulates the equivalent load resistance seen by the amplifier, thereby controlling the delivered power. While the present disclosure is not necessarily limited to such aspects, an understanding of specific examples in the following description may be understood from discussion in such specific contexts.STFD.470PCT (S25-020) 6

[0018] Accordingly, in the following description various specific details are set forth to describe specific examples presented herein. It should be apparent to one skilled in the art, however, that one or more other Oexamples and / or variations of these examples may be practiced without all the specific details given below. In other instances, well known features have not been described in detail so as not to obscure the description of the examples herein. For ease of illustration, the same connotation and / or reference numerals may be used in different diagrams to refer to the same elements or additional instances of the same element. Also, although aspects and features may in some cases be described in individual figures, it will be appreciated that features from one figure or embodiment can be combined with features of another figure or embodiment even though the combination is not explicitly show n or explicitly described as a combination. Further (and especially in connection with the following discussion and the discussion presented in the Appendix of the underlying U. S. provisional patent application), unless otherwise indicated ranges (of any, and all metrics) are merely exemplary of "approximate ranges7’ wherein this term may be understood to vary the bound(s) of the range (e.g., using improved and / or degraded material- or circuit-based design parameters) by a degree of anywhere from 10-to-20 percent (or in some instances from 5-35 percent), and, in the context of comparison to an improvement over a previously-reported effort, by a degree of improvement of 20 percent or greater.

[0019] Certain aspects of the present disclosure can be implemented to help improve the performance of current RF power systems, especially for applications such as plasma generation, semiconductor etching, wireless power transfer, and communication systems. In these and other applications, a variety of different processes and devices may be advantaged by such aspects disclosed in connection with the present disclosure, including aspects and examples in U. S. Provisional Application No. 63 / 754,314 filed on February 5, 2025 with an Appendix (STFD.470P1).

[0020] As specific examples in this regard, specific aspects of the present disclosure are directed to achieving ultra-fast power modulation with a single-phase power amplifier, to provide advantages over previously -known approaches (e.g., including voltage-rail regulation, out-phasing converter, and modularized on-off controls). For example, the voltage-rail regulation is usually slow and needs extra DC-DC power converter stages, increasing the cost of the overall system. The out-phasing and modular approaches require multi-phase power amplifiers, which cannot be implemented with single-phase systems.

[0021] In certain examples according to the present disclosure, an apparatus includes an amplifier (e.g., 0a s itched- mode power amplifier) and an impedance-regulation network.STFD.470PCT (S25-020) 7The amplifier and an impedance-regulation network are cooperatively configured to: drive a load, and control power delivered from the amplifier to the load by adjusting one or more frequencies of a signal coupled to drive the amplifier. The apparatus can be a power amplification circuit, any of a variety' of appliances that includes a power amplifier, and in some instances, the apparatus can be certain equipment specific to one of the applications as previously mentioned (e.g., plasma generation equipment for semiconductor etching, induction heating tools, communication systems, and magnetic-resonance imaging equipment).

[0022] Another specific example is related to the above-characterized exemplary- apparatus in the form of a method. The method includes: using an impedance-regulation network with an amplifier to drive the load; and controlling power delivered from the amplifier to the load by adjusting a frequency of a signal coupled to drive the amplifier. In more-specific examples and applicable to the above-characterized type of apparatus as well as the type of method, the network has a first port (driven by the amplifier), terminated with an associated first image impedance, and the network has a second port (driven from the amplifier) with an associated second image impedance that matches the first image impedance associated with the first port. By adjusting one or more frequencies, the impedance-regulation network and the amplifier are to cause the impedance-regulation network to modulate an equivalent load resistance as seen by the amplifier.[0023 J Consistent with the above-mentioned examples according to the present disclosure, FIG. 1 is a diagram of a pulsed RF power system, showing to the left side of FIG. 1 a generalized schematic of a power amplification circuit. To the right is a profile of pulses corresponding to an output from the system, and showing the pulse width being tens of microseconds at a power level of greater than 20 dB. The depicted system exemplifies how methods for power modulation can be combined with frequency modulation according to the present disclosure. As optional aspects, the pulsed RF power system shows rail regulation in dashed lines to the top of FIG. 1 and / or outphasing in dashed lines to the bottom of FIG. 1. Rail regulation, at the VDC power rail, is sometimes used to control and stabilize the DC supply voltages that power the output switching transistors. For example, with Class D amplifiers, the power supply voltage is modulated to create the output signal, and the rail regulation aids performance in terms of stability, efficiency and cleanliness of the voltage rails which power the amplifiers.

[0024] The outphasing aspect is depicted by a summer circuit (“+”) having as inputs different phases (0i, 02,... 0n) of related output signals driven by a parallel-arrangement ofSTFD.470PCT (S25-020) 8power amplifiers (PAi, PA2,... PAn). In this particular example of FIG. 1, each PA is driven by a different signal source having its associated frequency (ω₁ for PA₁, … ωₙ for PAₙ) in accordance with the present disclosure. More generally, outphasing involves breaking down the modulated signal into two constant-amplitude, phase-modulated signals, and as shown in FIG. 1. these two signals may then be combined to provide the combined output for driving a load.

[0025] In certain specific applications benefited by or requiring to maximize system efficiency, aspects of the present disclosure utilize the RRN power modulation technique with a switched-mode broadband power amplifier. This may be recognized, in one example, by considering practical design guidelines for certain types of broadband switched-mode amplifiers with reference to the loading effects of the RRN. In one experimental design, for example, a 300 W class-Φ2 prototype is successfully implemented and tested with realization of a peak efficiency of 94%. Operating between 13.2 MHz and 14.4 MHz, the amplifier is capable of doubling its output power within 500 ns while maintaining ZVS.

[0026] Accordingly, this type of design can be implemented to carry out high-speed RF power modulation using an impedance regulation network (sometimes referred to as a resistance regulation network, “RRN’'). As noted above, by adjusting the frequency, the RRN modulates the equivalent load resistance seen by the amplifier, thereby controlling the delivered power. In certain examples, such a design can be implemented with features (advantageous in comparison to previously-known methods including rail voltage regulation and / or out-phasing) including frequency modulation that enables ultra-fast transition speeds, minimal circuitry, high efficiency, compatibility with single-phase amplifiers (e.g.. offering reductions in size and power consumption), and the ability to complement existing power modulation techniques, providing the potential for improved performance (e.g., enhanced transient response) and a wider dynamic range of power levels when used in combination.

[0027] As a basis for designing such networks using image impedances, FIG. 2A-2B illustrate a generalized schematic of a circuit with an RRN, driven by a broadband power amplifier (PA) and loaded by a constant resistance (“R”). FIG. 2A depicts a generalized schematic showing a signal source with frequency control driving an input port of a PA, and the PA driving an RRN. FIG. 2B is a graph depicting a relationship between the angular frequency co and image impedance associated with each of the RRN ports.

[0028] The RRN provides frequency-dependent impedance control, designed to exhibit different driving point impedance (DPI) values as the excitation frequency changes.Equivalently, the RRN regulates a fixed load to a controllable DPI so that the powerSTFD.470PCT (S25-020) 9delivered to the network can be modulated. Assuming a lossless network, e.g., an LC network, the output power equals the power delivered to the network and thus can be directly adjusted by tuning the frequency.[00291 A trivial example of RRN is adding an inductor L between the amplifier and the toad. The amplitude of its DPI is the square root of (R2+ (ωL)2) with co being the angular frequency. This frequency dependence theoretically enables power modulation, as the output current is inversely proportional to the DPI. However, this RRN is less practical due to the inductive nature of its DPI. First, most power amplifiers are designed to drive resistive loads, making a variable inductive impedance highly undesirable. Such an impedance can lead to efficiency degradation and potential thermal issues in the amplifier. Additionally, achieving significant power modulation may require a large frequency shift, which can strain the amplifier’s bandwidth. For instance, at maximum power, it would be helpful if the DPI was to appear as resistive as possible to optimize semiconductor utilization within the amplifier. Assuming R = 10®L as an engineering approximation, when the power is reduced to 50% of its maximum, the RRN requires a frequency shift such that R ~ co'L. This implies a tenfold frequency change from co to co', which is difficult to implement efficiently.

[0030] Aspects of the present disclosure facilitate such circuitry so as to develop lossless RRNs with resistive DPI characteristics for improved efficiency and controllability. In these regards, the following discussion is helpful to appreciate theory and design examples, of such aspects according to the present disclosure.

[0031] In theory, the image impedances of a two-port network are defined such that when one port is terminated with its image impedance, the DPI at the other port matches the other image impedance. It is important to note that image impedances are specific to each port and are determined solely by the structure of the network. For clarity, the port driven by the amplifier is designated as port 1, with image impedance Zi 1 (co), and the port connected to the load is designated as port 2, with image impedance Zi2(co). Both Zil(co) and Zi2(co) are frequency-dependent.

[0032] According to the definition, if Zi2(co) = R holds across the entire bandwidth of interest, the DPI of the network is simply Zi 1 (co). In other words, the frequency profile of Zil(co) dictates the DPI value that loads the power amplifier at any specific frequency, which in turn determines the output power. When the network consists solely of lossless passive components, it is proven that both Z2i 1 (co) and Z2I2(OJ) are real numbers. Since real power is always being delivered to the load, the designed image impedances are guaranteed to be pure resistive. Therefore, its DPI remains resistive as long as Zi2(co) = R.STFD.470PCT (S25-020) 10

[0033] By shaping the frequency profile of Zi1(ω), one can design how the output power is modulated with frequency^ variations. For example, a large derivative of Zi 1 (co) indicates more sensitive power modulation in response to frequency changes, while a convex Zil(ro) profile leads to a concave power-versus frequency curve. In practice, it appears not to be physically possible to have Zi2(co) = R across the entire bandwidth. However, by constraining the first or even higher-order derivatives of Zi2(®) to zero, a good approximation can be achieved.

[0034] To illustrate the proposed RRN design methodology', one specific example is based on the inductively coupled double-tuned (ICDT) network. Note that this is only one of many possible RRNs networks. In FIG. 3A, a circuit diagram is shown with the coupling coefficient between the inductors denoted as k. The components are labeled with subscripts corresponding to their connected ports (its image impedances can be derived as (1) and (2) at the bottom of page 3 of the Appendix which forms part of the above-identified U. S.Provisional Application No. 63 / 754,314).

[0035] Under nominal conditions, it is assumed the RRN regulates the load R2 to a resistive DPI of Ri at the angular frequency wo. In terms of image impedances, this is equivalent to satisfying the following equation (identified as “3” with omission of 1 and 2 being intentional):...I /

[0036] First-order approximations are then applied around this nominal point to constrain the desired image impedance profiles. As will be shown, the resulting equations provide adequate accuracy across a wide variety' of designs. To approximate Zi2 ( ) = R2 over the bandwidth of interest, the derivative is set to zero at the nominal point:(4)

[0037] It suppresses the frequency sensitivity of Zi2 (w) at wo, creating a relatively flat profile around the nominal point and ensuring Zi2 (w) ~ R2. On the other hand, one can set the derivative of Zil (w) to a nonzero constant p as:= p f 0(5) 10038] This constrains the slope of Zii (w) at wo and results in a quasi-linear DPI profile. As a result, the Zii (w) and DPI can be approximated as:STFD.470PCT (S25-020) 11Zf / ’j. (u? ) ■■■■■■ p (tv — (g)

[0039] An example design is shown in FIGs. 4A-4B, where the nominal point is set at 13.56 MHz with Ri = 100 n and R2 = 50 n. To achieve a 50% DPI change within a 1 MHz bandwidth, p = 10 pOs / rad is chosen. Since the RRN has five unknown parameters while only three constraints are provided by equations (3) to (5), there is flexibility to select k = 0.9 so as to simplify the calculation. A detailed discussion on the impacts of different values of p and k is given in the next section. Substituting the values into equations (3) to (5) yields the following circuit parameters for LI and L2 as below at (7) as follows:LI = 11.58 pH, Cl = 137.9 pFL2 = 945.2 nH, C2 = 917.7 pF (7)

[0040] As illustrated by FIGs. 4A-4B, the profile of Zi2 (w) exhibits a flattened convex curvature around the nominal frequency. FIGs. 4A-4B depict a 1 MHz bandwidth, with the maximum deviation of Zi2(w) from R2 being approximately 10%, occur-ring at the frequency band's boundary. This corresponds to a reflection coefficient of 0.048, which validates the assumptions made in (4) and confirms that Zii(w) governs the DPI profile. FIGs.4A-4B compare Zii(w), the amplitude of DPI, and their linear approximation from Eqtn. (6). All three curves closely align within the 1 MHz bandwidth, demonstrating the effectiveness of the proposed design methodology. The linearity of Zii(w) is preserved relative to its tangent line, while the DPI closely tracks Zi ] (w] due to the nearly constant behavior of Zi2(w. Although the mismatch slightly increases at lower frequencies, the overall maximum-to-minimum impedance ratio of the DPI remains consistent with the predicted value from Ziifw ), approximately doubling from low to high frequencies within the band. Further calculations show that the phase of the DPI stays between 0° and -4° over the plotted frequency range, indicating that a near-resistive DPI is achieved. In conclusion, the example RRN with the ICDT topology validates the proposed design approach, demonstrating the ability to achieve doubled power modulation across a 1 MHz tuning bandwidth.

[0001] In connection with analysis of parameters, the performance of an RRN depends on its specific topology and circuit parameters. For instance, an ICDT network designed with different p values can exhibit varying power modulation sensitivity, while both p and k values influence the bandwidth and reactive current within the network. To examine theseSTFD.470PCT (S25-020) 12effects, the ICDT RRN is used as a case study, focusing on the following figures of merits (FOMs):• Nominal Bandwidth (BW) is based on a maximum tolerable Zi2imax.- If Wi < w < whrepresents the largest frequency band whereZi2(w) 5= Zi2) max> then the bandwidth is given by BW = wh— wt. Itsvalue is normalized to the nominal angular frequency wo.• Nominal Power Modulation Ratio (x) is the ratio of the maximum to minimum values of DPI within the band that defines BW.• Peak Reactive Current IPk is the maximum peak current flowing in the RRNat the nominal frequency. Its value is normalized to the load current.[0042 For the following discussion (e.g., in connection with FIGs. 5A-5D), normalized values are used to simplify the analysis and generalize the conclusions. In addition to the FOMs, the frequency is normalized to the nominal value wo. Zii(w) is normalized to Ri, and Z;2(w) is normalized to R2. FIGs. 5A-5D show the performance of the ICDT RRN with identical image impedance derivatives but varying the coupling coefficient k and a fixed image impedance slope. The same setting of Ri = 2R2 is maintained as in the previous example. In FIGs. 5A-5B, the image impedance curves show the profiles of Zi 1 (w) and Zi2(w) for different values of k (the darker the curve, the higher the coefficient k). In FIGs. 5C-5D, the FOM curves demonstrate the influence of k on the nominal bandwidth BW (with the nominal power modulation ratio x and the peak reactive current IPk of the RRN, and all values are normalized as hereinabove). For example, at the upper right of FIG. 5C where the k is greatest, the curves show the BW as slightly increasing over the normalized values.

[0043] As depicted in these performance curves, both Zii(w) and Zi2(w) exhibit consistent overall trends as k changes. When k decreases, the curvature of Zi2(w) becomes more pronounced, leading to a reduced flat section around the nominal frequency. This indicates that the first-order approximation of image impedances remains valid over a narrower bandwidth. To quantify this effect, Zi2 maxis set to be 10% higher than Ri o analyze the impact of varying k on the FOMs, as shown in FIGs. 5A-5D. The normalized profiles of B W and x are nearly identical, differing only by a scaling factor. This indicates that even for small the DPI maintains good linearity within the nanowed bandwidth. It also suggests that the proposed RRN methodology is applicable across a wide range of coupling coefficients in the ICDT network. The general trends in FIGs. 5A-5D demonstrate thatSTFD.470PCT (S25-020) 13increased k leads to both a wider nominal bandwidth (BW) and a higher power modulation ratio (x), while reducing the peak reactive current (Jpk). Since a lower reactive current typically enhances system efficiency, a larger coupling coefficient is generally desirable, provided the amplifier can operate across the required bandwidth.

[0044] To analyze how different image impedance derivatives affect the RRN's performance, the normalized slope Zii(w) is characterized as in (8) below:

[0045] With a fixed coupling coefficient of 0.95 and Ri = 2R2, the result of changing p is summarized in the plots of ICDT RRN performance curves of FIGs. 6A-6D, each with varying load port's image impedance slope p and a fixed coupling coefficient. In FIGs.6A and 6T3, the image impedance curves show the profiles of Zd(w) and Zj?(w) for different values of the normalized slope p. In FIG. 6A the darkness of the curves corresponds to a greater p as in tire upper plots to the right of center and to the lower plots to the left of center, and in FIG. 6B the darkness of the curves corresponds to a greater? as in the upper-most plots which meet at. center. In FIGs. 6C and 6D, the FOM curves demonstrate the influence of p on the nominal bandwidth BW, the nominal power modulation ratio x and the peak reactive current Ipk of the RRN All values are normalized as indicated above. The FOMs are calculated with the same Zi2of 110% R2. As p increases. Zii(w) displays the expected quasi-linear profile around the nominal frequency with a steeper slope. Meanwhile, Zi2(w) curls upward, leading to a narrower bandw idth. This reduced bandwidth counteracts the increased frequency sensitivity of the DPI, leading to diminishing returns when boosting X (FIG. 6C). Additionally, a higher p leads to a proportional increase in the peak reactive cunent (FIG. 6D), reducing the system's efficiency. Therefore, practical designs must balance power modulation capability with efficiency, and a moderate value of p is likely to offer the best overall performance.

[0046] By combining FIGs. 5A-5D and FIGs. 6A-6D, it can be concluded that the ICDT RRN network can comfortably achieve approximately a twofold power modulation with reasonably chosen parameters. It is important to note that the discussion in this section applies specifically to the ICDT network; RRNs with other topologies can behave differently. However, the general design methodology remains valid, and similar analyses can be conducted to assess the design parameters of those networks.STFD.470PCT (S25-020) 14

[0047] The impedance conversion ratio also plays a critical role in RRN design. While a different conversion ratio may not affect the normalized FOMs, it can still change the overall reactive power consumed by the network. Similar to conventional matching networks, a larger conversion ratio typically results in a higher quality factor, which can reduce the network's efficiency and tuning feasibility. Moreover, the impedance conversion ratio also impacts the power amplifier design, which must be capable of driving the resulting DPI while delivering the desired power. Hence, a moderate conversion ratio is generally more practical, as it balances the performance of both the power amplifier and the RRN.

[0048] In connection with an application involving a switched-mode broadband power amplifier, implementation of an RRN is benefitted by a broadband power amplifier (PA) with sufficient bandwidth, and switched-mode PAs are favored over linear ones due to their superior efficiency. According to recent studies, promising advancements have been shown in broadband switched-mode PA designs with various topologies, and in the following discussion is directed to an example amplifier, also in accordance with the present disclosure, being partitioned into a switched network and a broadband filter to carry out the design of a broadband Class-®? power amplifier. The loading effect is assessed separately on the switched network and filter when driving the RRN across a broad bandwidth. An exemplary holistic amplifier design, also according to the present disclosure, is disclosed hereinbelow, with all three circuit stages being combined and including the switched network, the broadband filter, and the RRN.

[0049] Using an example design with a Class-02 switched network, FIG. 7 shows a schematic of a typical Class-®? power amplifier, where the switched network contains LF, CF, LMR, CMR and the semiconductor switch.

[0050] The nominal operating frequency of the amplifier in FIG. 7 is set to 13.56 MHz when driving the nominal load resistance Ri = 100 n. According to the literature, a high-Q condition is important, if not necessary, for broadband operation and this imposes a constraint on the maximum LF, given by (9) as follows:rRi / .p ™ — - — ■*,, Z jF ZQXwhere w(j is the nominal angular frequency and QF is the desired quality factor. For a moderate resonating current in the switched network QF = 3.5 is chosen, leading to an LF of 335 nH. To account for the nonlinear Cossof the semiconductor switch, its on-state timeSTFD.470PCT (S25-020) 15is extended to 80% of the off-state time, resulting in a duty cycle of D = 0.44. The pole frequencies of the network, Wa and Wb, can thus be calculated by solving the equations at (10) below (as in Z. Ye and J. Rivas, " Broadband high frequency power conversion with frequency-tuning matching network," IEEE Open Journal of Power Electronics, vol. 6, pp. 120-129, 2025):where D' = 1 - D. A shape factor of r- = 0.4 is chosen to render a moderately flat voltage waveform across the switch (vds). And using this shape factor, based on the article by Z. Ye and J. Rivas, the shunt capacitance CF are determined as 165 pF, and the MR branch parameters are determined as CMR being equal to 82 pF and LMR being equal to 363 nH.

[0051] When the RRN is driven by an amplifier, it introduces loading effects that cause deviations from the intended nominal operation. These nonidealities can cause the amplifier to lose zero-voltage switching (ZVS) at high or low frequencies, ultimately restricting the range for frequency control and power modulation. With the aforementioned Class-fa network design, it is beneficial to implement the RRN with a positive Zi2 (w) slope for two reasons. First, even though the output voltage of the Class-fa network maintains consistent overall shape and amplitude, its fundamental component can have a slightly negative frequency dependency.

[0052] FIG. 8 illustrates the required duty cycle at different frequencies to achieve ZVS and the resultant fundamental amplitude of the switch's drain-to-source voltage | vds,i |. It is evident that | vds.i | drops by approximately 5% when the frequency is increased off the nominal value by the same percentage. Hence, it maximizes the power modulation ratio when combined with an RRN that has a positive impedance slope.

[0053] The second reason is that a positive Zi2(w) slope also helps maintain the high-Q condition to facilitate the amplifier operating across broadband. As shown in (9), for a given LF, the desired quality factor QF is proportional to the ratio of the load resistance and the frequency. A positive frequency slope of DPI thus keeps QF stay relatively constant around the nominal frequency and slowly decreases at lower frequencies. On the other hand,STFD.470PCT (S25-020) 16a negative frequency slope leads to a significantly reduced QF at high frequencies, resulting in the need for a smaller LF and higher resonant current in the switched network.

[0054] Because the loading effect reduces the quality factor of the switched network on one side of the bandwidth, the power amplifier with RRN will have an asymmetric power modulation performance below and above the nominal frequency. For example, with a positive Zi2(w) slope, the power amplifier is able to operate further above the nominal frequency than below without losing ZVS. Hence, the maximum power the power amplifier is able to output is set by the lowest frequency that ZVS is maintained.

[0055] Theoretically, there should be no limit on what broadband filter to be implemented in a broadband class-2 amplifier. The topology is selected as shown in FIG. 7 with the tuning to demonstrate a practical design and discuss its performance when loaded by an RRN. The two resonant branches resonant at the same nominal angular frequency wo, and their quality factors are defined in the following equation (identified as “13” with omission of 11 and 12 being intentional):VF ” - F"" - - - Trvr■••VAp Ri\ 1 - ) For discussion of such tuning and operation of the two resonant branches, see J. Xu, Z. Tong, and J. Rivas-Davila, "1 kw mhz wideband class e power amplifier," IEEE Open Journal of Power Electronics, Hol. 3, pp. 84-92, 2022. Intuitively, the two resonant branches counteract each other near the nominal frequency, leading to a relatively flat passband

[0025] , For demonstration, the same nominal conditions are used as in the above article by J. Xu, Z. Tong, and J. Rivas-Davila, with Ri = 1OOD at 13.56 MHz, and set Qs = 3 and Q p = 2. The resulting circuit parameters are below in (14):Ls = 3.6 pH, Cs = 39 pF / . / ? = 594 nH. Gp =230 pF (14)

[0056] Since the RRN exhibits a varying DPI across frequencies, the loading on the filter also changes accordingly. When the RRN’s DPI deviates from its nominal value Ri, the filter’s bandpass characteristics become less ideal, leading to increased signal attenuation and reflection. As a result, the filter’s DPI seen by the switched network can no longer be assumed to match the RRN’s DPI. This non-ideal loading effect depends on the specific topology and implementation of the broadband filter. Careful filter design can mitigate this effect within the desired frequency range.STFD.470PCT (S25-020) 17

[0057] FIG. 9 compares the DPI of the designed filter with the loading RRN's DPI. The comparison shows that around the nominal frequency, the two DPI curves overlap completely, indicating a good passband characteristic. As the frequency deviates from the nominal value, the DPI of the loaded filter exhibits a diminishing derivative compared to the RRN's DPI, leading to a reduced power modulation ratio. Notably, both DPI curves maintain near-zero phase values, suggesting resistive impedance transformation across the entire bandwidth.00 < S J The above discussion reveals that the switched network and the broadband filter are impacted differently by the RRN's loading effects. If the RRN is designed with a positive Zi2(w) slope, as in certain examples according to the present disclosure, the switched network helps increase the nominal power modulation ratio while the broadband filter attenuates it. The lowest tuning frequency is limited by the switched network to achieve ZVS, setting the maximum possible output power. The highest tuning frequency is limited by the filter attenuation, determining the lowest output power. Consequently, the practical achievable power modulation is controlled by an asymmetric frequency tuning range around the nominal frequency. See infra for further illustration of the loading effect (e.g., where a tuning range from approximately 13.2 MHz to approximately 14.4 MHz is achieved with a nominal frequency of approximately 13.56 MHz).

[0059] For example designs, according to the present disclosure, that include a broadband power amplifier with RRN loading, it is beneficial to design the RRN with a large coupling coefficient. Although achieving k > 0.9 with practical coupled inductors is challenging, the RRN's topology can be transformed into decoupled equivalent circuits, which are easier to implement. Moreover, the RRN can be integrated with the broadband filter stage in the pow er amplifier, further simplifying the circuit and reducing the component count.

[0060] FIGs. 10A-10B illustrate the conversion that combines the broadband filter and the RRN in such an example, (for converted-component values, see (15) of the Appendix in the above-identified U. S. Provisional Application No. 63 / 754,314). FIG. 10A is a generalized / conceptual schematic of the circuit design including the filter and the RRN for the design, and FIG. 10B is a generalized / conceptual schematic of an alternative circuit design in which circuitry related to that shown in FIG. 10A is decoupled as a simplified equivalent circuit.STFD.470PCT (S25-020) 18

[0061] For example, it is advantageous to use the designed broadband power amplifier to drive an RRN with k = 0.99 and p = 16 for Ri = 2R2 = 100 Q. Following the methodology proposed in Section I, the RRN parameters can be calculated as in (16) below:LI = 128.6 / / H, Cl = 130 pFL2 = 9.35 / H, C2 = 892 pF (16) Combining with the filter stage parameters designed in (14) renders the component values for the equivalent circuit in FIG. 10B as in (17) below:LH = 254 nH, CH= 892 pF, LT= 697 nHLG = 1564 nH, CG = 359 pF (17) [0062) The inductor values in (17) are significantly reduced (e.g., by roughly a hundred times). This conversion alleviates the challenges of implementing large inductors with high coupling while keeping the same power modulation capability. With the combined power amplifier and the RRN, its output power profile can be predicted by:(18)

[0063] FIG. 13 is a graph showing plots (also for the prototype of FIG. 11) of normalized power-frequency profiles comparing the theoretical analysis, simulation, and experiment, according to an example of the present disclosure, with the curves being normalized to the frequency and power at the nominal condition. In the graph of FIG. 13, this analytical (output power) profile is compared with simulation and experimental, indicating a good agreement between the analysis and experiment.

[0064] Specific experimental embodiments were used to verify the efficacy of certain of the generally-discussed examples disclosed herein. One such example is a type of circuit including an RRN implementation and a switched-mode broadband power amplifier operable within a frequency range having a lower limit on the order of one-half MHz and an upper limit on the order of tens of GHz. As a specify example of this type, a 300 W power amplifier prototype with RRN was constructed based on the design discussed in connection with FIG. 7. The prototype is implemented with a GaN transistor (e.g., GaN Systems Bt) on a 100 V to 150 V DC bus. For this experimental example prototype, a detailed description of components are generally described herein (and indicated at Table II of the Appendix in U. S. Provisional Application No. 63 / 754,314), and a photograph of the constructed prototype is show n in FIG. 11.STFD.470PCT (S25-020) 19

[0065] To verify the power modulation capability of the constructed prototype, the prototype was tested across a frequency range of 13.2 MHz to 14.4 MHz. FIG. 12 illustrates the experimental and measured output power (dBm) of the prototype at various frequencies (MHz) and DC voltages. In connection with such testing, an N1914A RF power meter is used to measure the output power, while the input power is monitored using an N5771 A DC power supply. The results show good agreement between the simulation and experimental data. With a 150 V DC input, the amplifier prototype can generate 304.7W (54.84 dBm) at 13.2 MHz and 159.8 W (52.03 dBm) at 14.4 MHz. The overall power modulation ratio achievable through frequency control is 1.91 (2.81 dB).

[0066] FIG.13 further compares the normalized power-frequency profiles from analysis, simulation, and experiment. The three curves exhibit the same trend and overlap near the nominal frequency. As discussed above in connection with FIG. 7, when the frequency drops below 13.2 MHz, the broadband amplifier loses ZVS due to a decrease in the quality factor of the switched network. On the other hand, frequencies above 14.4 MHz lead to additional attenuation by the filter network, resulting in significant impedance mismatch and non-ZVS switching.

[0067] It is recognized and appreciated that as specific examples, the abovecharacterized figures and discussion are provided to help illustrate certain aspects (and advantages in some instances) which may be used in the manufacture of such structures and devices. These structures and devices include the exemplary structures and devices described in connection with each of the figures as well as other devices, as each such described embodiment has one or more related aspects which may be modified and / or combined with the other such devices and examples as described hereinabove may also be found in the previously-identified Appendix (to U. S. Provisional Application No. 63 / 754,314, from which the noted equations and other discussion herein were derived).

[0068] The skilled artisan would also recognize various terminology as used in the present disclosure by way of their plain meaning. As examples, the Specification may describe and / or illustrates aspects useful for implementing the examples by way of various semiconductor materials / circuits which may be illustrated as or using terms such as layers, blocks, modules, device, system, unit, controller, and / or other circuit-type depictions. Such circuits, circuit elements and / or related circuitry may be used together with other elements to exemplify how certain examples may be carried out in the form or structures, steps, functions, operations, activities, etc. It would also be appreciated that terms to exemplify orientation, such as upper / lower, left / right, top / bottom and above / below, may be used hereinSTFD.470PCT (S25-020) 20to refer to relative positions of elements as shown in the figures. Also, it is appreciated that certain transistor-directed references to source and / or drain, may be reversed (as drain and / or source) depending on the transistor type and its polarities. It should be understood that the terminology is used for notational convenience only and that in actual use the disclosed structures may be oriented different from the orientation shown in the figures. Thus, the terms should not be construed in a limiting manner.

[0069] Based upon the above discussion and illustrations, those skilled in the art will readily recognize that various modifications and changes may be made to the various embodiments without strictly following the exemplary’ embodiments and applications illustrated and described herein. For example, methods as exemplified in the Figures may involve steps carried out in various orders, with one or more aspects of the embodiments herein retained, or may involve fewer or more steps. Such modifications do not depart from the true spirit and scope of various aspects of the disclosure, including aspects set forth in the claims.

Claims

1. STFD.470PCT (S25-020) 21What is claimed is:

1. An apparatus comprising:an amplifier; andan impedance-regulation network cooperatively configured with the amplifier to drive a load, andcontrol power delivered from the amplifier to the load by adjusting one or more frequencies of a signal coupled to drive the amplifier.

2. The apparatus of claim 1, wherein by adjusting one or more frequencies, the impedance-regulation network and the amplifier are to cause the impedance-regulation network to modulate, seen by the amplifier, an equivalent load resistance.

3. The apparatus of claim 1, wherein the impedance-regulation network has a first port, to be driven by the amplifier, terminated with an image impedance associated with the first port and has a second port, to be driven from the amplifier, with an image impedance associated with the second port that matches the image impedance associated with the first port.

4. The apparatus of claim 1, wherein the control power delivered from the amplifier is modulated with frequency variations by shaping, via the impedance-regulation network and the amplifier, a frequency profile of an image impedance specific to a port, of the impedanceregulation network, that is to be driven by the amplifier.

5. The apparatus of claim 1, wherein the amplifier is a switched-mode broadband power amplifier operable within a frequency range having a lower limit on the order of one-half MHz and an upper limit on the order of tens of GHz.

6. The apparatus of claim 1, wherein the impedance-regulation network has an image impedance specific to a first port of the impedance-regulation network that is to be driven by the amplifier and has an image impedance specific to a second port of the impedanceregulation network that is coupled to the load, each of the image impedances being frequency dependent and at least primarily defined by a manner in which the impedance-regulation network is designed.STFD.470PCT (S25-020) 227. The apparatus of claim 1, wherein the impedance-regulation network has an image impedance specific to a first port of the impedance-regulation network that is to be driven by the amplifier and has an image impedance specific to a second port of the impedanceregulation network that is coupled to the load.

8. The apparatus of claim 1, whereinthe impedance-regulation network is configured with a first port and a second port respectively connecting between the amplifier and the load and respectively having port specific first and second image impedances, andthe first image impedance is associated with a frequency profile that dictates a driving point impedance value that is to load the amplifier at any specific frequency and thereby determines output power of the amplifier9. The apparatus of claim 1, wherein the impedance-regulation network is composed of lossless passive components.

10. The apparatus of claim 1, wherein the impedance-regulation network is configured with a first port and a second port respectively connecting between the amplifier and the load and respectively having port-specific first and second purely-resistive image impedances.

11. The apparatus of claim 1, wherein the amplifier is to maintain zero-voltage-switching (ZVS) during switching transitions of the amplifier, and over different frequencies, from among the one or more frequencies, of the signal coupled to drive the amplifier.

12. The apparatus of claim 1, wherein the amplifier is single-phase power amplifier, and the control power delivered from the amplifier is to be increased, in response to adjusting one or more frequencies, at least by a factor of two, while the amplifier is operating at a frequency on the order of 10 MHz, within 1 microsecond.

13. The apparatus of claim 1, wherein the amplifier is a power amplifier using one or more other power modulation techniques; e.g., from among rail-voltage regulation, and out-phasing.STFD.470PCT (S25-020) 2314. The apparatus of claim 1, wherein the amplifier is a single-phase power amplifier using at least one amplifier-modulation technique involving a control signal adjustment other than said adjusting one or more frequencies of a signal coupled to drive the power amplifier.

15. The apparatus of claim 1, wherein the amplifier is a broadband class-D2 power amplifier, and the impedance-regulation network has a first port, to be driven by the amplifier, and has a second port that is coupled to the load and that is associated with a positively-sloped image impedance.

16. A method comprising:using an impedance-regulation network with an amplifier to drive a load; and controlling power delivered from the amplifier to the load by adjusting a frequency of a signal coupled to drive the amplifier.

17. The method of claim 1, further comprising using the impedance-regulation network, to facilitate said controlling power delivered to the load, to modulate the equivalent load resistance seen by the amplifier.

18. The method of claim 16, further including shaping, via the impedance-regulation network and the amplifier, a frequency profile of an image impedance specific to a port, of the impedance-regulation network, that is to be driven by the amplifier.

19. The method of claim 16, wherein in response to adjusting one or more frequencies, the impedance-regulation network modulates, seen by the amplifier, an equivalent load resistance.

20. The method of claim 16, further including increasing the power delivered from the amplifier, in response to adjusting one or more frequencies, at least by a factor of two, while the amplifier is operating at a frequency on the order of 10 MHz, within 1 microsecond.

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