A method for predicting S parameters of a reflective array antenna by combining a neural network with an equivalent circuit

Abstract

A method for predicting S parameters of a reflective array antenna by a neural network combined with an equivalent circuit, the method comprising the following steps: 1) constructing a model of a planar reflective antenna unit and setting its size parameters; 2) obtaining surface current density distributions along the x-axis and the y-axis at different frequencies; 3) updating the size parameters; 4) repeating steps 2) to 3) several times to obtain surface current density distributions along the x-axis and the y-axis at different frequencies and different size parameters; 5) constructing a BP neural network; constructing a training data set with the surface current density distributions along the x-axis and the y-axis, the corresponding frequencies and size parameters, and training the BP neural network to obtain a prediction model; 6) obtaining size parameters to be predicted and inputting them into the prediction model to obtain an approximate value of the surface current density; and 7) calculating the reflection coefficient S11 of the corresponding antenna by using a Floquet mode equivalent circuit method. The present application can quickly obtain S parameters at the initial design stage, thereby reducing the time required for design.

Description

Technical Field

[0001] This invention belongs to the field of planar reflective antennas, specifically relating to a method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit. Background Technology

[0002] A planar reflector antenna is an antenna with a flat reflector surface composed of hundreds of elements and an illumination-fed antenna. It combines some of the advantages of traditional parabolic antennas and large phased array antennas, achieving efficient high-gain microwave power transmission at a relatively low cost. Obtaining the S-curve of the planar reflector element is crucial for antenna design. Designers typically use full-wave simulation to obtain the S-curve, but relying solely on full-wave simulation and repeatedly changing element parameters and conducting simulation experiments to obtain a satisfactory S-curve requires a significant amount of time.

[0003] Existing technologies offer numerous examples of using machine learning methods to address the time consumption problem in reflected ray analysis. Machine learning methods that directly predict S-parameters involve taking multiple unit parameters as input and their corresponding S-parameters as output, combining this with a large amount of data for prediction. However, the relationship between unit parameters and S-parameters is non-linear. Predicting non-linear relationships requires building a network structure with three or more hidden layers, resulting in complex network design, long training times, and significant randomness in training performance. In particular, efficiency is low when the prediction network needs to be redesigned after unit changes.

[0004] Besides using machine learning to simplify the design of planar reflector antennas, the equivalent circuit method has also been favored by researchers in recent years. This method involves establishing an equivalent circuit that matches the element and solving the equivalent circuit to obtain the element parameters. However, the direct equivalent method requires a lot of simulations to obtain the relationship between the circuit parameters and the element. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, comprising the following steps:

[0006] 1) Construct a planar reflective antenna element model and set the size parameters of the planar reflective antenna element model.

[0007] 2) Obtain the surface current density distribution along the x-axis and y-axis of the planar reflective antenna element model at different frequencies.

[0008] 3) Update the size parameters of the planar reflective antenna element model.

[0009] 4) Repeat steps 2)-3) several times to obtain the surface current density distribution along the x-axis and y-axis of the reflective antenna element model under different frequencies and different size parameters.

[0010] 5) Construct a BP neural network.

[0011] A training dataset is constructed using the surface current density distribution along the x-axis and y-axis of the reflective antenna element model, as well as the corresponding frequency and size parameters. The BP neural network is then trained to obtain a surface current density distribution prediction model based on the BP neural network.

[0012] 6) Obtain the size parameters of the planar reflective antenna element model to be predicted, and input them into the surface current density distribution prediction model based on BP neural network to obtain the approximate value of surface current density.

[0013] 7) Based on the surface current density approximation, the reflection coefficient S11 of the plane reflective antenna element model to be predicted is calculated using the Floquet mode equivalent circuit method.

[0014] Furthermore, the planar reflective antenna element model includes a patch antenna and a substrate.

[0015] The lower surface of the patch antenna is connected to the upper surface of the substrate.

[0016] The patch antenna is polygonal in shape.

[0017] The dimensional parameters of the planar reflective antenna element model include the length of each side of the polygon and the thickness of the substrate.

[0018] Furthermore, before calculating the reflection coefficient S11 of the plane reflective antenna element model to be predicted using the Floquet mode equivalent circuit method, the dielectric constant and frequency of the substrate in the plane reflective antenna element model to be predicted are also obtained.

[0019] Furthermore, in step 7), the steps for calculating the S11 parameters of the corresponding antenna using the Floquet mode equivalent circuit method based on the surface current density approximation are as follows:

[0020] 7.1) Based on Floquet theory, the surface current density of the planar reflective antenna element model patch is expanded into a Fourier series-like form, decomposing the surface current density into scalar surface current densities in the x and y directions.

[0021] 7.2) Derive the equivalent surface impedance of the patch of the planar reflective antenna element model.

[0022] 7.3) Calculate the reflection coefficient S11 of the corresponding antenna based on the equivalent circuit.

[0023] Furthermore, the surface current density is decomposed into scalar surface current densities in the x and y directions, and the calculation formulas are as follows:

[0024]

[0025] In the formula, J(x,y) is the surface current density. denoted as scalar surface current densities in the x and y directions, respectively. m and n are both mode numbers. Let be the mode current after Fourier transform, and a and b be the length and width of the substrate of the planar reflective antenna element model, respectively.

[0026] Wherein, the Floquet wavenumber k of the mode corresponds to the x and y directions. xmn k ymn As shown below:

[0027]

[0028]

[0029] In the formula, k x0 k y0 These are the periodic wave vectors in the x and y directions, respectively. k0 is the periodic wave vector, and θ is the angle from the periodic wave vector to the z-axis. The angle between the periodic wave vector and the x-axis.

[0030] Furthermore, the equivalent surface impedance of the planar reflective antenna element model is as follows:

[0031]

[0032] In the formula, Z eq Let N be the equivalent surface impedance of the planar reflective antenna element model. N is a constant, and m and n are both mode numbers. ω represents the angular frequency. ho For the equivalent inductance of the high-order TE mode, C ho The equivalent capacitance for the higher-order TM mode. The higher-order TE mode has an electric field component perpendicular to the propagation direction of the incident wave. The higher-order TM mode has a magnetic field component perpendicular to the propagation direction of the incident wave.

[0033] Among them, the square of the equivalent transformer turns ratio T mn As shown below:

[0034]

[0035] In the formula, a and b are the length and width of the substrate of the planar reflective antenna element model, respectively. λ and y are the scalar surface current densities in the x and y directions, respectively. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively.

[0036] The sum of input admittance ymn As shown below:

[0037]

[0038] In the formula, The input admittance is the input inductance when looking outward in the L direction. This represents the input admittance when viewed outwards in the R direction. 'i' represents different media, i = 1 or 2. When i = 1, the medium is air in free space. When i = 2, the medium is a substrate. 'h' is the thickness of the substrate.

[0039] Wherein, the z-direction corresponds to the Floquet wavenumber of the mode. As shown below:

[0040]

[0041] In the formula, k0 is the periodic wave vector. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively. is the relative permittivity of the corresponding medium.

[0042] Modal admittance As shown below:

[0043]

[0044] In the formula, ε0 is the vacuum permittivity. μ0 is the vacuum permeability.

[0045] Furthermore, the formula for calculating the reflection coefficient S11 is as follows:

[0046]

[0047] In the formula, This represents the input admittance when the incident wave propagates, viewed from inside the patch antenna of the planar reflective antenna element model in the direction marked L. This represents the input admittance, as seen from the inside of the patch antenna in the planar reflector antenna element model, outwards along the R direction (marked as R). Free space is in the L direction of the patch antenna. The substrate is in the R direction of the patch antenna. TX represents the mode of the incident wave. This represents the square of the equivalent transformer turns ratio in TX mode when the incident wave does not contain a uniform plane wave. For Z eq The inverse operation of Z eq This is the equivalent surface impedance of the planar reflective antenna element model.

[0048] Furthermore, the incident wave mode TX includes higher-order TE mode and higher-order TM mode.

[0049] A smart terminal includes a processor and a memory. The memory stores a computer program, and the processor is communicatively connected to the memory. The processor executes a method for predicting the parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described above, through the computer program.

[0050] A computer-readable storage medium storing program data used to perform a method for predicting parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described above.

[0051] The technical effect of this invention is beyond doubt. This invention proposes to use a neural network to obtain an approximate distribution of the surface current density of the cell, instead of the direct S value, and then substitute the obtained approximate distribution of the surface current density into the ECM for calculation to obtain the corresponding S curve, thus obtaining a new auxiliary antenna design method.

[0052] This invention combines the Floquet equivalent circuit method with the BP neural network method, which can effectively reduce the number of full-wave simulations and reduce the complexity of the neural network (compared to directly predicting S-parameters).

[0053] Compared to existing technologies, which suffer from complex network design, long training times, high randomness in training results, and the need for redesigning the prediction network after unit changes, resulting in low efficiency, this invention uses the unit surface current density as the output. This has a stronger correlation with the unit parameters as input, thus simplifying network construction, improving prediction performance, and minimizing the impact of unit changes on the prediction network, thereby improving design efficiency. The method proposed in this invention enables rapid acquisition of S-parameters in the early stages of design, reducing the time required for design. Attached Figure Description

[0054] Figure 1 This is a flowchart of the calculation process of the present invention;

[0055] Figure 2 This is the equivalent circuit diagram of the Floquet expansion method of the present invention;

[0056] Figure 3 This is the equivalent circuit for the modal admittance of the present invention;

[0057] Figure 4 This is a schematic diagram of the rectangular patch unit of the present invention. Figure 4 a is the front view of the rectangular patch unit. Figure 4 b is a side view of the rectangular patch unit;

[0058] Figure 5 The normalized distribution of surface current density in the x-direction is given when w = 15 mm, t = 6 mm, and h = 1.25 mm.

[0059] Figure 6 To predict the normalized distribution of surface current density in the x-direction when w = 20 mm, t = 4 mm, and h = 1.25 mm;

[0060] Figure 7 The present invention calculates the phase-frequency variation curve of S11 when w = 20 mm, t = 4 mm, and h = 1.25 mm.

[0061] Figure 8 Calculate the S11 phase versus frequency curve for CST when w = 20 mm, t = 4 mm, and h = 1.25 mm;

[0062] Figure 9 To predict the normalized distribution of surface current density in the x-direction when w = 18 mm, t = 6 mm, and h = 1.25 mm;

[0063] Figure 10 The present invention calculates the phase-frequency variation curve of S11 when w = 18 mm, t = 6 mm, and h = 1.25 mm.

[0064] Figure 11 The S11 phase versus frequency curve was calculated for w = 18 mm, t = 6 mm, and h = 1.25 mm. Detailed Implementation

[0065] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0066] Example 1:

[0067] A method for rapidly designing a planar reflector antenna using Floquet equivalent circuitry and neural network technology includes the following steps:

[0068] 1) Construct a planar reflective antenna element model and set the size parameters of the planar reflective antenna element model.

[0069] 2) Obtain the surface current density distribution along the x-axis and y-axis of the planar reflective antenna element model at different frequencies.

[0070] 3) Update the size parameters of the planar reflective antenna element model.

[0071] 4) Repeat steps 2)-3) once or more to obtain the surface current density distribution along the x-axis and y-axis of the reflective antenna element model under different frequencies and different size parameters.

[0072] 5) Construct a BP neural network.

[0073] A training dataset is constructed using the surface current density distribution along the x-axis and y-axis of the reflective antenna element model, as well as the corresponding frequency and size parameters. The BP neural network is then trained to obtain a surface current density distribution prediction model based on the BP neural network.

[0074] 6) Obtain the size parameters of the planar reflective antenna element model to be predicted, and input them into the surface current density distribution prediction model based on BP neural network to obtain the approximate value of surface current density.

[0075] 7) Based on the surface current density approximation, the reflection coefficient S11 of the plane reflective antenna element model to be predicted is calculated using the Floquet mode equivalent circuit method.

[0076] Example 2:

[0077] A method for rapidly designing a planar reflector antenna using Floquet equivalent circuitry and neural network technology includes the following steps:

[0078] 1) Construct a planar reflective antenna element model and set the size parameters of the planar reflective antenna element model.

[0079] 2) Obtain the surface current density distribution along the x-axis and y-axis of the planar reflective antenna element model at different frequencies.

[0080] 3) Update the size parameters of the planar reflective antenna element model.

[0081] 4) Repeat steps 2)-3) M times, where M is a positive integer and M≥2; obtain the surface current density distribution along the x-axis and y-axis of the reflective antenna element model under different frequencies and different size parameters.

[0082] 5) Construct a BP neural network.

[0083] A training dataset is constructed using the surface current density distribution along the x-axis and y-axis of the reflective antenna element model, as well as the corresponding frequency and size parameters. The BP neural network is then trained to obtain a surface current density distribution prediction model based on the BP neural network.

[0084] 6) Obtain the size parameters of the planar reflective antenna element model to be predicted, and input them into the surface current density distribution prediction model based on BP neural network to obtain the approximate value of surface current density.

[0085] 7) Based on the surface current density approximation, the reflection coefficient S11 of the plane reflective antenna element model to be predicted is calculated using the Floquet mode equivalent circuit method.

[0086] The S-parameters are scattering parameters, which reveal almost all the characteristics of the transmission channel. The S-parameters include S11, S12, S21, and S22. S11 is the input reflection coefficient, which is the input return loss.

[0087] Example 3:

[0088] A method for rapidly designing a planar reflective antenna using Floquet equivalent circuit and neural network technology is provided. The main technical contents are described in either Embodiment 1 or 2. Furthermore, the planar reflective antenna unit model includes a patch antenna and a substrate.

[0089] The lower surface of the patch antenna is connected to the upper surface of the substrate.

[0090] The patch antenna is polygonal in shape.

[0091] The dimensional parameters of the planar reflective antenna element model include the length of each side of the polygon and the thickness of the substrate.

[0092] Example 4:

[0093] A method for rapidly designing planar reflective antennas using Floquet equivalent circuit and neural network technology is provided. The main technical contents are described in any one of Examples 1-3. Furthermore, before calculating the reflection coefficient S11 of the planar reflective antenna element model to be predicted using the Floquet modal equivalent circuit method, the dielectric constant and frequency of the substrate in the planar reflective antenna element model to be predicted are also obtained.

[0094] Example 5:

[0095] A method for rapidly designing a planar reflective antenna using Floquet equivalent circuit and neural network technology is provided. The main technical details are described in any one of Examples 1-4. Further, in step 7), the steps for calculating the S11 parameters of the corresponding antenna using the Floquet modal equivalent circuit method based on the approximate surface current density are as follows:

[0096] 7.1) Based on Floquet theory, the surface current density of the planar reflective antenna element model patch is expanded into a Fourier series-like form, decomposing the surface current density into scalar surface current densities in the x and y directions.

[0097] 7.2) Derive the equivalent surface impedance of the patch of the planar reflective antenna element model.

[0098] 7.3) Calculate the reflection coefficient S11 of the corresponding antenna based on the equivalent circuit.

[0099] Example 6:

[0100] A method for rapidly designing a planar reflective antenna using Floquet equivalent circuit and neural network technology is described in Example 5. Further, the surface current density is decomposed into scalar surface current densities in the x and y directions, and the calculation formulas are as follows:

[0101]

[0102] In the formula, J(x,y) is the surface current density. denoted as scalar surface current densities in the x and y directions, respectively. m and n are both mode numbers. Let be the mode current after Fourier transform, and a and b be the length and width of the substrate of the planar reflective antenna element model, respectively.

[0103] Wherein, the Floquet wavenumber k of the mode corresponds to the x and y directions. xmn k ymn As shown below:

[0104]

[0105]

[0106] In the formula, k x0 k y0 These are the periodic wave vectors in the x and y directions, respectively. k0 is the periodic wave vector, and θ is the angle from the periodic wave vector to the z-axis. The angle between the periodic wave vector and the x-axis.

[0107] Example 7:

[0108] A method for rapidly designing a planar reflective antenna using Floquet equivalent circuit and neural network technology is provided. The main technical details are described in any one of Examples 5-6. Furthermore, the equivalent surface impedance of the planar reflective antenna element model is as follows:

[0109]

[0110] In the formula, Z eq Let N be the equivalent surface impedance of the planar reflective antenna element model. N is a constant, and m and n are both mode numbers. ω represents the angular frequency. ho For the equivalent inductance of the high-order TE mode, C ho The equivalent capacitance for the higher-order TM mode. The higher-order TE mode has an electric field component perpendicular to the propagation direction of the incident wave. The higher-order TM mode has a magnetic field component perpendicular to the propagation direction of the incident wave.

[0111] Among them, the square of the equivalent transformer turns ratio T mn As shown below:

[0112]

[0113] In the formula, a and b are the length and width of the substrate of the planar reflective antenna element model, respectively. λ and y are the scalar surface current densities in the x and y directions, respectively. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively.

[0114] The sum of input admittance y mn As shown below:

[0115]

[0116] In the formula, The input admittance is the input inductance when looking outward in the L direction. This represents the input admittance when viewed outwards in the R direction. 'i' represents different media, i = 1 or 2. When i = 1, the medium is air in free space. When i = 2, the medium is a substrate. 'h' is the thickness of the substrate.

[0117] Wherein, the z-direction corresponds to the Floquet wavenumber of the mode. As shown below:

[0118]

[0119] In the formula, k0 is the periodic wave vector. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively. is the relative permittivity of the corresponding medium.

[0120] Modal admittance As shown below:

[0121]

[0122] In the formula, ε0 is the vacuum permittivity. μ0 is the vacuum permeability.

[0123] Example 8:

[0124] A method for rapidly designing a planar reflective antenna using Floquet equivalent circuit and neural network technology is provided. The main technical details are described in any one of Examples 5-7. Furthermore, the formula for calculating the reflection coefficient S11 is as follows:

[0125]

[0126] In the formula, This represents the input admittance when the incident wave propagates, viewed from inside the patch antenna of the planar reflective antenna element model in the direction marked L. This represents the input admittance, as seen from the inside of the patch antenna in the planar reflector antenna element model, outwards along the R direction (marked as R). Free space is in the L direction of the patch antenna. The substrate is in the R direction of the patch antenna. TX represents the mode of the incident wave. This represents the square of the equivalent transformer turns ratio in TX mode when the incident wave does not contain a uniform plane wave. For Z eq The inverse operation of Z eq This is the equivalent surface impedance of the planar reflective antenna element model.

[0127] Example 9:

[0128] A method for rapidly designing a planar reflector antenna using Floquet equivalent circuit and neural network technology is described in Example 8. Further, the incident wave mode TX includes a higher-order TE mode and a higher-order TM mode.

[0129] Example 10:

[0130] A smart terminal includes a processor and a memory. The memory stores a computer program, and the processor is communicatively connected to the memory. The processor executes, through the computer program, a method for rapidly designing a planar reflector antenna using Floquet equivalent circuit and neural network technology as described in any one of Embodiments 1-9.

[0131] Example 11:

[0132] A computer-readable storage medium storing program data, the program data being used to execute a method for rapidly designing a planar reflector antenna using Floquet equivalent circuitry and neural network technology as described in any one of Examples 1-9.

[0133] Example 12:

[0134] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit includes the following steps:

[0135] 1) Construct a planar reflective antenna element model and set the size parameters of the planar reflective antenna element model.

[0136] 2) Obtain the surface current density distribution along the x-axis and y-axis of the planar reflective antenna element model at different frequencies.

[0137] 3) Construct a BP neural network.

[0138] A training dataset is constructed using the surface current density distribution along the x-axis and y-axis of the reflective antenna element model, as well as the corresponding frequency and size parameters. The BP neural network is then trained to obtain a surface current density distribution prediction model based on the BP neural network.

[0139] 4) Obtain the size parameters of the planar reflective antenna element model to be predicted, and input them into the surface current density distribution prediction model based on BP neural network to obtain the approximate value of surface current density.

[0140] 5) Based on the surface current density approximation, the reflection coefficient S11 of the plane reflective antenna element model to be predicted is calculated using the Floquet mode equivalent circuit method.

[0141] The S-parameters are scattering parameters, which reveal almost all the characteristics of the transmission channel. The S-parameters include S11, S12, S21, and S22. S11 is the input reflection coefficient, which is the input return loss.

[0142] Example 13:

[0143] A method for predicting S-parameters of a reflective array antenna by combining a neural network with an equivalent circuit is described in Example 12. Further, the planar reflective antenna unit model includes a patch antenna and a substrate.

[0144] The lower surface of the patch antenna is connected to the upper surface of the substrate.

[0145] The patch antenna is polygonal in shape.

[0146] The dimensional parameters of the planar reflective antenna element model include the length of each side of the polygon and the thickness of the substrate.

[0147] Example 14:

[0148] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in either Example 12 or 13. Further, before calculating the reflection coefficient S11 of the planar reflective antenna element model to be predicted using the Floquet mode equivalent circuit method, the dielectric constant and frequency of the substrate in the planar reflective antenna element model to be predicted are also obtained.

[0149] Example 15:

[0150] A method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, the main technical contents of which are described in any one of Examples 12-14. Further, in step 7), the steps for calculating the corresponding antenna's S11 parameters using the Floquet mode equivalent circuit method based on the approximate surface current density are as follows:

[0151] 7.1) Based on Floquet theory, the surface current density of the planar reflective antenna element model patch is expanded into a Fourier series-like form, decomposing the surface current density into scalar surface current densities in the x and y directions.

[0152] 7.2) Derive the equivalent surface impedance of the patch of the planar reflective antenna element model.

[0153] 7.3) Calculate the reflection coefficient S11 of the corresponding antenna based on the equivalent circuit.

[0154] Example 16:

[0155] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in Example 15. Further, the calculation formula for decomposing the surface current density into scalar surface current densities in the x and y directions is shown below:

[0156]

[0157] In the formula, J(x,y) is the surface current density. denoted as scalar surface current densities in the x and y directions, respectively. m and n are both mode numbers. Let be the mode current after Fourier transform, and a and b be the length and width of the substrate of the planar reflective antenna element model, respectively.

[0158] Wherein, the Floquet wavenumber k of the mode corresponds to the x and y directions. xmn k ymn As shown below:

[0159]

[0160]

[0161] In the formula, k x0 k y0 These are the periodic wave vectors in the x and y directions, respectively. k0 is the periodic wave vector, and θ is the angle from the periodic wave vector to the z-axis. The angle between the periodic wave vector and the x-axis.

[0162] Example 17:

[0163] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in either Embodiment 15 or 16. Further, the equivalent surface impedance of the planar reflective antenna element model is as follows:

[0164]

[0165] In the formula, Zeq Let N be the equivalent surface impedance of the planar reflective antenna element model. N is a constant, and m and n are both mode numbers. ω represents the angular frequency. ho For the equivalent inductance of the high-order TE mode, C ho The equivalent capacitance for the higher-order TM mode. The higher-order TE mode has an electric field component perpendicular to the propagation direction of the incident wave. The higher-order TM mode has a magnetic field component perpendicular to the propagation direction of the incident wave.

[0166] Among them, the square of the equivalent transformer turns ratio T mn As shown below:

[0167]

[0168] In the formula, a and b are the length and width of the substrate of the planar reflective antenna element model, respectively. λ and y are the scalar surface current densities in the x and y directions, respectively. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively.

[0169] The sum of input admittance y mn As shown below:

[0170]

[0171] In the formula, The input admittance is the input inductance when looking outward in the L direction. This represents the input admittance when viewed outwards in the R direction. 'i' represents different media, i = 1 or 2. When i = 1, the medium is air in free space. When i = 2, the medium is a substrate. 'h' is the thickness of the substrate.

[0172] Wherein, the z-direction corresponds to the Floquet wavenumber of the mode. As shown below:

[0173]

[0174] In the formula, k0 is the periodic wave vector. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively. is the relative permittivity of the corresponding medium.

[0175] Modal admittance As shown below:

[0176]

[0177] In the formula, ε0 is the vacuum permittivity. μ0 is the vacuum permeability.

[0178] Example 18:

[0179] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is provided. The main technical details are described in any one of Examples 15-17. Furthermore, the formula for calculating the reflection coefficient S11 is as follows:

[0180]

[0181] In the formula, This represents the input admittance when the incident wave propagates, viewed from inside the patch antenna of the planar reflective antenna element model in the direction marked L. This represents the input admittance, as seen from the inside of the patch antenna in the planar reflector antenna element model, outwards along the R direction (marked as R). Free space is in the L direction of the patch antenna. The substrate is in the R direction of the patch antenna. TX represents the mode of the incident wave. This represents the square of the equivalent transformer turns ratio in TX mode when the incident wave does not contain a uniform plane wave. For Z eq The inverse operation of Z eq This is the equivalent surface impedance of the planar reflective antenna element model.

[0182] Example 19:

[0183] A method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in Example 18. Further, the incident wave mode TX includes a higher-order TE mode and a higher-order TM mode.

[0184] Example 20:

[0185] A smart terminal includes a processor and a memory. The memory stores a computer program. The processor is communicatively connected to the memory. The processor executes a method for predicting the parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described in any one of Examples 12-19, through the computer program.

[0186] Example 21:

[0187] A computer-readable storage medium storing program data used to perform a method for predicting parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described in any one of embodiments 12-19.

[0188] Example 22:

[0189] See Figures 1 to 11 A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit includes the following steps:

[0190] 1) Construct a planar reflective antenna element model and set the size parameters of the planar reflective antenna element model.

[0191] 2) At different frequencies, the surface current density distribution along the x-axis and y-axis of the planar reflective antenna element model is obtained using the H-field and Surface current sampling unit in CST, providing data for the subsequent training of the BP neural network.

[0192] 3) Update the size parameters of the planar reflective antenna element model.

[0193] 4) Repeat steps 2)-3) once or more to obtain the surface current density distribution along the x-axis and y-axis of the reflective antenna element model under different frequencies and different size parameters.

[0194] 5) Construct a BP neural network using the NeuralNet Fitting tool in MATLAB.

[0195] A training dataset is constructed using the surface current density distribution along the x-axis and y-axis of the reflective antenna element model, as well as the corresponding frequency and size parameters. The BP neural network is then trained to obtain a surface current density distribution prediction model based on the BP neural network.

[0196] 6) Obtain the size parameters of the planar reflective antenna element model to be predicted, and input them into the surface current density distribution prediction model based on BP neural network to obtain the approximate value of surface current density.

[0197] 7) Based on the surface current density approximation, the reflection coefficient S11 of the plane reflective antenna element model to be predicted is calculated using the Floquet mode equivalent circuit method.

[0198] The S-parameters are scattering parameters, which reveal almost all the characteristics of the transmission channel. The S-parameters include S11, S12, S21, and S22. S11 is the input reflection coefficient, which is the input return loss.

[0199] Example 23:

[0200] A method for predicting S-parameters of a reflective array antenna by combining a neural network with an equivalent circuit is described in Example 22. Further, the planar reflective antenna element model includes a patch antenna and a substrate.

[0201] The lower surface of the patch antenna is connected to the upper surface of the substrate.

[0202] The patch antenna is polygonal in shape. The patch shape is a simple overall pattern distributed along the x and y directions, and different shapes correspond to different element parameters.

[0203] The dimensional parameters of the planar reflective antenna element model include the length of each side of the polygon and the thickness of the substrate.

[0204] Example 24:

[0205] A method for predicting S-parameters of a reflective array antenna by combining a neural network with an equivalent circuit is described in Embodiment 23. Further, the patch antenna is rectangular in shape.

[0206] Example 25:

[0207] A method for predicting S-parameters of a reflective array antenna by combining a neural network with an equivalent circuit is described in Embodiment 23. Further, the patch antenna is I-shaped.

[0208] Example 26:

[0209] A method for predicting the S-parameters of a reflective array antenna by combining a neural network with an equivalent circuit is described in Example 23. Further, the patch antenna is cross-shaped.

[0210] Example 27:

[0211] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in any one of embodiments 24-26. Furthermore, in order to improve data processing efficiency, when there are two or more data points of the same length, only one of these data points of the same length is retained.

[0212] Example 28:

[0213] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in any one of Examples 22-27. Further, before calculating the reflection coefficient S11 of the planar reflective antenna element model to be predicted using the Floquet mode equivalent circuit method, the dielectric constant and frequency of the substrate in the planar reflective antenna element model to be predicted are also obtained.

[0214] Example 29:

[0215] A method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, the main technical contents of which are described in any one of Examples 22-28. Further, in step 7), the steps for calculating the corresponding antenna's S11 parameters using the Floquet mode equivalent circuit method based on the approximate surface current density are as follows:

[0216] 7.1) Due to the periodic structure, the surface current density will also exhibit periodicity according to Floquet theory. Utilizing this property, a Fourier-like series expansion is performed on the surface current density of the planar reflector antenna element model patch, decomposing the surface current density into scalar surface current densities in the x and y directions.

[0217] 7.2) Derive the equivalent surface impedance of the patch of the planar reflective antenna element model.

[0218] 7.3) Calculate the reflection coefficient S11 of the corresponding antenna based on the equivalent circuit.

[0219] Using this method, as long as the approximate distribution of the current density on the surface of the reflecting unit is known, the S11 parameters at the corresponding frequency can be derived.

[0220] Example 30:

[0221] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in Example 29. Further, it is generally assumed that the surface current density J(x,y,w) of the patch can be decomposed into: J(x,y,w)=A(w)J S (x,y)

[0222] Where A(w) represents the frequency-related coefficient, J S (x,y) represents a function that depends only on the spatial contour. This assumption allows the ECA method to have a good accuracy rate before the second resonance.

[0223] The formulas for calculating the surface current density, which is decomposed into scalar surface current densities in the x and y directions, are as follows:

[0224]

[0225] In the formula, J(x,y) is the surface current density. denoted as scalar surface current densities in the x and y directions, respectively. m and n are both mode numbers. Let be the mode current after Fourier transform, and a and b be the length and width of the substrate of the planar reflective antenna element model, respectively.

[0226] Wherein, the Floquet wavenumber k of the mode corresponds to the x and y directions. xmn k ymn As shown below:

[0227]

[0228]

[0229] In the formula, k x0 k y0These are the periodic wave vectors in the x and y directions, respectively. k0 is the periodic wave vector, and θ is the angle from the periodic wave vector to the z-axis. The angle between the periodic wave vector and the x-axis.

[0230] Example 31:

[0231] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is provided. The main technical details are described in any one of Examples 29-30. Furthermore, the equivalent surface impedance of the planar reflective antenna element model is as follows:

[0232]

[0233] In the formula, Z eq Let N be the equivalent surface impedance of the planar reflector antenna element model. N is a constant, generally N≤6 (TE / TM(0,0) indicates that the incident TE / TM uniform plane wave is not included). m and n are the mode numbers. ω represents the angular frequency, ω=2πf. L ho For the equivalent inductance of the high-order TE mode, C ho The equivalent capacitance for the higher-order TM mode. The higher-order TE mode has an electric field component perpendicular to the propagation direction of the incident wave. The higher-order TM mode has a magnetic field component perpendicular to the propagation direction of the incident wave.

[0234] Among them, the square of the equivalent transformer turns ratio Of course, 1 / ab will be canceled out when calculating the scattering parameters at the end, which has no effect on the result. The square of the equivalent transformer turns ratio T mn As shown below:

[0235]

[0236] In the formula, a and b are the length and width of the substrate of the planar reflective antenna element model, respectively. λ and y are the scalar surface current densities in the x and y directions, respectively. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively.

[0237] The sum of input admittance y mn As shown below:

[0238]

[0239] In the formula, The input admittance is the input inductance when looking outward in the L direction. The input admittance is the input looking outward in the R direction. i represents different media, i = 1 or 2. When i = 1, the medium is air in free space. When i = 2, the medium is a substrate. h is the thickness of the substrate. In this embodiment, a composite material of the Rogers RT5800 with ε = 2.2 is used for simulation. Of course, the substrate can be changed, and this only affects the calculation of the equivalent circuit.

[0240] Wherein, the z-direction corresponds to the Floquet wavenumber of the mode. As shown below:

[0241]

[0242] In the formula, k0 is the periodic wave vector. xmn k ymn These are the Floquet wavenumbers for the modes in the x and y directions, respectively. is the relative permittivity of the corresponding medium.

[0243] Modal admittance As shown below:

[0244]

[0245] In the formula, ε0 is the vacuum permittivity. μ0 is the vacuum permeability.

[0246] Example 32:

[0247] A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is provided. The main technical details are described in any one of Examples 29-31. Furthermore, the formula for calculating the reflection coefficient S11 is as follows:

[0248]

[0249] In the formula, This represents the input admittance when the incident wave propagates, viewed from inside the patch antenna of the planar reflective antenna element model in the direction marked L. This represents the input admittance, as seen from the inside of the patch antenna in the planar reflector antenna element model, outwards along the R direction (marked as R). Free space is in the L direction of the patch antenna. The substrate is in the R direction of the patch antenna. TX represents the mode of the incident wave. This represents the square of the equivalent transformer turns ratio in TX mode when the incident wave does not contain a uniform plane wave. For Z eq The inverse operation of Z eq This is the equivalent surface impedance of the planar reflective antenna element model.

[0250] like Figure 3The L direction represents looking from the inside to the left, because the left side is free space, so YL = Y1. The R direction represents looking from the inside to the right, and the right side is an electric wall that is equivalent to a short circuit, so YR = Y2*-jcot(k2h), which is the appearance presented by equation (6).

[0251] Example 33:

[0252] A method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit is described in Example 32. Further, the incident wave mode TX includes a higher-order TE mode and a higher-order TM mode.

[0253] Example 34:

[0254] A smart terminal includes a processor and a memory. The memory stores a computer program, and the processor is communicatively connected to the memory. The processor executes a method for predicting the parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described in any one of Examples 22-33, through the computer program.

[0255] Example 35:

[0256] A computer-readable storage medium storing program data used to perform a method for predicting parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described in any one of embodiments 22-33.

[0257] Example 36:

[0258] See Figures 1 to 11 A method for predicting the S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, the main contents of which include:

[0259] It is typically assumed that the surface current density J(x,y,w) of the patch can be decomposed into:

[0260] J(x,y,w)=A(w)J S (x,y) (1)

[0261] Where A(w) represents the frequency-related coefficient, J S (x,y) represents a function that depends only on the spatial contour. This assumption allows the ECA method to have a good accuracy rate before the second resonance.

[0262] J, as a two-dimensional vector, can be decomposed into x and y directions, i.e.

[0263]

[0264] Due to the periodic structure, the surface current density will also exhibit periodicity according to Floquet theory. Utilizing this property, a Fourier-like series expansion is performed. x J y The scalar surface current density in the x and y directions can be decomposed as:

[0265]

[0266] Where m and n are the number of modes. Let k be the modal current after Fourier transform. xmn k ymn This represents the Floquet wavenumber for the corresponding mode.

[0267]

[0268]

[0269] a and b are the length and width of the unit. and

[0270] Based on the derivation, the equivalent surface impedance can be expressed as:

[0271]

[0272] L ho The equivalent inductance for the higher-order TE mode is C. ho The equivalent capacitance of higher-order TM modes is generally N≤6 (TE / TM(0,0) indicates that the incident TE / TM uniform plane wave is not included). mn This is the square of the equivalent transformer turns ratio. Of course, when calculating the scattering parameters at the end, 1 / ab will be canceled out, which will not affect the result.

[0273]

[0274] Combining the above formula:

[0275]

[0276] y mn The sum of the input admittances looking outwards in the R and L directions (the reflection array is equivalent to a short circuit when viewed from the R direction):

[0277]

[0278]

[0279] For modal admittance, i = 1, 2, representing different media.

[0280]

[0281] Based on the equivalent circuit diagram, the reflection coefficient S11 can be calculated:

[0282]

[0283] TX stands for TE / TM, which is the mode of the incident wave.

[0284] Using this method, the S-parameters at the corresponding frequency can be derived once the approximate distribution of the surface current density of the reflecting unit is determined. Combining the Floquet equivalent circuit method with the BP neural network method can effectively reduce the number of full-wave simulations and the complexity of the neural network (compared to directly predicting the S-parameters). Figure 1 The diagram shows a flowchart of obtaining the S11 phase with the help of a neural network.

[0285] Here, rectangular patch units are used as the basic units for verification, such as... Figure 4 As shown, w(i) and t(i) (i = 1, 2, 3..., where w and t are input quantities that vary) are the length and width of the patch, a and b are the length and width of the cell, and h is the thickness of the substrate.

[0286] First, construct the unit model (w1, t1) in CST for simulation to derive the corresponding surface current density distribution. Repeat this step to obtain the original training data. Then, input the training data into the designed BP neural network for training and validation to obtain the prediction model, which predicts the change in surface current density distribution as the unit parameters change.

[0287] like Figure 5 The figure shows the normalized distribution of surface current density in the x-direction derived from CST Surface Current when w = 15 mm, t = 6 mm, and h = 1.25 mm (ignoring the variation with frequency, 6.5 GHz is selected as the reference frequency here).

[0288] Multiple sets of data were used as training data to obtain the model for prediction. The normalized distribution of surface current density in the x-direction when w = 20 mm, t = 4 mm, and h = 1.25 mm is shown in the figure below. Figure 6 As shown:

[0289] The predicted surface current density distribution is then used in the Floquet equivalent circuit algorithm to calculate the corresponding antenna's S11 parameters, such as... Figure 7 The figure shows the curve of S11 phase versus frequency calculated based on the predicted value:

[0290] The S11 phase diagram obtained from CST full-wave simulation is as follows: Figure 8 As shown:

[0291] The normalized distribution of surface current density in the x-direction is predicted to be as follows when w = 18 mm, t = 6 mm, and h = 1.25 mm. Figure 9 As shown:

[0292] Substituting the equivalent circuit algorithm of Floquet, the S11 phase curve is obtained, as follows: Figure 10 As shown:

[0293] CST calculates the phase curve of element S11 with w=18mm, t=6mm, and h=1.25mm, as follows: Figure 11 As shown:

[0294] Through the above simulation experiments, the S11 phase curves calculated by the neural network combined with the equivalent circuit algorithm and CST are largely the same. That is, the results obtained by the predicted values ​​are in good agreement with the full-wave simulation results, indicating that the method of combining neural networks with the Floquet equivalent circuit method can help in the calculation of S11 parameters in the early stage of the design of the planar reflector unit.

Claims

1. A method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, characterized in that, Includes the following steps: 1) Construct a planar reflective antenna element model and set the size parameters of the planar reflective antenna element model; 2) Obtain the surface current density distribution along the x-axis and y-axis of the planar reflective antenna element model at different frequencies; 3) Update the dimensional parameters of the planar reflector antenna element model; 4) Repeat steps 2)-3) several times to obtain the surface current density distribution along the x-axis and y-axis of the reflective antenna element model under different frequencies and different size parameters. 5) Construct a BP neural network; A training dataset is constructed using the surface current density distribution along the x-axis and y-axis of the reflective antenna element model, as well as the corresponding frequency and size parameters. The BP neural network is then trained to obtain a surface current density distribution prediction model based on the BP neural network. 6) Obtain the size parameters of the planar reflective antenna element model to be predicted, and input them into the surface current density distribution prediction model based on BP neural network to obtain an approximate value of surface current density; 7) Based on the surface current density approximation, the reflection coefficient S11 of the plane reflective antenna element model to be predicted is calculated using the Floquet mode equivalent circuit method; The formula for calculating the reflection coefficient S11 is as follows: （1） In the formula, This represents the input admittance when the incident wave propagates from inside the patch antenna of the planar reflective antenna element model and looks outward in the direction marked L. The input admittance, denoted as R, represents the input admittance of the patch antenna in the planar reflective antenna element model as the incident wave propagates, viewed from the inside to the outside. Free space is in the L direction of the patch antenna; the substrate is in the R direction of the patch antenna; TX represents the mode of the incident wave. This represents the square of the equivalent transformer turns ratio in TX mode when the incident wave does not contain a uniform plane wave. for The inverse operation, This is the equivalent surface impedance of the planar reflective antenna element model.

2. The method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, as described in claim 1, is characterized in that... The planar reflective antenna unit model includes a patch antenna and a substrate; The lower surface of the patch antenna is connected to the upper surface of the substrate; The patch antenna is polygonal in shape; The dimensional parameters of the planar reflective antenna element model include the length of each side of the polygon and the thickness of the substrate.

3. The method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, as described in claim 1, is characterized in that... Before calculating the reflection coefficient S11 of the plane reflective antenna element model to be predicted using the Floquet mode equivalent circuit method, the dielectric constant and frequency of the substrate in the plane reflective antenna element model to be predicted are also obtained.

4. The method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit according to claim 1, characterized in that, In step 7), the steps for calculating the S11 parameters of the corresponding antenna using the Floquet mode equivalent circuit method based on the surface current density approximation are as follows: 7.1) Based on Floquet theory, the surface current density of the planar reflective antenna element model patch is expanded into a Fourier series-like form, decomposing the surface current density into scalar surface current densities in the x and y directions. 7.2) Derive the equivalent surface impedance of the patch in the planar reflective antenna element model; 7.3) Calculate the reflection coefficient S11 of the corresponding antenna based on the equivalent circuit.

5. The method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, as described in claim 4, is characterized in that... The formulas for calculating the surface current density, which is decomposed into scalar surface current densities in the x and y directions, are as follows: （2） In the formula, Surface current density; , denoted as scalar surface current densities in the x and y directions, respectively; m and n are both modal numbers. Let be the mode current after Fourier transform, and a and b be the length and width of the substrate of the planar reflective antenna element model, respectively. Wherein, the Floquet wavenumbers of the modes correspond to the x and y directions. , As shown below: （3） （4） In the formula, , These are the periodic wave vectors in the x and y directions, respectively. , , For periodic wave vectors, The angle from the periodic wave vector to the z-axis. The angle between the periodic wave vector and the x-axis.

6. The method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit, as described in claim 4, is characterized in that... The equivalent surface impedance of the planar reflective antenna element model is shown below: （5） In the formula, Let N be the equivalent surface impedance of the planar reflective antenna element model; N is a constant, and m and n are both mode numbers; Indicates angular frequency; For the equivalent inductance of the high-order TE mode, The equivalent capacitance of the higher-order TM mode; the higher-order TE mode is in which the electric field component is perpendicular to the propagation direction of the incident wave; the higher-order TM mode is in which the magnetic field component is perpendicular to the propagation direction of the incident wave. Among them, the square of the equivalent transformer turns ratio As shown below: （6） In the formula, a and b are the length and width of the substrate of the planar reflective antenna element model, respectively; , denoted as scalar surface current densities in the x and y directions, respectively; , These are the Floquet wavenumbers for the modes in the x and y directions, respectively. Sum of input admittance As shown below: （7） In the formula, The input admittance is the input looking outward in the L direction; The input admittance is given by the R direction when looking outwards; i represents different media, i=1, 2; when i=1, it means the medium is air in free space; when i=2, it means the medium is a substrate; h is the thickness of the substrate; Wherein, the z-direction corresponds to the Floquet wavenumber of the mode. As shown below: （8） In the formula, It is a periodic wave vector; , These are the Floquet wavenumbers for the modes in the x and y directions, respectively. is the relative permittivity of the corresponding medium; Modal admittance As shown below: （9） In the formula, It is the vacuum dielectric constant; is the vacuum permeability.

7. The method for predicting S-parameters of a reflective array antenna using a neural network combined with an equivalent circuit according to claim 1, characterized in that, The incident wave mode TX includes higher-order TE mode and higher-order TM mode.

8. A smart terminal, characterized in that, The smart terminal includes a processor and a memory. The memory stores a computer program. The processor is communicatively connected to the memory. The processor executes, through the computer program, a method for predicting the parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program data that is used to perform a method for predicting parameters of a reflective array antenna S11 using a neural network combined with an equivalent circuit, as described in any one of claims 1-7.

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