Adjustable phase series 3*3 Norlan matrix unit, Norlan matrix and implementation method

Abstract

The invention relates to the technical field of communication, and provides a phase-series-adjustable 3x3 Nolan matrix unit, a 9x9 Nolan matrix, a multi-beam antenna array and an implementation method. Phase analysis is carried out on the 3 * 3 Noran matrix unit, the phase series delta alpha is defined to be equal to phi1, phi2 and pi / 2, the value of phi1 and the value of phi2 are adjusted, and adjustment of the phase difference can be achieved. And in the 9 * 9 Norlan matrix, the values of beta1-beta6 of the phase shifters are determined by deducing the phase relationship among the 3 * 3 Norlan matrix units, so that the adjustable phase series of the 9 * 9 Norlan matrix is realized.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and more particularly to a Nolan matrix in a beamforming network in a multi-beam antenna array. More particularly, the present invention relates to a 3x3 Nolan matrix unit with adjustable phase order, a 9x9 Nolan matrix, a multi-beam antenna array, and implementation methods thereof. Background Art

[0002] In modern communications and detection technologies, the demand for high data rates and excellent communication quality is increasing. This has led to the widespread use of multi-beam antenna arrays with large bandwidth and flexible beam steering. Beamforming networks (BFNs), as the core components of multi-beam antenna arrays, have characteristics that directly determine the array's beam scanning angle, gain, and radiation efficiency. The Butler Matrix (BM) and Nolen Matrix (NM) are key components in implementing beamforming. The traditional Butler matrix, with its symmetrical topology, is relatively simple to design and can achieve broadband performance. However, its limited number of ports (n is an integer), fixed phase progression, and limited beam steering range make it difficult to meet the diverse beam pointing requirements in complex communication scenarios. Furthermore, its topology lacks scalability, making it difficult to expand the number of ports to meet actual application requirements. Furthermore, its design is often based on multi-layer substrates, resulting in a complex structure and large size, increasing system cost and complexity. In contrast, the Nolan matrix offers a more flexible topology. By cascading couplers and phase shifters at the edges of the topology, the number of ports can be easily expanded, increasing the number of antenna array beams and the scanning range. However, the cascaded structure of the NM results in different electrical lengths for different internal paths between the input and output ports, thus narrowing the bandwidth. Furthermore, higher-order NM topologies require power distribution devices with a larger coupling range, further increasing the difficulty of achieving broadband characteristics.

[0003] Currently, achieving broadband performance, adjustable phase difference, and flexible port count within a single BM or NM topology is extremely challenging. Existing designs have numerous limitations in terms of phase level flexibility, port scalability, number of circuit layers, size, and bandwidth, failing to meet the demands of evolving communication and detection technologies. Summary of the Invention

[0004] In response to the requirements of existing multi-beam antenna arrays for beamforming networks, the embodiments of the present application provide a 3x3 Nolan matrix unit with adjustable phase level, and a 9x9 Nolan matrix constructed by the 3x3 Nolan matrix unit with adjustable phase level. At the same time, a multi-beam antenna array is provided, and an implementation method of the above-mentioned device is provided.

[0005] A 3x3 Nolan matrix unit with adjustable phase series includes a first input port, a second input port, a third input port, a first output port, a second output port, a third output port, a power distribution module, and a phase compensation module. The power distribution module includes a first orthogonal coupler, a second orthogonal coupler, a third orthogonal coupler, and a fourth phase shifter. The phase compensation module includes a first phase shifter, a second phase shifter, and a third phase shifter. The first input port is connected to input port 1 of the second orthogonal coupler, the second input port is connected to input port 1 of the first orthogonal coupler, and the third input port is connected to input port 2 of the first orthogonal coupler; Output port 1 of the first orthogonal coupler is connected to input port 2 of the second orthogonal coupler, and output port 2 of the first orthogonal coupler is connected to input port 2 of the third orthogonal coupler via a fourth phase shifter; The output port 1 of the second orthogonal coupler is connected to the first output port through the third phase shifter, and the output port 2 of the second orthogonal coupler is connected to the input port 1 of the third orthogonal coupler; The first output port of the third orthogonal coupler is connected to the second output port via the second phase shifter, and the second output port of the third orthogonal coupler is connected to the third output port via the first phase shifter.

[0006] Preferably, the coupling degree between the first orthogonal coupler and the third orthogonal coupler is 3.01 dB, and the coupling degree of the second orthogonal coupler is 4.77 dB; The phase adjustment value of the fourth phase shifter is (θ4-π / 2), θ4 is the phase shift value of the first orthogonal coupler from input port 2 to output port 2, the phase adjustment value of the first phase shifter is φ1, the phase adjustment value of the second phase shifter is φ2, and the phase adjustment value of the third phase shifter is (θ3+2φ2-φ1), θ3 is the phase shift value from input port 1 to output port 1 of the second orthogonal coupler.

[0007] The embodiment of the present application further provides a Nolan matrix with an adjustable phase series of 9x9, including six Nolan matrix units with an adjustable phase series of 3x3, and six phase shifters, respectively defined as Nolan matrix unit NM1, Nolan matrix unit NM2, Nolan matrix unit NM3, Nolan matrix unit NM4, Nolan matrix unit NM5, and Nolan matrix unit NM6; phase shifters β1, β2, β3, β4, β5, and β6; The input ports of the Nolan matrix unit NM1, the Nolan matrix unit NM2, and the Nolan matrix unit NM3 respectively constitute nine input ports of the 9x9 Nolan matrix; The first output port of the Nolan matrix unit NM1 is connected to the first input port of the Nolan matrix unit NM4, the second output port is connected to the first input port of the Nolan matrix unit NM5 through the phase shifter β1, and the third output port is connected to the first input port of the Nolan matrix unit NM6 through the phase shifter β2; The first output port of the Nolan matrix unit NM2 is connected to the second input port of the Nolan matrix unit NM4 through a phase shifter β3, the second output port is connected to the second input port of the Nolan matrix unit NM5, and the third output port is connected to the second input port of the Nolan matrix unit NM6 through a phase shifter β4; The first output port of the Nolan matrix unit NM3 is connected to the third input port of the Nolan matrix unit NM4 through a phase shifter β5, the second output port is connected to the third input port of the Nolan matrix unit NM5 through a phase shifter β6, and the third output port is connected to the third input port of the Nolan matrix unit NM6; The three output ports of the Nolan matrix unit NM4 respectively form the first output port, the fourth output port and the seventh output port of the 9x9 Nolan matrix; the three output ports of the Nolan matrix unit NM5 respectively form the second output port, the fifth output port and the eighth output port of the 9x9 Nolan matrix; the three output ports of the Nolan matrix unit NM6 respectively form the third output port, the sixth output port and the ninth output port of the 9x9 Nolan matrix.

[0008] Preferably, the system further includes two bridge networks, defined as bridge network CN1 and bridge network CN2. The first to ninth output ports of the 9x9 Nolan matrix are independently arranged in sequence, and the phase shifters β1, β2, β3, β4, β5, and β6 are connected to the input ports of the Nolan matrix units NM4, NM5, and NM6 via the bridge network CN1. The output ports of the Nolan matrix units NM4, NM5, and NM6 are connected to the first to ninth output ports of the 9x9 Nolan matrix via the bridge network CN2.

[0009] An embodiment of the present application also provides a broadband multi-beam antenna array, including a 9x9 Nolan matrix with adjustable phase levels, and an antenna array consisting of nine radiating elements, each radiating element being connected to one of the output ports of the 9x9 Nolan matrix.

[0010] The embodiment of the present application provides a method for implementing a Nolan matrix with adjustable phase levels of 9x9, including the following steps: S10, select 5.5GHz as the center frequency, and use Rogers 4003C material for circuit design, which has a relative dielectric constant of 3.38 and a thickness of 0.813mm; S20. Based on the topology of the aforementioned 3x3 Nolan matrix unit with adjustable phase order: improve the enhanced coupling structure to a grounded coplanar waveguide configuration to design a broadband coupler, while using a via-hole transmission structure to ensure that the outputs are on the same side, so as to design a first, second, and third orthogonal couplers with different coupling coefficients; when constructing the power distribution module, modify the 50-ohm transmission line to two parallel 100-ohm GCPW lines to implement the fourth phase shifter function and reduce the size; design a phase compensation module, using a delay line and a 90° short-circuit branch, and cascade it with the power distribution section, while optimizing the layout of the 90° short-circuit branch; S30. Implement a 9x9 Nolan matrix with adjustable phase levels, optimize the bridge network topology, and move some signal paths to the bottom layer to eliminate path crossings. Replace the three path intersections with transition via pairs and optimize the signal paths to straight lines. Connect the six designed 3 × 3 Nolan matrices, six phase shifters, and two bridge networks according to the topology of the 9x9 Nolan matrix design.

[0011] The 3x3 Nolan matrix unit with adjustable phase levels and the 9x9 Nolan matrix constructed based on the 3x3 Nolan matrix unit provided in the embodiments of the present application have the following technical effects compared to the prior art: (1) Flexible phase progression: Unlike most existing beamforming networks, the 9×9 Nolan matrix of the present invention can realize an adjustable phase progression in the topology structure, and can flexibly adjust the beam direction according to actual needs, thereby improving the accuracy and adaptability of communication and detection.

[0012] (2) Strong scalability: The 9×9 Nolan matrix built on the Nolan matrix can be expanded to multiple configurations of P×M input ports and Q×N output ports. Compared with the traditional Butler matrix with limited port numbers, it provides more options and can meet the needs of different scales and application scenarios.

[0013] (3) Superior circuit performance: The single-layer design with port alignment effectively reduces circuit complexity and cost. Compared with other similar designs, the maximum bandwidth is achieved while maintaining the minimum circuit size. For example, the 10 dB input return loss bandwidth measured by the 9×9 Nolan matrix can reach 62.30% - 90.91%, and the overall circuit size is only 2.58 × 2.24λg2, significantly improving the system integration and performance.

[0014] (4) Good broadband performance: Experimental verification shows that the broadband multi-beam antenna array constructed based on the 9×9 Nolan matrix has stable characteristics of nine individual beams in the frequency range of 4.2-6.4GHz (41.51%), making it suitable for a variety of broadband communication and detection application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or technical descriptions. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0016] Figure 1a Schematic diagram of the topological structure of a 9×9 Nolan matrix with adjustable phase levels; Figure 1b This is a schematic diagram of the topology of a 3×3 Nolan matrix unit with adjustable phase levels. It also illustrates the connection methods and port markings of each component, which helps to understand the Nolan matrix topology and signal transmission path. Figure 2a The circuit geometry and key parameters of the 4.77 dB and 3.01 dB quadrature couplers; Figure 2b This is a top view photo of the power distribution section of a 3×3 Nolan matrix; Figure 2c Simulated and measured insertion loss; presents the design details of the orthogonal coupler, the actual layout of the power distribution section, and the insertion loss performance of this section, helping to evaluate the effectiveness of power distribution and broadband performance; Figure 3a For NM1, Figure 3b This is the top view of NM2 and detailed configuration of phase shifters; Figure 3c For NM1 and Figure 3d The simulation and measurement results for the phase progression of NM2 are shown. The specific structures and phase shifter designs of different 3 × 3 Nolan matrices, as well as their phase progression performance, are demonstrated, validating the 3 × 3 Nolan matrix's ability to achieve adjustable phase progression. Figure 4a It is the evolutionary topology of broadband single-layer bridge network; Figure 4b A top view photo of the detailed configuration; Figure 4c Insertion loss simulation and measurement results, Figure 4d The simulation and measurement results of phase difference are presented; the optimization design process and actual performance of the cross-bridge network are presented, showing how to achieve single-layer design and good signal transmission performance through structural improvement; Figure 5a The top and bottom views of a broadband single-layer 9 × 9 Nolan matrix are shown; Figure 5b The simulation and measurement of reflection coefficients for each port demonstrate the overall structure of the 9 × 9 Nolan matrix and the reflection coefficient performance of each port, reflecting the matching and broadband characteristics of the matrix. Figure 6a Comparison of insertion loss simulation and measurement for port 5 of a 9×9 Nolan matrix; Figure 6bThis paper compares the simulated and measured phase difference of port 5 of a 9×9 Nolan matrix. It also analyzes the insertion loss and phase difference performance of the 9×9 Nolan matrix at specific ports, providing detailed data for evaluating the overall performance of the matrix. Figure 7a is the configuration of the magnetoelectric dipole antenna unit; Figure 7b A photo of the measurement environment and the broadband multi-beam antenna array, showing the radiating elements of the antenna array and the overall measurement environment. Figure 8a Measure reflection coefficient and achieved gain for broadband multi-beam antenna arrays; Figures 8b to 8d Ideal, simulated, and measured radiation patterns at three representative frequencies are shown. The antenna array's reflection coefficient, gain, and radiation pattern performance are presented, verifying the broadband performance and beamforming characteristics of the 9×9 Nolan matrix-based antenna array. Figure 9 : This paper presents an extended topology consisting of an ordered arrangement of P (M × N) and N (P × Q) sub-BFNs. This paper demonstrates the general structure of the scalable topology and provides a basis for understanding the implementation of different port number configurations. Figure 10 a is a schematic diagram of a 12 × 12 Nolan matrix; Figure 10b is a 3×3 Nolan matrix; Figure 10c is a 4 × 4 Nolan matrix; Figure 10d The simulated radiation pattern generated by the 12×12 Nolan matrix and the Huygens source array is presented in detail. The structure and components of the 12×12 Nolan matrix and its simulated radiation pattern are presented, verifying the effectiveness and flexibility of the scalable topology. DETAILED DESCRIPTION

[0017] Hereinafter, only certain exemplary embodiments are briefly described. As will be appreciated by those skilled in the art, the described embodiments may be modified in various ways without departing from the spirit or scope of the present invention. Therefore, the drawings and description are to be considered as illustrative in nature and not restrictive.

[0018] It should be noted that the terms "first," "second," "symmetrical," "array," etc. are used only to distinguish descriptions from positional descriptions and should not be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, limitations on features such as "first" and "symmetrical" may explicitly or implicitly include one or more of these features; similarly, when the number of certain features is not limited in the form of words such as "two" or "three," it should be noted that these features also explicitly or implicitly include one or more of the number of features. In the present invention, unless otherwise expressly specified or limited, terms such as "installation," "connection," and "fixation" should be understood broadly; for example, they may refer to fixed connection, detachable connection, or integral molding; they may refer to mechanical connection, direct connection, welding, or indirect connection through an intermediate medium; they may refer to internal communication between two components or interaction between two components. Those skilled in the art will be able to understand the specific meanings of the above terms in the present invention based on the specification and drawings in conjunction with specific circumstances.

[0019] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0020] Example 1: Design and implementation of a 9 × 9 Nolan matrix: like Figure 1a As shown, the embodiment of the present application provides a Nolan matrix with an adjustable phase series of 9x9, including six Nolan matrix units with an adjustable phase series of 3x3, six phase shifters and two bridge networks; respectively defined as Nolan matrix unit NM1, Nolan matrix unit NM2, Nolan matrix unit NM3, Nolan matrix unit NM4, Nolan matrix unit NM5, Nolan matrix unit NM6; phase shifters β1, phase shifter β2, phase shifter β3, phase shifter β4, phase shifter β5, phase shifter β6; bridge network CN1, bridge network CN2; Nolan matrix unit NM1, Nolan matrix unit NM2, and Nolan matrix unit NM3 are arranged in sequence, and their input ports respectively constitute the nine input ports of the 9x9 Nolan matrix, namely, input ports 1 to 9 marked at the top in FIG1 ; The first output port of the Nolan matrix unit NM1 (i.e., output port a in NM1) is connected to the first input port of the Nolan matrix unit NM4 (i.e., input port 1 in NM4), the second output port (i.e., output port b in NM1) is connected to the first input port of the Nolan matrix unit NM5 (i.e., input port 1 in NM5) via a phase shifter β1, and the third output port (i.e., output port c in NM1) is connected to the first input port of the Nolan matrix unit NM6 (i.e., input port 1 in NM6) via a phase shifter β2; The first output port of the Nolan matrix unit NM2 (i.e., output port a in NM2) is connected to the second input port of the Nolan matrix unit NM4 (i.e., input port 2 in NM4) via a phase shifter β3, the second output port (i.e., output port b in NM2) is connected to the second input port of the Nolan matrix unit NM5 (i.e., input port 2 in NM5), and the third output port (i.e., output port c in NM2) is connected to the second input port of the Nolan matrix unit NM6 (i.e., input port 2 in NM6) via a phase shifter β4; The first output port of the Nolan matrix unit NM3 (i.e., output port a in NM3) is connected to the third input port of the Nolan matrix unit NM4 (i.e., input port 3 in NM4) via a phase shifter β5, the second output port (i.e., output port b in NM3) is connected to the third input port of the Nolan matrix unit NM5 (i.e., input port 3 in NM5) via a phase shifter β6, and the third output port (i.e., output port c in NM3) is connected to the third input port of the Nolan matrix unit NM6 (i.e., input port 3 in NM6) via a phase shifter β6; The three output ports of the Nolan matrix unit NM4 respectively form the first output port a, the fourth output port d and the seventh output port g of the 9x9 Nolan matrix; the three output ports of the Nolan matrix unit NM5 respectively form the second output port b, the fifth output port e and the eighth output port h of the 9x9 Nolan matrix; the three output ports of the Nolan matrix unit NM6 respectively form the third output port c, the sixth output port f and the ninth output port i of the 9x9 Nolan matrix.

[0021] The adjustable phase series 3x3 Nolan matrix unit is the basic building block of the 9x9 Nolan matrix, providing power distribution and adjustable phase difference. The adjustable phase series 3x3 Nolan matrix unit provided in the embodiment of the present application is as follows: Figure 1b As shown, it includes a first input port 1, a second input port 2, a third input port 3, a first output port a, a second output port b, a third output port c, a power distribution module ① and a phase compensation module ②, the power distribution module includes a first orthogonal coupler, a second orthogonal coupler, a third orthogonal coupler and a fourth phase shifter, and the phase compensation module includes a first phase shifter, a second phase shifter and a third phase shifter; wherein the coupling degree of the first orthogonal coupler and the third orthogonal coupler is 3.01 dB, and the coupling degree of the second orthogonal coupler is 4.77 dB; The first input port 1 is connected to the input port 1 of the second orthogonal coupler (i.e., port 1 of the 4.77 dB orthogonal coupler), the second input port 2 is connected to the input port 1 of the first orthogonal coupler (i.e., port 1 of the first 3.01 dB orthogonal coupler), and the third input port is connected to the input port 2 of the first orthogonal coupler (i.e., port 4 of the first 3.01 dB orthogonal coupler); Output port 1 of the first orthogonal coupler (i.e., port 2 of the first 3.01dB orthogonal coupler) is connected to input port 2 of the second orthogonal coupler (i.e., port 4 of the 4.77dB orthogonal coupler), and output port 2 of the first orthogonal coupler (i.e., port 3 of the first 3.01dB orthogonal coupler) is connected to input port 2 of the third orthogonal coupler (i.e., port 4 of the second 3.01dB orthogonal coupler) via a fourth phase shifter. The output port 1 of the second orthogonal coupler (i.e., port 2 of the 4.77 dB orthogonal coupler) is connected to the first output port a through the third phase shifter, and the output port 2 of the second orthogonal coupler (i.e., port 3 of the 4.77 dB orthogonal coupler) is connected to the input port 1 of the third orthogonal coupler (i.e., port 1 of the second 3.01 dB orthogonal coupler); Output port 1 of the third orthogonal coupler (i.e., port 2 of the second 3.01dB orthogonal coupler) is connected to the second output port b through a second phase shifter, and output port 2 of the third orthogonal coupler (i.e., port 3 of the second 3.01dB orthogonal coupler) is connected to the third output port c through a first phase shifter.

[0022] The phase adjustment value of the fourth phase shifter is (θ4-π / 2), where θ4 is the phase shift value from input port 2 to output port 2 of the first orthogonal coupler (i.e., port 4 to port 3 of the first 3.01 dB orthogonal coupler). The phase adjustment value of the first phase shifter is φ1, the phase adjustment value of the second phase shifter is φ2, and the phase adjustment value of the third phase shifter is (θ3+2φ2-φ1). θ3 is the phase shift value from input port 1 to output port 1 of the second orthogonal coupler (i.e., port 1 to port 2 of the 4.77 dB orthogonal coupler).

[0023] Through rigorous phase analysis of the 3×3 Nolan matrix unit, the phase series Δα is defined as φ1−φ2+π / 2. Adjusting the values ​​of φ1 and φ2 allows for adjustment of the phase difference. In a 9×9 Nolan matrix, the phase relationships between each 3×3 Nolan matrix unit are derived to determine the values ​​of the phase shifters β1-β6, thereby achieving an adjustable phase series for the 9×9 Nolan matrix. For example, by setting a specific ΔP1 value (e.g., 40°), the other phase differences and phase shifter values ​​can be determined according to relevant formulas, completing the design of the 9×9 Nolan matrix, ensuring that its nine phase series exhibit specific coherence.

[0024] According to the required coupling coefficient and phase order, the orthogonal coupler and phase shifter in the 3×3 Nolan matrix unit are designed. The insertion phase is calculated and listed in Table I. ij It is used to represent the phase shift value of output port i when input port j is stimulated, where the value of i ranges from a to c and the value of j ranges from 1 to 3. In order to show the phase coherence between the inserted phases, a phase series parameter Δα=φ1−φ2+π / 2 is defined to represent the phase series.

[0025] Table I Insertion phase of 3×3 Nolan matrix unit

[0026] Table II Output phase relationship of 3×3 Nolan matrix unit

[0027] The relationship between the matrix insertion phases is shown in Table II. Adjusting the values ​​of φ1 and φ2 changes both the insertion phase and the phase progression. For ease of illustration, θ3, θ4, and φ2 are set to 0°. When φ1 is equal to −50° and 30°, θa1 and Δα are calculated to be −50° and 30°, and 40° and 120°, respectively. This demonstrates that the 3×3 Nolan matrix unit can flexibly change Δα by adjusting φ1 and φ2, thereby achieving an adjustable phase progression.

[0028] 9×9 Nolan matrix (such as Figure 1a ) consists of six 3×3 Nolan matrices (NM1- NM6), six phase shifters (β1- β6) and two bridge networks (CN1 - CN2). Since there are six 3×3 Nolan matrix units, the phase of the 3×3 Nolan matrix unit can be expressed as Δα x and θ ai,x To describe, where i ranges from 1 to 3 and x ranges from 1 to 6. x express Figure 1a The phase order when port 1 of NMx is excited. ai,x is the insertion phase corresponding to the signal path from port i to port a in NMx. The insertion phase of the 9×9 Nolan matrix can then be calculated. For verification, Table III shows the insertion phase when ports 1 and 2 are stimulated.

[0029] Table III Insertion phase of port 1 and port 2 in 9×9 Nolan matrix

[0030] The phase order of the 9×9 Nolan matrix can be calculated as shown in formula (1), where ΔP x (x = 1 to 9) is defined as the expected phase difference when port x is stimulated.

[0031]

[0032] Applying formula (1) to Table III, we can get θ a1 arrive θ i1 Inserting the phase of , we can get the following phase relationship:

[0033] Then substitute formulas (1), (2) and (3a) into θ 2 to θ i2 Inserting the phase gives

[0034] This means that the phase difference Δ P 1 and Δ P 2 is coherent, and its value is 2π / 3. By inserting the phase into ports 3 to 9 in the same way, we can get the following equations (3b) and (4b) from β 3 to β 6 Phase Shifters with Δ P 3 to Δ P 9 phase difference relationship to reflect the relationship between the phase differences. P 2 to P A phase difference of 9 is coherent.

[0035]

[0036] To simplify the design, a common 3 × 3 Nolan matrix (NM) structure is used as the building block from NM1 to NM3 and from NM4 to NM6. This premise can be summarized as follows:

[0037] Based on the above analysis, a 9 × 9 Nolan matrix (NM) with adjustable phase series can be designed. The nine phase series of the 9 × 9 Nolan matrix conform to the correlation of the formula. By selecting Δ P For a specific value of 1, the corresponding phase requirement can be obtained according to formulas (2), (5) and (6). P 1 is 40°, so Δ P 2 to Δ P The phase differences of 9 are 160°, -80°, 80°, -160°, -40°, 0°, 120° and -120° respectively. Then, according to formula (2), Δ α 4 to Δ α The phase difference of 6 is 120°. According to formula (5), Δ α 1 to Δ α The phase difference of 3 is set to 40°, and then the β 2 to β The phase shifter values ​​for 6 are 0°, 0°, -40°, 40°, 80°, and 40°.

[0038] Broadband single-layer 9×9 Nolan matrix implementation: 3×3 Nolan matrix unit design (such as Figure 2a 、 Figure 2b): With 5.5GHz as the center frequency, which is widely used in WLAN, WiMAX, Wi-Fi and other fields, a 3×3 Nolan matrix unit is designed using Rogers 4003C material with a relative dielectric constant of 3.38 and a thickness of 0.813 mm and a grounded coplanar waveguide (GCPW) structure. First, orthogonal couplers with different coupling coefficients are designed, and the enhanced coupling structure is modified to a grounded coplanar waveguide GCPW configuration. A port switching structure is added to the center of the coupling line, and a via transmission structure is used to ensure that the output ends are on the same side, so as to design orthogonal couplers with different coupling coefficients. Based on this, a power distribution module of the 3×3 Nolan matrix unit is constructed. The 50-ohm transmission line is modified into two parallel 100-ohm GCPW lines, and the parallel GCPW lines are used to achieve internal phase shifting and reduce size. By designing different phase compensation parts, phase levels of 40° and 120° are achieved, and the following are designed: Figure 2a 、 Figure 2b The 3×3 Nolan Matrix (NM) unit structure with phase shifters is shown. Figure 2c The test simulation results show that under the standard of 1.2 dB insertion loss imbalance, the bandwidth of different ports of the matrix can reach 69.03%, 77.55% and 57.39%. In order to achieve specific phase levels (such as 40° and 120°), different phase compensation parts are designed using delay lines and 90° short-circuit stubs, and cascaded with the power distribution part. The fabricated NM1 (40°) and NM2 (120°) are shown in Figure 2. Figure 3a 、 Figure 3b As shown in the figure, its structure is compact, with dimensions of 0.62 × 0.76λg2 and 0.62 × 0.76λg2 (where λg represents the wavelength corresponding to the center frequency), and it meets the ±5° phase difference imbalance standard, with good matching between different ports. The structural parameters of the coupler are optimized using electromagnetic simulation software to ensure good coupling performance over a wide bandwidth. For the phase shifter, precise phase adjustment is achieved by adjusting the length and shape of the parallel GCPW lines. Figure 3c 、 Figure 3d The test simulation results show that under the ±5° phase difference imbalance standard, the bandwidth performance of different ports is also very excellent, which fully proves the effectiveness and reliability of the design and production scheme.

[0039] 9×9 Nolan matrix design: Based on the GCPW structure, the cross-bridge network topology in the 9×9 Nolan matrix is ​​improved (its circuit structure is as follows Figure 4a 、 Figure 4b). Some signal paths were moved to the bottom layer of the circuit to reduce path crossings, and top-to-bottom via pairs were used to replace the three-way crossover in the center of the original bridge network. The optimized layout made all signal paths straight, making signal transmission more efficient and stable. Phase alignment was also achieved by using curved parallel GCPW lines of different lengths and shapes. The final 9×9 Nolan matrix is ​​shown below. Figure 5a As shown, the overall size is 2.58 × 2.24λg2. During the connection process, the length matching of the signal transmission path is strictly controlled, while ensuring effective signal isolation to avoid signal interference. In addition, the available space of the circuit is fully exploited to achieve a compact size design of the matrix to meet the space constraints required in practical applications. Figure 5b According to the test simulation results, each port achieved a 10 dB input return loss bandwidth of 62.30%-90.91%, and the overall operating bandwidth was 50% (4.2-7GHz). Figure 6a 、 Figure 6b The paper presents a comparison of simulation and measurement results at port 5 of a 9×9 Nolan matrix. Under the ±1.5 dB insertion loss imbalance standard, the average insertion loss is -12.99 dB (measured) and -12.14 dB (simulated). Under the ±1.5 dB insertion loss imbalance and -160°±10° phase difference standards, operating bandwidths of 48.54% (3.9-6.4 GHz) and 43.81% (4.1-6.4 GHz), respectively, are achieved. Taking all indicators into consideration, the minimum bandwidth of the 9×9 Nolan matrix is ​​41.51% (4.2-6.4 GHz).

[0040] During the fabrication and deployment phases, the 9×9 Nolan matrix was fabricated on Rogers 4003C material using a printed circuit board (PCB) process. During this process, precise control of circuit dimensions and parameters was crucial, particularly the key parameters of the couplers, as these directly impact the matrix's performance. Given the long signal transmission path and the presence of gaps that lead to additional losses, optimization of the signal transmission path was necessary to reduce unnecessary energy loss. Furthermore, debugging and calibration of the phase shifters were crucial. A network analyzer was used to thoroughly test the fabricated 9×9 Nolan matrix, measuring performance parameters such as input return loss, insertion loss, phase difference, and isolation. The measured results were carefully compared with simulation results. Any performance deviations were promptly adjusted and optimized to ensure the matrix accurately achieved the designed phase value, thereby ensuring that the overall performance of the 9×9 Nolan matrix met the design requirements.

[0041] Wideband multi-beam antenna array applications: The magnetoelectric dipole antenna is selected as the radiation unit, and a broadband multi-beam antenna array is constructed according to the design requirements. It is ensured to have good radiation performance in a wide frequency band to verify the effectiveness of the designed Nolan matrix. The antenna unit structure is as follows Figure 7a As shown in the figure, the unit spacing in the antenna array is 31 mm, and the antenna array is connected to the 9×9 Nolan matrix output port through nine uniform cables to ensure the stability of the connection and the accuracy of signal transmission. Figure 7b As shown in the figure, the reflection coefficient is measured in a microwave anechoic chamber using the Keysight ENA Network Analyzer E5080A, and the antenna radiation characteristics are tested using the Satimo 3D AntennaMeasurement System StarLab BTS. The beam characteristics and broadband performance of the antenna array at different frequencies are analyzed. Figures 8a to 8d Measurement results show that the antenna array exhibits broadband characteristics within the 4.2-6.4 GHz bandwidth. Although the return loss of some ports at specific frequencies deviates slightly due to transmission path issues, the overall matching performance is still well maintained. The beam performance of the antenna array at different frequencies was verified by measuring ideal, simulated, and actual normalized gain. The measured beam coverage of the nine beams at 4.2 GHz, 5.5 GHz, and 6.4 GHz was −72° to 69°, −51° to 51°, and −42° to 45°, respectively, verifying the effectiveness of the 9×9 Nolan matrix in broadband multi-beam antenna arrays.

[0042] Scalable topology design: To meet diverse port configuration requirements, the Nolan matrix topology can be expanded as follows: Figure 9 . This structure uses different Nolan matrices as basic building blocks. By orderly arranging P M×N and N P×Q sub-beamforming networks BFNs, P×M and N×Q multiple port configurations can be achieved. For example, when P=Q=2, M=N=4 / 8 / 16, traditional 8×8, 16×16 and 32×32 Butler matrices can be obtained; this configuration method reflects the scalability and flexibility of the topology, and can adjust the matrix size according to different application scenarios. Taking the 12×12 Nolan matrix as an example (topology structure as Figure 10a 、 Figure 10b 、 Figure 10c (As shown in the figure), when M=N=3 and P=Q=4, it consists of four 3×3 Nolan matrix units and three 4×4 Nolan matrix units. Using a design process similar to the 9×9 Nolan matrix, the phase order is determined and verified through simulation. Using electromagnetic simulation software, the designed 12×12 Nolan matrix is ​​simulated to analyze its phase and amplitude characteristics under different port excitations. Figure 10dSimulation results show that the antenna array driven by a 12×12 Nolan matrix can provide one broadside beam, one dual beam in an end-fire radiation pattern, and ten pencil beams with high spatial resolution, effectively verifying the effectiveness and flexibility of the scalable topology.

[0043] The core of the 9×9 Nolan matrix and its scalable topology proposed in the present invention lies in the innovative topology design. This design uses the 3×3 Nolan matrix unit as the basic unit, and cleverly combines the phase shifter and the bridge network to achieve flexible and adjustable phase series; at the same time, the grounded coplanar waveguide (GCPW) structure and specific materials are used to achieve the goal of broadband, compact single-layer design; in addition, a scalable topology is constructed by orderly arranging the sub-beamforming network (BFN). These innovations together constitute the main protection content of the present invention, covering the matrix topology, the connection method and design method of each component, the scalable topology architecture and its related design ideas. With these innovations, the present invention can effectively solve the problems existing in the existing beamforming network and significantly improve the overall performance.

[0044] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various modifications and substitutions within the technical scope disclosed in the present invention, and such modifications and substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A 3x3 Nolan matrix unit with adjustable phase sequence, characterized in that: The device comprises a first input port, a second input port, a third input port, a first output port, a second output port, a third output port, a power distribution module, and a phase compensation module, wherein the power distribution module comprises a first orthogonal coupler, a second orthogonal coupler, a third orthogonal coupler, and a fourth phase shifter, and the phase compensation module comprises a first phase shifter, a second phase shifter, and a third phase shifter; The first input port is connected to input port 1 of the second orthogonal coupler, the second input port is connected to input port 1 of the first orthogonal coupler, and the third input port is connected to input port 2 of the first orthogonal coupler; Output port 1 of the first orthogonal coupler is connected to input port 2 of the second orthogonal coupler, and output port 2 of the first orthogonal coupler is connected to input port 2 of the third orthogonal coupler via a fourth phase shifter; The output port 1 of the second orthogonal coupler is connected to the first output port through the third phase shifter, and the output port 2 of the second orthogonal coupler is connected to the input port 1 of the third orthogonal coupler; The first output port of the third orthogonal coupler is connected to the second output port via the second phase shifter, and the second output port of the third orthogonal coupler is connected to the third output port via the first phase shifter.

2. The 3x3 Nolan matrix unit with adjustable phase sequence according to claim 1, wherein: The coupling degree between the first and third orthogonal couplers is 3.01 dB, and the coupling degree between the second orthogonal coupler is 4.77 dB. The phase adjustment value of the fourth phase shifter is (θ4 - π / 2), θ4 is the phase shift value of the first orthogonal coupler from input port 2 to output port 2, the phase adjustment value of the first phase shifter is φ1, the phase adjustment value of the second phase shifter is φ2, and the phase adjustment value of the third phase shifter is (θ3+2φ2-φ1), θ3 is the phase shift value from input port 1 to output port 1 of the second orthogonal coupler.

3. A 9x9 Nolan matrix with adjustable phase series, characterized in that: It includes six 3x3 Nolan matrix units with adjustable phase series as described in claim 1 or claim 2, and six phase shifters; respectively defined as Nolan matrix unit NM1, Nolan matrix unit NM2, Nolan matrix unit NM3, Nolan matrix unit NM4, Nolan matrix unit NM5, and Nolan matrix unit NM6; phase shifter β1, phase shifter β2, phase shifter β3, phase shifter β4, phase shifter β5, and phase shifter β6; The input ports of the Nolan matrix unit NM1, the Nolan matrix unit NM2, and the Nolan matrix unit NM3 respectively constitute nine input ports of the 9x9 Nolan matrix; The first output port of the Nolan matrix unit NM1 is connected to the first input port of the Nolan matrix unit NM4, the second output port is connected to the first input port of the Nolan matrix unit NM5 through the phase shifter β1, and the third output port is connected to the first input port of the Nolan matrix unit NM6 through the phase shifter β2; The first output port of the Nolan matrix unit NM2 is connected to the second input port of the Nolan matrix unit NM4 through a phase shifter β3, the second output port is connected to the second input port of the Nolan matrix unit NM5, and the third output port is connected to the second input port of the Nolan matrix unit NM6 through a phase shifter β4; The first output port of the Nolan matrix unit NM3 is connected to the third input port of the Nolan matrix unit NM4 through a phase shifter β5, the second output port is connected to the third input port of the Nolan matrix unit NM5 through a phase shifter β6, and the third output port is connected to the third input port of the Nolan matrix unit NM6; The three output ports of the Nolan matrix unit NM4 respectively form the first output port, the fourth output port and the seventh output port of the 9x9 Nolan matrix; the three output ports of the Nolan matrix unit NM5 respectively form the second output port, the fifth output port and the eighth output port of the 9x9 Nolan matrix; the three output ports of the Nolan matrix unit NM6 respectively form the third output port, the sixth output port and the ninth output port of the 9x9 Nolan matrix.

4. The 9x9 Nolan matrix with adjustable phase series according to claim 3, wherein: It also includes two bridge networks, defined as bridge network CN1 and bridge network CN2. The first output port to the ninth output port of the 9x9 Nolan matrix are arranged in sequence and independently set. The phase shifter β1, phase shifter β2, phase shifter β3, phase shifter β4, phase shifter β5, and phase shifter β6 are connected to the input ports of the Nolan matrix unit NM4, Nolan matrix unit NM5, and Nolan matrix unit NM6 through the bridge network CN1. The output ports of the Nolan matrix unit NM4, Nolan matrix unit NM5, and Nolan matrix unit NM6 are connected to the first output port to the ninth output port of the 9x9 Nolan matrix through the bridge network CN2.

5. A broadband multi-beam antenna array, comprising a 9x9 Nolan matrix with adjustable phase levels as described in claim 3 or claim 4, and an antenna array consisting of nine radiating elements, each radiating element being connected to one of the output ports of the 9x9 Nolan matrix.

6. The broadband multi-beam antenna array according to claim 5, wherein: The radiation unit is a magnetoelectric dipole antenna.

7. The broadband multi-beam antenna array according to claim 6, wherein: The distance between the radiation units is 31 mm.

8. A method for implementing a 9x9 Nolan matrix with adjustable phase series, characterized in that: The following steps are involved: S10, select 5.5GHz as the center frequency, and use Rogers 4003C material for circuit design, which has a relative dielectric constant of 3.38 and a thickness of 0.813mm; S20. According to the topology of the 3x3 Nolan matrix unit with adjustable phase sequence as claimed in claim 1 or 2: improve the enhanced coupling structure to a grounded coplanar waveguide configuration to design a broadband coupler, and use a via-hole transmission structure to ensure that the outputs are on the same side, so as to design a first orthogonal coupler, a second orthogonal coupler, and a third orthogonal coupler with different coupling coefficients; when constructing the power distribution module, modify the 50-ohm transmission line to two parallel 100-ohm GCPW lines to realize the fourth phase shifter function and reduce the size; design a phase compensation module, use a delay line and a 90° short-circuit branch, and cascade it with the power distribution part, and optimize the layout of the 90° short-circuit branch; S30. Implement a 9x9 Nolan matrix with adjustable phase levels, optimize the bridge network topology, transfer part of the signal path to the bottom layer to eliminate path crossings; replace the three path intersections with transition via pairs, and optimize the signal path to a straight line; connect the six designed 3×3 Nolan matrices, six phase shifters, and two bridge networks according to the topological structure designed as claimed in claim 3 or 4.

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