Electric scanning array antenna performance calculation method based on reflection electromagnetic metasurface

Abstract

The invention discloses an electric scanning array antenna performance calculation method based on a reflection electromagnetic metasurface, and solves the problem of rapid calculation of the electric scanning array antenna performance based on the reflection electromagnetic metasurface. According to the principle that all units of the reflection electromagnetic metasurface are located in a far field of a feed source, firstly, the electric field intensity of the electromagnetic metasurface units is obtained through calculation, and the reflection power and phase of all the reflection electromagnetic metasurface units are obtained on the basis. And on the basis of the reflected power and phase of the unit, the directional diagram data of the antenna is quickly calculated by using a fast Fourier transform technology, so that various performance indexes of the antenna are solved. The method has the advantages of simplicity and high efficiency, can quickly calculate the antenna performance, is high in universality, does not depend on a specific feed source and electromagnetic metasurface unit form, and can be widely applied to the field of radar and communication antennas.

Description

Technical Field

[0001] The present invention belongs to the field of microwave antenna feeder technology, and in particular is a method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface. Background Art

[0002] With the rapid development of electronic science and technology, active phased array antennas conform to radar platforms and have incomparable advantages in observing high-speed moving targets, realizing multiple radar functions and multi-target tracking. They are widely used in radar systems. The electronically scanned array antenna based on the reflective electromagnetic metasurface includes a feed source and an electromagnetic metasurface unit array, and has a large electrical size. Directly using full-wave simulation calculation methods to design and evaluate the performance of the antenna results in large hardware resource overhead and low computational efficiency. Summary of the invention

[0003] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a method for quickly evaluating the performance of an electronically scanned array antenna, so as to solve the problem of quickly and accurately evaluating the performance of an electronically scanned array antenna. To achieve the above purpose, the present invention is implemented by the following method.

[0004] A method for calculating performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface, comprising:

[0005] S1: Rectangular meshing of electromagnetic metasurface unit array;

[0006] S2: Taking the feed source as the reference, coordinate transformation is performed on all grid nodes of the electromagnetic metasurface unit array, and the normal vector and grid area at each grid node are calculated;

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

[0008] S4: according to the angle relationship between the direction vector and the normal direction of the feed source and the normal direction of the metasurface unit, the amplitude values ​​of the normalized directional patterns of the feed source and the metasurface unit at the direction vector are obtained respectively;

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

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

[0011] S7: determining the theoretical excitation phase of each unit according to the beam pointing of the electromagnetic metasurface unit array and the spacing between the electromagnetic metasurface units;

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

[0013] S9: Calculate the antenna pattern using fast Fourier transform according to the excitation amplitude and phase at each unit, and determine various performance parameters of the antenna 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 ) is the global coordinate of the i-th grid node of the r-th unit cell of the electromagnetic metasurface unit array, (XGs_ r,i+1 , YGs_ r,i+1 , ZGs_ r,i+1 ) is the global coordinate of the i+1th grid node of the rth unit cell of the electromagnetic metasurface array, (XGs_ r,i+3 , YGs_ r,i+3 , ZGs_ r,i+3 ) is the global coordinate of the i+3th grid node of the rth unit cell of the electromagnetic metasurface unit 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 unit of the electromagnetic metasurface unit array is:

[0018]

[0019] In the formula, (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 array, (X feed , Y feed, Z feed ) is the feed source position coordinate.

[0020] Preferably, the direction vector between the feed source and the i-th grid node of the r-th unit of the electromagnetic metasurface unit 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 source output power into the excitation voltage intensity is:

[0023]

[0024] Where γ is the air wave impedance and Pow is the feed output power.

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

[0026]

[0027] Where c is the propagation speed of electromagnetic waves, E feed is the voltage value corresponding to the transmission power of the feed horn, Gfeed is the maximum gain of the feed source, is the amplitude value of the normalized radiation pattern of the feed source at (θ_Nr,i,φ_Nr,i), is the amplitude value of the normalized pattern of the rth electromagnetic metasurface unit at (θ_Sr,i,φ_Sr,i), Dis r,i is the Euclidean distance between the feed source and the i-th grid node of the r-th unit of the electromagnetic metasurface unit array, F 0 is 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 the Poincaré vector is:

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

[0030] Where 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 value and the initial phase of each unit of the electromagnetic metasurface are calculated according to the incident power of each unit, and the relative phase value is determined according to the initial phase, specifically:

[0032] The relative excitation amplitude value of the rth 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 actual phase to be configured for the rth electromagnetic metasurface unit is determined according to the initial phase: delt_Phs(r)=Phs_s r -Phs(r), Phs_s r is the theoretical excitation phase

[0035] Quantize the phase actually required to be configured to obtain the actual quantized phase delt_Phs_nbit(r) required to be configured for the r-th electromagnetic metasurface unit;

[0036] According to the phase actually required to be configured after quantization, the relative phase value is determined: Phs_cell(r)=delt_Phs_nbit(r)+Phs(r).

[0037] Compared with the prior art, the present invention has the following significant advantages:

[0038] ① The present invention has the advantage of high computational efficiency. It uses the principle that the near field in the array is the unit far field to realize the rapid calculation of the excitation field of the metasurface array 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 The present 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 The present invention has strong versatility. The present invention does not rely on specific feed source and electromagnetic metasurface unit forms. The feed source and metasurface unit radiation patterns and relative positions can be conveniently configured according to the actual array antenna, and has strong versatility.

[0041] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the performance calculation method of electronically scanned array antenna based on reflective electromagnetic metasurface.

[0043] Figure 2This is a schematic diagram of an electronically scanned array antenna based on a reflective electromagnetic metasurface, in which 1 is the electromagnetic metasurface unit array and 2 is the feed source.

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

[0045] Figure 4 It is the distribution diagram of electric field intensity on the surface of electromagnetic metasurface unit array.

[0046] Figure 5 It is the antenna pattern calculated by the present invention. DETAILED DESCRIPTION

[0047] The present invention proposes a performance calculation method for an electronically scanned array antenna based on a reflective electromagnetic metasurface, and takes a reflective electromagnetic metasurface electronically scanned array antenna as an example to illustrate the rapid calculation of the antenna performance.

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

[0049] S1: Rectangular meshing of electromagnetic metasurface unit array;

[0050] S2: Taking the feed source as the reference, coordinate transformation is performed on all grid nodes of the electromagnetic metasurface unit array, and the normal vector and grid area at each grid node are calculated;

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

[0052] S4: according to the angle relationship between the direction vector and the normal direction of the feed source and the normal direction of the metasurface unit, the amplitude values ​​of the normalized directional patterns of the feed source and the metasurface unit at the direction vector are obtained respectively;

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

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

[0055] S7: determining the theoretical excitation phase of each unit according to the beam pointing of the electromagnetic metasurface unit array and the spacing between the electromagnetic metasurface units;

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

[0057] S9: Calculate the antenna pattern using fast Fourier transform according to the excitation amplitude and phase at each unit, and determine various performance parameters of the antenna based on the antenna radiation pattern.

[0058] As an embodiment, before calculation, the relevant parameters of the electronic scanning array antenna are determined, including the operating frequency F0, the feed source is a horn antenna, and the normalized directional pattern Maximum gain G feed =16.2dB=42, feed horn feed power Pow=200W, feed position coordinates (X feed , Y feed , Z feed ) is (0,0,0) and the backward angle N feed =35°, the electromagnetic metasurface unit array has 96 rows and 96 columns, the row and column spacing of the metasurface units are both 8mm, the array center is 600mm in front of the feed source and 390mm above, the normalized radiation pattern of the electromagnetic metasurface unit array Metasurface unit phase shift number N_Bit = 1, array antenna beam pointing The schematic diagram of the electronically scanned array antenna is as follows Figure 2 As shown, in the figure, 1 is the electromagnetic metasurface unit array, and 2 is the feed source;

[0059] As an embodiment, a method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface is provided. Figure 2 As shown, including:

[0060] S1: Mesh the electromagnetic metasurface unit array, and divide the area occupied by the rth, r=1,2,3...9216th metasurface units into rectangular meshes to obtain I mesh node coordinates (XLs_r,i, YLs_r,i, ZLs_r,i), r=1,2,3...9216; i=1,2,3...64;

[0061] S2: According to the relative position relationship between the feed source and the electromagnetic metasurface unit array, the coordinates of the electromagnetic metasurface area grid are transformed to obtain the global coordinates (XGs_ r,i , YGs_ r,i ,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 , YGs_r,i+3-YGs_r,i, 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 cross product, the area of ​​the parallelogram formed by the two vectors is the modulus value of the vector after the cross product of the two vectors. The schematic diagram of the grid node is as follows 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 source and the rth, r=1, 2, 3...9216th unit of the electromagnetic metasurface array, the ith, i=1, 2, 3...64th grid node And the direction vector V_r,i=(X feed -XGs_r,i,Y feed -YGs_r,i,Z feed -ZGs_r,i);

[0063] S4: Known feed source normal vector VNL_feed = (0,0,1), according to the tilt angle N feed = 20 to transform the coordinates, and obtain the transformed normal vector VNG_feed = (0, 0.5736, 0.8192), and solve the direction vector V_ r,i Angle with the normal vector VNG_feed Solve the direction vector V_r,i and the node normal vector VNs_ r,i Angle And according to the angular coordinate, the normalized value of the feed source and the electromagnetic metasurface unit array antenna unit pattern is obtained. and It is common knowledge in the art to obtain the angular coordinates of a known direction vector in the local coordinate system of the antenna unit. It is also common knowledge in the art to obtain the normalized value of the antenna unit radiation pattern at that angle by using a table lookup or interpolation method.

[0064] S5: Convert the transmission power of the feed horn into a voltage value Calculate the electric field strength at the i-th grid node of the r-th unit of the electromagnetic metasurface Where c is the propagation speed of electromagnetic waves, and according to the formula Pyt(r,i)=mag(Es (r,i)) 2 / 377*exp(j*angle(E s (r,i))) calculates the Poynting vector Pyt(r,i), (r=1,2,3......9216;i=1,2,3......64) at the node, and calculates the Poynting vectors at all 64 grid nodes in turn. The electromagnetic metasurface unit array is located in the near field relative to the feed source, but the metasurface array unit is in the far field relative to the feed source. Therefore, the electric field strength at the i-th grid node in this step can be calculated using the far field electric field. The electric field strength distribution of the electromagnetic metasurface unit array calculated in this example is as follows Figure 4 As shown;

[0066] S6: Calculate the surface integral of the Poynting vector Pyt(r,i),(r=1,2,3......9216;i=1,2,3......64) at the area occupied by the rth,(r=1,2,3......9216)th electromagnetic metasurface unit to obtain the incident power Ps_cell(r) at the rth,(r=1,2,3......9216)th unit;

[0067] According to the above steps, all cells and grids are calculated to obtain the data of all cells and grids.

[0068] S7: Beam pointing based on electromagnetic metasurface array The theoretical excitation phase Phs_s required for each unit can be obtained by comparing the distance between the electromagnetic metasurface units. r , (r=1,2,3......9216), the calculation method of the excitation phase is common knowledge in the art and will not be repeated here;

[0069] S8: Calculate the relative excitation amplitude value and the initial phase of each unit of the electromagnetic metasurface according to the incident power at each unit, and determine the relative phase value according to the initial phase;

[0070] The relative excitation amplitude value of the rth electromagnetic metasurface unit is: Es_cell(r)=|Ps_cell(r)|^0.5; the initial phase Phs(r)=angle(Ps_cell(r));

[0071] The actual phase to be configured for the rth electromagnetic metasurface unit is determined according to the initial phase: delt_Phs(r)=Phs_s r-Phs(r), in this example, the phase shift number N_Bit of the electromagnetic metasurface unit is 1, that is, the quantized phase is only 0° and 180°, and the actual quantized phase delt_Phs_nbit(r) required to be configured for the r-th electromagnetic metasurface unit is obtained. It is common knowledge in the art to obtain the quantized phase with the known phase shift number N_Bit, which will not be described here;

[0072] According to the phase actually required to be configured after quantization, determine the relative phase value: Phs_cell(r)=delt_Phs_nbit(r)+Phs(r)

[0073] S9: Based on the obtained relative excitation amplitude value Es_cell(r) and phase Phs_cell(r) of the electromagnetic metasurface unit, and the spacing between electromagnetic metasurface units, the radiation pattern is calculated using the fast Fourier transform technology to obtain the radiation pattern of the electronically scanned array antenna. Direction diagram Figure 5 As shown, based on the radiation pattern, the radiation pattern beam width, side lobe, pointing, directivity coefficient and other indicators can be easily calculated. It is common knowledge to calculate these indicators based on the known radiation pattern data and will not be repeated here.

[0074] Furthermore, the normalized radiation pattern of the feed source in the first step of the calculation method shown is Normalized Directivity Pattern in Electromagnetic Metasurface Array It can be obtained by actual measurement or simulation calculation. In this example, the known electromagnetic metasurface unit array unit excitation amplitude and phase value of each unit calculates the radiation pattern using fast Fourier transform technology, which is common knowledge in the field and will not be repeated.

[0075] In order to verify the correctness of the method described in the present invention, a full-wave simulation calculation verification was carried out on the antenna, and the calculation time was 24 hours, 56 minutes and 36 seconds, while the calculation time of the method described in the present invention was 42 seconds.

[0076] The antenna performance calculated by the method of the present invention is as follows:

[0077] Azimuth beamwidth: 1.92°, azimuth sidelobe: -25.3dB, elevation beamwidth: 1.84°, elevation sidelobe: -20.1dB, directivity coefficient: 37.5dB.

[0078] The antenna performance calculated by full-wave simulation is as follows:

[0079] Azimuth beamwidth: 1.96°, azimuth sidelobe: -24.3dB, elevation beamwidth: 1.87°, elevation sidelobe: -19.4dB, directivity coefficient: 36.7dB.

[0080] It can be seen from the above results that the full-wave simulation time is more than 2100 times that of the method described in the present invention, and the antenna performance is well consistent.

Claims

1. A method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface, characterized in that: include: S1: Rectangular meshing of electromagnetic metasurface unit array; S2: Taking the feed source as the reference, coordinate transformation is performed on all grid nodes of the electromagnetic metasurface unit array, and the normal vector and grid area at each grid node are calculated; S3: Calculate the Euclidean distance and direction vector between the feed source and the i-th grid node of the r-th unit of the electromagnetic metasurface unit array, r = 1, 2, ..., R, i = 1, 2, ..., I, R is the total number of units, and I is the grid node of each unit; S4: according to the angle relationship between the direction vector and the normal direction of the feed source and the normal direction of the metasurface unit, the amplitude values ​​of the normalized directional patterns of the feed source and the metasurface unit at the direction vector are obtained respectively; S5: convert the output power of the feed source into the excitation voltage intensity, calculate the electric field intensity value at each grid node of the electromagnetic metasurface unit array and convert it into the Poincaré vector; S6: Calculate the power surface integral of the area occupied by each electromagnetic metasurface unit to obtain the incident power at each unit; S7: determining the theoretical excitation phase of each unit according to the beam pointing of the electromagnetic metasurface unit array and the spacing between the electromagnetic metasurface units; S8: Calculate the relative excitation amplitude value and the initial phase of each unit of the electromagnetic metasurface according to the incident power at each unit, and determine the relative phase value according to the initial phase; S9: Calculate the antenna pattern using fast Fourier transform according to the excitation amplitude and phase at each unit, and determine various performance parameters of the antenna based on the antenna radiation pattern.

2. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 1, characterized in that: The normal vector at the node 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 )×(XGs_ r,i+3 -XGs_ r,i ,YGs_ r,i+3 -YGs_ r,i ,ZGs_ r,i+3 -ZGs_ r,i ) In the formula, (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 array, (XGs_ r,i+1 , YGs_ r,i+1 , ZGs_ r,i+1 ) is the global coordinate of the i+1th grid node of the rth unit cell of the electromagnetic metasurface array, (XGs_ r,i+3 , YGs_ r,i+3 , ZGs_ r,i+3 ) is the global coordinate of the i+3th grid node of the rth unit cell of the electromagnetic metasurface unit array.

3. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 1, characterized in that: The specific formula for calculating the Euclidean distance between the feed source and the i-th grid node of the r-th unit of the electromagnetic metasurface unit array is: In the formula, (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 array, (X feed , Y feed , Z feed ) is the feed source position coordinate.

4. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 3, characterized in that: The direction vector of the i-th grid node of the r-th unit of the electromagnetic metasurface unit array is specifically: V_ r,i (X feed -XGs_ r,i ,Y feed -YGs_ r,i ,Z feed -ZGs_ r,i )。 5. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 1, characterized in that: The specific formula for converting the feed output power into the excitation voltage intensity is: Where γ is the air wave impedance and Pow is the feed output power.

6. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 1, characterized in that: The specific formula for calculating the electric field strength value at any grid node of the electromagnetic metasurface unit array is: Where c is the propagation speed of electromagnetic waves, E feed is the voltage value corresponding to the transmission power of the feed horn, Gfeed is the maximum gain of the feed source, is the amplitude value of the normalized radiation pattern of the feed source at (θ_Nr,i,φ_Nr,i), is the amplitude value of the normalized pattern of the rth electromagnetic metasurface unit at (θ_Sr,i,φ_Sr,i), Dis r,i is the Euclidean distance between the feed source and the i-th grid node of the r-th unit of the electromagnetic metasurface unit array, and F0 is the operating frequency of the electronically scanned array antenna.

7. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 6, characterized in that: The specific formula for converting the electric field strength value at any grid node into the Poincaré vector is: Question(r,i)=mag(E s (r,i)) 2 / γ*exp(j*angle(E s (r,i))) Where angle() represents the complex-valued phase function, mag() represents the complex-valued amplitude function, and γ is the air wave impedance.

8. The method for calculating the performance of an electronically scanned array antenna based on a reflective electromagnetic metasurface according to claim 1, characterized in that: The relative excitation amplitude value and initial phase of each unit of the electromagnetic metasurface are calculated according to the incident power of each unit, and the relative phase value is determined according to the initial phase, specifically: The relative excitation amplitude value of the rth electromagnetic metasurface unit is: Es_cell(r)=|Ps_cell(r)|^0.5, where Ps_cell(r) is the incident power; Initial phase Phs(r)=angle(Ps_cell(r)); The phase that actually needs to be configured for the rth electromagnetic metasurface unit is determined according to the initial phase, specifically: delt_Phs(r)=Phs_s r -Phs(r), Phs_s r is the theoretical excitation phase Quantize the phase actually required to be configured to obtain the actual quantized phase delt_Phs_nbit(r) required to be configured for the r-th electromagnetic metasurface unit; According to the phase actually required to be configured after quantization, the relative phase value is determined: Phs_cell(r)=delt_Phs_nbit(r)+Phs(r).

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