Analysis method of multi-element rotating circularly polarized yagi antenna and yagi antenna

Abstract

The application provides a kind of multi-element rotating circularly polarized yagi antenna analysis method and its five-element structure related to the technical field of antenna, comprising the following steps: S1, establishing antenna model and analyzing magnetic vector potential and scalar potential;S2, electric field double-bit integral equation is established;S3, based on the theory of moment method, the integral equation to be solved is discretized;S4, impedance matrix is solved, and then far-field electric field is obtained;S5, the expression of far-field electric field is expanded, considering the rotating oscillator unit vector, the linear antenna array electric field calculation formula of rotating oscillator is obtained;S6, according to the formula of circularly polarized pattern, the polarization pattern is calculated and compared with simulation;S7, a five-element structure is designed according to the theory and the performance is analyzed.The application calculates the three-dimensional spatial arrangement of the oscillator rotation, and the conclusion obtained effectively explains the reason why the axial rotating antenna array generates circularly polarized wave, and provides better theoretical support for antenna design.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of antenna, in particular, to a method for analyzing a multi-element rotating circularly polarized Yagi antenna and a five-element structure thereof. BACKGROUND

[0002] With the rapid development of wireless communication technology, the circularly polarized antenna is widely concerned because the circularly polarized wave has the advantages of suppressing multipath fading and being not affected by the Faraday rotation effect in the ionosphere. The Yagi-Uda antenna is a classic design that has been widely used in the history of antennas. Its simple structure, small longitudinal size, high gain, low sidelobe level, excellent directivity and other advantages make it last forever. Many domestic and foreign scholars have tried to generate circularly polarized waves on the basis of this antenna to expand its application range. However, many circularly polarized Yagi antennas provide less theoretical explanation because of their additional feed network or complex unit shape design. The present application provides a theoretical calculation method for the circularly polarized Yagi antenna composed of simple rotating dipoles, explains the reason for the generation of circularly polarized waves in principle, and is conducive to guiding the design of the same type of antenna. SUMMARY

[0003] In view of the defects in the prior art, the purpose of the present application is to provide a method for analyzing a multi-element rotating circularly polarized Yagi antenna and a five-element structure thereof.

[0004] According to the method for analyzing a multi-element rotating circularly polarized Yagi antenna provided by the present application, the method comprises the following steps:

[0005] S1, establishing an antenna model and analyzing the magnetic vector potential and the scalar potential;

[0006] S2, establishing an electric field double integral equation;

[0007] S3, discretizing the integral equation to be solved based on the method of moments theory;

[0008] S4, solving the impedance matrix to obtain the far-field electric field;

[0009] S5, expanding the far-field electric field expression, considering the rotating dipole unit vector, and obtaining the linear antenna array electric field calculation formula of the rotating dipole;

[0010] S6, calculating the polarization pattern according to the circularly polarized pattern formula and comparing with the simulation;

[0011] S7, designing a five-element structure according to the theory and analyzing the performance.

[0012] Preferably, in step S1, a model of a linear antenna with an arbitrary length L and a radius a is established, and a is much smaller than L and the wavelength; the field intensity E0 at the feed point is known; the magnetic vector potential A and the scalar potential Φ are calculated according to the formulae: iunder the action of the antenna current i(l), in the far field has a point P(x p ,y p ,z p ), the radiation field strength of the point is E s , according to the boundary condition of the ideal conductor surface has

[0013] The magnetic vector potential and scalar potential of the antenna are:

[0014] Magnetic vector potential:

[0015] Scalar potential:

[0016] Wherein, μ: magnetic permeability, ε: dielectric constant, ω: angular frequency, Field point vector radius, Source point vector radius, l is the length variable of the field point along the axis direction, l' is the length variable of the source point along the axis direction, along the antenna current i(l'), k: wave number, j is a complex imaginary unit.

[0017] Preferably, in step S2, the magnetic vector potential and the scalar potential are substituted into the boundary condition to obtain:

[0018]

[0019] Preferably, in step S3, the oscillator current is discretized, based on the theory of moment method, the impulse function and the unit impulse function are selected as the expansion function matrix and the weighting matrix of the linear combination of the current respectively, and then the integral equation is discretized into the following:

[0020]

[0021] In the formula, m - , n - , m, n, m + , n + Are the starting point, midpoint and end point of the mth segment and nth segment of the antenna differential segment; △l m , △l n Is the differential length of the mth segment and nth segment, I(n) is the differential current of the nth segment, and Ψ(m, n) is the transition function.

[0022] Preferably, in step S4, if there is only one excitation oscillator center feed in the antenna, the electric field is written as:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Among them, v m Let z be the voltage matrix. mn Let R be the impedance matrix between segments m and n; when m = n, the obtained value is the self-impedance, and when m ≠ n, the obtained value is the mutual impedance. m It is the distance between the m-th and n-th segments, according to By obtaining the matrix formed by the current in each differential segment, the expression for the radiated electric field can be derived:

[0030]

[0031]

[0032]

[0033]

[0034] in, Radiated electric field vector : The theta component of the radiated electric field : The φ component of the radiated electric field The basis vectors in the r, θ, φ directions of the spherical coordinate system are the unit vectors in the rectangular coordinate system; the unit vector along the antenna direction in the spherical coordinate system. The unit vector that is always perpendicular to the direction φ Therefore, its projection in the φ direction is always 0; the radiated electric field only contains E. θ Without E Φ Therefore, the antenna array produces linearly polarized radiation.

[0035] Preferably, in step S5, when the oscillator deviates from the z-axis at a certain axial angle α, the unit vector along the tilted antenna direction... Not everywhere a unit vector They are perpendicular, and the planes in which they lie are parallel to each other, meaning that their projections in the φ direction are not zero;

[0036]

[0037] Because the oscillator is tilted at a certain axial angle α relative to the z-axis, the unit vector along the antenna direction changes:

[0038]

[0039] Meanwhile, the basis vectors of the spherical coordinate system are the unit vectors in the rectangular coordinate system. and

[0040]

[0041]

[0042]

[0043] Substituting this into the radiation electric field, the extended expression is:

[0044]

[0045] Preferably, since different antenna elements have corresponding axial angles α, the component of the electric field in the φ direction is no longer always 0, and the linear antenna array with axial rotation angle will no longer purely radiate linearly polarized waves; when each linear antenna selects a suitable axial deflection angle, antenna length, number of linear antenna elements, and mutual spacing, the two perpendicular electric fields E in the far field are made more uniform. Φ and E θ The amplitudes are equal, and because the phases differ by 90 degrees, the circular polarization condition is met, thus achieving different degrees of circular polarization radiation.

[0046] Preferably, in step S6, the calculated E is used θ and E Φ The directional function F is easily obtained. θ and F Φ An elliptic polarized wave can be composed of two linearly polarized waves or the sum of two linearly polarized waves, when F θ and F Φ When the phase difference is an integer multiple of π / 2 and the amplitudes are the same, a circularly polarized wave is formed, and the composition relationship is as follows:

[0047]

[0048]

[0049] Among them, F θ : The pattern function in the θ direction, F Φ : The radiation pattern function in the φ direction, F L : Left-handed circularly polarized pattern, F R Right-handed circular polarization pattern Left-handed circularly polarized pattern unit vector The unit vector of the right-hand circular polarization pattern; the calculated circular polarization pattern is normalized and compared with the simulation results. If they match, the theory is valid.

[0050] Preferably, in step S7, the transverse electric field radiation caused by rotation is such that the Yagi antenna no longer radiates only linearly polarized waves, so that the algorithm not only provides simple design guidance for this type of circularly polarized Yagi antenna, but also explains the reason why a rotating dipole can form a circularly polarized wave in principle.

[0051] The application also provides a five-element structure using the analysis method of the multi-element rotating circularly polarized Yagi antenna.

[0052] Compared with the prior art, the application has the following beneficial effects:

[0053] The mathematical method of the application is different from the calculation method of the conventional common linearly polarized Yagi antenna, and it is extended on the basis of the original two-dimensional arrangement of dipoles to become a three-dimensional space arrangement that can calculate the rotation of the dipoles, wherein the conclusion effectively explains the reason why the axially rotating antenna array produces a circularly polarized wave, and guides the design of a circularly polarized Yagi antenna with better performance, which is consistent with the calculation result, and provides better theoretical support for the design of this type of antenna. BRIEF DESCRIPTION OF DRAWINGS

[0054] Other features, objects and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments, made with reference to the accompanying drawings:

[0055] Figure 1 The specific implementation schematic diagram of the application;

[0056] Figure 2 The theoretical analysis schematic diagram of a unit linear antenna of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0057] Figure 3 The theoretical analysis schematic diagram of two parallel linear antennas of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0058] Figure 4 The theoretical analysis schematic diagram of two linear antennas with an axial rotation angle of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0059] Figure 5 The comparison of the theoretical calculation and simulation of the circularly polarized normalized directional diagram of the xoy plane at 2.41 GHz of the three-element circularly polarized Yagi antenna with axial rotation of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0060] Figure 6 The comparison of the theoretical calculation and simulation of the circularly polarized normalized directional diagram of the zox plane at 2.41 GHz of the three-element circularly polarized Yagi antenna with axial rotation of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0061] Figure 7 A 3D structure schematic diagram of an example five-element structure designed under the guidance of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0062] Figure 8 A side view (zoy) structure schematic diagram of the example five-element structure designed under the guidance of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0063] Figure 9 A side view (zox) structure schematic diagram of the example five-element structure designed under the guidance of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0064] Figure 10 An axial ratio and S11 parameter schematic diagram of the example five-element structure designed under the guidance of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application.

[0065] Figure 11 A circularly polarized directional diagram of the example five-element structure designed under the guidance of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application in the xoy plane at 2.41 GHz.

[0066] Figure 12 A circularly polarized directional diagram of the example five-element structure designed under the guidance of the analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application in the zox plane at 2.41 GHz.

[0067] Figure label:

[0068] 1-active vibrator, 2-first root director, 3-second root director, 4-third root director, 5-feed point, 6-reflection vibrator. DETAILED DESCRIPTION

[0069] The application will be described in detail below with specific embodiments. The following embodiments will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the application. These are within the scope of protection of the application.

[0070] Example 1

[0071] The analysis method of the multi-element rotating circularly polarized Yagi antenna provided by the application comprises the following steps:

[0072] S1, establishing an antenna model and analyzing magnetic vector potential and scalar potential

[0073] Firstly, a model of linear antenna with arbitrary length L and radius a is established as shown in Figure 2 The length L is much larger than the radius a and the wavelength. Under the action of the known field intensity E i at the feed point, the current i(l) along the antenna can be obtained. In the far field, there is a point P(x p ,y p ,z p ) and the radiation field intensity at this point is E s . According to the boundary condition of the ideal conductor surface, we have

[0074] However, for a linear antenna, the magnetic vector potential and the scalar potential are as follows:

[0075] Magnetic vector potential:

[0076] Scalar potential:

[0077] Where μ is the magnetic permeability, ε is the dielectric constant, ω is the angular frequency, The vector radius of the field point, The vector radius of the source point, l is the length variable of the field point along the axis of the antenna, l' is the length variable of the source point along the axis of the antenna, the current along the antenna is i(l'), k is the wave number, and j is the complex imaginary unit.

[0078] S2, Electric field double integral equation

[0079] Substitute the magnetic vector potential and the scalar potential into the boundary condition to obtain:

[0080]

[0081] S3, Discretization of the integral equation to be solved based on the theory of the method of moments

[0082] Discretize the current of the oscillator, select the impulse function and the unit impulse function as the expansion function matrix and the weighting matrix of the linear combination of the current, respectively, and then discretize the integral equation into the following form:

[0083]

[0084] Where m - , n - , m, n, m + , n + are the start point, the midpoint and the end point of the mth segment and the nth segment of the antenna differential segment, respectively. △l m , △l n are the differential lengths of the mth segment and the nth segment, I(n) is the differential current of the nth segment, and Ψ(m, n) is the transition function.

[0085] S4, solve the impedance matrix, and then the far-field electric field

[0086] If there is only one excitation vibrator in the center of the antenna, the electric field can be written as:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] where v m is the voltage matrix, z mn is the impedance matrix between the mth and nth segments. When m = n, the self-impedance is obtained, and when m ≠ n, the mutual impedance is obtained, R m is the distance between the mth and nth segments. According to the matrix of the current of each differential segment can be obtained, and then the expression of the radiation electric field can be obtained:

[0094]

[0095]

[0096]

[0097]

[0098] where, the radiation electric field vector, : the radiation electric field θ component, : the radiation electric field φ component, the unit vectors of the r, θ, and φ directions of the spherical coordinate system in the rectangular coordinate system. The above calculation process can effectively calculate the single dipole antenna or multiple parallel linear antenna arrays distributed on the same plane as shown in Figure 2 and Figure 3 In the spherical coordinate system, the unit vector along the direction of the antenna is always perpendicular to the unit vector in the φ direction Therefore, its projection in the φ direction is always 0. The radiation electric field only contains E θ but not E ΦTherefore, the antenna array generates linear polarization radiation; so the right side of the above formula can be used as a general formula for calculating the radiation electric field of a linearly polarized Yagi antenna placed in two dimensions in parallel.

[0099] S5, expand the far-field electric field expression, considering the unit vector of the rotating oscillator, to obtain the linear antenna array electric field calculation formula of the rotating oscillator

[0100] However, when the oscillator deviates from the z-axis as shown in Figure 4 , the unit vector along the direction of the inclined antenna is not perpendicular to the unit vector at all, but the planes in which they are located are parallel to each other. That is, the projection in the φ direction is not 0; therefore, we expand the original parallel linear antenna radiation electric field calculation formula:

[0101]

[0102] At this time, because the oscillator is inclined to the z-coordinate axis at a certain axial angle α, the unit vector along the direction of the antenna changes:

[0103]

[0104] At the same time, the unit vectors of the basis vectors of the spherical coordinate system in the rectangular coordinate system and

[0105]

[0106]

[0107]

[0108] Substituting it into the radiation electric field, the expanded expression is:

[0109]

[0110] From the above formula, it can be seen that because there is a corresponding axial angle α for different antenna elements, the component of the electric field in the φ direction is no longer always 0, so the linear antenna array with an axial rotation angle will no longer purely radiate linearly polarized waves; it can be reasonably speculated that if each linear antenna selects a suitable axial deviation angle, antenna length, number of linear antenna elements, and mutual distance, the amplitudes of the two perpendicular electric fields E Φ and E θ in the far field can be equal, and because the phase difference is 90 degrees, it satisfies the circular polarization condition, and different degrees of circular polarization radiation can be achieved;

[0111] S6, calculate the polarization pattern according to the circular polarization pattern formula and compare it with the simulation

[0112] Using the calculated E θ and E Φ The directional function F is easily obtained. θ and F Φ Elliptically polarized waves can be composed of two linearly polarized waves or the sum of two linearly polarized waves; when F θ and F Φ When the phase difference is an integer multiple of π / 2 and the amplitudes are the same, a circularly polarized wave is formed, and the composition relationship is as follows:

[0113]

[0114]

[0115] Among them, F θ : The pattern function in the θ direction, F Φ : The radiation pattern function in the φ direction, F L : Left-handed circularly polarized pattern, F R Right-handed circular polarization pattern Left-handed circularly polarized pattern unit vector The unit vector of the right-hand circular polarization pattern. The calculated circular polarization pattern is normalized and compared with the simulation results; if they match, the theory is valid.

[0116] like Figure 5 , Figure 6 As shown, the normalized circular polarization pattern of the three-element circularly polarized Yagi antenna was analyzed and processed using the above theory in MATLAB software and the electromagnetic simulation software HFSS. The results showed good agreement, thus proving that the theory is valid.

[0117] S7. Design a five-element structure based on theory and analyze its performance.

[0118] Based on the above theory, we know that the transverse electric field radiation caused by rotation allows the Yagi antenna to radiate more than just linearly polarized waves. Therefore, this algorithm not only provides simplified design guidance for this type of circularly polarized Yagi antenna but also explains in principle why a rotating element can form a circularly polarized wave. Therefore, following the traditional Yagi antenna design approach, we increase the number of guiding elements to improve circular polarization performance under the guidance of this theory. We designed a five-element structure as an example of this theoretical guidance and analyzed its performance. Figures 7-12 As shown.

[0119] More specifically, starting from the Yagi antenna prototype composed of parallel linear antenna elements, its electromagnetic parameter calculation formulas can be derived using the method of moments and two-position integral equations. Figures 2-3 After analysis, the far-field radiation expression of its electric field can be obtained as follows: However, further introduction of rotating oscillators, such as...Figure 4 As shown more specifically, an axial angle a is formed in the x-axis direction, a unit vector along the vibrator direction is solved, and a radiation expression of a far-field electric field is expanded to obtain

[0120]

[0121] We find that the electric field components not only fall in the theta direction, but also exist in the phi direction, so if appropriate axial angle, antenna length, number of linear antenna elements, and mutual distance are selected, the magnitudes of the two perpendicular electric fields E Φ and E θ are equal, and because the phase difference is 90 degrees, the circular polarization condition is satisfied, and different degrees of circular polarization radiation can be achieved. According to the design experience of traditional linear polarization Yagi antennas, we find that if the number of director vibrators is increased, the electromagnetic waves radiated, reflected, and coupled are directionally propagated, which effectively improves the gain. According to the theory described in this paper, if the number of director vibrators is increased, because each director vibrator is at different distances from the excitation point, different axial angles need to be assigned to each director vibrator to tune the magnitudes of the orthogonal electric fields in the far field until they are the same, and then the circular polarization performance is improved.

[0122] Example 2

[0123] The present application refers to a five-element structure, which uses the analysis method of the multi-element rotating circularly polarized Yagi antenna in embodiment 1.

[0124] As shown in Figures 7-9 , it includes an active vibrator 1, a first director vibrator 2, a second director vibrator 3, a third director vibrator 4, a reflector vibrator 6, and a feed at the center feed point 5 of the active vibrator. The reflector vibrator 6 and the director vibrators 2-4 are located on both sides of the active vibrator 1, the active vibrator 1, the reflector vibrator 6, and the three director vibrators 2-4 form different included angles γ with each other, and the active vibrator 1, the reflector vibrator 6, and the director vibrators 2-4 are located on different planes. More specifically, the reflector vibrator 6 and the active vibrator 1 maintain a certain distance and form a certain axial angle, and are located on one side of the active vibrator, and the planes where the two vibrators are located are parallel to each other. The three director vibrators 2-4 and the active vibrator 1 each maintain a certain distance and form a certain axial angle, and the planes where the vibrators are located are parallel to each other. The center feed point 5 of the active vibrator 1 is normally fed as an antenna radiator; the reflector vibrator 6 reflects the electromagnetic waves radiated by the active vibrator; the director vibrators 2-4 guide the radiated and reflected electromagnetic waves and couple them to directionally propagate, and because of the axial angle, there are appropriate electric field components in the orthogonal direction, which radiate in a circularly polarized manner.

[0125] Specifically, a space rectangular coordinate system o-xyz includes an origin o, an x-axis, a y-axis, and a z-axis.

[0126] The circularly polarized Yagi-Uda antenna is parallel to the yoz plane of the spatial rectangular coordinate system;

[0127] The five oscillators are kept at a certain distance and have a certain axial angle, wherein the size of the oscillators, the axial angle, and the distance are as follows: the length of the active oscillator 1 is 58.2 mm, the length of the reflecting oscillator 6 is 65.00 mm, and the length of the three directing oscillators 2-4 is 52.00 mm;

[0128] The active oscillator 1 and the reflecting oscillator 6 form an angle of 47° in the ZOY plane direction as shown in FIG. 5, and the active oscillator 1 and the directing oscillators 2-4 form angles of 28°, 53°, and 76° in the ZOY plane direction as shown in FIG. 6, respectively; Figure 8 Figure 8 The active oscillator 1 and the reflecting oscillator 6 form an angle of 47° in the ZOY plane direction as shown in FIG. 5, and the active oscillator 1 and the directing oscillators 2-4 form angles of 28°, 53°, and 76° in the ZOY plane direction as shown in FIG. 6, respectively;

[0129] The active oscillator 1 and the reflecting oscillator 6 are kept at a distance of 9.46 mm in the ZOX plane direction as shown in FIG. 7, and the active oscillator 1 and the directing oscillators 2-4 are kept at distances of 9.46 mm, 18.92 mm, and 28.38 mm in the ZOX plane direction as shown in FIG. 8, respectively; Figure 9 Figure 9 The active oscillator 1 and the reflecting oscillator 6 are kept at a distance of 9.46 mm in the ZOX plane direction as shown in FIG. 7, and the active oscillator 1 and the directing oscillators 2-4 are kept at distances of 9.46 mm, 18.92 mm, and 28.38 mm in the ZOX plane direction as shown in FIG. 8, respectively;

[0130] Working principle : By feeding the active oscillator 1, the active oscillator 1 starts to radiate electromagnetic waves to the periphery, and the electromagnetic waves propagate to the reflecting oscillator 6 on one side. Since the reflecting oscillator 6 is a metal conductor, it largely reflects the electromagnetic waves back to the original path. The reflected and radiated electromagnetic waves pass through the directing oscillators 2-4. Due to the different axial angles of the reflecting oscillator and the three directing oscillators, a phase difference is caused. According to the theory described in this article, the three directing oscillators are arranged from near to far from the excitation source, so the angles of the directing oscillators are kept increasing to a certain extent, the amplitudes of the orthogonal electric fields in the far field are adjusted to be equal, thereby forming a circular polarization condition, and a circularly polarized wave is formed after coupling and propagates in a certain direction.

[0131] The gain and polarization effect are better after testing, as shown in FIG. 9, which is a schematic diagram of the axial ratio and S11 parameter curve of the antenna, Figure 10 Figure 11 Figure 12

[0132] ​​​​​In the description of the present application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like refer to the orientation or positional relationship shown in the drawings, and are only intended to facilitate the description of the present application and simplify the description, and are not intended to indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0133] The specific embodiments of the present application are described above. It should be understood that the present application is not limited to the above specific embodiments, and various changes or modifications can be made by those skilled in the art within the scope of the claims, which do not affect the essential content of the present application. The embodiments of the present application and the features in the embodiments can be arbitrarily combined with each other without conflict, provided that they do not conflict.

Claims

1. An analytical method for a multi-element rotating circularly polarized Yagi antenna, characterized in that, Includes the following steps: S1. Establish the antenna model and analyze the magnetic vector potential and scalar potential; S2, Establishment of the electric field two-position integral equation; S3. Discretize the integral equation to be solved based on the method of moments theory; S4. Solve for the impedance matrix, and then obtain the far-field electric field; S5. Extend the far-field electric field expression, considering the unit vector of the rotating dipole, to obtain the electric field calculation formula of the linear antenna array of the rotating dipole. S6. Calculate the polarization pattern according to the formula for circular polarization pattern and compare it with the simulation results; S7. Design a five-element structure and analyze its performance; In step S5, when the oscillator deviates from the z-axis at a certain axial angle α, the unit vector along the tilted antenna direction... Not everywhere a unit vector They are perpendicular, and the planes in which they lie are parallel to each other, meaning that their projections in the φ direction are not zero; μ: permeability, ω: angular frequency, k: wave number, j: complex imaginary unit, Δl n Let be the differential length of the nth segment. Because the oscillator is tilted to the z-axis at a certain axial angle α, the unit vector along the antenna direction changes: Meanwhile, the basis vectors of the spherical coordinate system are the unit vectors in the rectangular coordinate system. and : Substituting this into the radiation electric field, the extended expression is: in, : Field point vector diameter; Because different antenna elements have corresponding axial angles α, the component of the electric field in the φ direction is no longer always zero. Therefore, a linear antenna array with an axial rotation angle will no longer purely radiate linearly polarized waves. When each linear antenna is configured with a suitable axial deflection angle, antenna length, number of linear antenna elements, and spacing, the two perpendicular electric fields E in the far field become... Φ and E θ The amplitudes are equal, and because the phases differ by 90 degrees, the circular polarization condition is met, thus achieving different degrees of circular polarization radiation.

2. The analysis method for a multi-element rotating circularly polarized Yagi antenna according to claim 1, characterized in that, In step S1, a model of a line antenna of arbitrary length L and radius a is established, where a is much smaller than L and wavelength; the field strength E at the known feed point is... i Under the influence of the antenna current i(l), a point P(x) can be obtained in the far field. p ,y p ,z p The radiation field strength at this point is E. s According to the boundary conditions of an ideal conductor surface, we have The magnetic vector potential and scalar potential of the antenna are: Magnetic vector position: Scalar potential: Where μ is the magnetic permeability, ε is the permittivity, and ω is the angular frequency. : Field point vector diameter, : Source point radius vector, l is the length variable of the field point along the line axis, l' is the length variable of the source point along the line axis, along the antenna current i(l'), k: wave number, j is the complex imaginary unit.

3. The analysis method for a multi-element rotating circularly polarized Yagi antenna according to claim 2, characterized in that, In step S2, substituting the magnetic vector potential and scalar potential into the boundary conditions, we obtain:

4. The analysis method for a multi-element rotating circularly polarized Yagi antenna according to claim 3, characterized in that, In step S3, the oscillator current is discretized. Based on the method of moments theory, the impulse function and the unit impulse function are selected as the expansion function matrix and weighting matrix of the linear combination of currents, respectively. Then, the integral equation is discretized as follows: In the formula, m - n - ,m,n,m + n + These represent the start point, midpoint, and end point of the m-th and n-th segments of the antenna differential segment, respectively; Δl m Δl n Let I(n) be the differential length of the m-th and n-th segments, I(n) be the differential current of the n-th segment, and Ψ(m,n) be the transition function.

5. The analysis method for a multi-element rotating circularly polarized Yagi antenna according to claim 4, characterized in that, In step S4, if the antenna has only one excitation element center-fed, the electric field is written as: Among them, v m Let z be the voltage matrix. mn Let R be the impedance matrix between segments m and n; when m = n, the obtained value is the self-impedance, and when m ≠ n, the obtained value is the mutual impedance. m It is the distance between the m-th and n-th segments, according to By obtaining the matrix formed by the current in each differential segment, the expression for the radiated electric field can be derived: in, : Radiation electric field vector : The theta component of the radiated electric field : The v component of the radiated electric field : The unit vectors of the basis vectors in the r, θ, φ directions of the spherical coordinate system in the rectangular coordinate system; the unit vector along the antenna direction in the spherical coordinate system. The unit vector that is always perpendicular to the direction φ Therefore, its projection in the φ direction is always 0; the radiated electric field only contains E. θ Without E Φ Therefore, the antenna array produces linearly polarized radiation.

6. The analysis method for a multi-element rotating circularly polarized Yagi antenna according to claim 1, characterized in that, In step S6, using the calculated E θ and E Φ The directional function F is easily obtained. θ and F Φ An elliptical polarized wave can be composed of two linearly polarized waves or the sum of two linearly polarized waves, when F θ and F Φ When the phase difference is an integer multiple of π / 2 and the amplitudes are the same, a circularly polarized wave is formed, and the composition relationship is as follows: Among them, F θ : The pattern function in the θ direction, F Φ : The pattern function in the φ direction, F L : Left-handed circularly polarized pattern, F R Right-handed circular polarization pattern : Left-handed circularly polarized pattern unit vector : Right-hand circular polarization pattern unit vector; Normalize the calculated circular polarization pattern and compare it with the simulation results. If they match, the theory is valid.

7. The analysis method for a multi-element rotating circularly polarized Yagi antenna according to claim 1, characterized in that, In step S7, the lateral electric field radiation caused by the rotation causes the Yagi antenna to no longer radiate only linearly polarized waves.

8. A five-element structure construction device, characterized in that, The analysis method for the multi-element rotating circularly polarized Yagi antenna as described in any one of claims 1-7 is adopted.

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