High-frequency high-efficiency self-shielded inductor

Abstract

According to some embodiments, a high-frequency (HF) self-shielded inductor includes: an outer shell having a distributed or quasi-distributed gap and two or more notches; an inner core disposed within the outer shell and having a distributed or quasi-distributed gap; a coil winding disposed between the inner core and the outer shell; two endcaps disposed at opposite ends of the inner core and the outer shell; and a conductive shield disposed around the outer shell.

Description

HIGH-FREQUENCY HIGH-EFFICIENCY SELF-SHIELDED INDUCTOR CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit under 35 U.S.C. §119 of U.S. Provisional Patent Application No.63 / 496,456 filed on April 17, 2023, which is hereby incorporated by reference herein in its entirety. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] N / A BACKGROUND

[0003] High-frequency (HF) power converters operating between 3-30 MHz offer several advantages, such as improved performance, reduced energy storage requirements, and miniaturization. In some applications, such as RF plasma generation and HF wireless power transfer, HF operation is a natural requirement. At lower frequencies, cored magnetic components are used for miniaturization, high efficiency, and self-shielding. However, core materials traditionally used for power applications, such as MnZn ferrites, perform poorly at frequencies above a few MHz due to high core loss. Additionally, skin and proximity effects make it challenging to efficiently carry large currents at HF, and techniques such as litz wire used to compensate for these losses become impractical at frequencies above a few MHz for manufacturing reasons. The design of cored magnetic components is, therefore, challenging for HF applications as both copper and core losses significantly increase with frequency. As a result, air-core inductors currently dominate power applications in the HF (3-30 MHz) and VHF (30-300 MHz) ranges. SUMMARY

[0004] A limitation of air-core RF inductors, such as coreless solenoids, is that their magnetic fields are not shielded and can couple with other components in the system, causing electromagnetic interference (EMI) and significant losses due to induced eddy currents. To maintain high efficiency, RF air-core inductors often require significant physical volume and are placed in a metal enclosure, separated from the control circuitry, to mitigate EMI. As a result, they often contribute significantly to an overall system’s sizeand loss and can be a bottleneck for system miniaturization, such as in tunable matching networks.

[0005] To achieve higher efficiencies and power densities for RF applications, progress has been made in the measurement and characterization of high-performance magnetic materials at HF. Low-permeability NiZn ferrite materials have been found to be suitable for high-frequency AC inductor design, and proper design of cored inductors leveraging these materials can provide better combinations of size and efficiency than coreless inductors. However, achieving high-performance cored HF inductors requires design techniques to address skin and proximity losses. Field balancing, single-layer winding, and quasi-distributed gaps can be used to minimize these losses.

[0006] Recent work using these new design techniques and low-permeability RF magnetic materials has achieved impressive combinations of size and efficiency. However, many of these designs result in significant magnetic fields surrounding the inductor, leading to EMI concerns. For example, the high-power cored inductor in achieves a high Q but generates considerable external fringing flux, similar to its air-core solenoid counterpart. The unshielded external field from this inductor can couple with surrounding components and induce EMI and losses. Therefore, there is a need for cored HF inductors that can deliver high efficiency while also providing self-shielding to minimize induced losses and EMI in surrounding components.

[0007] This disclosure presents a new design and model for the HF cored self-shielded inductor. The refined design includes specific strategies to minimize losses that result from 3D effects. Additionally, the refined model takes these effects into consideration, resulting in a more accurate estimation of losses and enabling the attainment of an optimized design. A thermal model is also presented to prevent the ferrite from overheating and potentially entering thermal runaway.

[0008] According to one aspect of the present disclosure, a high-frequency (HF) self- shielded inductor includes: an outer shell having a distributed or quasi-distributed gap and two or more notches; an inner core disposed within the outer shell and having a distributed or quasi-distributed gap; a coil winding disposed between the inner core and the outer shell;two endcaps disposed at opposite ends of the inner core and the outer shell; and a conductive shield disposed around the outer shell.

[0009] In some embodiments, the two or more notches of the outer shell have a total angular length sufficient to limit phi-directed flux density in the outer shell to less than 25% of z-directed flux density in the outer shell. In some embodiments, a reluctance of the outer shell is less than a reluctance of the inner core. In some embodiments, the outer shell reluctance is between 20% and 80% of the inner core reluctance. In some embodiments, the outer shell reluctance is between 30% and 70% of the inner core reluctance. In some embodiments, the outer shell reluctance is between 40% and 60% of the inner core reluctance. In some embodiments, the conductive shield comprises a copper shield.

[0010] In some embodiments, the coil winding is a single-layer helical winding. In some embodiments, the conductive winding is disposed within a window formed between the inner core and outer shell, and two leads of the a single-layer helical winding are brought through the outer shell with a spacing in a z direction that is less than or equal to 10% of a total height of the window. In some embodiments, the coil winding comprises two single-layer helical windings configured to carry current in opposite directions.

[0011] In some embodiments, the coil winding comprises a double-layer helical winding. In some embodiments, the inner core is constructed of alternating magnetic and non-magnetic spacer material discs. In some embodiments, the outer shell is constructed of alternating pieces of magnetic and non-magnetic material and provides a return path for flux to flow. In some embodiments, the coil winding has evenly spaced turns wound around the inner core. In some embodiments, the two or more notches have a total notch length sufficient to limit fringing at said notches to induce proximity to an amount less than or equal to other proximity effect losses of the HF self-shielded inductor.

[0012] In some embodiments, the conductive shield wraps the inner core, outer shell, two end caps, and the coil winding to reject leakage flux flowing out of the HF self- shielded inductor. In some embodiments, the conductive shield is shorted. In some embodiments, relative values of a z-directed field in the inner core and in the outer shell are selected to minimize total loss. In some embodiments, the outer shell and the inner core both have a spiral core structure.

[0013] It should be appreciated that individual elements of different embodiments described herein may be combined to form other embodiments not specifically set forth above. Various elements, which are described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. It should also be appreciated that other embodiments not specifically described herein are also within the scope of the following claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The manner of making and using the disclosed subject matter may be appreciated by reference to the detailed description in connection with the drawings, in which like reference numerals identify like elements.

[0015] Fig.1A is a polar cutaway view of a self-shielded inductor.

[0016] Fig.1B is a three-dimensional (3D) cutaway view of the self-shielded inductor of Fig. 1A.

[0017] Fig.2 is a schematic diagram showing a two-dimensional (2D) model of a self- shielded inductor.

[0018] Fig.3A is a perspective view of a coil winding that can be provided within a self-shielded inductor, illustrating z-directed current.

[0019] Fig.3B is a top view of a self-shielded inductor, illustrating phi-directed fields associated with z-directed current.

[0020] Fig.4A is a top view of a self-shielded inductor having a notched outer shell core piece.

[0021] Fig.4B is a diagram showing a circuit for modeling the outer shell core piece of Fig. 4A.

[0022] Figs.5A–D are perspective views of different types of coil windings that can be provided within a self-shielded inductor to reduce Z-directed current, according to some embodiments.

[0023] Figs.6A and 6B are graphical diagrams illustrating H-field on the YZ cross- section of a shielded inductor.

[0024] Figs.7A–C are graphical diagrams illustrating B-field on the YZ cross-section of a shielded inductor.

[0025] Fig.8 is a schematic diagram of a coil winding window, illustrating a derivation of window gap reluctance to model flux jumping across the top and bottom of the winding window.

[0026] Fig.9 is a diagram showing a magnetic circuit for z-directed magnetic flux, according to some embodiments.

[0027] Figs.10A–C are perspective views of spiral core structures that may be provided within a self-shielded inductor to reduce current crowding, according to some embodiments.

[0028] Figs.11A and 11B are graphical diagrams showing magnitude of H-field on the YZ cross-section for a spiral core structure.

[0029] Fig.12 shows thermal resistance modules used to define thermal resistance network, according to some embodiments.

[0030] Fig.13 is a diagram showing an example of how modular thermal modules can be connected to define the complete thermal resistance network, according to some embodiments.

[0031] The drawings are not necessarily to scale, or inclusive of all elements of a system, emphasis instead generally being placed upon illustrating the concepts, structures, and techniques sought to be protected herein. DETAILED DESCRIPTION

[0032] Figs.1A and 1B show a self-shielded inductor 100 such as described in U.S. Pat. Pub. No. 2022 / 0262561, published on August 18, 2022, and entitled “Self-Shielded High Frequency Inductor.” Inductor 100 includes a “pot core” structure 102 and a conductive outer shield 104 (e.g., copper foil) disposed thereabout. Core structure 102 isformed of an inner core 106 (sometimes referred to as an “inner post”), an outer shell 108 (sometimes referred to as a “outer core”), a coil winding window 110 (or “window) is formed between the inner core 106 and outer shell 108, a first endcap 112, and a second endcap 114. Window 110 provides a distribution gap (or “void”) in which coil winding 111 (e.g., single-layer winding) can be located. Endcaps 112, 114, which can both have a cylindrical shape, are positioned to form top and bottom walls of the window 110, as shown.

[0033] As shown, inner core 106, outer shell 108 and window 110 can have a height ℎ^. Core structure 102 has a radius R. For example, R may correspond to the endcap radius. Inner core 106 has a radius bR, where b is a number between 0 and 1. Outer shell 108 has an inner radius cR, where c is a number between 0 and 1, The cores 106 and 108 have relative, effective permeabilities ^^^^and ^^^^, respectively. Endcaps 112, 114 each have a relative permeability ^^and a height of ℎ^⁄2 (depicted in Fig.2).

[0034] Outer shell 108 canone or more notches that are not visible in Figs.1A and 2B. For example, notches may be provided to remove the winding 111 from the window 110 and / or to help reduce a magnetic field component.

[0035] Inner core 106 and / or outer shell 108 can have a quasi-distributed gap structure. For example, as illustrated in Fig.1B, inner core 106 and outer shell 08 can be formed of alternating magnetic core pieces (e.g., ferrite discs) and non-magnetic spacers (e.g., discs of non-magnetic material), stacked up along the z-direction.

[0036] The design methodology presented in and U.S. Pat. Pub. No.2022 / 0262561 and in R. S. Bayliss, R. S. Yang, A. J. Hanson, C. R. Sullivan, and D. J. Perreault, “Design, implementation, and evaluation of high-efficiency high-power radio-frequency inductors,” in 2021 IEEE Applied Power Electronics Conference and Exposition (APEC), 2021, pp.881–888, utilizes a two-dimensional (2D) representation of the system to create a shielded inductor. A script was developed to determine the most efficient inductor construction for a given volume based on this 2D analysis.

[0037] Fig.2 shows a 2D model 200 of a self-shielded inductor, with the left side of the figure showing a front reivew of the inductor and the right side of the figure showing atop view of the inductor. The following dimensions that may be used to design a self- shielded inductor are depicted: ^ inner core radius bR; ^ outer shell inner radius cR; ^ spacing between outer shield and endcaps ^^^^; ^ total inductor radius ^^^^; ^ endcap radius ^; ^ height of inner core piece ℎ^^; ^ height of inner core gap (e.g., spacer height) ℎ^^; ^ height of outer shell core piece ℎ^^; ^ height of outer shell gap (e.g., spacer height) ℎ^^; ^ endcap height ℎ^⁄2 ; ^ height of the window ^ℎ; ^ total indcutor height ℎ; ^ winding height ℎ^^^^^^^; ^ turn-over-turn winding spacing ^^^; and ^ angular length of an outer shell notch α, shown distributed among four notches each having an angular length α⁄4.

[0038] The self-shielded inductor described in U.S. Pat. Pub. No.2022 / 0262561 can be simulated using a 3D simulator (e.g., ANSYS MAXWELL 3D) and the inductor losses compared to losses predicted from the 2D model 200 Fig.2. A large inductance difference can be found, as a result of the energy storage associated with phi-directed fields not being accounted for in the model. The mismatch between the loss predicted by the 2D model and the loss simulated by the 3D simulator indicates the need to consider additional effects that affect loss.

[0039] 2D analysis may not be suitable for designing inductors with low turn counts (such as two or three turns) as the helical nature of the winding at low turn counts overrides 2D symmetry, resulting in infeasible designs if three-dimensional (3D) effects are not considered. In addition, thermal modeling is crucial, as the self-shielded inductor has a significantly lower effective volume. Therefore, determining the acceptable level of loss is essentially a question of determining acceptable thermal levels.

[0040] Described hereinbelow is a new design and model for the HF cored self- shielded inductor. The refined design includes specific strategies to minimize losses that result from 3D effects. Additionally, the refined model takes these effects into consideration, resulting in a more accurate estimation of losses and enabling the attainment of an optimized design. A thermal model is also presented to prevent the ferrite from overheating and potentially entering thermal runaway.

[0041] A script (e.g., a MATLAB script) can be used to determine the minimum loss geometry for the refined design, with the geometry parameterized, such as shown in Fig. 2. This script can be built on the code developed in C. R. Sullivan, “Prospects for advances in power magnetics,” in CIPS 2016; 9th International Conference on Integrated Power Electronics Systems, 2016, pp.1–9, and G. Zulauf and J. M. Rivas-Davila, “Single- turn air-core coils for high-frequency inductive wireless power transfer,” IEEE Transactions on Power Electronics, vol.35, no.3, pp.2917–2932, 2020, but expanded to include the additional loss mechanisms described below.

[0042] Table I losses predicted from a model to 3D simulation results for a prior art self-shielded inductor design compared to a disclosed self-shielded inductor design. As shown in the table, the disclosed design matches well with the simulation, providing credence to the validity of the modeling. The proposed model is able to achieve a better- optimized design with more than 50% reduction in total loss.Table I Prior art design Disclosed design Predicted from L (nH) 500 495 model Core loss (W) 33 29 Copper loss (W) 56 44 3D simulation results L (nH) 790 466 Core loss (W) 191 34 Copper loss (W) 82 61 Total loss (W) 273 95

[0043] Turning to Figs.3A and 3B, when assuming a 2D model, helical coil turns are represented as concentric circles that run parallel to each other. However, in real-life applications, these turns are interconnected, resulting in a net current directed towards the z-axis. For example, as shown in Fig. 3A, current ^ flowing through coil winding 300 having helical turns inevitably produces a net current of the same value in the z-direction. As shown in Fig.3B, this z-directed current generates phi-directed fields, ^^, in an outer shell 322 of a self-shielded inductor 320. In contrast, these fields cancelin the inner core 324. Note that Fig.3B displays a notch 326 in the outer shell 322 that serves as a manufacturing requirement to remove the winding from the window 328 and helps reduce the magnetic field component.

[0044] The net z-directed current generates a magnetomotive force (MMF) that drives each piece and gap of the outer shell 322 in parallel. Additionally, there is always at least one notch in the outer shell (e.g., notch 326) to enable the coil to exit the core window.

[0045] Fig.4A shows a piece 400 of an outer shell having a notch 402. Fig.4B shows a circuit model 420 for the outer shell core piece 400. The model 420 includes a first reluctance 422a associated with the shell, ℛ^,^, in series with a second reluctance 422b associated with the notch, ℛ^^^^^and driven by a by an MMF 424 associated with the net z-directed current, ^ (the same value as the driving current).

[0046] The shell reluctance can be modeled as follows:ℛ^,^ =(^^^^)(^^^)^^^^^^^^^(1) where, ^ represents the angularaverage radius of the shell, ^^is the permeability of free space, ^^is the relative permeability of the core, and ℎ^^represents the thickness (or “height”) of the outer shell core piece.

[0047] The energy stored in the fields also contributes to the inductance of the structure. Specifically, as the fields are perpendicular to the “normal” z-directed fields, the inductance associated with the phi-fields can be defined as: ^^=^ℛ^,^^^(2) where, ℛ^,^^^denotes the net reluctance

[0048] It is appreciated herein that, with this model, the reluctance modeling choice described above is insufficient to estimate core loss due to phi-directed fields, leading to an underestimation of this loss component. One reason for this is that the notch reluctance estimate is conservatively high since the increased cross-sectional area of the fringing path is not accounted for. In designs with a higher shell gap height compared to the shell core thickness, the peak flux density was found to be much higher than expected from the model.

[0049] To account for the fringing field path, the model can be updated to employ two parallel notch reluctances, one associated with the thickness of the shell and another related to the thickness of the gap (e.g., spacer) between shell pieces. This update yields better matching of the core loss, and further adjustments to the parallel reluctance estimate may lead to an improved design. ℛ^^^^^,^=^(^^^)^^^^^^^(3) where ℎ^^is the thickness (orcan yield significantly better matching of the core loss.

[0050] To mitigate phi-directed fields, embodiments of the present disclosure can employ either, or both, of the following strategies: (1) increase the reluctance of the phi-field path, and (2) use winding constructions that reduce or eliminate net z-directed current flowing through the window, such as illustrated in Figs. 5A–D.

[0051] Referring back to Fig. 2, one approach to reducing phi-fields is to increase the length (e.g., angular length) of the notch, which can be distributed symmetrically around the outer shell to avoid issues with a single large notch. For example, as shown in the figure, four (4) notches can be formed, each having angular length α⁄4 (in radians, for example). However, this reduces the cross-sectional area for z-directed fields in the outer shell.

[0052] Another strategy to mitigate the phi-directed fields and the associated core loss is to eliminate the z-directed currents that give rise to these fields. This approach focuses on modifying the winding configuration or structure of the inductor. Various winding constructions for reducing or ideally removing net Z-directed current are described below, according to embodiments of the present disclosure. The disclosed winding constructions may effectively eliminate phi-directed fields, for example by limiting them to less than 5% of the total field.

[0053] Fig.5A shows a segmented winding construction 500, where the coil is divided into multiple single-turn segments 502a, 502b, 502c, etc. that can be connected in parallel. This construction 500 can reduce the net z-directed current flowing through the window and the overall capacitance of the structure.

[0054] Fig.5B shows another winding construction 520 whereby a return pathway 522 for the winding can be provided inside the outer shell to eliminate or minimize the net z- directed current and the associated phi-directed fields and core losses. This allows both leads 524, 526 of the winding to be brought through the outer shell with a spacing 527 in a z direction sufficiently close to effectively eliminate the phi-directed field. For example, the lead spacing 527 in the z direction may be less than or equal to 10% of the total window height. By incorporating a dedicated pathway 522 for the return current within the outer core, the overall magnetic flux distribution is balanced, resulting in zero net z- directed current. A notch space in the outer shell can be used to house this return path.

[0055] Fig.5C shows another winding construction 540 whereby the coil is split into two mirrored halves, namely an upper portion 542 having leads 544, 546 and a lowerportion 548 having leads 550, 552, with the two coil portions 542, 548 connected in parallel, for example. As illustrated by lead arrows in the figure, the upper portion 542 can be connected to carry a net positive z-directed current and the lower portion 548 can be connected to carry a net negative z-directed current. This configuration maintains the excitation of the z-directed field while halving the phi-directed fields for the same core geometry. Consequently, core losses associated with the phi-directed fields are significantly reduced.

[0056] Fig.5D shows another winding construction 560 whereby a helix is wound in two layers, with a first layer 562 wound “up” from a first lead 568 and a second layer 564 wound “down” to a second lead 570, and with a connection 566 provided between the two layers 562, 564. This double winding arrangement can eliminate the z-directed fields.

[0057] The choice of strategy for mitigating phi-directed fields can be selected based on the specific application and design requirements. In some embodiments, a combination of disclosed strategies may also be used within a self-shielded inductor.

[0058] The helical winding of the coil creates an “asymmetry” between the arrangement of the circular core pieces (which have no variation in the z-direction) and how the helical winding evolves through the window. In 2D, individual turns can be identified and discussed, starting and ending without any change in their z-directed displacement, like the core structure. However, in 3D, the turns are displaced in the z- direction by their height and an additional turn-to-turn spacing. This phenomenon is especially important at the ends of the windings, where it changes how flux traverses through the region and introduces current crowding associated with fields that jump across the winding window.

[0059] To understand these effects, one can consider how the z-directed flux paths are impacted by the geometry at the ends of the inductor. For example, Figs.6A–B and 7A–C show the magnitude of the H-field and B-field, respectively, on the YZ cross-section of the shielded inductor.

[0060] Figs.6A and 6B are graphical diagrams illustrating H-field on the YZ cross- section of a shielded inductor, showing the tendency for fields to jump the winding gapnear the ends of the window, with Fig.6A showing an unobstructed view with arrows pointing to ‘lost gaps’ and Fig.6B showing core shell locations.

[0061] Figs.7A–C are graphical diagrams illustrating B-field on the YZ cross-section of a shielded inductor, showing the tendency for fields to jump the winding gap near the ends of the window, with Fig. 7A showing core shell locations, Fig.7B showing unobstructed view and arrows pointing to ‘lost gaps’, and Fig.7C showing endcap locations.

[0062] In Fig.6A, one can observe that the H-field weakens gradually in the gaps as we move from top to bottom on the left side until it is nearly zero for the bottom three gaps. One can see a similar weakening of the H-field as one moves from bottom to top on the right side, indicating that magnetic field is jumping across the window near the ends of the windings. Looking at the endcap regions in Figs. 7A–C shows a similar phenomenon where the B-field is preferentially on one side of the core, suggesting that the other part of the endcap carries minimal flux (consistent with fields jumping across the gap).

[0063] The impact of end-turn effects on the 2D design is as summarized. The core’s net reluctance is lower than expected due to some gaps being bypassed, resulting in a higher simulated inductance compared to the designed inductance, combined with the inductance associated with phi-directed fields. The upper and lower edges of the helix experience a crowding of current, leading to a significant increase in copper loss for the helical winding.

[0064] The limitations of 2D analysis in accounting for these effects make it difficult to accurately optimize the design for loss using this method. As a solution, this disclosure provides a method to incorporate the lost gaps effect into an equivalent magnetic circuit model, enabling accurate optimization of the design for loss and achieve precise results. Additionally, the disclosures provides strategies for mitigating the current crowding effect at the ends.

[0065] Figs.6A–B show that the last three gaps, viewed on the YZ cross-section, appear to be un-used. This may be a result of field jumping across the window if that is a lower reluctance path than the alternative shell and inner gap path. In order to model this phenomenon, the possible paths for magnetic field across the winding window can beaccounted for. Assuming that the only viable path is through the non-conductive portions of the window (i.e., that the windings will reject flux attempting to pass through them), the model can be updated by including reluctances associated with the “r-directed” window paths. Although the spaces between the gaps present a viable path for flux (e.g., as evidenced in Figs. 6A–B by the field hotspots between the turns), it can be assumed that all of this window jumping happens near the ends of the winding in order to derive a tractable model.

[0066] Turning to Fig. 8, a coil winding window 800 to can be bounded by top and bottom endcaps 802, 804. As shown in Fig.8 (and also by the arrows of Figs. 6A–B), gaps can be present at the top and bottom of the window 800 due to the helical shape of coil winding 806. A derivation of the window gap reluctance is provided in order to model flux jumping across the top and bottom of the winding window.

[0067] Under previous described assumptions, the height of the region where fields can jump the window varies (or “evolves”) with the position of the helix as shown in the right side of Fig. 8. The effective reluctance associated with this window-jumping path is ℛ^^^^^^=(^^^)^^^^^^,^^^(4) where the effective area of this path^^^,^^^= ^^^^^^^^^ℎ^^^^^^^= ^ℎ^^^^^^^^^^^^ ^^. (5)

[0068] Thusℛ^^^^^^=^ ^^^^^^^^^^^^^^^^^^^ (6)

[0069] It can be assumed that this reluctance is in parallel with the number of outer shell core pieces and outer shell gaps that are encompassed within the height of one winding. That is ^^^,^^^^=^^^^^^^(7)

[0070] For example, in Figs. 6A–B, the number of lost gaps is equal to 3.9. Thus, instead of using the full outer shell and outer gap reluctances, a reluctance model as in Fig. 9 can be used.

[0071] Fig.9 shows a magnetic circuit 900 for z-directed magnetic flux. The illustrative circuit 900 includes an excitation current source 902 connected in series with reluctances 904a–g. Another reluctance 904h can be connected at one end between reluctances 904a, 904b and at the other end between reluctances 904d, 904e. Another reluctance 904i can be connected at one end between current source 902 and reluctance 904g, and at the other end between reluctances 904e, 904f. The reluctances can be defined in terms of various elements as shown in Fig.9, with the elements described in Table II. Table II Element Description ^ Excitation current ℛ^^Reluctance of inner core piece in the z-direction ℛ^^Reluctance of inner gap piece in the z-direction ℛ^^Reluctance of outer shell core piece in the z-direction ℛ^^Reluctance of outer shell gap piece in the z-direction ^^Total number of gaps in the inner core section (equal to number of outer gaps) ^^,^^^^Number of gaps that compete with window reluctance path ℛ^^^^^^Reluctance of the window path ℛ^Reluctance of the endcaps

[0072] Turning to Figs.10A–C, as mentioned above, a challenge with some self- shielded inductor designs that the helical winding evolves in the z-direction while the core remains static. With the small number of turns in these designs, 2D symmetry is broken, resulting in a significant current crowding phenomenon. To address this effect, embodiments of the present disclosure use a core structure that evolves helically, maintaining symmetry. This core structure ensures that each segment of the winding sits in an identical core and gap geometry, which creates a perfect shroud over the windings. Theshroud is to convince z-directed flux to traverse through the endcap instead of jumping across the window.

[0073] Figs.10A–C show examples of spiral core structures that can be provided within a self-shielded inductor, according to some embodiments.

[0074] Fig.10A shows a spiral core structure 1000 having a spiral-shaped inner core 1002 and a spiral-shaped outer shell 1004, both without phi-direction notches.

[0075] Fig.10B shows a spiral core structure 1020 having a spiral-shaped inner core 1022 having a plurality of phi-direction notches (e.g., notch 1026) and a spiral-shaped outer shell 1024 also having a plurality of phi-direction notches (e.g., notch 1028). In the example shown, both cores 1022, 1024 have eight (8) phi notches, although other numbers of phi notches can be selected (e.g., based on application requirements and using modeling techniques described herein). In other embodiments, only the outer shell 1024 can have phi notches.

[0076] Fig.10C shows a how a spiral core structure can be fitted with spiral endcaps 1042, 1044. In the case of phi-notched cores, endcaps 1042, 1044 may also be notched in the phi direction (as shown in the figure). In the case of non-phi-notched cores, the endcaps may not have phi notches.

[0077] Figs.11A and 11B demonstrate the resulting H-field distribution on the YZ cross-section of a spiral core without (Fig. 11A) and with (Fig.11B) spiral endcaps. Without the endcaps, the winding loss is similar to that of self-shielded inductors without a spiral core. With the spiral endcap, current crowding fields no longer exist, and the simulated winding loss is equal to what would be estimated without accounting for this current-crowding effect.

[0078] These results confirm that a significant reduction of in the winding loss (e.g., a 20% reduction) can be achieved by employing a core geometry that better mimics the 2D conditions used for design. In particular, a construction similar to those illustrated in Figs. 10A–C can provide a winding loss that is equal to what is estimated from a simple 2D analysis.

[0079] In practice, it may be necessary or desirable to formulate a thermal model for a self-shielded HF cored inductor design. The conductive outer shield (e.g., copper shield) greatly reduces the inductor’s “effective” volume, resulting in a much higher “effective” energy density that causes high magnetic flux densities within the ferrite which could lead to thermal stress, thermal runaway, and potentially breaking the ferrite. Therefore, it may be important to develop a comprehensive thermal model in order to select the most optimal cooling solution that will ensure the success of the inductor.

[0080] Here, a 2D (cylindrical) thermal model is presented, which is based on conductive and convective thermal resistances. The model may be useful for evaluating the relative impact of changing specific parameters, such as increasing the number of gaps. The system can be distributed into thermal modules as shown in Fig.12. As shown, module 1202 represents an inner core piece plus winding mount, module 1204 represents an inner gap piece plus winding mount, module 1206 represents an outer shell core piece plus shield mount, module 1208 represents an outer gap piece plus shell amount, module 1210 represents a winding, module 1212 represents an endcap, and module 1214 represents the outer shell. The definitions for each thermal resistance in Fig.12 are listed in Tables III and IV.

[0081] The modules for the core pieces and gaps can be repeated to match the number of core pieces and gaps in the designed inductor. Fig. 13 shows an example of how the modular thermal modules of Fig.12 can be connected to define the complete thermal resistance network 1300, with like reference numerals identifying like elements in the two figures. In this example, perfect 2D symmetry is assumed, which means that phi-directed are not included in the model. After comparing the results of the proposed thermal model with a thermal simulation (e.g., a simulation conducted in ANSYS ICEPAK), a satisfactory level of agreement can be observed between the two.Table III Parameter Equation Description Inner core ^^^,^^,^ℎ^^From center of an innerpiece plus ^^^^^^^^^ ^( )^core piece to the top orwinding^^ bottom. ℎ^^ is the innermount core piece height. ^^^,^^ ,^ 1^^^^^^^^“Radial” thermal^ℎ^^ resistance from centerto window. Take average cross-sectional area as ^ℎ^^(^^). (mean circumference*h from 0 to ^^). Length is ^^. ^^^,^^^^,^ ^ ^^^^^^^^^ ,^^ℎ“Radial” thermal^^(^^^ + 2^^) resistance of windingmount. Take average cross-sectional area as ^^^^^(^^^^^^^^^)^ . Length is ^^^. Assume that heat will convect in the small part of the spacer that it attaches to. Each inner ^^^,^^,^Same as ^^^,^^,^but with z-Rth to the middle of gap piece plus ℎ^^and ^^^^the gap. ℎ^^is the inner winding core piece height. mount ^^^,^^,^Same as ^^^,^^,^but with r-Rth from the center to ℎ^^and ^^^^the window ^^^ ,^^^^,^Same as ^^^,^^^^,^but r-Rth from the edge of with ℎ^^the window to the winding Inner support^^^ ,^^,^Same as ^^^,^^,^but with z-Rth to the middle of pieces ℎ^inner support piece ^^^ ,^^,^Same as ^^^,^^,^but with r-Rth to the core ℎ^window from themiddle of the inner support piece ^^^ ,^^^^,^Same as ^^^,^^^^,^but r-Rth of the holder of with ℎ^the copper winding Each outer ^^^,^^,^Same as ^^^,^^,^but with shell coreℎ changed tplus(^^^ o ℎ^) → (1 − ^^)^.piece^ ^ ^^shield mount ^^^,^^,^^^^^^^^^(1 − ^) “Radial” thermal2^ℎ^^(1 + ^) resistance from centerof outer shell. Take average cross-sectional area as ^ℎ^^^^(1 + ^)^. (mean of circumference*h from cR to R). Length is(^ − ^^)⁄ 2 = (1 −^)^⁄ 2 ^^^,^^^^,^ ^^ ^^^^^^^^^ℎ^^^^^^^ is the spacer^^(^^^ + 2^) used to mount theshell. Take average cross-sectional area as ^^^^^(^^^^^^^)^Table IV Parameter Equation Description Each outer gap^^^,^^,^ Same as ^^^,^^,^ butpiece pluswithshield mount ℎ^^and ^^^^^^^,^^,^ Same as ^^^,^^,^ butwithℎ^^and ^^^^^^^,^^^^,^ Same as ^^^,^^^^,^ butwith ℎ^^Endcap^^^,^^^,^ h^^^^(^^)^Forced air convective cooling. ℎ^^^= 12.12− 1.16^+11.6^^ / ^^^^,^^,^ ^^^ ,^^,^ , change h^^ → ℎ^To the middle ofthe endcap in the z direction ^^^,^^,^ ^^^ ,^^,^ , change h^^ → ℎ^To the edge of theendcap portion in the r direction ^^^,^^^,^ h^^^^^^(^^+ ^^)^To the middle of the endcap in the second portion ^^^,^^,^ Same as ^^^,^^,^, but withh^^ → ℎ^(^^)^ → (^^ − ^^)^^^^^,^^,^^^^^^^^^(^ − ^)2^ℎ^(^ + ^)^^^,^^^,^h^^^^^^(1 − ^^) ^^^,^^,^Same as ^^^,^^,^, but with h^^→ ℎ^^^^,^^,^^^^,^^,^h^^→ ℎ^^^^ ,^^^,^ ^^^,^^^^,^ Radial thermalh^^ → ℎ^resistance fromedge of endcap toshell Outer shell ^^^ ,^^,^h^^^(2^^)(2ℎ^− ℎ^) Winding ^^^,^^^^370 W / m.K ^^^^^^^^^^^^^^^^

[0082] As used in the claims or elsewhere herein, the term “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality.

[0083] Various embodiments of the concepts systems and techniques are described herein with reference to the related drawings. Alternative embodiments can be devised without departing from the scope of the described concepts. It is noted that various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth between elements in the claims, detailed description, and drawings. These connections and / or positional relationships, unless specified otherwise, can be direct or indirect, and the claimed inventions are not intended to be limiting in this respect. Accordingly, a coupling / connection of entities can refer to either a direct or an indirect coupling / connection, and a positional relationship between entities can be a direct or indirect positional relationship. As an example of an indirect positional relationship, references in the present description to element or structure A coupled / connected to element or structure B include situations in which one or more intermediate elements or structures (e.g., element C) is provided between elements A and B regardless of whether the characteristics and functionalities of elements A and / or B are substantially changed by the intermediate element(s).

[0084] Furthermore, it should be appreciated that relative, directional or reference terms (e.g. such as “above,” “below,” “left,” “right,” “top,” “bottom,” “vertical,” “horizontal,” “front,” “back,” “rearward,” “forward,” etc.) and derivatives thereof are usedonly to promote clarity in the description of the figures. Such terms are not intended as, and should not be construed as, limiting. Such terms may simply be used to facilitate discussion of the drawings and may be used, where applicable, to promote clarity of description when dealing with relative relationships, particularly with respect to the illustrated embodiments. Such terms are not, however, intended to imply absolute relationships, positions, and / or orientations. For example, with respect to an object or structure, an “upper” or “top” surface can become a “lower” or “bottom” surface simply by turning the object over. Nevertheless, it is still the same surface and the object remains the same.

[0085] The terms “disposed over,” “overlying,” “atop,” “on top,” “positioned on” or “positioned atop” mean that a first element, such as a first structure, is present on a second element, such as a second structure, where intervening elements or structures (such as an interface structure) may or may not be present between the first element and the second element. The term “direct contact” means that a first element, such as a first structure, and a second element, such as a second structure, are connected without any intermediary elements or structures between the interface of the two elements. The term “connection” can include an indirect connection and a direct connection.

[0086] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0087] The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. The term “substantially equal” may be used to refer to values that are within ±20% of one another in some embodiments, within ±10% of one another in some embodiments, within ±5% of one another in some embodiments, and yet within ±2% of one another in some embodiments.

[0088] The term “substantially” may be used to refer to values that are within ±20% of a comparative measure in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and yet within ±2% in some embodiments. For example, a first direction that is “substantially” perpendicular to a second direction may refer to a first direction that is within ±20% of making a 90° angle with the second direction in some embodiments, within ±10% of making a 90° angle with the second direction in some embodiments, within ±5% of making a 90° angle with the second direction in some embodiments, and yet within ±2% of making a 90° angle with the second direction in some embodiments.

[0089] In the foregoing detailed description, various features are grouped together in one or more individual embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that each claim requires more features than are expressly recited therein. Rather, inventive aspects may lie in less than all features of each disclosed embodiment.

[0090] References in the disclosure to “one embodiment,” “an embodiment,” “some embodiments,” or variants of such phrases indicate that the embodiment(s) described can include a particular feature, structure, or characteristic, but every embodiment can include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment(s). Further, when a particular feature, structure, or characteristic is described in connection knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

[0091] The disclosed subject matter is not limited in its application to the details of construction and to the arrangements of the components set forth in the detailed description or illustrated in the drawings. The disclosed subject matter is capable of other embodiments and of being practiced and carried out in various ways. As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for the designing of other structures, methods, and systems for carrying out the several purposes of the disclosed subject matter. Therefore, the claims should be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the disclosed subject matter.

[0092] Although the disclosed subject matter has been described and illustrated in the foregoing exemplary embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the disclosed subject matter may be made without departing from the spirit and scope of the disclosed subject matter.

[0093] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

[0094] The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to obtain an advantage.

[0095] Any reference signs in the claims should not be construed as limiting the scope.

[0096] All publications and references cited herein are expressly incorporated herein by reference in their entirety.

Claims

CLAIMS 1. A high-frequency (HF) self-shielded inductor comprising: an outer shell having a distributed or quasi-distributed gap and two or more notches; an inner core disposed within the outer shell and having a distributed or quasi- distributed gap; a coil winding disposed between the inner core and the outer shell; two endcaps disposed at opposite ends of the inner core and the outer shell; and a conductive shield disposed around the outer shell.

2. The HF self-shielded inductor of claim 1, wherein the two or more notches of the outer shell have a total angular length sufficient to limit phi-directed flux density in the outer shell to less than 25% of z-directed flux density in the outer shell.

3. The HF self-shielded inductor of claim 1 wherein a reluctance of the outer shell is less than a reluctance of the inner core.

4. The HF self-shielded inductor of claim 3 wherein the outer shell reluctance is between 20% and 80% of the inner core reluctance.

5. The HF self-shielded inductor of claim 3 wherein the outer shell reluctance is between 30% and 70% of the inner core reluctance.

6. The HF self-shielded inductor of claim 3 wherein the outer shell reluctance is between 40% and 60% of the inner core reluctance.

7. The HF self-shielded inductor of claim 1 wherein the conductive shield comprises a copper shield.

8. The HF self-shielded inductor of claim 1, wherein the coil winding is a single-layer helical winding.

9. The HF self-shielded inductor of claim 8, wherein the conductive winding is disposed within a window formed between the inner core and outer shell, and two leads of the a single-layer helical winding are brought through the outer shell with a spacing in a z direction that is less than or equal to 10% of a total height of the window.

10. The HF self-shielded inductor of claim 1, where the coil winding comprises two single-layer helical windings configured to carry current in opposite directions.

11. The HF self-shielded inductor of claim 1, where the coil winding comprises a double-layer helical winding.

12. The HF self-shielded inductor of claim 1, wherein the inner core is constructed of alternating magnetic and non-magnetic spacer material discs.

13. The HF self-shielded inductor of claim 1, wherein the outer shell is constructed of alternating pieces of magnetic and non-magnetic material and provides a return path for flux to flow.

14. The HF self-shielded inductor of claim 1, wherein the coil winding has evenly spaced turns wound around the inner core.

15. The HF self-shielded inductor of claim 1, wherein the two or more notches have a total notch length sufficient to limit fringing at said notches to induce proximity to an amount less than or equal to other proximity effect losses of the HF self-shielded inductor.

16. The HF self-shielded inductor of claim 1, wherein the conductive shield wraps the inner core, outer shell, two end caps, and the coil winding to reject leakage flux flowing out of the HF self-shielded inductor.

17. The HF self-shielded inductor of claim 16, wherein the conductive shield is shorted.

18. The HF self-shielded inductor of claim 1, wherein relative values of a z-directed field in the inner core and in the outer shell are selected to minimize total loss.

19. The HF self-shielded inductor of claim 1, wherein the outer shell and the inner core both have a spiral core structure.

20. A high-frequency (HF) self-shielded inductor comprising: an inner core; an outer shell; two end caps; a single-layer winding, wherein the two leads of the winding are brought through the outer shell with a close spacing in a z direction in order to limit core loss owing to phi-directed flux to a value that is small compared to core loss owing to z- directed; and a copper shield.

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