wilkinson power divider

CN224934976UActive Publication Date: 2026-11-03MOBILE ANTENNA TECH SHENZHEN +5
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Patent Information

Application Number
CN202522514794.X
Authority / Receiving Office
CN · China
Patent Type
Utility models(China)
Current Assignee / Owner
Filing Date
2025-11-26
Publication Date
2026-11-03
Estimated Expiration
2035-11-26

AI Technical Summary

Technical Problem

Traditional Wilkinson power dividers have insufficient isolation and are too large in size over a wide frequency range, making them difficult to adapt to miniaturized RF modules.

Method used

It adopts a folded λ/4 transmission line structure and a dual isolation resistor design, including a dielectric substrate, RF transmission line, and first and second isolation resistors. The isolation and size are optimized through a U-shaped folding design and a temperature compensation sheet.

Benefits of technology

Significantly improves isolation, reduces size, meets the needs of miniaturized RF modules, and ensures high isolation and low insertion loss.

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Abstract

The application provides a Wilkinson power divider, which comprises a dielectric substrate, a radio frequency transmission line, a first isolation resistor and a second isolation resistor; the radio frequency transmission line is arranged on one side of the dielectric substrate, the radio frequency transmission line adopts a folded λ / 4 transmission line structure and comprises an input transmission line, a first branch transmission line and a second branch transmission line, the input transmission line is connected to one end of the first branch transmission line and the second branch transmission line through a T-shaped node respectively, and the first branch transmission line and the second branch transmission line both adopt a twice U-shaped folding design; two ends of the first isolation resistor are electrically connected to one end of the first branch transmission line and the second branch transmission line away from the input transmission line respectively, and two ends of the second isolation resistor are electrically connected between two U-shaped folds of the first branch transmission line and the second branch transmission line. The Wilkinson power divider has high isolation and small size.
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Description

Technical Field

[0001] This application relates to the field of radio frequency and microwave technology, and in particular to a Wilkinson power divider. Background Technology

[0002] As a core component in radio frequency and microwave systems for signal distribution and synthesis, the performance (isolation, insertion loss, amplitude and phase consistency) and structural dimensions of Wilkinson power dividers directly affect the stability and integration of the entire system. In practical applications, traditional Wilkinson power dividers have significant drawbacks. Firstly, insufficient isolation: Microstrip Wilkinson power dividers typically rely on a single isolation resistor to achieve isolation between output ports. When the operating frequency covers a wide frequency band (e.g., 1GHz-6GHz), the matching performance of the isolation resistor degrades, resulting in an isolation level of less than 20dB between output ports. This easily leads to crosstalk between ports, affecting the system's receiving sensitivity. Secondly, excessive size: The transmission lines of traditional Wilkinson power dividers must meet the λ / 4 wavelength requirement (λ being the operating wavelength). At low frequencies (e.g., 1GHz), the λ / 4 transmission line length exceeds 75mm, making it difficult to adapt to miniaturized RF modules (e.g., 5G terminal RF units with dimensions <50mm×50mm). It is important to note that the techniques described in this section are not necessarily those previously conceived or adopted. Unless otherwise specified, no technique described in this section should be assumed to be prior art simply because it is included in this section. Similarly, unless otherwise specified, the issues mentioned in this section should not be considered to be recognized in any prior art. Utility Model Content

[0003] This application provides a Wilkinson power divider designed to address the technical problems of insufficient isolation and excessive size in existing Wilkinson power dividers.

[0004] To achieve the above objectives, this application provides a Wilkinson power divider, the Wilkinson power divider comprising: Dielectric substrate; A radio frequency (RF) transmission line is disposed on one side of the dielectric substrate. The RF transmission line adopts a folded λ / 4 transmission line structure. The RF transmission line includes an input transmission line, a first branch transmission line, and a second branch transmission line. One end of the input transmission line is used to connect to an input port. The other end of the input transmission line is connected to one end of the first branch transmission line and one end of the second branch transmission line through a T-shaped node. The end of the first branch transmission line away from the input line is used to connect to a first output port. The end of the second branch transmission line away from the input line is used to connect to a second output port. Both the first branch transmission line and the second branch transmission line adopt a double U-shaped fold design. A first isolation resistor, one end of which is electrically connected to the end of the first branch transmission line away from the input transmission line, and the other end of the first isolation resistor is electrically connected to the end of the second branch transmission line away from the input transmission line; and The second isolation resistor has one end electrically connected between the two U-shaped folds of the first branch transmission line, and the other end electrically connected between the two U-shaped folds of the second branch transmission line.

[0005] Optionally, the dielectric substrate is an Al2O3 ceramic substrate with εr=9.8 and tanδ<0.001; or, the dielectric substrate is an AlN ceramic substrate with εr=8.8 and tanδ=0.0005.

[0006] Optionally, the thickness of the dielectric substrate is 0.5 mm to 1 mm.

[0007] Optionally, the surface of the dielectric substrate is covered with copper foil, the thickness of which is 35μm~50μm.

[0008] Optionally, the edge of the radio frequency transmission line has a rounded transition structure with a radius of 0.1mm to 0.2mm.

[0009] Optionally, the first isolation resistor is made of nickel-chromium alloy material, the first isolation resistor is packaged as a bare die, the rated power of the first isolation resistor is ≥0.5W, the first isolation resistor is fixed to the dielectric substrate by conductive silver paste, the first isolation resistor and the first branch transmission line are ultrasonically welded, and the solder joint thickness between the first isolation resistor and the first branch transmission line is 5μm~8μm.

[0010] Optionally, the two ends of the second isolation resistor are respectively connected to the portion of the first branch transmission line and the second branch transmission line that is λ / 8 away from the T-node.

[0011] Optionally, the Wilkinson power divider includes: A temperature compensation plate is disposed on the side of the radio frequency transmission line away from the dielectric substrate. The temperature compensation plate is made of a negative temperature coefficient ceramic material, and the εr temperature coefficient of the negative temperature coefficient ceramic material is -20ppm / ℃.

[0012] Optionally, the temperature compensation patch covers the λ / 8 segment of the first branch transmission line and the second branch transmission line, and the area of ​​the temperature compensation patch covering the first branch transmission line and the second branch transmission line accounts for 30% to 40% of the total area of ​​the radio frequency transmission line.

[0013] Optionally, the Wilkinson power divider includes: A grounding layer is disposed on the side of the dielectric substrate opposite to the radio frequency transmission line.

[0014] The Wilkinson power divider of this application has the following beneficial effects: (1) significantly improved isolation. Since the position between the two U-shaped folds is equivalent to the midpoint between the first output terminal / second output terminal and the T-shaped node in terms of electrical length, the second isolation resistor and the first isolation resistor form a dual isolation mechanism, which can improve the overall isolation performance of the Wilkinson power divider, effectively suppress signal crosstalk between ports, and achieve high isolation; (2) greatly reduced size. The two U-shaped folds design enables the RF transmission line to achieve an electrical length of λ / 4 in a limited space, and the overall size of the Wilkinson power divider can be relatively small, thereby adapting to miniaturized RF modules.

[0015] It should be understood that the description in this section is not intended to identify key or important features of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent from the following description. Attached Figure Description

[0016] The accompanying drawings exemplify embodiments and form part of the specification, working together with the textual description to explain exemplary implementations of the embodiments. The drawings shown are for illustrative purposes only and do not limit the scope of the claims. Throughout the drawings, the same reference numerals refer to similar but not necessarily identical elements.

[0017] Figure 1 This is a top view of an embodiment of the Wilkinson power divider of this application.

[0018] Figure 2 A stereoscopic view of another embodiment of the Wilkinson power divider of this application Figure 1 ; Figure 3 for Figure 2 The three-dimensional embodiment shown Figure 2 ; Explanation of reference numerals in the attached figures: Detailed Implementation

[0019] To make the inventive objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0021] In the description of the embodiments of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The term "multiple" means two or more, unless otherwise explicitly specified. The term "comprising" indicates the presence of the described feature, whole, step, operation, element, and / or component, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or sets thereof. The term "and / or" describes the relationship between related objects, indicating that three relationships may exist. For example, A and / or B may include three cases: A existing alone, A and B existing simultaneously, and B existing alone. The character " / " generally indicates that the related objects before and after are in an "or" relationship.

[0022] Unless otherwise defined, all technical terms used in the embodiments of this application have the same meaning as commonly understood by one of ordinary skill in the art; the terms used in the embodiments of this application are for the purpose of describing specific embodiments only and are not intended to limit this application; the terms "comprising" and "having" and any variations thereof in the specification, claims and foregoing description of the drawings of this application are intended to cover non-exclusive inclusion.

[0023] Furthermore, terms such as "exemplary," "for example," and "optional" are used to indicate illustrative purposes. Any technical solution described by the above terms in the embodiments of this application should not be construed as being more preferred or advantageous than other technical solutions. Specifically, these terms are intended to present the relevant technical concepts in terms of specific implementation methods.

[0024] This application provides a Wilkinson power divider, which can be mainly used in communication systems (such as 5G / 6G base stations, satellite communication equipment), radar systems, test and measurement instruments, and RF front-end modules to achieve equal or unequal power distribution / combination of RF signals. It is especially suitable for high-density integrated RF circuit scenarios with strict size constraints, high isolation requirements, and low insertion loss. This Wilkinson power divider includes a dielectric substrate, an RF transmission line, a first isolation resistor, and a second isolation resistor. The RF transmission line is located on one side of the dielectric substrate and employs a folded λ / 4 transmission line structure. The RF transmission line includes an input transmission line, a first branch transmission line, and a second branch transmission line. One end of the input transmission line is connected to an input port, and the other end is connected via a T-junction to one end of the first branch transmission line and one end of the second branch transmission line. The end of the first branch transmission line furthest from the input transmission line is connected to a first output port, and the end of the second branch transmission line furthest from the input line is connected to a second output port. Both the first and second branch transmission lines employ a double U-shaped fold design. One end of the first isolation resistor is electrically connected to the end of the first branch transmission line furthest from the input line, and the other end of the first isolation resistor is electrically connected to the end of the second branch transmission line furthest from the input line. One end of the second isolation resistor is electrically connected between the two U-shaped folds of the first branch transmission line, and the other end of the second isolation resistor is electrically connected between the two U-shaped folds of the second branch transmission line.

[0025] The Wilkinson power divider of this application has the following beneficial effects: (1) significantly improved isolation. Since the position between the two U-shaped folds is equivalent to the midpoint between the first output terminal / second output terminal and the T-shaped node in terms of electrical length, the second isolation resistor and the first isolation resistor form a dual isolation mechanism, which can improve the overall isolation performance of the Wilkinson power divider, effectively suppress signal crosstalk between ports, and achieve high isolation; (2) greatly reduced size. The two U-shaped folds design enables the RF transmission line to achieve an electrical length of λ / 4 in a limited space, and the overall size of the Wilkinson power divider can be relatively small, thereby adapting to miniaturized RF modules.

[0026] Please combine Figures 1 to 3 The Wilkinson power divider 1 of this application will be described in detail below.

[0027] The Wilkinson power divider 1 of this application includes a dielectric substrate 11. In some embodiments, the dielectric substrate 11 is an Al2O3 ceramic substrate with εr = 9.8 and tanδ < 0.001. In other embodiments, the dielectric substrate 11 is an AlN ceramic substrate with εr = 8.8 and tanδ = 0.0005. Both Al2O3 (alumina) and AlN (aluminum nitride) ceramic substrates are high-frequency, low-loss substrates, and both have high dielectric constants, which can reduce the physical size of the transmission line. The extremely low loss tangent of the Al2O3 and AlN ceramic substrates can minimize the dielectric loss of the RF signal during transmission, ensuring the low insertion loss characteristics of the Wilkinson power divider 1. The AlN ceramic substrate also has higher thermal conductivity, which can adapt to the heat dissipation requirements of high-power scenarios and expand the application range of the Wilkinson power divider 1.

[0028] The thickness of the dielectric substrate 11 is 0.5mm to 1mm. A dielectric substrate 11 that is too thin (<0.5mm) will result in insufficient mechanical strength, brittleness, and high processing difficulty. A dielectric substrate 11 that is too thick (>1mm) will not only increase the overall size of the Wilkinson power divider 1, which conflicts with the miniaturization design of the folded transmission line, but will also increase the dielectric loading effect deviation of the RF transmission line 12, resulting in a decrease in impedance matching accuracy.

[0029] The surface of the dielectric substrate 11 is covered with copper foil, the thickness of which is 35μm to 50μm. The copper foil possesses high conductivity and low loss characteristics. The 35μm to 50μm thickness of the copper foil meets the requirements of the "skin effect," avoiding increased skin loss due to insufficient thickness and ensuring low conductor loss of the RF transmission line 12. The copper foil of this thickness exhibits excellent adhesion to the dielectric substrate 11 (achieved through a high-temperature copper plating process), is not prone to detachment or cracking, and can withstand mechanical stress during photolithography, etching, and other processing. This allows for the fabrication of the fine patterns (two U-shaped folds) of the first branch transmission line 122 and the second branch transmission line 123. Furthermore, the etching accuracy of the 35μm to 50μm copper foil can reach ±0.01mm, accurately replicating the folded structure and dimensions of the RF transmission line 12, ensuring the accuracy of the λ / 4 electrical length, and thus ensuring impedance matching accuracy.

[0030] This Wilkinson power divider 1 includes an RF transmission line 12, which adopts a folded λ / 4 transmission line structure. The RF transmission line 12 includes an input transmission line 121, a first branch transmission line 122, and a second branch transmission line 123. One end of the input transmission line 121 is connected to an input port, and the other end of the input transmission line 121 is connected to one end of the first branch transmission line 122 and one end of the second branch transmission line 123 via a T-junction. The end of the first branch transmission line 122 furthest from the input line 121 is connected to a first output port, and the end of the second branch line 123 furthest from the input line 121 is connected to a second output port. Both the first branch line 122 and the second branch line 123 employ a double U-shaped fold design. This double U-shaped fold design allows the RF transmission line 12 to achieve a λ / 4 electrical length within a limited space, resulting in a smaller overall size for the Wilkinson power divider 1, thus enabling it to be adapted to miniaturized RF modules.

[0031] The edges of the RF transmission line 12 are rounded. If the edges of the RF transmission line 12 were right angles, it would not only cause abrupt impedance changes and signal reflections, but also result in additional radiation loss and interference with surrounding circuits. The rounded transition structure, with its smooth curve connection, allows for continuous impedance variation, avoiding these drawbacks.

[0032] The radius of the arc-shaped transition structure is 0.1mm~0.2mm. This 0.1mm~0.2mm radius design avoids distortion of the effective width of the RF transmission line due to an excessively large radius, while also preventing the inability to effectively smooth impedance due to an excessively small radius. 0.1mm~0.2mm is the optimal range for industrial mass production, with etching precision reaching ±0.01mm, accurately replicating the design and avoiding etching residue or linewidth loss caused by an excessively small radius.

[0033] The Wilkinson power divider 1 of this application includes a first isolation resistor 131. One end of the first isolation resistor 131 is electrically connected to the end of the first branch transmission line 122 away from the input transmission line 121, and the other end of the first isolation resistor 131 is electrically connected to the end of the second branch transmission line 123 away from the input transmission line 121. The first isolation resistor 131 provides basic isolation for direct coupling signals between the first port and the second port.

[0034] The first isolation resistor 131 is made of nickel-chromium alloy and is packaged as a bare die. Its rated power is ≥0.5W. The first isolation resistor 131 is fixed to the dielectric substrate 11 using conductive silver paste. The first isolation resistor 131 and the first branch transmission line 122 are ultrasonically welded, with a solder joint thickness of 5μm~8μm. Nickel-chromium alloy possesses high resistivity and a low temperature coefficient, meeting the stability requirements of RF scenarios. The bare die package eliminates the need for a separate casing, aligning with the miniaturized design of the Wilkinson power divider 1. A rated power of ≥0.5W satisfies the loss tolerance requirements for medium-to-high power signal transmission. The conductive silver paste provides both mechanical stability and low contact resistance. Ultrasonic welding ensures a reliable electrical connection between the first isolation resistor 131 and the first branch transmission line 122. The solder joint thickness of 5μm~8μm ensures welding strength while avoiding excessive parasitic capacitance due to excessive solder joint thickness, thus not affecting high-frequency performance. The first isolation resistor 131 and the second branch transmission line 123 can also be ultrasonically welded, and the thickness of the solder joint with the second branch transmission line 123 can be 5μm~8μm.

[0035] The Wilkinson power divider 1 of this application includes a second isolation resistor 132. One end of the second isolation resistor 132 is electrically connected between the two U-shaped folds of the first branch transmission line 122, and the other end of the second isolation resistor 132 is electrically connected between the two U-shaped folds of the second branch transmission line 123. The second isolation resistor 132 forms secondary isolation for the coupled signals in the middle section of the first branch transmission line 122 and the second branch transmission line 123, thereby improving the overall isolation.

[0036] The two ends of the second isolation resistor 132 are respectively connected to the portions of the first branch transmission line 122 and the second branch transmission line 123 at a distance of λ / 8 from the T-node. λ / 8 is a critical node for signal voltage division / isolation. The positioning at λ / 8 ensures that the second isolation resistor 132 can accurately act on the middle section of the strongest coupled signal, complementing the first isolation resistor 131, and will not interfere with the impedance matching of the RF transmission line 12.

[0037] The materials and connection method of the second isolation resistor 132 can be the same as those of the first isolation resistor 131, and will not be described in detail here.

[0038] Please see Figure 2 and Figure 3 In some embodiments, the Wilkinson power divider 1 includes a temperature compensation plate 14, which is disposed on the side of the RF transmission line 12 away from the dielectric substrate 11. The temperature compensation plate 14 is made of a negative temperature coefficient ceramic material with an εr temperature coefficient of -20ppm / ℃. The temperature compensation plate 14 of the negative temperature coefficient (NTC) ceramic material can counteract the positive drift of the εr of the dielectric substrate 11 by utilizing its own characteristic that εr decreases with increasing temperature, thereby achieving overall stability of εeff over a wide temperature range. The temperature compensation plate 14 is disposed on the side of the RF transmission line 12 away from the dielectric substrate 11, which neither compromises the connection reliability between the RF transmission line 12 and the dielectric substrate 11, nor does it directly affect the electromagnetic transmission environment of the RF transmission line 12, ensuring compensation efficiency, and without occupying additional surface space of the dielectric substrate 11, thus meeting the design goal of miniaturization.

[0039] Temperature compensation patch 14 covers the λ / 8 segment of the first branch transmission line 122 and the second branch transmission line 123. The area covered by temperature compensation patch 14 accounts for 30% to 40% of the total area of ​​the RF transmission line 12. The λ / 8 segment of the first branch transmission line 122 / second branch transmission line 123 is a critical performance area of ​​the Wilkinson power divider 1, which is more sensitive to dielectric constant drift. This area is also the connection point of the second isolation resistor 132. The reliability of the electrical connection between the second isolation resistor 132 and the first branch transmission line 122 / second branch transmission line 123 is also affected by temperature. Covering this area with temperature compensation patch 14 can simultaneously stabilize the dielectric environment of the first branch transmission line 122 / second branch transmission line 123 and the temperature characteristics of the connection area of ​​the second isolation resistor 132. The 30% to 40% coverage avoids material waste and increased parasitic parameters caused by over-compensation, and accurately solves the temperature drift problem in the core area (i.e., the λ / 8 segment).

[0040] Please see Figure 2 and Figure 3In some embodiments, the Wilkinson power divider 1 includes a ground layer 15, which is disposed on the side of the dielectric substrate 11 facing away from the radio frequency transmission line 12. The radio frequency transmission line 12 of the Wilkinson power divider 1 of this application is in the form of a microstrip line (copper foil + dielectric substrate 11). The ground layer 15 has the functions of providing a signal return path, suppressing electromagnetic radiation and crosstalk, and stabilizing the characteristic impedance of the transmission line. The placement of the ground layer 15 neither occupies the signal layer space where the radio frequency transmission line 12 is located, nor does it maximize the dielectric isolation effect of the dielectric substrate 11, ensuring a stable electric field distribution between the ground layer 15 and the radio frequency transmission line 12.

[0041] The above embodiments are only used to illustrate the present application and are not intended to limit it. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included within the protection scope of the present application.

Claims

1. A Wilkinson power divider, characterized in that, include: Dielectric substrate; A radio frequency (RF) transmission line is disposed on one side of the dielectric substrate. The RF transmission line adopts a folded λ / 4 transmission line structure. The RF transmission line includes an input transmission line, a first branch transmission line, and a second branch transmission line. One end of the input transmission line is used to connect to an input port. The other end of the input transmission line is connected to one end of the first branch transmission line and one end of the second branch transmission line through a T-shaped node. The end of the first branch transmission line away from the input line is used to connect to a first output port. The end of the second branch transmission line away from the input line is used to connect to a second output port. Both the first branch transmission line and the second branch transmission line adopt a double U-shaped fold design. A first isolation resistor has one end electrically connected to the end of the first branch transmission line away from the input transmission line, and the other end of the first isolation resistor is electrically connected to the end of the second branch transmission line away from the input transmission line. as well as The second isolation resistor has one end electrically connected between the two U-shaped folds of the first branch transmission line, and the other end electrically connected between the two U-shaped folds of the second branch transmission line.

2. The Wilkinson power divider according to claim 1, characterized in that, The dielectric substrate is an Al2O3 ceramic substrate with εr=9.8 and tanδ<0.001; or, the dielectric substrate is an AlN ceramic substrate with εr=8.8 and tanδ=0.0005.

3. The Wilkinson power divider according to claim 1, characterized in that, The thickness of the dielectric substrate is 0.5mm to 1mm.

4. The Wilkinson power divider according to claim 1, characterized in that, The surface of the dielectric substrate is covered with copper foil, the thickness of which is 35μm~50μm.

5. The Wilkinson power divider according to claim 1, characterized in that, The edge of the radio frequency transmission line has a rounded transition structure with a radius of 0.1mm to 0.2mm.

6. The Wilkinson power divider according to claim 1, characterized in that, The first isolation resistor is made of nickel-chromium alloy material, the first isolation resistor is packaged as a bare die, the rated power of the first isolation resistor is ≥0.5W, the first isolation resistor is fixed to the dielectric substrate by conductive silver paste, the first isolation resistor and the first branch transmission line are ultrasonically welded, and the thickness of the solder joint between the first isolation resistor and the first branch transmission line is 5μm~8μm.

7. The Wilkinson power divider according to claim 1, characterized in that, The two ends of the second isolation resistor are respectively connected to the first branch transmission line and the portion of the second branch transmission line that is λ / 8 away from the T-shaped node.

8. The Wilkinson power divider according to claim 1, characterized in that, The Wilkinson power divider includes: A temperature compensation plate is disposed on the side of the radio frequency transmission line away from the dielectric substrate. The temperature compensation plate is made of a negative temperature coefficient ceramic material, and the εr temperature coefficient of the negative temperature coefficient ceramic material is -20ppm / ℃.

9. The Wilkinson power divider according to claim 8, characterized in that, The temperature compensation sheet covers the λ / 8 segment of the first branch transmission line and the second branch transmission line, and the area of ​​the temperature compensation sheet covering the first branch transmission line and the second branch transmission line accounts for 30% to 40% of the total area of ​​the radio frequency transmission line.

10. The Wilkinson power divider according to claim 1, characterized in that, The Wilkinson power divider includes: A grounding layer is disposed on the side of the dielectric substrate opposite to the radio frequency transmission line.