A performance calculation method of an electrically scanning array antenna based on a reflective electromagnetic metasurface

Abstract

The application discloses a performance calculation method of an electric scanning array antenna based on a reflective electromagnetic super surface, and solves the problem of fast calculation of the performance of the electric scanning array antenna based on the reflective electromagnetic super surface. According to the principle that each unit of the reflective electromagnetic super surface is located in the far field of a feed source, the electric field intensity at the unit of the electromagnetic super surface is calculated first, and then the reflection power and phase of each unit of the reflective electromagnetic super surface are obtained. The directional diagram data of the antenna are calculated quickly by using the fast Fourier transform technology based on the reflection power and phase of the unit, so that various performance indexes of the antenna are obtained. The application has the advantages of simplicity and high efficiency, can quickly calculate the performance of the antenna, has strong universality, is independent of specific forms of the feed source and the unit of the electromagnetic super surface, and can be widely applied in the fields of radar and communication antennas.

Description

Technical Field

[0001] This invention pertains to microwave antenna feeder technology, specifically a method for calculating the performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface. Background Technology

[0002] With the rapid development of electronic science and technology, active phased array antennas, with their conformal characteristics to radar platforms, possess unparalleled advantages in observing high-speed moving targets, realizing multiple radar functions, and multi-target tracking, and are widely used in radar systems. Electrically scanned array antennas based on reflective electromagnetic metasurfaces include a feed source and an electromagnetic metasurface element array, resulting in a relatively large electrical size. Directly employing full-wave simulation calculations for antenna design and performance evaluation incurs significant hardware resource costs and low computational efficiency. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a rapid calculation method for evaluating the performance of electrically scanned array antennas, thereby solving the problem of rapid and accurate performance evaluation of electrically scanned array antennas. To achieve the above objective, the present invention is implemented through the following method.

[0004] A method for calculating the performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface includes:

[0005] S1: Perform rectangular meshing on the electromagnetic metasurface unit array;

[0006] S2: Using the feed source as a reference, perform coordinate transformation on all grid nodes of the electromagnetic metasurface unit array, and calculate the normal vector and grid area at each grid node;

[0007] S3: Calculate the Euclidean distance and direction vector between the feed and the i-th grid node of the r-th element in the electromagnetic metasurface array, where r = 1, 2, ..., R, i = 1, 2, ..., I, R is the total number of elements, and I is the grid node of each element;

[0008] S4: Based on the angular relationship between the direction vector and the feed normal and the metasurface element normal, obtain the normalized radiation pattern amplitude values ​​of the feed and metasurface element at the direction vector respectively;

[0009] S5: Convert the feed output power into excitation voltage intensity, calculate the electric field strength at each grid node of the electromagnetic metasurface unit array and convert it into Poincaré vector;

[0010] S6: Calculate the power area integral of the area occupied by each electromagnetic metasurface unit to obtain the incident power at each unit.

[0011] S7: Determine the theoretical excitation phase of each element based on the beam direction of the electromagnetic metasurface element array and the spacing between the electromagnetic metasurface elements;

[0012] S8: Calculate the relative excitation amplitude and initial phase of each element of the electromagnetic metasurface based on the incident power at each element, and determine the relative phase value based on the initial phase;

[0013] S9: Calculate the antenna radiation pattern using Fast Fourier Transform based on the excitation amplitude and phase at each unit, and determine the antenna performance parameters based on the antenna radiation pattern.

[0014] Preferably, the normal vector at the node is specifically:

[0015] VNs_ r,i =(XGs_ r,i+1 -XGs_ r,i YGs_ r,i+1 -YGs_ r,i ZGs_ r,i+1 -ZGs_ r,i )×(XGs_ r,i+3 -XGs_ r,i YGs_ r,i+3 -YGs_ r,i ZGs_ r,i+3 -ZGs_ r,i )

[0016] In the formula, (XGs_ r,i YGs_ r,i ZGs_ r,i (XGs_) represents the global coordinates of the i-th grid node in the r-th element of the electromagnetic metasurface array. r,i+1 YGs_ r,i+1 ZGs_ r,i+1 (XGs_) represents the global coordinates of the (i+1)th mesh node in the r-th element of the electromagnetic metasurface array. r,i+3 YGs_ r,i+3 ZGs_ r,i+3 ) represents the global coordinates of the (i+3)th grid node of the r-th cell in the electromagnetic metasurface array.

[0017] Preferably, the specific formula for calculating the Euclidean distance between the feed source and the i-th grid node of the r-th element of the electromagnetic metasurface array is as follows:

[0018]

[0019] In the formula, (XGs_ r,i YGs_ r,i ZGs_ r,i Let (X) be the global coordinates of the i-th grid node in the r-th element of the electromagnetic metasurface array. feed Y feedZ feed () represents the coordinates of the feed source position.

[0020] Preferably, the direction vector of the feed source and the i-th grid node of the r-th element in the electromagnetic metasurface array is specifically:

[0021] V_ r,i =(X feed -XGs_ r,i Y feed -YGs_ r,i Z feed -ZGs_ r,i ).

[0022] Preferably, the specific formula for converting the feed output power into the excitation voltage intensity is as follows:

[0023]

[0024] In the formula, γ is the air wave impedance and Pow is the feed output power.

[0025] Preferably, the specific formula for calculating the electric field strength at any grid node of the electromagnetic metasurface element array is as follows:

[0026]

[0027] In the formula, c is the propagation speed of electromagnetic waves, and E feed Here, represents the voltage value corresponding to the transmitting power of the feedhorn, and Gfeed represents the maximum gain of the feedhorn. Let be the amplitude value of the normalized radiation pattern of the feed at (θ_Nr,i,φ_Nr,i). Dis represents the amplitude value of the normalized pattern of the r-th electromagnetic metasurface unit at (θ_Sr,i,φ_Sr,i). r,i Let be the Euclidean distance between the feed source and the i-th grid node of the r-th element in the electromagnetic metasurface array. F 0 represents the operating frequency of the electronically scanned array antenna.

[0028] Preferably, the specific formula for converting the electric field strength value at any grid node into a Poincaré vector is as follows:

[0029] Pyt(r,i)=mag(Es(r,i)) 2 / γ*exp(j*angle(E s (r,i)))

[0030] In the formula, angle() represents the complex-valued phase function, mag() represents the complex-valued amplitude function, and γ is the air wave impedance.

[0031] Preferably, the relative excitation amplitude and initial phase of each element of the electromagnetic metasurface are calculated based on the incident power of each element, and the relative phase value is determined based on the initial phase, specifically as follows:

[0032] The relative excitation amplitude of the r-th electromagnetic metasurface unit is: Es_cell(r)=|Ps_cell(r)|^0.5, where Ps_cell(r) is the incident power;

[0033] Initial phase Phs(r) = angle(Ps_cell(r));

[0034] The phase that the r-th electromagnetic metasurface unit actually needs to be configured is determined based on the initial phase, specifically: delt_Phs(r) = Phs_s r -Phs(r), Phs_s r Theoretical excitation phase

[0035] The phase that actually needs to be configured is quantized to obtain the actual quantized phase delt_Phs_nbit(r) that needs to be configured for the r-th electromagnetic metasurface unit.

[0036] The relative phase value is determined based on the phase configured according to the actual needs after quantization: Phs_cell(r) = delt_Phs_nbit(r) + Phs(r).

[0037] Compared with the prior art, the significant advantages of this invention are:

[0038] ① This invention has the advantage of high computational efficiency. It realizes the rapid calculation of the excitation field of the metasurface array unit by utilizing the principle that the near field of the array is the far field of the unit. At the same time, it uses the fast Fourier transform algorithm to accelerate the calculation of the array pattern, which greatly improves the computational efficiency.

[0039] ② This invention can also conveniently calculate the power value at the electromagnetic metasurface unit, thereby providing a reference for the selection of electromagnetic metasurface control devices;

[0040] ③ This invention has strong versatility. It does not depend on a specific feed source and electromagnetic metasurface element form. The feed source and metasurface element radiation pattern and relative position can be conveniently configured according to the actual array antenna, which makes it highly versatile.

[0041] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0042] Figure 1 This is a flowchart of a method for calculating the performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface.

[0043] Figure 2This is a schematic diagram of an electrically scanned array antenna based on a reflective electromagnetic metasurface. In the diagram, 1 is the electromagnetic metasurface element array, and 2 is the feed source.

[0044] Figure 3 Schematic diagram of electromagnetic metasurface unit array mesh division.

[0045] Figure 4 This is a diagram showing the surface electric field intensity distribution of an electromagnetic metasurface unit array.

[0046] Figure 5 This is the antenna radiation pattern calculated using this invention. Detailed Implementation

[0047] This invention proposes a method for calculating the performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface. Taking an electrically scanned array antenna with a reflective electromagnetic metasurface as an example, the method provides a rapid calculation and explanation of the antenna performance.

[0048] like Figure 1 As shown, a method for calculating the performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface includes:

[0049] S1: Perform rectangular meshing on the electromagnetic metasurface unit array;

[0050] S2: Using the feed source as a reference, perform coordinate transformation on all grid nodes of the electromagnetic metasurface unit array, and calculate the normal vector and grid area at each grid node;

[0051] S3: Calculate the Euclidean distance and direction vector between the feed and the i-th grid node of the r-th element in the electromagnetic metasurface array, where r = 1, 2, ..., R, i = 1, 2, ..., I, R is the total number of elements, and I is the grid node of each element;

[0052] S4: Based on the angular relationship between the direction vector and the feed normal and the metasurface element normal, obtain the normalized radiation pattern amplitude values ​​of the feed and metasurface element at the direction vector respectively;

[0053] S5: Convert the feed output power into excitation voltage intensity, calculate the electric field strength at each grid node of the electromagnetic metasurface unit array and convert it into Poincaré vector;

[0054] S6: Calculate the power area integral of the area occupied by each electromagnetic metasurface unit to obtain the incident power at each unit.

[0055] S7: Determine the theoretical excitation phase of each element based on the beam direction of the electromagnetic metasurface element array and the spacing between the electromagnetic metasurface elements;

[0056] S8: Calculate the relative excitation amplitude and initial phase of each element of the electromagnetic metasurface based on the incident power at each element, and determine the relative phase value based on the initial phase;

[0057] S9: Calculate the antenna radiation pattern using Fast Fourier Transform based on the excitation amplitude and phase of each element, and determine the antenna performance parameters based on the antenna radiation pattern.

[0058] As one embodiment, before calculation, the relevant parameters of the electronically scanned array antenna are determined, including the operating frequency F0, the feed source being a horn antenna, and the normalized radiation pattern. Maximum gain G feed =16.2dB=42, feed power of the horn Pow=200W, feed location coordinates (X feed Y feed Z feed (0,0,0) and the pitch angle N feed =35°, electromagnetic metasurface element array size 96 rows 96 columns, metasurface element row spacing and column spacing are both 8mm, array center distance is 600mm in front of the feed and 390mm above it, normalized radiation pattern in electromagnetic metasurface element array. Metasurface element phase shift number N_Bit = 1, array antenna beam pointing A schematic diagram of an electrically scanned array antenna is shown below. Figure 2 As shown in the figure, 1 is the electromagnetic metasurface unit array, and 2 is the feed source;

[0059] As one embodiment, a method for calculating the performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface is provided, such as... Figure 2 As shown, it includes:

[0060] S1: Mesh the electromagnetic metasurface unit array. Divide the area occupied by the r-th metasurface unit (r=1,2,3......9216) into a rectangular mesh to obtain the coordinates of the I mesh nodes (XLs_r,i, YLs_r,i, ZLs_r,i), where r=1,2,3......9216 and i=1,2,3......64.

[0061] S2: Based on the relative positional relationship between the feed and the electromagnetic metasurface element array, perform coordinate transformation on the grid coordinates of the electromagnetic metasurface region to obtain the global coordinates (XGs_) of the i-th grid node of the r-th element in the electromagnetic metasurface element array. r,i YGs_ r,i Let ZGs_r,i), r=1,2,3......9216; i=1,2,3......64, and calculate the normal vector VNs_r,i=(XGs_r,i+1-XGs_ r,i YGs_ r,i+1 -YGs_ r,i ZGs_ r,i+1 -ZGs_r,i )×(XGs_ r,i+3 -XGs_ r,i The grid consists of YGs_r,i+3-YGs_r,i and ZGs_r,i+3-ZGs_r,i), r = 1, 2, 3...9216; i = 1, 2, 3...64, and the area of ​​the i-th node element Sr,i = |VNs_r,i|, r = 1, 2, 3...9216; i = 1, 2, 3...64. In this step, "×" represents the cross product, and the area of ​​the parallelogram formed by the two vectors is the magnitude of the vector after the cross product. A schematic diagram of the grid nodes is shown below. Figure 3 As shown in the figure, 1 represents the i-th node, 2 represents the (i+1)-th node, 3 represents the (i+2)-th node, and 4 represents the (i+3)-th node.

[0062] S3: Calculate the Euclidean distance between the feed and the i-th, i=1,2,3...9216th element of the electromagnetic metasurface array. And the direction vector V_r,i=(X feed -XGs_r,i,Y feed -YGs_r,i,Z feed -ZGs_r,i);

[0063] S4: Given the feed normal vector VNL_feed = (0,0,1), based on the pitch angle N... feed Perform a coordinate transformation on the coordinate system, resulting in the transformed normal vector VNG_feed = (0, 0.5736, 0.8192). Solve for the direction vector V_ r,i The angle between the vector and the normal vector VNG_feed Solve for the direction vector V_r,i and the node normal vector VNs_ r,i The included angle The normalized values ​​in the radiation patterns of the feed and electromagnetic metasurface array antenna elements are then obtained based on these angular coordinates. and It is common knowledge in the field to find the angular coordinates of a given direction vector in the local coordinate system of an antenna element. It is also common knowledge in the field to find the normalized value of the antenna element pattern at that angle by using table lookup or interpolation methods.

[0064] S5: Convert the transmitting power of the feedhorn into a voltage value. Calculate the electric field strength at the i-th grid node of the r-th element of the electromagnetic metasurface. In the formula, c is the propagation speed of electromagnetic waves, and is expressed by the formula Pyt(r,i)=mag(Es (r,i)) 2 / 377*exp(j*angle(E s Calculate the Poynting vector Pyt(r,i) at node (r=1,2,3......9216; i=1,2,3......64), and calculate the Poynting vector at all 64 grid nodes in sequence. The electromagnetic metasurface array is located in the near-mid field relative to the feed, but the metasurface array elements are in the far field relative to the feed. Therefore, the electric field strength at the i-th grid node in this step can be obtained using the far-field electric field calculation. The electric field strength distribution of the electromagnetic metasurface array calculated in this example is as follows: Figure 4 As shown;

[0065] S6: Calculate the area integral of the Poynting vector Pyt(r,i), (r=1,2,3......9216; i=1,2,3......64) at the area occupied by the r-th (r=1,2,3......9216) electromagnetic metasurface unit to obtain the incident power Ps_cell(r) at the r-th (r=1,2,3......9216) unit;

[0066] Following the steps described above, calculations are performed on all cells and meshes to obtain data for all cells and meshes.

[0067] S7: Based on the beam direction of the electromagnetic metasurface unit array The theoretical excitation phase Phs_s required for each element can be obtained by considering the spacing between the electromagnetic metasurface elements. r (r = 1, 2, 3... 9216), the calculation method for the excitation phase is common knowledge in this field and will not be elaborated further;

[0068] S8: Calculate the relative excitation amplitude and initial phase of each element of the electromagnetic metasurface based on the incident power at each element, and determine the relative phase value based on the initial phase;

[0069] The relative excitation amplitude of the r-th electromagnetic metasurface unit is: Es_cell(r)=|Ps_cell(r)|^0.5; the initial phase Phs(r)=angle(Ps_cell(r));

[0070] The phase that the r-th electromagnetic metasurface unit actually needs to be configured is determined based on the initial phase, specifically: delt_Phs(r) = Phs_s r-Phs(r), in this example, the phase shift number N_Bit = 1 for the electromagnetic metasurface unit, that is, the quantized phase is only 0° and 180°. The actual quantized phase delt_Phs_nbit(r) to be configured for the r-th electromagnetic metasurface unit is obtained. It is common knowledge in the field to obtain the quantized phase given the phase shift number N_Bit, so it will not be elaborated here.

[0071] The relative phase value is determined based on the phase configuration required after quantization: Phs_cell(r) = delt_Phs_nbit(r) + Phs(r)

[0072] S9: Based on the obtained relative excitation amplitude values ​​Es_cell(r) and phase Phs_cell(r) of the electromagnetic metasurface elements, and the spacing between the electromagnetic metasurface elements, the radiation pattern of the electrically scanned array antenna is obtained by calculating the radiation pattern using the Fast Fourier Transform technique. directional pattern as follows Figure 5 As shown, based on this radiation pattern, the beamwidth, sidelobes, pointing, directivity coefficient, and other indicators can be easily obtained. It is common knowledge that the determination of these indicators is known from radiation pattern data, so it will not be elaborated further.

[0073] Furthermore, in the first step of the calculation method shown, the feed normalization pattern is... Normalized pattern in electromagnetic metasurface unit array It can be obtained through actual measurement or simulation calculation. In this example, the radiation pattern was calculated using the Fast Fourier Transform technique, which is common knowledge in the field and will not be elaborated further.

[0074] To verify the correctness of the method described in this invention, a full-wave simulation calculation was performed on the antenna. The calculation time was 24 hours, 56 minutes, and 36 seconds, while the calculation time of the method described in this invention was 42 seconds.

[0075] The antenna performance calculated by the method described in this invention is as follows:

[0076] Azimuth width: 1.92°, azimuth sidelobes: -25.3dB, elevation width: 1.84°, elevation sidelobes: -20.1dB, directivity coefficient: 37.5dB.

[0077] The antenna performance calculated using full-wave simulation is as follows:

[0078] Azimuth width: 1.96°, azimuth sidelobe: -24.3dB, elevation width: 1.87°, elevation sidelobe: -19.4dB, directivity coefficient: 36.7dB.

[0079] The results above show that the full-wave simulation time is more than 2100 times that of the method described in this invention, and the antenna performance is well matched.

Claims

1. A method for calculating performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface, characterized in that, Comprise: S1: three-dimensional space rectangular grid partitioning is carried out to electromagnetic super surface unit array; S2: all grid nodes of electromagnetic super surface unit array are coordinate transformed with feed as benchmark, normal vector and grid area at each grid node are calculated; S3: the Euclidean distance and direction vector of feed and the i-th grid node of the r-th unit of electromagnetic super surface unit array are calculated, r=1, 2,..., R, i=1, 2,..., I, R is the total number of units, I is the grid node of each unit; S4: according to the angle relationship of direction vector, feed normal and super surface unit normal, the amplitude value of the normalized directional diagram of feed and super surface unit at the direction vector is obtained; S5: the output power of feed is converted into excitation voltage intensity, the electric field intensity value at each grid node of electromagnetic super surface unit array is calculated and converted into Poynting vector; S6: the power area of each electromagnetic super surface unit is calculated, and the incident power at each unit is obtained; S7: the theoretical excitation phase of each unit is determined according to the beam pointing of electromagnetic super surface unit array and the distance between electromagnetic super surface units; S8: the relative excitation amplitude value and initial phase of each unit of electromagnetic super surface are calculated according to the incident power at each unit, and the relative phase value is determined according to the initial phase; S9: the antenna directional diagram is calculated according to the excitation amplitude and phase at each unit, and the performance parameters of the antenna are determined based on the antenna radiation directional diagram.

2. The method of claim 1, wherein the method is performed by a computer system. The specific formula for calculating the Euclidean distance of the i-th grid node of the r-th unit of feed and electromagnetic super surface unit array is: VNs_ r,i = (XGs_ r,i+1 - XGs_ r,i , YGs_ r,i+1 - YGs_ r,i , ZGs_ r,i+1 - ZGs_ r,i ) x (XGs_ r,i+3 - XGs_ r,i , YGs_ r,i+3 - YGs_ r,i , ZGs_ r,i+3 - ZGs_ r,i ) wherein (XGs r,i , YGs r,i , ZGs r,i ) is the global coordinate of the i-th grid node of the r-th unit cell of the electromagnetic metasurface unit cell array, (XGs r,i+1 , YGs r,i+1 , ZGs r,i+1 ) is the global coordinate of the i+1-th grid node of the r-th unit cell of the electromagnetic metasurface unit cell array, and (XGs r,i+3 , YGs r,i+3 , ZGs r,i+3 ) is the global coordinate of the i+3-th grid node of the r-th unit cell of the electromagnetic metasurface unit cell array.

3. The method of claim 1, wherein the method is performed by a computer system. The specific formula for calculating the Euclidean distance of the i-th grid node of the r-th unit of feed and electromagnetic super surface unit array is: wherein (XGs r,i , YGs r,i , ZGs r,i ) are global coordinates of the rth element of the array of electromagnetic metasurface elements, and (X feed , Y feed , Z feed ) are coordinates of the feed position.

4. The method of claim 3, wherein the method is performed by a computer system. The specific formula for converting the output power of feed into excitation voltage intensity is: V_ r,i = (X feed - Xs r,i , Y feed - Ys r,i , Z feed - Zs r,i ).

5. The method of claim 1, wherein, In the formula, γ is air wave impedance, and Pow is the output power of feed. The specific formula for calculating the electric field intensity value at any grid node of electromagnetic super surface unit array is:

6. The method of claim 1, wherein, The specific formula for converting the electric field intensity value at any grid node into Poynting vector is: where c is the electromagnetic wave propagation speed, E feed is the voltage value corresponding to the transmit power of the feed horn, Gfeed is the maximum gain of the feed, is the amplitude value of the normalized directional pattern of the feed at (θ_Nr,i, φ_Nr,i), is the amplitude value of the normalized directional pattern of the rth electromagnetic metasurface unit at (θ_Sr,i, φ_Sr,i), Dis r,i is the Euclidean distance between the feed and the i-th grid node of the rth unit of the electromagnetic metasurface unit array, F0 is the operating frequency point of the electrically scanned array antenna.

7. The method of claim 6, wherein the method is performed by a computer system. In the formula, angle() represents the phase function of complex value, mag() represents the amplitude function of complex value, and γ is air wave impedance. Pyt(r,i) = mag(E s (r,i)) 2 / γ * exp(j * angle(E s (r,i))) The specific formula for calculating the relative excitation amplitude value and initial phase of each unit of electromagnetic super surface according to the incident power at each unit is:

8. The method of claim 1, wherein the method is a method of calculating performance of an electrically scanned array antenna based on a reflective electromagnetic metasurface. The relative excitation amplitude value of the r-th electromagnetic super surface unit is: Es_cell(r)=|Ps_cell(r)|^0.5, wherein Ps_cell(r) is the incident power; The initial phase Phs(r)=angle(Ps_cell(r)); The actual phase to be configured of the r-th electromagnetic super surface unit is determined according to the initial phase, which is: The actual quantized phase to be configured of the r-th electromagnetic super surface unit is obtained by quantizing the actual phase to be configured; delt_Phs(r) = Phs_s r - Phs(r), Phs_s r for the theoretical excitation phase The relative phase value Phs_cell(r)=delt_Phs_nbit(r)+Phs(r) is determined according to the quantized actual phase to be configured. ​

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