Transformer having bypass magnetic core, and on-board charger

By integrating multiple power magnetic devices in the vehicle-mounted charger into one transformer, using bypass core and flux adjustment, the problems of large losses, serious heat generation and large volume in the prior art are solved, and efficient miniaturization and cost reduction are achieved.

WO2025152299A1PCT designated stage expired Publication Date: 2025-07-24SHENZHEN VMAX NEW ENERGY CO LTD
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Patent Information

Application Number
PCT/CN2024/092011
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2024-01-16
Filing Date
2024-05-09
Publication Date
2025-07-24

AI Technical Summary

Technical Problem

In existing vehicle-mounted chargers, multiple power magnetic devices lead to large total losses, serious heat generation, large volume, high cost, and difficult to design and control the leakage inductance, making it difficult to achieve efficient miniaturization.

Method used

Using a transformer with a bypass core, four power magnetic components are integrated into one transformer. The leakage inductance is obtained as a resonant inductor by controlling the coupling between the transformer windings, reducing the number of magnetic devices, and optimizing flux adjustment by adjusting the magnetic circuit parameters.

Benefits of technology

The number of magnetic devices of the converter is reduced, the cost is reduced, the power density is improved, the overall loss is reduced, and the efficiency is improved.

✦ Generated by Eureka AI based on patent content.

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Abstract

A transformer having a bypass magnetic core, and an on-board charger. The transformer comprises a first C-shaped magnetic core (1) and a second C-shaped magnetic core (2), wherein the first C-shaped magnetic core and the second C-shaped magnetic core form a closed magnetic ring, and a bypass magnetic core (3) is arranged in the middle of the magnetic ring, and divides the interior of the magnetic ring into a first cavity (4) and a second cavity (5); a first winding (W1), a first strand of a second winding (W2), a third winding (W3) and a fourth winding (W4) are wound round the first C-shaped magnetic core, and pass through the first cavity; and a second strand of the second winding is wound round the second C-shaped magnetic core, and passes through the second cavity. The transformer reuses a magnetic core, and controls the coupling between transformer windings, so as to obtain leakage inductance acting as resonant inductance; and four power magnetic elements in the prior art are integrated into a transformer, and the transformer is then applied to an on-board charger. Thus, the number of magnetic devices of a converter is reduced; the power density of the converter is significantly improved; the overall loss of the converter is reduced, and the efficiency is improved; and the costs of the magnetic devices of the converter are reduced.
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Description

A transformer with bypass magnetic core and a vehicle charger Technical Field

[0001] The utility model relates to a transformer, in particular to a transformer with a bypass magnetic core and integrating multiple coils, and a vehicle-mounted charger. Background Art

[0002] In existing on-board charger technology, the DC conversion circuit is generally divided into two stages. The front-stage circuit is a bidirectional high-voltage DC conversion circuit, whose output is connected to the on-board power battery and provides a high-voltage DC charging current. This circuit topology is generally an LLC resonant circuit, in which the resonant inductor and the main transformer are independent of each other and are used in the circuit as two discrete components. The rear-stage circuit is a low-voltage DC conversion circuit, whose input is connected in parallel with the on-board power battery to the output of the front-stage bidirectional high-voltage DC conversion circuit, and the output is connected to the low-voltage battery and other low-voltage loads. Its circuit topology is also often an LLC resonant circuit, in which the transformer and resonant inductor are independent of each other and are used as two discrete components. Referring to the circuit diagram of the existing on-board charger transformer shown in Figure 1, the two-stage DC conversion circuit has a total of two resonant inductors, two transformers, and a total of four power magnetic devices. For on-board integrated charging products, there are the following problems: 1. The total loss of multiple power magnetic devices is large, which is not conducive to improving product efficiency; 2. The multiple power magnetic devices generate severe heat overall, and the heat dissipation cost is high; 3. The total volume of multiple magnetic components is large, which is not conducive to the high power density and miniaturization development of the product; 4. The total cost of multiple magnetic components is high.

[0003] Although some transformers in existing technical solutions mention the use of leakage inductance as a resonant inductor, the following problems still exist: 1. The design and control of leakage inductance are relatively difficult; 2. In multi-level output applications such as in-vehicle charging products, the front- and rear-stage DC conversion circuits still require the use of more than two power magnetic devices, which results in relatively high power consumption and cost. Utility Model Content

[0004] In order to solve the above-mentioned defects in the prior art, the present invention proposes a transformer with a bypass magnetic core and an on-board charger.

[0005] The technical solution adopted by the present invention is: a transformer with a bypass core, comprising a base, and a first C-shaped core and a second C-shaped core installed on the base, wherein the two ends of the first C-shaped core and the two ends of the second C-shaped core are butted together to form a closed magnetic ring, the transformer also comprises a second winding and a bypass core, the bypass core is arranged in the middle of the magnetic ring, dividing the interior of the magnetic ring into a first chamber and a second chamber; the second winding comprises a first strand of the second winding and a second strand of the second winding connected in series with each other; the first winding, the first strand of the second winding, the third winding and the fourth winding are wound on the first C-shaped core, and the second strand of the second winding is wound on the second C-shaped core.

[0006] Optionally, at least one of the two joints between the first C-shaped magnetic core and the second C-shaped magnetic core is provided with a magnetic flux regulating block, and the magnetic flux regulating block is clamped between the ends of the first C-shaped magnetic core and the second C-shaped magnetic core.

[0007] Optionally, a flux regulating block is provided at both joints of the first C-shaped magnetic core and the second C-shaped magnetic core, and the flux regulating block is clamped between the ends of the first C-shaped magnetic core and the second C-shaped magnetic core; wherein, one end of the bypass magnetic core is connected to one end of the first C-shaped magnetic core, and the other end of the bypass magnetic core is connected to the other end of the first C-shaped magnetic core; or, one end of the bypass magnetic core is connected to one end of the second C-shaped magnetic core, and the other end of the bypass magnetic core is connected to the other end of the second C-shaped magnetic core; or, one end of the bypass magnetic core is connected to one end of the first C-shaped magnetic core, and the other end of the bypass magnetic core is connected to the flux regulating block; or, the bypass magnetic core is connected between two flux regulating blocks.

[0008] Optionally, the first winding and the first strand of the second winding are wound closely around the first C-shaped magnetic core 1 , the third winding is wound outside the first winding, and the fourth winding is wound outside the third winding.

[0009] In an optional scheme, the number of turns of the third winding and the fourth winding is 1, and the third winding and the fourth winding adopt the same structure, both including a wrapping part and a connecting part electrically connected to each other; the connecting part is long and strip-shaped and installed close to the base; the cross-section of the wrapping part is U-shaped and is inverted above the first winding; the wrapping part and the connecting part are surrounded to form a circle.

[0010] In another optional solution, the first winding, the first strand of the second winding, the third winding and the fourth winding are all wound closely around the first C-shaped magnetic core.

[0011] Optionally, the first C-shaped magnetic core includes a winding portion and two connecting arms; the winding portion is cylindrical, with a connecting arm connected to each of its two ends, the first winding, the first strand of the second winding, the third winding and the fourth winding are wound around the outer circumference of the winding portion, the cross-section of the connecting arm is rectangular, and can be connected to the end of the second C-shaped magnetic core; the cross-sectional area of ​​the winding portion is equal to the cross-sectional area of ​​the connecting arm; the cross-sectional area of ​​the second C-shaped magnetic core is rectangular.

[0012] Optionally, the bypass magnetic core includes multiple magnetic sheets, and air gaps are provided between connected magnetic sheets.

[0013] Optionally, the third winding and the fourth winding are connected in series.

[0014] The present utility model also designs an on-board charger, which includes, in addition to the above-mentioned transformer with a bypass magnetic core, a bidirectional high-voltage DC conversion circuit connected to the first winding, a primary side conversion circuit connected to the second winding, and a low-voltage DC conversion circuit connected to the third winding and the fourth winding.

[0015] The beneficial effects of the technical solution provided by the utility model are:

[0016] The utility model reuses a magnetic core and controls the coupling between the transformer windings to obtain leakage inductance as a resonant inductance, integrates four power magnetic components in the prior art into an integrated transformer, and is applied to a three-port power supply circuit. It has the following advantages: 1. The number of magnetic components of the converter is reduced, thereby reducing costs; 2. The power density of the converter is greatly improved; 3. The overall loss of the converter is reduced, thereby improving efficiency; 4. The cost of the converter's magnetic components is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be described in detail below with reference to the embodiments and accompanying drawings, wherein:

[0018] Figure 1 is a circuit diagram of a conventional vehicle-mounted charger transformer;

[0019] Figure 2 is an exploded view of the present invention;

[0020] Figure 3 is a three-dimensional view of the present invention;

[0021] FIG4 is a perspective schematic diagram of the third and fourth single-turn windings of the present invention;

[0022] Figure 5 is an exploded view of each magnetic core of the present invention;

[0023] Figure 6 is a schematic diagram of the structure of the integrated transformer of the utility model;

[0024] Figure 7 is a schematic diagram of the winding and magnetic circuit of the integrated transformer of the present invention;

[0025] FIG8 is a schematic diagram of an integrated transformer having only one magnetic sheet according to the present invention;

[0026] FIG9 is a schematic diagram of an integrated transformer in which a bypass core is connected between two magnetic sheets according to the present invention;

[0027] FIG10 is a schematic diagram of an integrated transformer having a plurality of air gaps in a magnetic sheet according to the present invention;

[0028] Figure 11 is a functional block diagram of the vehicle-mounted charger of the present invention;

[0029] Figure 12 is a circuit diagram of the vehicle-mounted charger of the present utility model;

[0030] Explanation of reference numerals: first C-shaped magnetic core (1), winding portion (1a), two connecting arms (1b), second C-shaped magnetic core (2), bypass magnetic core (3), magnetic sheet (3a), air gap (3b), first chamber (4), second chamber (5), magnetic flux regulating block (6), first winding (W1), second winding (W2), first strand of second winding (W2a), second strand of second winding (W2b), third winding (W3), wrapping portion (W3a) of third winding, connecting portion (W3b) of third winding, pin (3Wb1) of third winding (W3), fourth winding (W4), wrapping portion (W4a) of fourth winding (W4), pin (4Wa1) of fourth winding (W4), connecting portion (W4b) of fourth winding (W4), common pin (4Wb1) of third winding (W3) and fourth winding (W4), base (10), jack (11). DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0032] The utility model discloses a transformer with a bypass magnetic core. The utility model reuses one magnetic core, controls the coupling between transformer windings to obtain leakage inductance as resonant inductance, and integrates four power magnetic elements into one integrated transformer. As can be seen from the exploded view shown in FIG2 and the stereoscopic view shown in FIG3 , the transformer with a bypass core includes a base 10, and a first C-shaped core 1 and a second C-shaped core 2 mounted on the base 10. The two ends of the first C-shaped core 1 and the two ends of the second C-shaped core 2 are butted together to form a closed magnetic ring. The transformer also includes a second winding W2 and a bypass core 3. The bypass core 3 is disposed in the middle of the magnetic ring, dividing the interior of the magnetic ring into a first chamber 4 and a second chamber 5. The second winding W2 includes a first strand W2a and a second strand W2b of the second winding connected in series. The first C-shaped core 1 is wound with a first winding W1, a first strand W2a of the second winding, a third winding W3, and a fourth winding W4, while the second C-shaped core 2 is wound with a second strand W2b of the second winding. The pins of the first winding W1, the second winding W2, the third winding W3, and the fourth winding W4 extend downward through the base 10 for soldering to the circuit board.

[0033] The first winding W1, the first strand W2a of the second winding, the third winding W3, and the fourth winding W4 pass through the first chamber 4 on the left, while the second strand W2b of the second winding passes through the second chamber 5 on the right. Referring to the transformer winding and magnetic circuit schematic diagram shown in FIG7 , the first C-shaped magnetic core 1 and the second C-shaped magnetic core 2 form the main magnetic circuit, and the bypass magnetic core 3 forms the bypass magnetic circuit. By adjusting the magnetic circuit length, cross-sectional area, and magnetic permeability of the first C-shaped magnetic core 1, the second C-shaped magnetic core 2, the bypass magnetic core 3, and the flux regulating block 6, the magnetic resistance of the flux regulating block 6 and the bypass magnetic core 3 are changed to control the excitation inductance of the first winding W1 and the leakage inductance of the first winding W1 to the second winding W2. These functions serve as the resonant inductance of the resonant power supply circuit, thereby eliminating the need for discrete inductance, as shown in FIG12 as the resonant inductance Lr.

[0034] To achieve the purpose of regulating magnetic flux, a magnetic flux regulating block 6 is provided at least at one of the two joints between the first C-shaped magnetic core 1 and the second C-shaped magnetic core 2. The magnetic flux regulating block 6 is sandwiched between the ends of the first C-shaped magnetic core 1 and the second C-shaped magnetic core 2. Figure 8 shows a schematic diagram of an integrated transformer with only one magnetic flux regulating block 6.

[0035] Referring to another optional embodiment shown in Figure 6, a flux adjustment block 6 is provided at both joints of the first C-shaped magnetic core 1 and the second C-shaped magnetic core 2, and the flux adjustment block 6 is clamped between the ends of the first C-shaped magnetic core 1 and the second C-shaped magnetic core 2; wherein, one end of the bypass magnetic core 3 is connected to one end of the first C-shaped magnetic core 1, and the other end of the bypass magnetic core 3 is connected to the other end of the first C-shaped magnetic core 1.

[0036] In one optional embodiment, one end of the bypass core 3 is connected to one end of the second C-shaped core 2, and the other end of the bypass core 3 is connected to the other end of the second C-shaped core 2 (not shown in the figure for this example). In another optional embodiment, one end of the bypass core 3 is connected to one end of the first C-shaped core 1, and the other end of the bypass core 3 is connected to the flux regulating block 6 (not shown in the figure for this example). Figure 9 shows a modified embodiment: flux regulating blocks 6 are provided at both joints of the first C-shaped core 1 and the second C-shaped core 2, and the flux regulating blocks 6 are sandwiched between the ends of the first C-shaped core 1 and the second C-shaped core 2; the bypass core 3 is connected between the two flux regulating blocks 6.

[0037] 6 shows a winding method, the first winding W1 and the second winding first strand W2a are wound closely around the first C-shaped magnetic core 1, the third winding W3 is wound around the outside of the first winding W1, and the fourth winding W4 is wound around the outside of the third winding W3.

[0038] In some applications (such as applications of the present invention in on-board chargers), the third and fourth windings W3 and W4 each have one turn. Referring to the exploded view of the transformer shown in Figure 2 and the perspective view of the transformer shown in Figure 3, the third and fourth windings W3 and W4 share the same structure, including electrically connected wrapping portions W3a and W4a and connecting portions W3b and W4b. Referring to the perspective diagram of the single-turn third and fourth windings shown in Figure 4, W3a and W3b represent the wrapping and connecting portions of the third winding W3, while W4a and W4b represent the wrapping and connecting portions of the fourth winding W4. The connecting portions W3b and W4b are elongated and mounted close to the base 10. The wrapping portions W3a and W4a have a U-shaped cross-section and are inverted above the first winding W1. The wrapping portions W3a and W4a and the connecting portions W3b and W4b form a circle, encircling the first C-shaped magnetic core 1 at its center. Icon 3Wb1 is a pin of the third winding W3, which is connected to the connection portion W3b of the third winding W3. Icon 4Wb1 is a common pin of the third winding W3 and the fourth winding W4, which is connected to the connection portion W4b of the fourth winding W4. Icon 4Wa1 is a pin of the fourth winding W4, which is connected to the wrapped portion of the fourth winding W4. The connection portion W3b of the third winding W3 is provided with a socket 11. The plug of the wrapped portion W3a of the third winding W3 is inserted into this socket 11, connecting the connection portion W3b and the wrapped portion W3a of the third winding W3 to form a complete turn. The connection portion W4b of the fourth winding W4 is provided with two sockets 11, which can be plugged into the plug of the wrapped portion W3a of the third winding W3 and the plug of the wrapped portion W4a of the fourth winding W4, respectively, to connect the connection portion W4b and the wrapped portion W4a of the fourth winding W4 to form a complete turn and connect the third winding W3 and the fourth winding W4.

[0039] 7 shows another winding method, the second winding first strand W2 a , the first winding W1 , the third winding W3 , and the fourth winding W4 are all wound closely around the first C-shaped magnetic core 1 .

[0040] Referring to the exploded view of each magnetic core shown in Figure 5, the first C-shaped magnetic core 1 comprises a winding portion 1a and two connecting arms 1b. The winding portion 1a is cylindrical, with a connecting arm 1b connected at each end. The first winding W1, the first strand W2a of the second winding, the third winding W3, and the fourth winding W4 are wound around the outer periphery of the winding portion 1a. The connecting arms 1b have a rectangular cross-section and can mate with the ends of the second C-shaped magnetic core 2. The cross-sectional area of ​​the winding portion 1a is equal to that of the connecting arms 1b. The second C-shaped magnetic core 2 also has a rectangular cross-section. The total thickness of the first winding W1, the first strand W2a of the second winding, the third winding W3, and the fourth winding W4 wound around the winding portion 1a is slightly less than the length of the connecting arms 1b. The middle portion of the second C-shaped magnetic core 2 is recessed, where the second strand W2b of the second winding is wound. The thickness of the second strand W2b of the second winding is slightly less than the length of the bent portions at either end of the second C-shaped magnetic core 2. It should be pointed out that the connecting arm 1b is designed to be flat (with a rectangular cross-section) instead of being cylindrical like the winding portion 1a. This is because if the connecting arm 1b is also cylindrical, the longitudinal length of the entire transformer will be longer, which is not conducive to the miniaturization of the integrated transformer. The present invention can greatly improve the power density of the integrated transformer.

[0041] To change the magnetic reluctance of bypass core 3, an air gap can be provided in bypass core 3 in an alternative solution. Referring to Figure 10 , which shows a schematic diagram of an integrated transformer, bypass core 3 comprises multiple magnetic sheets 3a, with air gaps 3b disposed between connected magnetic sheets 3a. By varying the number and size of the air gaps, the magnetic reluctance of bypass core 3 can be varied.

[0042] In one embodiment, the third winding W3 and the fourth winding W4 are connected in series. It should be noted that the third winding W3 and the fourth winding W4 can be two independent windings, or they can be connected in series to form a complete winding, or they can be connected to each other to form a three-tap winding with three taps. The complete winding can be adapted to a full-bridge rectifier circuit. The three-tap winding can be connected to a full-wave rectifier circuit. The full-wave rectifier circuit uses a dual winding with taps, such as the on-board charger circuit diagram shown in Figure 12, plus two rectifier tubes, which is equivalent to a full-bridge rectifier circuit consisting of a complete winding plus four rectifier tubes.

[0043] The present invention discloses an on-board charger. Referring to the block diagram of the on-board charger principle shown in FIG11, the on-board charger includes, in addition to the aforementioned transformer with a bypass core, a bidirectional high-voltage DC conversion circuit connected to the first winding W1, a primary-side conversion circuit connected to the second winding W2, and a low-voltage DC conversion circuit connected to the third and fourth windings W3 and W4. The third and fourth windings W3 and W4 may be three-tapped windings. By adjusting the magnetic path length, cross-sectional area, and magnetic permeability of the first C-shaped magnetic core 1, the second C-shaped magnetic core 2, the bypass core 3, and the flux regulating block 6, the magnetic resistance of the flux regulating block 6 and the bypass core 3 are changed, thereby controlling the excitation inductance of the first winding W1 and the leakage inductance of the first winding W1 to the second winding W2. FIG12 shows a circuit diagram of the on-board charger of the present invention.

[0044] The above embodiments are for illustration only and are not intended to be limiting. Any equivalent modifications or variations made thereto without departing from the spirit and scope of this application should be included in the scope of the claims of this application.

Claims

1. A transformer with a bypass magnetic core, comprising a base (10), a first C-shaped magnetic core (1) and a second C-shaped magnetic core (2) mounted on the base (10), wherein two ends of the first C-shaped magnetic core (1) and two ends of the second C-shaped magnetic core (2) are butt-jointed in pairs to enclose a closed magnetic ring, and is characterized in that: The transformer further includes a second winding (W2) and a bypass magnetic core (3). The bypass magnetic core (3) is disposed in the middle of the magnetic ring, dividing the interior of the magnetic ring into a first chamber (4) and a second chamber (5). The second winding (W2) includes a first strand (W2a) and a second strand (W2b) of the second winding connected in series with each other. The first C-shaped magnetic core (1) is wound with a first winding (W1), the first strand (W2a) of the second winding, a third winding (W3), and a fourth winding (W4), and the second C-shaped magnetic core (2) is wound with the second strand (W2b) of the second winding.

2. The transformer with a bypass core as claimed in claim 1, wherein: At least one of the two docking joints of the first C-shaped magnetic core (1) and the second C-shaped magnetic core (2) is provided with a magnetic flux regulating block (6), and the magnetic flux regulating block (6) is clamped between the ends of the first C-shaped magnetic core (1) and the second C-shaped magnetic core (2).

3. The transformer with a bypass core as claimed in claim 2, wherein: Both of the two docking joints of the first C-shaped magnetic core (1) and the second C-shaped magnetic core (2) are provided with magnetic flux regulating blocks (6), and the magnetic flux regulating blocks (6) are clamped between the ends of the first C-shaped magnetic core (1) and the second C-shaped magnetic core (2); wherein, One end of the bypass magnetic core (3) is connected to one end of the first C-shaped magnetic core (1), and the other end of the bypass magnetic core (3) is connected to the other end of the first C-shaped magnetic core (1); or, One end of the bypass magnetic core (3) is connected to one end of the second C-shaped magnetic core (2), and the other end of the bypass magnetic core (3) is connected to the other end of the second C-shaped magnetic core (2); or, One end of the bypass magnetic core (3) is connected to one end of the first C-shaped magnetic core (1), and the other end of the bypass magnetic core (3) is connected to the magnetic flux regulating block (6); or, The bypass magnetic core (3) is connected between two magnetic flux regulating blocks (6).

4. The transformer with a bypass core as claimed in claim 1, wherein: The first winding (W1) and the first strand (W2a) of the second winding are wound closely around the first C-shaped magnetic core (1). The third winding (W3) is wound outside the first winding (W1), and the fourth winding (W4) is wound outside the third winding (W3).

5. The transformer with a bypass core according to claim 4, wherein: The number of turns of the coils of the third winding (W3) and the fourth winding (W4) is 1. The third winding (W3) and the fourth winding (W4) have the same structure and both include a wrapping portion (W3a, W4a) and a connecting portion (W3b, W4b) electrically connected to each other. The connecting portion (W3b, W4b) is strip-shaped and is installed close to the base (10). The cross-section of the wrapping portion (W3a, W4a) is U-shaped and is buckled above the first winding (W1). The wrapping portion (W3a, W4a) and the connecting portion (W3b, W4b) enclose a circle.

6. The transformer with a bypass core as described in claim 1, characterized in that: The first winding (W1), the first strand (W2a) of the second winding, the third winding (W3), and the fourth winding (W4) are all wound closely around the first C-shaped magnetic core (1).

7. The transformer with a bypass core as claimed in claim 1, wherein: The first C-shaped magnetic core (1) includes a winding portion (1a) and two connecting arms (1b); the winding portion (1a) is cylindrical, with one connecting arm (1b) connected to each of its two ends. The first winding (W1), the first strand of the second winding (W2a), the third winding (W3), and the fourth winding (W4) are wound around the outer periphery of the winding portion (1a). The cross-section of the connecting arm (1b) is rectangular and can be butted against the end of the second C-shaped magnetic core (2); the cross-sectional area of the winding portion (1a) is equal to the cross-sectional area of the connecting arm (1b); the cross-section of the second C-shaped magnetic core (2) is rectangular.

8. The transformer with a bypass core as claimed in claim 1, wherein: The bypass magnetic core (3) includes a plurality of magnetic sheets (3a), and an air gap (3b) is provided between adjacent magnetic sheets (3a).

9. The transformer with a bypass core as claimed in claim 1, wherein: The third winding (W3) and the fourth winding (W4) are connected in series with each other.

10. A vehicle-mounted charger, characterized in that: In addition to the transformer with a bypass magnetic core according to any one of claims 1 to 9, the on-vehicle charger further includes: a bidirectional high-voltage DC conversion circuit connected to the first winding (W1), a primary conversion circuit connected to the second winding (W2), and a low-voltage DC conversion circuit connected to the third winding (W3) and the fourth winding (W4).

Citation Information

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