Ultra-wideband rectangular waveguide-slot gap waveguide mixed transition power divider

By designing an ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider, the problem of poor electrical contact in rectangular waveguide power dividers in high-frequency communication is solved. This achieves a compact combination of rectangular waveguide and slot gap waveguide, improves the integration and robustness of the communication system, and provides ultra-wideband characteristics to meet the needs of high-speed and high-capacity communication.

CN121602007APending Publication Date: 2026-03-03TONGYU COMM INC
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Patent Information

Application Number
CN202511736532.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-11-25
Publication Date
2026-03-03

AI Technical Summary

Technical Problem

Existing rectangular waveguide power dividers suffer from poor electrical contact in high-frequency communications, leading to increased losses and deteriorated matching. Furthermore, the existing rectangular waveguide-slot gap waveguide transition structure is difficult to meet the requirements for miniaturization and ultra-wideband.

Method used

An ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider is designed. By setting periodic metal pins on a metal plate to form an electromagnetic bandgap, and combining it with a U-shaped partition and a matching ridge, a compact combination of rectangular waveguide and slot gap waveguide is achieved to form an E-plane waveguide T-junction, thus optimizing impedance matching and mode transition.

Benefits of technology

It realizes mode transition and power splitting functions between rectangular waveguides and slot gap waveguides, improves the integration and robustness of communication systems, has ultra-wideband characteristics, covers high-frequency communication bands, meets the requirements of high speed and high capacity, and ensures stable and reliable signal transmission.

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Abstract

The invention discloses an ultra wide band rectangular waveguide-slot gap waveguide mixed transition power divider, which comprises a first metal plate and a second metal plate which are oppositely arranged, metal pins which are respectively arranged on the left side and the right side and are periodically arranged are arranged on the first metal plate, and a first air gap A1 is arranged between the metal pins and the second metal plate to form an electromagnetic band gap; an input rectangular waveguide and a matching rectangular waveguide are arranged on the first metal plate; a U-shaped partition plate, two output slot gap waveguides and two matching ridges are arranged in the electromagnetic band gap; the output slot gap waveguide is communicated with the input rectangular waveguide through the matching rectangular waveguide; mode transition between a rectangular waveguide main mode TE10 and a slot gap waveguide main mode quasi TE10 and the core function of the power divider are achieved, the impedance bandwidth of an input port S11 is smaller than or equal to-20 dB and is higher than 54.65%, the high-frequency V wave band and E wave band of two millimeter waves are comprehensively covered, the ultra-wideband characteristic is achieved, and the high-speed and large-capacity communication requirements can be met.
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Description

Technical Field

[0001] This invention relates to the field of power dividers, and in particular to an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider. Background Technology

[0002] As a core passive device in microwave communication, the power divider's core function is to distribute the energy of one input signal to multiple output ports in a specific ratio. In reverse operation, it can combine multiple signals (i.e., a combiner), and is widely used in power distribution / combining and array antenna feed networks. Rectangular waveguide power dividers, with their advantages of high power capacity and low insertion loss, have become a key choice for high-frequency communication systems. However, with the rapid development of 5G / 6G communication, millimeter-wave communication, satellite communication, and vehicle-to-everything (V2X) communication, the demand for transmission capacity and speed in communication systems is exploding, driving the rapid evolution of rectangular waveguide power dividers towards higher frequencies, wider bandwidth, and miniaturization.

[0003] Traditional rectangular waveguide power dividers consist of two layers of metal plates. Loose physical bonding between these plates can easily create gaps, leading to poor electrical contact and electromagnetic leakage. This problem increases losses and deteriorates matching, becoming increasingly severe with higher frequency bands, particularly in the V-band (57-66 GHz), E-band (71-76 GHz, 81-86 GHz), and higher millimeter-wave high-frequency bands. To address this issue of poor electrical contact, slot-gap waveguides, a novel electromagnetic transmission structure based on the non-contact electromagnetic bandgap (EBG) principle, have emerged. They form an electromagnetic bandgap through periodic electromagnetic structures. This non-contact design not only avoids electrical contact problems but also offers advantages such as wide bandwidth, high flexibility, and ease of integration.

[0004] However, current microwave test equipment (such as vector network analyzers) mostly uses rectangular waveguide interfaces. Testing slot-gap waveguide devices requires a rectangular waveguide-slot-gap waveguide transition structure. In existing technologies, the rectangular waveguide-slot-gap waveguide transition and the slot-gap waveguide power divider are mostly designed independently, resulting in large space requirements when combined, making it difficult to meet the miniaturization and integration needs of electronic devices. Furthermore, the impedance bandwidth (S) of the disclosed slot-gap waveguide power divider schemes is limited. 11 The bandwidth (≤-20dB) is typically only about 20%, which is far from meeting the actual needs of ultra-wideband applications and limits its promotion and application in the field of high-frequency communication. Summary of the Invention

[0005] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention proposes an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider.

[0006] The technical solution adopted by an embodiment of the present invention to solve its technical problem is: an ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider, including a first metal plate and a second metal plate arranged opposite to each other, the first metal plate is provided with metal pins arranged periodically on the left and right sides, and a first air gap A1 is provided between the metal pins and the second metal plate to form an electromagnetic band gap; An input rectangular waveguide and a matching rectangular waveguide are provided on the first metal plate; The electromagnetic bandgap contains a U-shaped partition, two output slot gap waveguides, and two matching ridges. The output slot gap waveguide and the input rectangular waveguide are connected via a matching rectangular waveguide to form an E-plane waveguide T-junction; The output slot gap waveguides are directly connected, and the longitudinal cross-section of the wide side coincides with the longitudinal cross-section of the wide side of the input rectangular waveguide, while the transverse cross-section of the narrow side is orthogonal to the vertical cross-section of the narrow side of the input rectangular waveguide. The longitudinal cross-section of the matching ridge coincides with the longitudinal cross-section of the output slot gap waveguide, and the bottom surface coincides with the bottom surface of the output slot gap waveguide; The U-shaped partition is set on the second metal plate, with its wide side longitudinal cross-section coinciding with the wide side longitudinal cross-section of the input rectangular waveguide and its narrow side vertical cross-section coinciding with the narrow side vertical cross-section of the input rectangular waveguide.

[0007] As one of the preferred embodiments of the present invention, the wide side of the matching rectangular waveguide is set to 85%-95% of the wide side of the input rectangular waveguide, the narrow side of the matching rectangular waveguide is set to 90%-99% of the narrow side of the input rectangular waveguide, and the height of the matching rectangular waveguide is set to one-quarter of the waveguide wavelength of the input rectangular waveguide.

[0008] As one of the preferred embodiments of the present invention, the matching ridge comprises a plurality of matching steps arranged in a stepped manner, wherein the height of the matching steps is not higher than the height of the metal pin.

[0009] As one of the preferred embodiments of the present invention, the length of the matching step is set to one-quarter of the waveguide wavelength of the output slot gap waveguide, and the width is set to 20%-50% of the width of the output slot gap waveguide.

[0010] As one of the preferred embodiments of the present invention, the U-shaped partition is provided with a first column and a second column extending downward at both ends, and a second air gap A2 is provided between the lower end face of the first column and the second column and the first metal plate.

[0011] As one of the preferred embodiments of the present invention, a concave impedance matching groove is provided in the middle of the U-shaped partition, and the height of the impedance matching groove is set to 15% to 25% of the width of the output slot gap waveguide.

[0012] As one of the preferred embodiments of the present invention, the metal pin is integrally formed with the first metal plate.

[0013] As one of the preferred embodiments of the present invention, the U-shaped partition and the second metal plate are integrally formed.

[0014] The beneficial effects of this invention are: (1) Multifunctional integration: It realizes both the rectangular waveguide master mode TE and the multifunctional integration of the rectangular waveguide master mode TE. 10 Mode and slot gap waveguide master mode quasi-TE 10 The mode transition between modules also serves as the core function of a power divider, enhancing the integration and functional diversity of the communication system. (2) Simple and compact structure: The present invention cleverly combines the rectangular waveguide-slot gap waveguide transition and the slot gap waveguide power divider, successfully achieving a minimalist layout. Its structure is very compact, effectively reducing unnecessary space occupation and conforming to the trend of miniaturization. (3) Simple processing technology: Although the two devices are integrated, the structure is still simple and easy to process. In particular, the U-shaped partition is integrated into the upper plate and forms an interlaced structure with the periodic electromagnetic structure (metal pin) of the lower plate, which further optimizes the structural layout, makes the processing simpler, and facilitates large-scale production. (4) Excellent performance: Simulation results of the embodiments of the present invention show that the input port S 11 With an impedance bandwidth of ≤-20dB, it has a bandwidth of over 54.65% (49.6-86.9GHz), fully covering the V-band (57-66GHz) and E-band (71-76GHz, 81-86GHz) of the two millimeter wave high frequencies. It has ultra-wideband characteristics, which not only conforms to the trend of high frequency development, but also meets the needs of high-speed and high-capacity communication. At the same time, the amplitude consistency of the two output signals is good within the above frequency bands, and the signal transmission is stable and reliable. (5) Excellent robustness: Due to the adoption of gap waveguide technology, the problem of poor electrical contact in traditional rectangular waveguide power dividers is effectively solved, and the robustness is significantly improved, which helps to greatly improve the pass rate of mass production. Attached Figure Description

[0015] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a schematic diagram of the first structure of an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider. Figure 2 This is a schematic diagram of the second structure of an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider; Figure 3 An exploded view of an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider; Figure 4This is a cross-sectional view of an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider; Figure 5 The instantaneous electric field distribution diagram of an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider is shown. Figure 6 A schematic diagram of the S-parameter curves of an ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider; Figure 7 This is a schematic diagram of the phase curves of the two branches of a hybrid transition power divider consisting of an ultrawideband rectangular waveguide and a slot gap waveguide. Detailed Implementation

[0016] This section will describe in detail specific embodiments of the present invention. Preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the drawings is to supplement the textual description with graphics, so that people can intuitively and vividly understand each technical feature and overall technical solution of the present invention, but they should not be construed as limiting the scope of protection of the present invention.

[0017] In the description of this invention, "multiple" means two or more; "greater than," "less than," and "exceeding" are understood to exclude the stated number; "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0018] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0019] In this invention, unless otherwise explicitly defined, the terms "setting," "installing," and "connecting" should be interpreted broadly. For example, they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to a fixed connection, a detachable connection, or an integrally formed connection; they can refer to a mechanical connection; they can refer to the internal connection of two components or the interaction between two components. Those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0020] Reference Figures 1-7An ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider includes a first metal plate 10 and a second metal plate 20 arranged opposite to each other. Metal pins 30 are arranged periodically on the left and right sides of the first metal plate 10. A first air gap A1 is provided between the metal pins 30 and the second metal plate 20 to form an electromagnetic band gap 40. An input rectangular waveguide 51 and a matching rectangular waveguide 52 are provided on the first metal plate 10; The electromagnetic bandgap 40 is provided with a U-shaped partition 60, two output slot gap waveguides 70 and two matching ridges 80; The output slot gap waveguide 70 and the input rectangular waveguide 51 are connected via a matching rectangular waveguide 52 to form an E-plane waveguide T-junction. The output slot gap waveguides 70 are directly connected, and their wide-side longitudinal cross-sections coincide with the wide-side longitudinal cross-sections of the input rectangular waveguide 51, while their narrow-side transverse cross-sections are orthogonal to the narrow-side vertical cross-sections of the input rectangular waveguide 51. The longitudinal cross-section of the matching ridge 80 coincides with the longitudinal cross-section of the output slot gap waveguide 70, and its bottom surface coincides with the bottom surface of the output slot gap waveguide 70. The U-shaped partition 60 is disposed on the second metal plate 20, and its wide-side longitudinal cross-section coincides with the wide-side longitudinal cross-section of the input rectangular waveguide 51, while its narrow-side vertical cross-section coincides with the narrow-side vertical cross-section of the input rectangular waveguide 51. It should be noted that the hybrid transition power divider provided by the present invention is geometrically symmetrical about the longitudinal and vertical cross-sections.

[0021] Reference Figures 1-4 This invention constructs an electromagnetic bandgap (EBG) structure using a first metal plate 10, a second metal plate 20, and a periodically arranged array of metal pins 30. This avoids the problem of poor electrical contact in principle. Specifically, the metal pins 30 on the first metal plate 10 are arranged in a specific period. The first air gap A1 formed between the upper end face of the metal pins 30 and the lower end face of the second metal plate 20 ensures that electromagnetic waves can only propagate within the output slot gap waveguide 70 area enclosed by the metal pins 30 during propagation. The periodic metal structure will produce a "bandgap effect" on electromagnetic waves of a specific frequency band, preventing electromagnetic waves from leaking to the outside. At the same time, the non-contact design of the air gap completely eliminates signal loss and matching degradation caused by loose metal bonding, which is especially suitable for the transmission requirements of millimeter-wave high-frequency bands. Preferably, the metal pins 30 and the first metal plate 10 are integrally formed.

[0022] Reference Figures 1-4 An input rectangular waveguide 51 and a matching rectangular waveguide 52 are disposed on the first metal plate 10, and a U-shaped partition 60, two output slot gap waveguides 70, and two matching ridges 80 are disposed within the electromagnetic band gap 40. The output slot gap waveguides 70 are connected to the input rectangular waveguide 51 via the matching rectangular waveguide 52 to form an E-plane waveguide T-junction. Preferably, the U-shaped partition 60 is integrally formed with the second metal plate 20. (Refer to...) Figure 5The dominant mode transmitted by the input rectangular waveguide 51 is TE. 10 The dominant mode of the output slot gap waveguide 70, whose electric field distribution is polarized along the wide side, is quasi-TE. 10 The electric field distribution of the mode needs to be adapted to the constraint characteristics of the gap structure. The hybrid transition power divider provided by this invention can achieve smooth mode transition: 1. The cross-sectional design of the output slot gap waveguide 70 with the wide side coinciding with the wide side of the input rectangular waveguide 51 and the narrow side orthogonal to it makes the electric field polarization direction naturally adapted; 2. The size of the matching rectangular waveguide 52 is designed according to the specific proportion of the input rectangular waveguide 51 to form a quarter-wavelength impedance transformation section to compensate for the characteristic impedance difference between the two waveguide structures; 3. The cross-sections of the wide and narrow sides of the U-shaped partition 60 are completely fitted to the corresponding cross-sections of the input rectangular waveguide 51 to form an electromagnetic constraint channel, ensuring that the field distribution of the TE10 mode changes continuously during the transition process and avoiding reflection loss caused by mode abrupt change.

[0023] Reference Figures 1-4 In some embodiments, the wide side of the matching rectangular waveguide 52 is set to 85%-95% of the wide side of the input rectangular waveguide 51, the narrow side of the matching rectangular waveguide 52 is set to 90%-99% of the narrow side of the input rectangular waveguide 51, and the height of the matching rectangular waveguide 52 is set to one-quarter of the waveguide wavelength of the input rectangular waveguide 51. This utilizes the transmission line impedance transformation principle to achieve preliminary impedance matching between the rectangular waveguide and the slot gap waveguide. The dimensions of the input rectangular waveguide 51 can refer to GB 11450.2-1989, designed to match the rectangular waveguide interface of microwave test equipment such as vector network analyzers for easy testing. The above are only preferred values; suitable dimensions can also be obtained through waveguide transmission line theory calculations based on the required operating frequency band and power requirements.

[0024] Reference Figures 1-4 In other embodiments, the matching ridge 80 comprises a plurality of matching steps 81 arranged in a stepped manner, the height of which is not higher than the height of the metal pin 30; the length of the matching step 81 is set to one-quarter of the waveguide wavelength of the output slot gap waveguide 70, and the width is set to 20%-50% of the width of the output slot gap waveguide 70, thus forming a continuous impedance gradient channel to compensate for impedance abrupt changes at the power branch and extend the effective frequency band of impedance matching.

[0025] Reference Figures 1-4 In a further embodiment, a recessed impedance matching slot 63 is provided in the middle of the U-shaped partition 60. The height of the impedance matching slot 63 is set to 15% to 25% of the width of the output slot gap waveguide 70. By adjusting the slot depth (height), the electromagnetic coupling strength at the branch is changed, further optimizing the impedance characteristics in the wide frequency band, so that the input port S 11 With an impedance bandwidth of ≤-20dB exceeding 54.65%, ultra-wideband coverage is achieved.

[0026] Reference Figures 1-4 In a further embodiment, the geometrically symmetrical structure of the E-plane waveguide T-junction serves as the basis for power equalization. The output slot gap waveguides 70 are designed to be directly connected, and with the symmetrical constraint of the U-shaped partition 60, the input signal is evenly split into two paths at the branch point. The first pillar 61 and the second pillar 62 at both ends of the U-shaped partition 60 are equivalent to metal pins 30, and the first pillar 61 and the second pillar 62 form a second air gap A2 with the first metal plate 10. At the same time, the matching ridge 80 is completely symmetrical about the longitudinal cross section, ensuring that the transmission path impedance of the two signals is consistent, and finally achieving equal amplitude and inverse phase output, and the phase difference remains stable within the target frequency band. This invention achieves integration through functional structure fusion. The electromagnetic bandgap 40 serves as both the waveguide structure of the slot gap waveguide 70 and provides an electromagnetic shielding environment for the power divider. The U-shaped partition 60 not only participates in the electromagnetic constraint of mode transition but also undertakes the branch isolation function of power distribution. Furthermore, the matching ridge 80 optimizes bandwidth characteristics and ensures power distribution accuracy. Each structure carries multiple functions simultaneously without the need for additional components, achieving a minimalist and compact layout design.

[0027] The advantages of this invention are: (1) Multifunctional integration: It realizes the mode transition between the rectangular waveguide main mode TE10 mode and the slot gap waveguide main mode quasi-TE10 mode, and also has the core function of the power divider, which improves the integration and functional diversity of the communication system; (2) Simple and compact structure: This invention cleverly combines the rectangular waveguide-slot gap waveguide transition and the slot gap waveguide power divider, and successfully achieves a minimalist layout. Its structure is very compact, effectively reducing unnecessary space occupation and conforming to the trend of miniaturization; (3) Simple processing technology: Although the two devices are integrated, the structure is still simple and easy to process. In particular, the U-shaped partition is integrated into the upper plate and forms an interlaced structure with the periodic electromagnetic structure (metal pin) of the lower plate, which further optimizes the structural layout, makes the processing simpler, and facilitates large-scale production; (4) Excellent performance: Referring to Figures 6-7 Simulation results of the present invention show that the impedance bandwidth of the input port S11≤-20dB is higher than 54.65% (49.6-86.9GHz), fully covering the V-band (57-66GHz) and E-band (71-76GHz, 81-86GHz) of the two millimeter wave high frequencies, and has ultra-wideband characteristics. It not only conforms to the trend of high frequency development, but also meets the needs of high-speed and large-capacity communication. At the same time, the amplitude consistency of the two output signals is good in the above frequency bands, and the signal transmission is stable and reliable. (5) Excellent robustness: Due to the use of gap waveguide technology, the problem of poor electrical contact of traditional rectangular waveguide power dividers is effectively solved, and the robustness is significantly improved, which helps to greatly improve the pass rate of mass production.

[0028] Of course, the present invention is not limited to the above-described embodiments. Those skilled in the art can make equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications and substitutions are included within the scope defined by the claims of this application.

Claims

1. A hybrid transition power divider of ultrawideband rectangular waveguide and slot gap waveguide, characterized in that: It includes a first metal plate (10) and a second metal plate (20) arranged opposite to each other. The first metal plate (10) is provided with metal pins (30) arranged periodically on the left and right sides. A first air gap A1 is provided between the metal pins (30) and the second metal plate (20) to form an electromagnetic band gap (40). An input rectangular waveguide (51) and a matching rectangular waveguide (52) are provided on the first metal plate (10). The electromagnetic bandgap (40) is provided with a U-shaped partition (60), two output slot gap waveguides (70) and two matching ridges (80). The output slot gap waveguide (70) and the input rectangular waveguide (51) are connected through the matching rectangular waveguide (52) to form an E-plane waveguide T-junction; The output slot gap waveguides (70) are straight through each other, and the longitudinal cross-section of the wide side coincides with the longitudinal cross-section of the wide side of the input rectangular waveguide (51), while the transverse cross-section of the narrow side is orthogonal to the vertical cross-section of the narrow side of the input rectangular waveguide (51). The longitudinal cross-section of the matching ridge (80) coincides with the longitudinal cross-section of the output slot gap waveguide (70), and the bottom surface coincides with the bottom surface of the output slot gap waveguide (70). The U-shaped partition (60) is disposed on the second metal plate (20) and its wide longitudinal cross section coincides with the wide longitudinal cross section of the input rectangular waveguide (51), and its narrow vertical cross section coincides with the narrow vertical cross section of the input rectangular waveguide (51).

2. The ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 1, characterized in that: The wide side of the matching rectangular waveguide (52) is set to 85%-95% of the wide side of the input rectangular waveguide (51), the narrow side of the matching rectangular waveguide (52) is set to 90%-99% of the narrow side of the input rectangular waveguide (51), and the height of the matching rectangular waveguide (52) is set to one-quarter of the waveguide wavelength of the input rectangular waveguide (51).

3. The ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 1, characterized in that: The matching ridge (80) comprises a plurality of matching steps (81) arranged in a stepped manner, and the height of the matching steps (81) is not higher than the height of the metal pin (30).

4. The ultrawideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 3, characterized in that: The length of the matching step (81) is set to one-quarter of the waveguide wavelength of the output slot gap waveguide (70), and the width is set to 20%-50% of the width of the output slot gap waveguide (70).

5. The ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 1, characterized in that: The U-shaped partition (60) has a first column (61) and a second column (62) extending downward at both ends. A second air gap A2 is provided between the lower end face of the first column (61) and the second column (62) and the first metal plate (10).

6. The ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 1, characterized in that: The U-shaped partition (60) has a recessed impedance matching groove (63) in the middle, and the height of the impedance matching groove (63) is set to 15% to 25% of the width of the output slot gap waveguide (70).

7. The ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 1, characterized in that: The metal pin (30) is integrally formed with the first metal plate (10).

8. The ultra-wideband rectangular waveguide-slot gap waveguide hybrid transition power divider according to claim 1, characterized in that: The U-shaped partition (60) is integrally formed with the second metal plate (20).

Citation Information

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