Wideband phase shifter based on pixelated structure, design method thereof and electronic device

The broadband phase shifter, optimized through pixelation structure and genetic algorithm, solves the technical problems that were not addressed in the prior art, achieving stable phase difference output and low loss over a wide bandwidth, and is suitable for broadband phased array antennas and beam scanning systems.

CN123034110APending Publication Date: 2026-11-03GUANGDONG UNIV OF TECH
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Patent Information

Application Number
CN202611081696.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-07-21
Publication Date
2026-11-03

AI Technical Summary

Technical Problem

Traditional electrically tunable phase shifters based on PIN diodes have narrow operating bandwidth and high insertion loss, making it difficult to meet the application requirements of broadband systems. Furthermore, the phase state is only accurate within a narrow band.

Method used

A wideband phase shifter is designed with a pixelated structure. By optimizing the connection or disconnection state of each pixel unit and combining it with a genetic algorithm for global optimization search, a multi-port network model is constructed to achieve a stable 90-degree phase difference output. A DC bias network and switching devices are introduced to ensure good impedance matching and low loss.

Benefits of technology

It achieves stable 90-degree phase difference output over a wide frequency range, maintains good impedance matching performance, and is suitable for broadband phased array antennas and beam scanning systems, significantly improving operating bandwidth and design flexibility.

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Abstract

The application discloses a kind of wideband phase shifter based on pixel structure and its design method, electronic equipment, the wideband phase shifter includes microstrip feed structure, dielectric substrate, metal floor and reconfigurable pixelized phase shift structure, the microstrip feed structure and reconfigurable pixelized phase shift structure are set on the upper surface of dielectric substrate, microstrip feed structure has two microstrip line feed ports, for realizing the input and output of radio frequency signal, reconfigurable pixelized phase shift structure is connected with microstrip feed structure, reconfigurable pixelized phase shift structure is composed of multiple pixel units, the metal floor is set on the lower surface of dielectric substrate.The application can realize stable 90 degree phase difference output in relatively wide frequency range, while maintaining good impedance matching performance, so as to lay the core foundation for wideband beam scanning array.
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Description

Technical Field

[0001] This invention relates to a broadband phase shifter based on a pixelated structure, its design method, and electronic equipment, belonging to the field of antenna design technology. Background Technology

[0002] In modern wireless communication and radar systems, achieving fast and accurate beam scanning is a critical requirement. Reconfigurable antennas offer a solution by dynamically adjusting radiation characteristics, with PIN diode-based electrically tunable phase shifters being widely adopted due to their low cost, ease of integration, and fast switching. However, traditional designs typically rely on resonant structures, resulting in narrow operating bandwidth, high insertion loss, and precise phase states only within a narrow band, making them unsuitable for broadband system applications.

[0003] To overcome this bandwidth bottleneck, pixelation technology has been introduced into phase shifter design. This technology discretizes a continuous metal surface into a two-dimensional grid array, and by optimizing the connection or disconnection state of each pixel unit, the electromagnetic response of the structure can be flexibly and precisely customized. This pixelation method provides a high degree of freedom for designing high-performance microwave devices. Summary of the Invention

[0004] The first objective of this invention is to solve the problems of the prior art, such as narrow operating bandwidth, high insertion loss, poor phase stability, and the fact that its discrete phase state is only accurate within a narrow band, making it difficult to meet the application requirements of broadband systems. This invention provides a broadband phase shifter based on a pixelated structure, which can achieve a stable 90-degree phase difference output over a wide frequency range while maintaining good impedance matching performance, thereby laying a core foundation for broadband beam scanning arrays.

[0005] A second objective of the present invention is to provide an electronic device comprising the aforementioned broadband phase shifter.

[0006] The third objective of this invention is to provide a design method for the aforementioned broadband phase shifter.

[0007] The first objective of this invention can be achieved by adopting the following technical solution:

[0008] A broadband phase shifter based on a pixelated structure includes a microstrip feed structure, a dielectric substrate, a metal ground plane, and a reconfigurable pixelated phase shift structure. The microstrip feed structure and the reconfigurable pixelated phase shift structure are disposed on the upper surface of the dielectric substrate. The microstrip feed structure has two microstrip line feed ports for realizing the input and output of radio frequency signals. The reconfigurable pixelated phase shift structure is connected to the microstrip feed structure and is composed of multiple pixel units. The metal ground plane is disposed on the lower surface of the dielectric substrate.

[0009] Furthermore, it also includes a DC bias network disposed on the upper surface of the dielectric substrate, and the DC bias network is connected to the microstrip feeding structure and the reconfigurable pixelated phase shifting structure, respectively.

[0010] Furthermore, the DC bias network includes a current-limiting resistor, an RF isolation inductor, a bypass capacitor, and a grounding inductor. One end of the current-limiting resistor is connected to a feed point, and the other end of the current-limiting resistor is connected to one end of the RF isolation inductor and one end of the bypass capacitor, respectively. The other end of the RF isolation inductor is connected to a microstrip feed structure, and one end of the grounding inductor is connected to a reconfigurable pixelated phase-shifting structure.

[0011] Furthermore, a first switching device is provided at the connection point between the reconfigurable pixelated phase-shifting structure and the microstrip feeding structure.

[0012] Furthermore, the pixel unit consists of G×H units, and each pixel unit is arranged according to a predetermined spacing rule to form a two-dimensional discrete structure. Each pair of adjacent pixel units is coupled to each other through several connection nodes.

[0013] Furthermore, a second switching device is provided at the connection node.

[0014] The second objective of this invention can be achieved by adopting the following technical solution:

[0015] An electronic device comprising the aforementioned broadband phase shifter.

[0016] The third objective of this invention can be achieved by adopting the following technical solution:

[0017] A design method for a broadband phase shifter, wherein the broadband phase shifter is the broadband phase shifter described above, the method comprising:

[0018] The reconfigurable pixelated phase-shifting structure is modeled as a multi-port network model with external input / output ports and N internal ports.

[0019] A genetic algorithm is introduced to perform a global optimization search on the pixel connection state of the multi-port network model in order to determine the reconfigurable pixelated phase-shifting structure;

[0020] After determining the reconfigurable pixelated phase-shifting structure, the broadband phase shifter was fabricated.

[0021] Furthermore, the voltage and current relationship between the external input / output ports and internal ports of the multi-port network model is as follows:

[0022] ;

[0023] in, This indicates the voltage at the external input / output port. This indicates the current at the external input / output port. This indicates the voltage at the internal port. Indicates the current at the internal port. This represents the self-impedance matrix of the external input / output ports. This represents the self-impedance matrix of the internal ports. This represents the mutual impedance matrix between external input / output ports and internal ports. = ;

[0024] Internal port terminals are load balancers The corresponding voltage and current satisfy the following equation:

[0025] ;

[0026] Will Substituting the voltage and current relationships, the input impedance matrix at the external input / output ports is derived:

[0027] ;

[0028] Based on the input impedance matrix, the reflection coefficient of the input port is derived:

[0029] ;

[0030] in, Indicates the reference impedance. Represents the identity matrix.

[0031] Furthermore, the optimization objectives of the global optimization search include a first objective and a second objective;

[0032] The first objective is to sample frequency points within the target frequency band. Reflectance at location An evaluation was conducted to ensure the amplitude was as small as possible. 10 dB, the corresponding objective function is defined as:

[0033] ;

[0034] in, Indicates the number of frequency sampling points. This indicates that only the positive values ​​are accumulated;

[0035] The second objective is to maintain a phase difference of approximately 90 degrees between the two operating states of the broadband phase shifter, in order to achieve precise phase accuracy. The corresponding objective function is defined as:

[0036] ;

[0037] in, and These represent the transmission phases under the two switching states, respectively.

[0038] The present invention has the following advantages over the prior art:

[0039] 1. This invention applies a pixelated structure to the design of a broadband phase shifter for a reconfigurable antenna. Under different operating conditions, it can maintain smooth and continuous phase change characteristics over a wide frequency range, achieving a stable phase difference output close to 90 degrees. At the same time, it has low insertion loss and good return loss performance, making it suitable for phase control applications in broadband phased array antennas and broadband beam scanning systems.

[0040] 2. This invention introduces a pixelated phase-shifting structure modeling method based on an internal multi-port approach, which improves the design accuracy and phase stability of broadband phase shifters. By constructing a cost function that includes impedance matching and phase difference constraints, global optimization of pixel connection states is achieved, enabling broadband phase shifters to maintain a stable 90-degree phase difference output across a wide bandwidth. A system design method based on pixel connection state optimization is proposed, which avoids the bandwidth limitation problem of traditional phase shifters and significantly improves the operating bandwidth and design flexibility of phase shifters. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0042] Figure 1 This is a three-dimensional structural diagram of a broadband phase shifter based on a pixelated structure according to an embodiment of the present invention.

[0043] Figure 2 This is a top view of a broadband phase shifter based on a pixelated structure according to an embodiment of the present invention.

[0044] Figure 3 This is a magnified view of a pixel portion of a broadband phase shifter based on a pixelated structure according to an embodiment of the present invention.

[0045] Figure 4 This is a circuit model diagram of a reconfigurable pixelated phase shifter based on a pixelated structure, according to an embodiment of the present invention.

[0046] Figure 5 This is an equivalent circuit diagram of the on / off state of the first switching device of the broadband phase shifter based on a pixelated structure according to an embodiment of the present invention.

[0047] Figure 6 The figures show the test and simulation results of a broadband phase shifter based on a pixelated structure according to an embodiment of the present invention.

[0048] Wherein, 1-first microstrip line feed port, 2-second microstrip line feed port, 5-feed point, 6-current limiting resistor, 7-RF isolation inductor, 8-bypass capacitor, 9-grounding inductor, 10-first switching device, 11-pixel unit, 12-second switching device. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0050] Example:

[0051] like Figures 1-3 As shown, this embodiment provides a broadband phase shifter based on a pixelated structure. The broadband phase shifter includes a microstrip feed structure, a dielectric substrate 3, a metal ground plane 4, and a reconfigurable pixelated phase shifting structure. The microstrip feed structure and the reconfigurable pixelated phase shifting structure are disposed on the upper surface of the dielectric substrate 3. The microstrip feed structure has two microstrip line feed ports, namely the first microstrip line feed port 1 and the second microstrip line feed port 2, which are used to realize the input and output of radio frequency signals, that is, as the input port and output port of the broadband phase shifter. The reconfigurable pixelated phase shifting structure is connected to the microstrip feed structure and is composed of multiple pixel units 11. The metal ground plane 4 is disposed on the lower surface of the dielectric substrate to form a standard microstrip transmission environment, thereby ensuring the impedance continuity and transmission stability of the radio frequency signal during transmission.

[0052] In this embodiment, the dielectric substrate 3 is made of Arlon AD255A material with a thickness of 1 mm. Its relative permittivity ξr is 2.55, and the dielectric loss tangent tanδ is 0.0014. This material has low dielectric loss in the microwave band, which is beneficial for reducing the overall insertion loss of the broadband phase shifter and improving the transmission efficiency. The microstrip feed structure is directly connected to the pixelated phase shift structure, so that the radio frequency signal propagates along the equivalent transmission path composed of multiple pixel units 11 after entering the pixelated region. Through the overall design of the microstrip line width, trace length, and its connection method with the pixelated phase shift structure, the broadband phase shifter can maintain good impedance matching characteristics throughout the entire operating frequency band, thereby effectively reducing reflection loss and ensuring that the signal has stable and consistent transmission characteristics in different phase shift states. The microstrip line width of the microstrip feed structure is finally determined to be 2 mm to meet the impedance matching requirements while taking into account the structural size and fabrication feasibility.

[0053] like Figure 2 As shown, the broadband phase shifter in this embodiment also includes a DC bias network. The DC bias network is disposed on the upper surface of the dielectric substrate 3. The DC bias network can be located in the peripheral region of the reconfigurable pixelated phase shifting structure and is connected to the microstrip feeding structure and the reconfigurable pixelated phase shifting structure, respectively.

[0054] Furthermore, the DC bias network includes a current-limiting resistor 6, an RF isolation inductor 7, a bypass capacitor 8, and a grounding inductor 9. One end of the current-limiting resistor 6 is connected to the feed point 5, and the other end of the current-limiting resistor 6 is connected to one end of the RF isolation inductor 7 and one end of the bypass capacitor 8, respectively. The other end of the RF isolation inductor 7 is connected to the microstrip feed structure, and one end of the grounding inductor 9 is connected to the reconfigurable pixelated phase-shifting structure.

[0055] In this embodiment, the current-limiting resistor 6 has a resistance of 50 Ω and is used to limit the bias current flowing through the switching device to prevent the device from being damaged due to overcurrent; the RF isolation inductor 7 has an inductance of 100 nH and is used to form a high impedance in the RF band, thereby suppressing the leakage of RF signals to the DC path; the bypass capacitor 8 has a capacitance of 100 pF and is used to provide a stable AC ground for the DC bias; the grounding inductor 9 has an inductance of 27 nH and is used to further improve the isolation effect of the DC bias network on the RF signal.

[0056] Furthermore, a first switching device 10 is provided at the connection point between the reconfigurable pixelated phase-shifting structure and the microstrip feeding structure. The first switching device 10 is a PIN diode of model MA4SPS402, used to switch the electrical connection or disconnection states between the pixel units 11. Through the synergistic effect of the aforementioned DC bias network and the first switching device 10, the switching of pixel connection states can be completed without significantly affecting the RF transmission characteristics, thereby ensuring that the broadband phase shifter still has a consistent insertion loss level and good phase stability under different operating states.

[0057] like Figure 3 As shown, the pixel unit in this embodiment is G×H, where G=5 and H=19. Each pixel unit is arranged according to a predetermined spacing rule to form a two-dimensional discrete structure. Each pair of adjacent pixel units is coupled to each other through several connection nodes. The reconfigurable pixelated phase-shifting structure formed by each pixel unit forms different equivalent impedance distributions and equivalent electrical lengths in an electromagnetic sense, thereby causing different transmission phase responses when the radio frequency signal passes through the structure.

[0058] Furthermore, the reconfigurable pixelated phase-shifting structure can be equivalent to a multi-port network model containing external input / output ports and multiple internal ports. The input and output ports are used for the transmission of radio frequency signals, and the internal ports correspond to the connection nodes between pixel units. A second switching device 12 is provided at the connection node. The terminal state of the internal port is determined by the on or off state of the second switching device 12. Different states correspond to different equivalent electromagnetic topologies, thereby forming different phase-shifting working modes. The second switching device 12 is also a PIN diode of model MA4SPS402.

[0059] The broadband phase shifter in this embodiment adopts a planar structure, with all functional units integrated on the same planar level. It is compact, easy to manufacture and integrate into the system. The input and output ports of the broadband phase shifter are connected to the reconfigurable pixelated phase shift structure through a microstrip feeding structure, so that the radio frequency signal forms electromagnetic coupling with the pixel unit when passing through the reconfigurable pixelated phase shift structure. This achieves the predetermined phase modulation effect during transmission and maintains smooth and continuous phase change characteristics over a wide frequency range under different operating conditions. It achieves a stable and accurate 90-degree phase difference output, while having low insertion loss and good return loss performance. It is suitable for phase control applications in broadband phased array antennas and broadband beam scanning systems.

[0060] To quantitatively describe the impact of pixel connection state changes on the electrical performance of the broadband phase shifter, this embodiment uses a multi-port network modeling method to analyze the reconfigurable pixelated phase shift structure, such as... Figure 4As shown, the reconfigurable pixelated phase-shifting structure is modeled as a multi-port network model with external input / output ports and N internal ports. The voltage and current relationships of the external input / output ports and internal ports of the multi-port network model are as follows:

[0061] (1);

[0062] in, This indicates the voltage at the external input / output port. This indicates the current at the external input / output port. This indicates the voltage at the internal port. Indicates the current at the internal port. This represents the self-impedance matrix of the external input / output ports. This represents the self-impedance matrix of the internal ports. This represents the mutual impedance matrix between external input / output ports and internal ports. = .

[0063] Internal port terminals are load balancers The corresponding voltage and current satisfy the following equation:

[0064] (2);

[0065] Substituting equation (2) into the voltage-current relationship, i.e., equation (1), we can derive the input impedance matrix at the external input / output port:

[0066] (3);

[0067] Based on the input impedance matrix, the reflection coefficient of the input port is derived:

[0068] (4);

[0069] in, Indicates the reference impedance. Represents the identity matrix.

[0070] The above modeling method can accurately describe the impact of pixel connection state on the electrical performance of broadband phase shifters at the theoretical level, providing a mathematical basis for subsequent optimization.

[0071] This embodiment employs a reconfigurable pixelated phase-shifting structure in the width phase shifter to broaden its operating bandwidth. For example... Figure 3As shown, the pixel surface is discretized into 5×19 pixel units, each pixel unit is a 1.1mm square, and the spacing between each pixel unit is 0.2mm, ultimately forming M=166 possible connections; each connection is modeled as an internal port, represented in binary form as a short circuit or open circuit; the structure is modeled as a multi-port network, with input / output ports as external ports, providing M=166 internal ports. Each pixel connection can be regarded as an internal port, and its connection state is represented in binary form: when the connection state is short circuit, it is denoted as... =0; when the connection state is open, it is denoted as =∞; Thus, the entire reconfigurable pixelated phase-shifting structure can be modeled as a multi-port network model with external input / output ports and N internal ports.

[0072] Based on this, a genetic algorithm is introduced to perform a global optimization search on the pixel connection state of the multi-port network model in order to determine the reconfigurable pixelated phase-shifting structure; wherein the optimization objectives include a first objective and a second objective.

[0073] Furthermore, the first objective is to sample frequency points within the target frequency band. Reflectance at location An evaluation was conducted to ensure the amplitude was as small as possible. 10 dB, the corresponding objective function is defined as:

[0074] (5);

[0075] in, Indicates the number of frequency sampling points. This indicates that only the positive values ​​are accumulated;

[0076] Furthermore, the second objective is to maintain a phase difference of approximately 90 degrees between the two operating states of the broadband phase shifter, in order to achieve precise phase accuracy. The corresponding objective function is defined as follows:

[0077] (6);

[0078] in, and These represent the transmission phases under the two switching states, respectively.

[0079] The genetic algorithm in this embodiment minimizes the combined cost function formed by the above objective function to obtain the optimal pixel connection configuration. The final reconfigurable pixelated phase-shifting structure is as follows: Figure 3 As shown, the circled areas represent connected pixels, while the uncircled areas represent disconnected pixels.

[0080] After determining the reconfigurable pixelated phase-shifting structure, the broadband phase shifter was fabricated. Figure 5 The equivalent circuit models of the first switching device (i.e., the PIN diode) in the on-state and off-state are shown respectively. In this embodiment, an MA4SPS402 type PIN diode is used, and its equivalent parameters include: on-resistance Rs = 3 Ω, off-resistance Rb = 85 kΩ, and junction capacitance Cb = 0.025 pF; Figure 6 As shown, the test results demonstrate a high degree of consistency between the simulation and experimental results. A stable 90-degree phase shift can be achieved within the 3.5 GHz to 3.9 GHz frequency range, with a maximum phase deviation of less than 5 degrees. The simulated transmission amplitude range is −0.3 dB to −0.9 dB, while the experimental result is approximately 1 dB lower. This difference primarily stems from non-ideal factors such as parasitic losses in the PIN diode, additional losses introduced by the soldering process and DC bias network, and manufacturing tolerances.

[0081] In summary, this invention applies a pixelated structure to the design of a broadband phase shifter for reconfigurable antennas. Under different operating conditions, it can maintain smooth and continuous phase change characteristics over a wide frequency range, achieving a stable phase difference output close to 90 degrees. At the same time, it has low insertion loss and good return loss performance, making it suitable for phase control applications in broadband phased array antennas and broadband beam scanning systems.

[0082] Although the invention has been described herein with reference to embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the drawings themselves. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple components. While different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0083] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the invention and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications fall within the scope of the invention and its equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A broadband phase shifter based on a pixelated structure, characterized in that, The device includes a microstrip feed structure, a dielectric substrate, a metal ground plane, and a reconfigurable pixelated phase-shifting structure. The microstrip feed structure and the reconfigurable pixelated phase-shifting structure are disposed on the upper surface of the dielectric substrate. The microstrip feed structure has two microstrip line feed ports for realizing the input and output of radio frequency signals. The reconfigurable pixelated phase-shifting structure is connected to the microstrip feed structure and is composed of multiple pixel units. The metal ground plane is disposed on the lower surface of the dielectric substrate.

2. The broadband phase shifter according to claim 1, characterized in that, It also includes a DC bias network disposed on the upper surface of the dielectric substrate, and the DC bias network is connected to the microstrip feeding structure and the reconfigurable pixelated phase shifting structure, respectively.

3. The broadband phase shifter according to claim 2, characterized in that, The DC bias network includes a current-limiting resistor, an RF isolation inductor, a bypass capacitor, and a grounding inductor. One end of the current-limiting resistor is connected to a feed point, and the other end of the current-limiting resistor is connected to one end of the RF isolation inductor and one end of the bypass capacitor, respectively. The other end of the RF isolation inductor is connected to a microstrip feed structure, and one end of the grounding inductor is connected to a reconfigurable pixelated phase-shifting structure.

4. The broadband phase shifter according to claim 1, characterized in that, A first switching device is provided at the connection between the reconfigurable pixelated phase-shifting structure and the microstrip feeding structure.

5. The broadband phase shifter according to claim 1, characterized in that, The number of pixel units is G×H. Each pixel unit is arranged according to a predetermined spacing rule to form a two-dimensional discrete structure. Each pair of adjacent pixel units is coupled to each other through several connection nodes.

6. The broadband phase shifter according to claim 5, characterized in that, A second switching device is provided at the connection node.

7. An electronic device, characterized in that, Includes the broadband phase shifter as described in any one of claims 1-6.

8. A design method for a broadband phase shifter, wherein the broadband phase shifter is the broadband phase shifter according to any one of claims 1-6, characterized in that, The method includes: The reconfigurable pixelated phase-shifting structure is modeled as a multi-port network model with external input / output ports and N internal ports. A genetic algorithm is introduced to perform a global optimization search on the pixel connection state of the multi-port network model in order to determine the reconfigurable pixelated phase-shifting structure; After determining the reconfigurable pixelated phase-shifting structure, the broadband phase shifter was fabricated.

9. The design method according to claim 8, characterized in that, The voltage and current relationships between the input / output ports and internal ports of the multi-port network model are as follows: ; in, This indicates the voltage at the external input / output port. This indicates the current at the external input / output port. This indicates the voltage at the internal port. Indicates the current at the internal port. This represents the self-impedance matrix of the external input / output ports. This represents the self-impedance matrix of the internal ports. This represents the mutual impedance matrix between external input / output ports and internal ports. = ; Internal port terminals are load balancers The corresponding voltage and current satisfy the following equation: ; Will Substituting the voltage and current relationships, the input impedance matrix at the external input / output ports is derived: ; Based on the input impedance matrix, the reflection coefficient of the input port is derived: ; in, Indicates the reference impedance. Represents the identity matrix.

10. The design method according to claim 8, characterized in that, The optimization objectives of the global optimization search include a first objective and a second objective; The first objective is to sample frequency points within the target frequency band. Reflectance at location An evaluation was conducted to ensure the amplitude was as small as possible. 10 dB, the corresponding objective function is defined as: ; in, Indicates the number of frequency sampling points. This indicates that only the positive values ​​are accumulated; The second objective is to maintain a phase difference of approximately 90 degrees between the two operating states of the broadband phase shifter, in order to achieve precise phase accuracy. The corresponding objective function is defined as: ; in, and These represent the transmission phases under the two switching states, respectively.