A method for predicting the radiation field of deformed flexible antenna based on infinitesimal dipoles

Abstract

The present invention proposes a method for predicting the radiation field of a deformed flexible antenna based on infinitesimal dipoles, and the implementation steps are: initializing parameters; calculating the initial spatial position and posture of each infinitesimal dipole; calculating the dipole moment of each infinitesimal dipole; calculating the change in the posture of the infinitesimal dipole after the flexible antenna is deformed; and obtaining the prediction result of the radiation field of the flexible antenna after deformation. The present invention has an infinitesimal dipole at the center of each finite element unit, and the flexible antenna is equivalent to a plurality of infinitesimal dipoles. The radiation field of the flexible antenna after deformation is calculated by calculating the dipole moment of each infinitesimal dipole, as well as the dyadic Green's function matrix and posture matrix after the flexible antenna is deformed. The method can adapt to the deformation of the flexible antenna in different dimensions, avoid the defect of the prior art that the radiation field is calculated by the surface current of a one-dimensional bending deformation model, and give priority to broadening the scope of application of the prediction while ensuring the prediction accuracy and efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of flexible antennas, and relates to a method for predicting electrical performance of a flexible antenna after deformation, and specifically to a method for predicting radiation field of a flexible antenna after deformation based on an infinitesimal dipole. Background Art

[0002] Flexible antennas are made of flexible materials and can be bent, folded, and deformed while ensuring electrical performance as much as possible. They are widely used in scenarios such as drone belly antennas, flexible electronic devices, and wearable devices. The radiation field of flexible antennas in the initial state is the ideal state of their design, with the best radiation characteristics. However, in actual applications, flexible antennas will deform due to design requirements, and deformation will significantly affect the current distribution and radiation field on their surface.

[0003] Flexible antennas can be deformed in various forms, depending on the actual design requirements. For example, a flexible antenna that conforms to the cylindrical belly of a drone undergoes cylindrical deformation in actual operation, a flexible antenna that conforms to the head of the radome undergoes spherical deformation in actual operation, and a wearable flexible antenna that conforms to the human body undergoes irregular multi-dimensional deformation in actual operation. In existing studies, the prediction of the radiation field of a deformed flexible antenna often assumes that the antenna undergoes one-dimensional deformation, i.e., cylindrical deformation. Therefore, predicting the electrical properties after other complex deformations is crucial to ensuring the stability of the flexible antenna in complex environments and reducing the adverse effects of bending deformation on the electrical properties of the flexible antenna.

[0004] In order to improve the prediction efficiency, for example, in the patent application with the application publication number CN 115374631 A and the name "Rapid prediction method for electrical performance of one-dimensional deformation of flexible antenna", a method for rapid prediction of radiation field of one-dimensional deformation of flexible antenna is proposed. The invention establishes a microstrip antenna primitive model in feko, divides the antenna primitive model into triangular meshes with RWG basis functions, calculates the surface current of microstrip antenna according to the triangular mesh nodes and the corresponding node coordinates, and then calculates the radiation field according to the surface current. The invention solves the technical problems of long time consumption and low efficiency in the existing prediction methods, but the bending deformation model used in the invention to represent the bending state of the microstrip antenna is a one-dimensional model, which can only realize the prediction of the radiation field of the flexible antenna after single-dimensional deformation, limiting the practicality and promotion and application of the method. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a method for predicting the radiation field of a flexible antenna after deformation based on infinitesimal dipoles, aiming to solve the technical problem of narrow application scope in the prior art while ensuring prediction accuracy and efficiency.

[0006] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Initialization parameters:

[0008] The flexible antenna initially distributed in the Cartesian coordinate system includes N finite element units, each finite element unit includes I unit nodes, and the initial spatial position of the i-th unit node in the n-th finite element unit is d ni , after the flexible antenna undergoes arbitrary deformation ni The change in Δd ni ; The infinitesimal dipole placed at the center of the nth finite element is ID n ; The radiation field of the flexible antenna in the initial state is E, the observation point P with the microwave probe installed is located in the far field region with a distance D from the geometric center of the upper surface of the flexible antenna, and the number of observation points of the observation point P is K, where N≥2, I≥3, K≥180, D≥10λ, λ is the working wavelength of the flexible antenna;

[0009] (2) Calculate the initial spatial position and posture of each infinitesimal dipole:

[0010] By the initial spatial position d of each unit node ni Calculate the infinitesimal dipole ID in each finite element n The initial spatial position r n ′ and spatial attitude τ n ;

[0011] (3) Calculate the dipole moment of each infinitesimal dipole:

[0012] The pitch angle direction vector passing through the spatial position of the kth observation point and the azimuth direction vector Calculate the observation point position matrix The spatial position r of the kth observation point k and each infinitesimal dipole ID n The initial spatial position r n 'Calculate the dyadic Green function matrix G of the initial state of the flexible antenna; through the direction vectors of the x-axis, y-axis and z-axis of the Cartesian coordinate system where the flexible antenna is located Calculate the Cartesian coordinate direction matrix I xyz ; By ID n The initial spatial posture τ n Calculate the attitude matrix T of the initial state of the flexible antenna; through the pitch angle component E of the radiation field of the initial state of the flexible antenna at the kth observation point θk and the horizontal angle component Calculate the initial electric field component matrix E 0 ; and through G.I xyz , T, E 0Calculate each infinitesimal dipole ID n The dipole moment M n ;

[0013] (4) Calculate the change in position of the infinitesimal dipole after the flexible antenna is deformed:

[0014] The spatial position change Δd of the i-th unit node in the n-th finite element unit after the flexible antenna is deformed ni , calculate the ID of each infinitesimal dipole after the flexible antenna is deformed n The spatial position r n The change of 'Δr n ′ and spatial attitude τ n The change in Δτ n ;

[0015] (5) Obtain the prediction results of the radiation field after the flexible antenna is deformed:

[0016] Through the spatial position r of each observation point k k , each infinitesimal dipole ID n The initial spatial position r n ′ and the spatial position change Δr n 'Calculate the dyadic Green's function matrix G' after the deformation of the flexible antenna; through each infinitesimal dipole ID n The initial spatial posture τ n And the spatial attitude change Δτ n Calculate the attitude matrix T′ after the deformation of the flexible antenna; and use G′, T′ and each infinitesimal dipole ID n The dipole moment M n Calculate the radiation field E′ of the flexible antenna after deformation.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] The present invention has an infinitesimal dipole at the center of each finite element unit, and the flexible antenna is equivalent to a plurality of infinitesimal dipoles. The radiation field of the flexible antenna after deformation is calculated by calculating the dipole moment of each infinitesimal dipole, as well as the dyadic Green's function matrix and the attitude matrix of the flexible antenna after deformation. The invention can adapt to the deformation of the flexible antenna in different dimensions, and avoids the defect of the prior art of calculating the radiation field through the surface current of a one-dimensional bending deformation model. Under the premise of ensuring the prediction accuracy and efficiency, the application scope of the prediction is preferentially broadened. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flow chart for implementing the present invention.

[0020] Figure 2 It is a schematic diagram of the division of the finite element unit of the flexible antenna adopted in the embodiment of the present invention.

[0021] Figure 3 It is the pitch angle / azimuth direction of the spatial position of the observation point of the present invention. DETAILED DESCRIPTION

[0022] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0023] Reference Figure 1 , the present invention comprises the following steps:

[0024] Step 1) Initialize parameters:

[0025] The flexible antenna initially distributed in the Cartesian coordinate system includes N finite element units, each finite element unit includes I unit nodes, and the initial spatial position of the i-th unit node in the n-th finite element unit is d ni , after the flexible antenna undergoes arbitrary deformation ni The change in Δd ni , arbitrary deformation includes one-dimensional deformation (cylindrical deformation) and non-one-dimensional deformation (spherical deformation, etc.); the infinitesimal dipole placed at the center of the nth finite element unit is ID n ; The radiation field of the flexible antenna in the initial state is E, the observation point P with the microwave probe installed is located in the far field region with a distance D from the geometric center of the upper surface of the flexible antenna, and the number of observation points of the observation point P is K, where N≥2, I≥3, K≥180, D≥10λ, λ is the working wavelength of the flexible antenna;

[0026] Reference Figure 2 , the flexible antenna of this embodiment includes a flexible substrate, an upper ideal electrical conductor and a lower ideal electrical conductor. The geometric center of the upper surface of the flexible substrate with a size of 50mm×80mm×2.87mm is coated with an upper ideal electrical conductor with a size of 31.18mm×46.65mm, and the lower surface is coated with a lower ideal electrical conductor with a size of 50mm×80mm. Each finite element unit includes I unit nodes, which refers to the number of vertices of a triangle, quadrilateral, or a cube with a triangular or quadrilateral cross section that forms a finite element unit. The finite strain shell unit used in this embodiment is a cube with a quadrilateral cross section, containing 8 vertices, that is, I=8, the upper ideal electrical conductor of the flexible antenna includes 6×8 finite strain shell units, the flexible substrate includes 10×12 finite strain shell units, the lower ideal electrical conductor includes 10×12 finite strain shell units, and the flexible antenna includes a total of 288 finite strain shell units, that is, N=288.

[0027] Reference Figure 3In this embodiment, the flexible antenna is distributed in the Cartesian coordinate system, the upper surface of the flexible antenna coincides with the xoy plane, and the origin o of the Cartesian coordinate system is located at the geometric center of the upper surface of the flexible antenna. The kth observation point P is located on a spherical surface at a distance D from the origin o of the coordinate system. The pitch angle θ of the spatial position of P is k Defined as the angle between the line connecting the point and the origin o and the z-axis, the pitch angle direction is the value along the sphere θ k The direction of increase; azimuth It is defined as the angle between the projection of the line connecting the point and the origin o on the xoy plane and the positive direction of the x-axis. Along the sphere Increased direction.

[0028] An infinitesimal dipole is an idealized electromagnetic source with an extremely short length and uniform current distribution. The current distributed on it is quantified by the parameter "dipole moment". The length of the infinitesimal dipole is extremely small relative to the wavelength involved, so it is often regarded as a point source in electromagnetic field analysis, and is superimposed and approximated as a basic unit. The present invention has an infinitesimal dipole at the center of each finite element unit, and the flexible antenna is equivalent to multiple infinitesimal dipoles, so that the influence of the deformation of the flexible antenna on the radiation field is reflected in the spatial position and posture change of the infinitesimal dipole, which has nothing to do with the structure of the antenna itself. Therefore, the defect of the prior art of calculating the radiation field through the surface current of a one-dimensional bending deformation model is avoided, and it can adapt to the deformation of the flexible antenna in different dimensions. Since the present invention uses a large number of observation points (K≥180) of the radiation field of the flexible antenna in the initial state to calculate the dipole moment of the infinitesimal dipole equivalent to it, it is ensured that the prediction accuracy of the method meets the needs of actual engineering. When analyzing different deformation states of a flexible antenna, the present invention calculates the dipole moment of an infinitesimal dipole equivalent to the flexible antenna through the radiation field of the initial state of the flexible antenna. When the antenna undergoes different deformations, it is only necessary to calculate the different spatial positions and postures of the infinitesimal dipole under different deformation states through step 4, and then obtain the radiation field prediction result after the deformation of the flexible antenna through step 5, thereby ensuring that the efficiency of the method meets the needs of actual engineering.

[0029] Step 2) Calculate the initial spatial position and attitude of each infinitesimal dipole:

[0030] By the initial spatial position d of each unit node ni Calculate the infinitesimal dipole ID in each finite element n The initial spatial position r n ′ and spatial attitude τ n ;

[0031] Infinitesimal dipole ID in each finite element n The initial spatial position rn ′ and spatial attitude τ n , the calculation formulas are:

[0032]

[0033] ζ n =d n21 ∧d n31

[0034] d n21 =d n2 -d n1

[0035] d n31 =d n3 -d n1

[0036] Among them, d n21 is the vector formed by connecting the two nodes i=1 and i=2 of the nth finite element, d n31 is a vector formed by connecting the two nodes i=1 and i=3; ∧ is an outer product operation; <·,·> is an inner product operation; To obtain the unit length operation; [,] T is the transpose operation.

[0037] Step 3) Calculate the dipole moment of each infinitesimal dipole:

[0038] The pitch angle direction vector passing through the spatial position of the kth observation point and the azimuth direction vector Calculate the observation point position matrix The spatial position of the kth observation point and refer to Figure 3 ; Through the spatial position r of the kth observation point k and each infinitesimal dipole ID n The initial spatial position r n 'Calculate the dyadic Green function matrix G of the initial state of the flexible antenna; through the direction vectors of the x-axis, y-axis and z-axis of the Cartesian coordinate system where the flexible antenna is located Calculate the Cartesian coordinate direction matrix I xyz ; By ID n The initial spatial posture τ n Calculate the attitude matrix T of the initial state of the flexible antenna; through the pitch angle component E of the radiation field of the initial state of the flexible antenna at the kth observation point θk and the horizontal angle component Calculate the initial electric field component matrix E 0 ; and through G.I xyz, T, E 0 Calculate each infinitesimal dipole ID n The dipole moment M n ;

[0039] Observation point location matrix Dyadic Green function matrix G, Cartesian coordinate direction matrix I xyz , attitude matrix T, initial electric field component matrix E 0 、Each infinitesimal dipole ID n The dipole moment M n , the calculation formulas are:

[0040]

[0041] c=-jωμ

[0042] Among them, c is a constant term; j is an imaginary unit; ω is the angular velocity of the electromagnetic wave; and μ is the magnetic permeability.

[0043] Step 4) Calculate the position change of the infinitesimal dipole after the flexible antenna is deformed:

[0044] The spatial position change Δd of the i-th unit node in the n-th finite element unit after the flexible antenna is deformed ni , calculate the ID of each infinitesimal dipole after the flexible antenna is deformed n The spatial position r n The change of 'Δr n ′ and spatial attitude τ n The change in Δτ n ;

[0045] Each infinitesimal dipole ID after the flexible antenna is deformed n The spatial position r n The change of 'Δr n ′ and spatial attitude τ n The change in Δτ n , the calculation formulas are:

[0046]

[0047] d n ' i =d ni +Δd ni

[0048] Among them, N i represents the finite element shape function, which depends on the type of finite element element; (s, t, h) represents ID n The spatial position in the local coordinate system of the element; t i is the shell element thickness at the i-th element node; d n1and d n2 are the two nodes i=1 and i=2 of the nth finite element; d n ' 21 is the vector formed by connecting the two nodes i=1 and i=2 of the nth finite element unit after the flexible antenna is deformed, d n ' 31 It is a vector formed by connecting the two nodes i=1 and i=3.

[0049] Step 5) Obtain the prediction result of the radiation field after the flexible antenna is deformed:

[0050] Through the spatial position r of each observation point k k , each infinitesimal dipole ID n The initial spatial position r n ′ and the spatial position change Δr n 'Calculate the dyadic Green's function matrix G' after the deformation of the flexible antenna; through each infinitesimal dipole ID n The initial spatial posture τ n And the spatial attitude change Δτ n Calculate the attitude matrix T′ after the deformation of the flexible antenna; and use G′, T′ and each infinitesimal dipole ID n The dipole moment M n Calculate the radiation field E′ of the flexible antenna after deformation.

[0051] The calculation formulas of the dyadic Green's function matrix G', the posture matrix T' after the flexible antenna is deformed, and the radiation field E' after the flexible antenna is deformed are:

[0052]

Claims

1. A method for predicting the radiation field of a flexible antenna after deformation based on infinitesimal dipoles, characterized in that: The steps include: (1) Initialization parameters: The flexible antenna initially distributed in the Cartesian coordinate system includes N finite element units, each finite element unit includes I unit nodes, and the initial spatial position of the i-th unit node in the n-th finite element unit is d ni , after the flexible antenna is deformed ni The change in Δd ni ; The infinitesimal dipole placed at the center of the nth finite element is ID n ; The radiation field of the flexible antenna in the initial state is E, the observation point P with the microwave probe installed is located in the far field region with a distance D from the geometric center of the upper surface of the flexible antenna, and the number of observation points of the observation point P is K, where N≥2, I≥3, K≥180, D≥10λ, λ is the working wavelength of the flexible antenna; (2) Calculate the initial spatial position and posture of each infinitesimal dipole: By the initial spatial position d of each unit node ni Calculate the infinitesimal dipole ID in each finite element n The initial spatial position r n ′ and spatial attitude τ n ; (3) Calculate the dipole moment of each infinitesimal dipole: The pitch angle direction vector passing through the spatial position of the kth observation point and the azimuth direction vector Calculate the observation point position matrix The spatial position r of the kth observation point k and each infinitesimal dipole ID n The initial spatial position r n 'Calculate the dyadic Green function matrix G of the initial state of the flexible antenna; through the direction vectors of the x-axis, y-axis and z-axis of the Cartesian coordinate system where the flexible antenna is located Calculate the Cartesian coordinate direction matrix I xyz ; By ID n The initial spatial posture τ n Calculate the attitude matrix T of the initial state of the flexible antenna; through the pitch angle component E of the radiation field of the initial state of the flexible antenna at the kth observation point θk and the horizontal angle component Calculate the initial electric field component matrix E0; and G.I xyz , T, E0 calculate each infinitesimal dipole ID n The dipole moment M n ; (4) Calculate the change in the position of the infinitesimal dipole after the flexible antenna is deformed: The spatial position change Δd of the i-th unit node in the n-th finite element unit after the flexible antenna is deformed ni , calculate the ID of each infinitesimal dipole after the flexible antenna is deformed n The spatial position r n The change of 'Δr n ′ and spatial attitude τ n The change in Δτ n ; (5) Obtain the radiation field prediction results after the flexible antenna is deformed: Through the spatial position r of each observation point k k , each infinitesimal dipole ID n The initial spatial position r n ′ and spatial position change Δr n 'Calculate the dyadic Green's function matrix G' after the deformation of the flexible antenna; through each infinitesimal dipole ID n The initial spatial posture τ n And the spatial attitude change Δτ n Calculate the attitude matrix T′ after the deformation of the flexible antenna; and use G′, T′ and each infinitesimal dipole ID n The dipole moment M n Calculate the radiation field E′ of the flexible antenna after deformation.

2. The method according to claim 1, characterized in that Each finite element unit described in step (1) includes I unit nodes, which refers to the number of vertices that form a finite element unit triangle, quadrilateral, or a cube with a triangular or quadrilateral cross section.

3. The method according to claim 1, characterized in that: The infinitesimal dipole ID in each finite element described in step (2) n The initial spatial position r n ′ and spatial attitude τ n , the calculation formulas are: g n =d n21 ∧d n31 d n21 =d n2 -d n1 d n31 =d n3 -d n1 Among them, d n21 is the vector formed by connecting the two nodes i=1 and i=2 of the nth finite element, d n31 is a vector formed by connecting the two nodes i=1 and i=3; ∧ is an outer product operation; <·,·> is an inner product operation; To obtain the unit length operation; [·] T is the transpose operation.

4. The method according to claim 3, characterized in that The observation point position matrix described in step (3) Dyadic Green function matrix G, Cartesian coordinate direction matrix I xyz , attitude matrix T, initial electric field component matrix E0, each infinitesimal dipole ID n The dipole moment M n , the calculation formulas are: c=-jωμ Among them, c is a constant term; j is an imaginary unit; ω is the angular velocity of the electromagnetic wave; and μ is the magnetic permeability.

5. The method according to claim 3, characterized in that: After the flexible antenna is deformed as described in step (4), each infinitesimal dipole ID n The spatial position r n The change of 'Δr n ′ and spatial attitude τ n The change in Δτ n , the calculation formulas are: d n ′ i =d ni +Δd ni Among them, N i represents the finite element shape function, which depends on the type of finite element element; (s, t, h) represents ID n The spatial position in the local coordinate system of the element; t i is the shell element thickness at the i-th element node; d n1 and d n2 are the two nodes i=1 and i=2 of the nth finite element; d n ' 21 is the vector formed by connecting the two nodes i=1 and i=2 of the nth finite element unit after the flexible antenna is deformed, d n ' 31 It is a vector formed by connecting the two nodes i=1 and i=3.

6. The method according to claim 5, characterized in that The calculation formulas of the dyadic Green's function matrix G', the posture matrix T' after the flexible antenna is deformed, and the radiation field E' after the flexible antenna is deformed in step (5) are:

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