Method for improving quality factor of ltcc wound inductor and wound inductor

By pre-setting a clearance area and setting a spaced grounding layer on the substrate, the problem of low quality factor of LTCC wire-wound inductors is solved, the performance of wire-wound inductors is improved, the loss of matching circuits is reduced, and the overall performance of wireless communication chips is improved.

CN121011451BActive Publication Date: 2026-02-17LANSUS TECH INC
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Patent Information

Application Number
CN202511538220.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-10-27
Publication Date
2026-02-17
Estimated Expiration
2045-10-27

AI Technical Summary

Technical Problem

The existing LTCC wire-wound inductors have a low quality factor, which leads to increased losses in the matching circuit and affects the performance of wireless communication chips.

Method used

A clearance area is pre-defined on the substrate, and the wire-wound inductor layer is placed within the clearance area. Electrical connection is achieved through metal vias. The ground layer and the wire-wound inductor layer are spaced apart to meet specific distance conditions, thereby increasing the clearance area and the distance between the ground layer and the wire-wound inductor layer, and improving the quality factor of the wire-wound inductor.

Benefits of technology

By increasing the clearance area and the spacing between the grounding layer and the wire-wound inductor layer, the insertion loss of the matching circuit is reduced, and the performance of the LTCC wire-wound inductor is improved. The overall method is simple, efficient, low-cost, and easy to process, thereby improving the performance of the wireless communication chip.

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Abstract

The present application relates to wireless communication technology field, provide a kind of method for improving LTCC winding inductance quality factor and winding inductance, method includes the following steps: presetting clearance area;Provide first winding inductance layer, first winding inductance layer is set in clearance area;The upper surface of the first winding inductance layer is provided with the first metal via hole post with via hole;The upper surface of the second winding inductance layer is provided with the second metal via hole post with via hole, the third winding inductance layer is set in the end of the second metal via hole post away from the second winding inductance layer;Wherein, the winding turns of the first winding inductance layer, the second winding inductance layer and the third winding inductance layer are all 2-4 turns;Provide ground layer, the ground layer is set in the side of the first winding inductance layer away from the second winding inductance layer;And the ground layer and the first winding inductance layer are mutually spaced apart.The present application can improve winding inductance quality factor Q value.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless communication technology, and particularly relates to a method for improving the quality factor of a LTCC winding inductor and the winding inductor. BACKGROUND

[0002] In recent years, under the wave of continuous iteration of mobile communication technology, the fifth generation mobile communication system (5G) has become the core of the attention of academia and industry. The driving force for the rapid development of 5G mainly comes from two aspects: first, the fourth generation mobile communication (4G) network has matured and is widely used in the world, and users and industries have high expectations for the new application scenarios (such as immersive experience, Internet of Things) that the next generation of communication technology can enable; the second is the deepening of social informationization, and the data traffic is growing explosively, and the network connection density and rate requirements are unprecedentedly high. The inherent ability of the 4G network has been shown to be inadequate in dealing with complex demands such as future smart society, industrial Internet, and massive Internet of Things device access. It is necessary to accelerate the research and development and deployment of 5G systems with better performance. Among the many core radio frequency chips, the power amplifier (PA) plays a crucial role as the last stage of the transmit chain. It directly determines the output power, system coverage, and overall energy efficiency of the signal, and its linearity, efficiency, and bandwidth performance are particularly critical and challenging to meet the requirements of 5G high-frequency and high-data-rate. Therefore, it is of great technical value and urgent industrial demand to tailor a high-performance and high-efficiency power amplifier for the 5G communication system.

[0003] The key indicators of the existing PA design mainly include output power, gain, efficiency, and linearity. The matching circuit at each stage has the greatest impact on these indicators during the design process. The architecture and matching value of the matching circuit are critical. Usually, the architecture and matching value of the matching circuit can be adjusted to the optimal state through simulation and debugging, but there may still be a small difference between the above state and the target performance. At this time, it is necessary to improve the Q value (Quality Factor) of each part of the matching circuit. Improving the Q value can effectively reduce the transmission loss in the circuit, thereby improving the performance of the PA. However, the usual method for improving the Q value is to use SMD devices with higher Q values or larger SMD devices. Although this method is simple and efficient, it significantly increases the cost and size of the chip. LTCC (Low Temperature Co-fired Ceramic) technology has a wide range of applications in radio frequency front-end due to its unique material and process advantages. LTCC technology has the advantages of high Q value, low dielectric loss, multi-layer three-dimensional wiring, and low cost. However, how to fully utilize the high Q value of LTCC technology has become a design difficulty.

[0004] In related technologies, a winding inductor is designed, such as Figure 1As shown, the wire-wound inductor includes a ground layer 4a (metal6), a first winding layer 1a (metal5), a second winding layer 2a (metal3), a third winding layer 3a (metal1), a first via 5a connecting the first winding layer 1a and the second winding layer 2a, and a second via 6a connecting the second winding layer 2a and the third winding layer 3a. The spacing between adjacent winding layers of the first winding layer 1a, the second winding layer 2a, and the third winding layer 3a is greater than the spacing between the first winding layer 1a and the ground layer 4a. Simulation results of the wire-wound inductor are shown below. Figures 2a-2b As shown, the inductance of the wire-wound inductor A is 14.8 nH (@2.35 GHz), and its Q value is 24.1 (@2.35 GHz). Based on design experience, this wire-wound inductor's Q value is too small, which will increase the losses in the matching circuit.

[0005] However, theoretical analysis is used to improve the Q value of the aforementioned wire-wound inductor. The Q value is defined as follows: (Stored energy) / (Energy consumed per cycle), as its definition shows, increasing the Q value can be achieved by increasing the stored energy or decreasing the consumed energy. The consumed energy includes ohmic losses, dielectric losses, leakage losses, and radiation losses. Figure 1 Analysis revealed that the first winding layer of the wire-wound inductor uses metal5 for winding, which is close to the ground layer 4a and has a large parasitic capacitance. This causes some energy to leak into the ground layer 4a, thus consuming the stored energy and resulting in a decrease in the Q value. Summary of the Invention

[0006] To address the shortcomings of the existing technology, this invention proposes a method to improve the quality factor of LTCC wire-wound inductors, thereby solving the problem of low quality factor in existing LTCC wire-wound inductors.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] In a first aspect, embodiments of the present invention provide a method for improving the quality factor of LTCC wire-wound inductance, the method comprising the following steps:

[0009] A substrate is provided, and a clearance area is pre-defined on the substrate;

[0010] A first wound inductor layer is provided, and the first wound inductor layer is disposed within the clearance area;

[0011] A first metal via post with a via is provided on the upper surface of the first wire-wound inductor layer, and a second wire-wound inductor layer is provided at the end of the first metal via post away from the first wire-wound inductor layer.

[0012] A second metal via column with a via hole is arranged on the upper surface of the second winding inductance layer, and a third winding inductance layer is arranged at the end of the second metal via column away from the second winding inductance layer; wherein the number of turns of the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 2-4 turns;

[0013] A ground layer is provided, which is arranged on the side of the first winding inductance layer away from the second winding inductance layer; and the ground layer and the first winding inductance layer are spaced from each other; wherein the distance between the first winding inductance layer and the second winding inductance layer is defined as L1, the distance between the second winding inductance layer and the third winding inductance layer is defined as L2, and the distance between the first winding inductance layer and the ground layer is defined as L3, which satisfies the following conditions: L1 < L3, L2 < L3.

[0014] Preferably, the distance between the ground of the clearance area and the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is greater than or equal to 100 um.

[0015] Preferably, the distance between the ground of the clearance area and the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 150 um.

[0016] Preferably, the distance between the ground of the clearance area and the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 300 um.

[0017] Preferably, L1 = L2.

[0018] Preferably, the first winding inductance layer, the second winding inductance and the third winding inductance layer are octagonal winding structures, respectively.

[0019] Preferably, the first winding inductance layer, the second winding inductance and the third winding inductance layer are circular winding structures, respectively.

[0020] Preferably, the first winding inductance layer is a first metal layer, the second winding inductance layer is a second metal layer, and the third winding inductance layer is a third metal layer.

[0021] In a second aspect, an embodiment of the present application provides a winding inductance prepared based on the above method for improving the quality factor of the LTCC winding inductance.

[0022] Compared with the related art, in the embodiment of the present application, by presetting a clearance area on the substrate, the first winding inductance layer is arranged in the clearance area; the first metal via column with a via hole is arranged on the upper surface of the first winding inductance layer, the second winding inductance layer is arranged on the side of the first metal via column away from the first winding inductance layer; the second metal via column with a via hole is arranged on the upper surface of the second winding inductance layer, the third winding inductance layer is arranged on the side of the second metal via column away from the second winding inductance layer; wherein the number of turns of the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 2-4 turns; the ground layer is arranged on the side of the first winding inductance layer away from the second winding inductance layer; and the ground layer and the first winding inductance layer are spaced from each other; wherein the distance between the first winding inductance layer and the second winding inductance layer is defined as L1, the distance between the second winding inductance layer and the third winding inductance layer is defined as L2, and the distance between the first winding inductance layer and the ground layer is defined as L3, which satisfies the following conditions: L1 < L3, L2 < L3; by increasing the clearance area and the distance between the ground layer and the first winding inductance layer, the quality factor (Q value) of the winding inductance can be improved, the matching circuit insertion loss can be reduced, the performance of the LTCC winding inductance can be improved, the overall method is simple and efficient, the manufacturing cost is low, and the processing is convenient; and the performance of the wireless communication chip can be further improved. BRIEF DESCRIPTION OF DRAWINGS

[0023] The present application will be described in detail below with reference to the accompanying drawings. The above or other aspects of the present application will become more apparent and more readily appreciated by referring to the following detailed description, taken in conjunction with the accompanying drawings. In the drawings:

[0024] Figure 1 A structure schematic diagram of the LTCC winding inductance provided by the prior art;

[0025] Figure 2a A simulation diagram of the frequency and inductance of the LTCC winding inductance provided by the prior art;

[0026] Figure 2b A simulation diagram of the frequency and Q value of the LTCC winding inductance provided by the prior art;

[0027] Figure 3 A flowchart of the method for improving the quality factor of the LTCC winding inductance provided by the embodiment of the present application;

[0028] Figure 4 A top view of the winding inductance of the method for improving the quality factor of the LTCC winding inductance provided by the embodiment of the present application;

[0029] Figure 5 A front view of the winding inductance of the method for improving the quality factor of the LTCC winding inductance provided by the embodiment of the present application;

[0030] Figure 6a Simulation diagrams of frequency and inductance for improving the quality factor of LTCC wire-wound inductors provided in embodiments of the present invention;

[0031] Figure 6b Simulation diagrams showing the frequency and Q value for improving the quality factor of LTCC wire-wound inductors provided in embodiments of the present invention;

[0032] Figure 7 A front view of a circular wire-wound inductor used in an embodiment of the present invention to illustrate a method for improving the quality factor of LTCC wire-wound inductors.

[0033] Figure 8a for Figure 7 Simulation diagram of frequency and inductance;

[0034] Figure 8b for Figure 7 Simulation graphs of frequency and Q value;

[0035] Figure 9a for Figure 7 Simulation plot of frequency and Q value for a metal with a thickness of 12µm;

[0036] Figure 9b for Figure 7 Simulation graphs of frequency and Q value for a metal with a thickness of 20 μm;

[0037] Figure 10a The simulation diagram of frequency and inductance for a 100µm ground-layout wire-wound inductor provided in an embodiment of the present invention;

[0038] Figure 10b Simulation diagram of frequency and Q value of 100µm ground-distance wire-wound inductor provided in an embodiment of the present invention;

[0039] Figure 11a The simulation diagram of frequency and inductance for a 150µm ground-layout winding inductor provided in an embodiment of the present invention;

[0040] Figure 11b Simulation diagram of frequency and Q value of 150µm ground-distance wire-wound inductor provided in an embodiment of the present invention;

[0041] Figure 12a The simulation diagram of frequency and inductance for a 300µm ground-layout wire-wound inductor provided in an embodiment of the present invention;

[0042] Figure 12b The simulation diagram shows the frequency and Q value of the 300µm ground-layout winding inductor provided in the embodiment of the present invention.

[0043] Wherein, 100, winding inductance, 1, first winding inductance layer, 2, second winding inductance layer, 3, third winding inductance layer, 4, ground layer, 5, first metal via column, 6, second metal via column, 7, keepout area. DETAILED DESCRIPTION

[0044] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used in the description herein is for describing particular embodiments only and is not intended to be limiting of the application; the use herein of terms such as "comprise", "have" and "include" or variations such as "comprises", "comprising", "includes" and "including", is intended to be construed in a non-exclusive manner. The terminology used in the description herein is for describing particular embodiments only and is not intended to be limiting of the application.

[0045] Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase "in an embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily all directed to the same embodiment, or to a single alternative embodiment.

[0046] The technical solutions in the embodiments of the present application will be described clearly and completely in connection with the drawings of the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0047] Embodiment one

[0048] Please refer to Figures 3-9b As shown in the drawings, the embodiments of the present application provide a method for improving the quality factor of LTCC winding inductance, which comprises the following steps:

[0049] S1, providing a substrate, and presetting a keepout area 7 on the substrate. Wherein, the keepout area 7 (Keepout Area) refers to the area which is drawn around a specific element (such as winding inductance, antenna, high-frequency oscillator, etc.) to avoid the adverse effects of the surrounding environment (especially the ground layer 4, other conductors or elements) on the specific element, and the area is prohibited to arrange specific structures (such as ground plane, conductor trace, component, etc.).

[0050] The size of the clearance area 7 has a significant impact on the winding inductance Q value. This is mainly because the winding inductance has a parasitic capacitance with its surrounding ground layer 4, and the smaller the ground distance from the winding inductance, the larger the parasitic capacitance, thereby causing more energy to be leaked through the parasitic capacitance to the ground layer 4. However, in the actual design process, the clearance area 7 cannot be set to be infinitely large, so it is necessary to find a suitable clearance area 7 size for actual engineering. Therefore, continuing to increase the clearance area 7 can increase the Q value of the winding inductance.

[0051] S2, provide a first winding inductance layer 1, and set the first winding inductance layer 1 in the clearance area 7.

[0052] S3, a first metal via column 5 with a via is arranged on the upper surface of the first winding inductance layer 1, and a second winding inductance layer 2 is arranged at the end of the first metal via column 5 away from the first winding inductance layer 1. The first metal via column 5 can realize the electrical connection between the first winding inductance layer 1 and the second winding inductance layer 2.

[0053] S4, a second metal via column 6 with a via is arranged on the upper surface of the second winding inductance layer 2, and a third winding inductance layer 3 is arranged at the end of the second metal via column 6 away from the second winding inductance layer 2. The second metal via column 6 can realize the electrical connection between the second winding inductance layer 2 and the third winding inductance layer 3. The number of turns of the first winding inductance layer 1, the second winding inductance layer 2 and the third winding inductance layer 3 is 2-4 turns. The number of turns of the winding inductance is moderate, which can improve the Q value of the winding inductance.

[0054] Optionally, the first metal via column 5 and the second metal via column 6 are made of copper, aluminum or silver material, which has high structural strength and good conductivity.

[0055] S5, provide a ground layer 4, which is arranged on the side of the first winding inductance layer 1 away from the second winding inductance layer 2; and the ground layer 4 and the first winding inductance layer 1 are spaced from each other; wherein the distance between the first winding inductance layer 1 and the second winding inductance layer 2 is defined as L1, the distance between the second winding inductance layer 2 and the third winding inductance layer 3 is defined as L2, and the distance between the first winding inductance layer 1 and the ground layer 4 is defined as L3. The following conditions are met: L1

[0056] Specifically, by the steps S1-S5, by increasing the distance between the clearance area 7 and the ground layer 4 and the first winding inductance layer 1, the Q value of the winding inductance can be improved, the matching circuit insertion loss can be reduced, the performance of the LTCC winding inductance can be improved, the overall method is simple and efficient, the manufacturing cost is low, and the processing is convenient; and the performance of the wireless communication chip can be further improved.

[0057] In this embodiment, the distance between the ground of the clearance area 7 and the first winding inductance layer 1, the second winding inductance layer 2 and the third winding inductance layer 3 is greater than or equal to 100um. Among them, the ground distance is represented as the minimum straight line distance between the ground plane (ground) around the first winding inductance layer 1 (usually the outermost edge of the inductance) and the edge of the winding inductance is 100um (micron). Specifically, "ground" here refers to the metal plane (such as the ground layer 4) on the PCB for grounding, and "distance" is the shortest vertical distance from the edge of the winding inductance to the edge of the ground plane.

[0058] As shown in Figures 10a-10b , the ground distance of the winding inductance is 100um, as shown in Figure 7 , the simulation is carried out, and the simulation results are shown in Figure 10a and Figure 10b . By comparing Figure 10b and Figure 6b , it is found that in the case of the same inductance value, Figure 6b , the Q value in Figure 10b is 12.8 (@2.35GHz) higher.

[0059] In this embodiment, the distance between the ground of the clearance area 7 and the first winding inductance layer 1, the second winding inductance layer 2 and the third winding inductance layer 3 is 150um.

[0060] As shown in Figures 11a-11b , the ground distance of the winding inductance is 150um, as shown in Figure 11b , the simulation is carried out. Compared with Figure 10b , Figure 11b , the Q value in Figure 6b is only 5.3 (@2.35GHz) higher. If the Q value requirement is not very strict, the ground distance of the winding inductance can be ensured to be 150um. But if the Q value requirement is higher, the clearance area 7 needs to be further increased.

[0061] In this embodiment, the distance between the ground of the clearance area 7 and the first winding inductance layer 1, the second winding inductance layer 2 and the third winding inductance layer 3 is 300um.

[0062] Specifically, as shown in Figures 12a-12bAs shown, the ground is arranged to be 300um away from the winding inductance, as Figure 12b As shown, the simulation is performed, as Figure 12b As shown from the figure, the Q value is only 1.6 higher than Figure 6b Therefore, in the design process of the winding inductance with high Q value requirement, it is necessary to ensure that the ground distance of the winding inductance is greater than 300um.

[0063] In this embodiment, the distance between the second winding inductance layer 2 and the first winding inductance layer 1 is equal to the distance between the second winding inductance layer 2 and the third winding inductance layer 3; L1=L2. Optionally, the distance between the first winding inductance layer 1 and the second winding inductance layer 2 is 1 / 2 of the distance between the first winding inductance layer 1 and the ground layer 4; the arrangement is convenient.

[0064] In this embodiment, the first winding inductance layer 1, the second winding inductance layer 2 and the third winding inductance layer 3 are octagonal winding structures.

[0065] In this embodiment, as shown, Figures 7-8b The first winding inductance layer 1, the second winding inductance layer 2 and the third winding inductance layer 3 are circular winding structures. In the design process of the LTCC winding inductance, firstly, the area of the clearance area near the winding inductance needs to be ensured, and the ground distance of the winding is at least 150um, secondly, in the winding process, the metal layer far away from the ground layer 4 should be selected as much as possible, and if the size allows, the circular winding can be used instead of the octagonal winding. There is also an optimal corresponding relationship between the winding width and the Q value, too narrow will cause the resistance to become large, too wide will cause the space utilization to become low and increase the eddy current loss. The number of turns of the winding should not be too large, and 2-4 can be selected.

[0066] Optionally, due to different stack structures, the simulation results of different thicknesses are as follows, Figure 9a As shown, the Q value of the metal thickness of 12um and the dielectric constant of 3.7 is 49.082. As shown, Figure 9b The Q value of the metal thickness of 20um and the dielectric constant of 2.2 is 59.438. Therefore, the thickness increases and the dielectric constant decreases to increase the Q value.

[0067] In the embodiment, the first winding inductance layer 1 is a first metal layer, the second winding inductance layer 2 is a second metal layer, and the third winding inductance layer 3 is a third metal layer. Optionally, the first metal layer is a metal1 winding inductance, the second metal layer is a metal2 winding inductance, and the third metal layer is a metal3 winding inductance; the metal1 winding inductance, the metal2 winding inductance, and the metal3 winding inductance are all made of the same metal material, and their inductance values are different due to their different spatial positions; wherein the inductance values of the metal1 winding inductance, the metal2 winding inductance, and the metal3 winding inductance decrease in turn.

[0068] Specifically, the winding inductance of the prior art is improved, and the LTCC winding inductance of the present application is designed, in which the winding layer is replaced by a metal1 winding inductance, a metal2 winding inductance, and a metal3 winding inductance, as shown in FIG. 2. Figure 4 The winding inductance is simulated, and the simulation result is shown in FIG. 3. Figure 6b The simulation result shows that the inductance value of the LTCC winding inductance of the present application is similar to that of the winding inductance of the prior art, but the Q value is increased by 34 (@2.35 GHz), and the Q value is obviously improved.

[0069] Embodiment Two

[0070] The embodiment of the present application provides a winding inductance 100, which is made based on the above-mentioned method for improving the quality factor of the LTCC winding inductance. It should be noted that the above-described various embodiments with reference to the accompanying drawings are only used to illustrate the present application and not to limit the scope of the present application, and those skilled in the art should understand that the modifications or equivalent replacements of the present application without departing from the spirit and scope of the present application should be covered within the scope of the present application. In addition, unless otherwise indicated in the context, the word in singular form includes the plural form, and vice versa. In addition, unless specifically stated, all or part of any embodiment can be used in combination with all or part of any other embodiment.

Claims

1. A method for improving the quality factor of LTCC wound inductors, characterized in that, The method comprises the following steps: providing a substrate and presetting a clearance area on the substrate; providing a first winding inductance layer, and arranging the first winding inductance layer in the clearance area; arranging a first metal via column with a via on the upper surface of the first winding inductance layer, and arranging a second winding inductance layer at the end of the first metal via column away from the first winding inductance layer; arranging a second metal via column with a via on the upper surface of the second winding inductance layer, and arranging a third winding inductance layer at the end of the second metal via column away from the second winding inductance layer; wherein the number of turns of the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 2-4 turns; providing a ground layer, and arranging the ground layer on the side of the first winding inductance layer away from the second winding inductance layer; and the ground layer and the first winding inductance layer are spaced apart; wherein the distance between the first winding inductance layer and the second winding inductance layer is defined as L1, the distance between the second winding inductance layer and the third winding inductance layer is defined as L2, and the distance between the first winding inductance layer and the ground layer is defined as L3, which satisfies the following conditions: L1 < L3, L2 < L3; L1 = L2; The distance between the ground of the clearance area and the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is greater than or equal to 100 um.

2. The method of improving the quality factor of LTCC wound inductors of claim 1, wherein, The distance between the ground of the clearance area and the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 150 um.

3. The method of improving the quality factor of a LTCC wound inductor of claim 1, wherein, The distance between the ground of the clearance area and the first winding inductance layer, the second winding inductance layer and the third winding inductance layer is 300 um.

4. The method of improving the quality factor of a LTCC wound inductor of claim 1, wherein, The first winding inductance layer, the second winding inductance layer and the third winding inductance layer are octagonal winding structures respectively.

5. The method of improving the quality factor of LTCC wound inductors of claim 1, wherein, The first winding inductance layer, the second winding inductance layer and the third winding inductance layer are circular winding structures respectively.

6. The method of improving the quality factor of a LTCC wound inductor of claim 1, wherein, The first winding inductance layer is a first metal layer, the second winding inductance layer is a second metal layer, and the third winding inductance layer is a third metal layer.

7. A wire wound inductor, characterized by, The winding inductance is prepared based on the method for improving the quality factor of the LTCC winding inductance according to any one of claims 1-6.

Citation Information

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