CN105161860B - Deformation planar array electrical performance compensation method based on mechanical-electric coupling and Fourier transformation - Google Patents
Deformation planar array electrical performance compensation method based on mechanical-electric coupling and Fourier transformation Download PDFInfo
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Abstract
The invention discloses a kind of deformation planar array electrical performance compensation method based on mechanical-electric coupling and Fourier transformation, including：1) parameter of i.e. M linear array antenna of planar array is determined；2) finite element analysis obtains the malformation amount of planar array under vibration environment；3) electrical property after i-th of linear array antenna deformation is calculated using linear array antenna electromechanical Coupling Model；4) electrical property is decomposed into preferable linear array electrical property and linear array electrical property changes item；5) the exciting current amplitude of antenna spatial phase errors and the adjustment amount of phase are compensated to 4) carrying out Fast Fourier Transform (FFT) respectively；6) judge whether to have calculated the adjustment amount of all exciting current amplitudes and phase；7) adjustment amount of exciting current amplitude and phase is entered into electromechanical Coupling Model, calculates deformation planar array electrical property；8) judge whether the deformation planar array electrical property after compensation meets index request.The present invention can ensure there is good electrical properties to the planar array of military service.
Description
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to an electrical property compensation method of a deformed area array antenna based on electromechanical coupling and Fourier transform.
Background
Antennas are widely used in radio systems for communication, broadcasting, television, radar, navigation, etc., and are devices that radiate and receive radio waves, which are indispensable in radio communication. Compared with a single antenna, the area array antenna has the advantages of high radiation intensity, high reliability, multiple functions, strong detection and tracking capabilities and good stealth performance, and is widely applied to the fields of various radar systems, navigation systems, electronic countermeasures and the like.
The antenna is a core component of a radar system, the performance of which depends to a large extent on the electrical performance of the antenna. The antenna structure is a carrier for realizing the electrical performance of the antenna, and the amplitude and the phase distribution of an electromagnetic field of the antenna in space are directly influenced by the change of a displacement field of the antenna. When the antenna is in service, the structural performance of the antenna is changed by the load of the working environment such as dead weight, rain and snow, solar irradiation, vibration, impact and the like, so that structural errors are generated on the antenna, random errors are generated on the structure of the antenna in the processing and assembling processes, and position errors are generated on the antenna radiation unit, and finally, the gain of the antenna is reduced, the side lobe is raised, and the pointing deviation is caused. The reduction in the electrical performance of the antenna directly results in a reduction in the performance of the radar system, which is even impossible to achieve. Therefore, in order to reduce the influence of the structural error on the electrical performance of the area array antenna and ensure that the radar system can normally work, the electrical performance of the antenna must be compensated.
The active compensation method is a main mode of antenna electrical performance compensation, and the active compensation is carried out on the antenna electrical performance, namely, the change of the antenna electrical performance is compensated by adjusting the excitation current of the antenna radiation unit, so that the key for accurately obtaining the compensation quantity of the excitation current of the deformed antenna and the electrical performance of the deformed antenna in the active compensation method is whether the compensation method is effective or not. Researchers at home and abroad have performed many works on compensating the electrical property of a deformed antenna by using an active compensation method, for example, in Svensson B, Lanne M, windard J, et al, element position error compensation is performed on a unit position error of the antenna by adjusting an excitation current of the antenna, however, the unit position error is assumed to obey gaussian distribution and is not an antenna structure error under an actual working condition, and therefore, the excitation current compensation amount obtained by the method is not to compensate the electrical property change caused by the actual antenna structure error. In addition, in the Tsao j.adaptive phase compensation for distorted phase array minimum minor dimension and performance international symposium. measuring Technologies for the 90's. digest. ieee,1990: 1466-phase 1469 operation, compensation of the electrical performance of the deformed phased array antenna can be achieved only by adjusting the phase of the excitation current of the antenna element, however, adjusting the phase of the excitation current can only compensate the beam pointing direction of the antenna, the secondary lobe level of the antenna cannot be effectively compensated, and the amplitude of the excitation current is directly related to the antenna gain, the secondary lobe level and the like, so that the phase and amplitude of the excitation current should be adjusted at the same time to meet the electrical performance of the antenna.
Therefore, how to compensate the electrical performance of the deformed area array antenna under the actual working condition by adjusting the amplitude and the phase of the exciting current in order to ensure the normal operation of the area array antenna under the service environment has become a technical problem to be solved in the field at present.
Disclosure of Invention
Based on the above problems, in order to compensate for the decrease of the electrical performance of the area array antenna in the actual working environment, the invention uses the array antenna electric coupling model to obtain the variation of the electrical performance of the antenna under the load of the working environment, and adjusts the amplitude and the phase of the excitation current of all the area array antenna radiation units by combining the FFT method to compensate the electrical performance of the deformed array antenna, thereby ensuring that the area array antenna can normally work under the service environment. The method can effectively solve the problem of electrical property deterioration of the area array antenna caused by working load, ensure the normal work of the area array antenna in a service environment, and can quickly realize compensation of the electrical property of the deformed area array antenna and provide theoretical guidance for compensating the electrical property of the antenna in real time.
The technical scheme for realizing the invention is that the structural parameters and the electromagnetic parameters of M rows and N columns of area array antennas, namely M linear array antennas, are determined; establishing a finite element model of the area array antenna structure according to the area array antenna structure parameters, and analyzing to obtain the deformation of the area array antenna structure; extracting the ith (i is more than or equal to 1 and less than or equal to M) linear array antenna, and calculating the electrical property of the ith linear array antenna after deformation in an airborne environment by using a linear array antenna electric coupling model; decomposing the electrical property of the ith deformed linear array antenna into the electrical property change items of the ideal linear array and the electrical property change items of the linear array caused by the structural deformation, and respectively carrying out Fast Fourier Transform (FFT) on the electrical property change items of the ideal linear array and the electrical property change items of the linear array to obtain the amplitude and the phase adjustment quantity of the excitation current for compensating the spatial phase error of the antenna; judging whether the adjustment quantity of the excitation current amplitude and the phase of all the linear array antennas is calculated, if so, obtaining the adjustment quantity of the excitation current amplitude and the phase of the area array antenna unit, and if not, extracting the next linear array antenna for calculation; bringing the obtained adjustment quantity of the amplitude and the phase of the exciting current of the area array antenna unit into an area array antenna electric coupling model, and calculating the electric performance of the deformed area array antenna; judging whether the electrical property of the compensated deformed array antenna meets the index requirement, if so, indicating that the excitation current amplitude and the phase adjustment quantity with the optimal electrical property of the compensated deformed array antenna are obtained, so that the area array antenna achieves the optimal working performance in the service environment; otherwise, modifying the structural parameters of the area array antenna, and repeating the steps until the requirements are met.
The invention is realized by the following technical scheme:
the electrical property compensation method of the deformed area array antenna based on electromechanical coupling and Fourier transform comprises the following processes:
(1) determining geometric model parameters and material attributes of the area array antenna and simultaneously determining working parameters of the area array antenna according to structural parameters of the area array antenna with M rows and N columns, namely M linear array antennas;
(2) establishing a finite element model of the area array antenna structure according to the geometric model parameters and the material attributes of the area array antenna; determining constraint conditions of an antenna finite element model according to the installation form of the area array antenna; applying airborne random vibration power spectrum to the finite element model of the area array antenna, calculating the structural deformation of the area array antenna, and extracting the position offset of the central node of the radiation unit of the area array antenna in the x, y and z directions;
(3) extracting the position offset of the ith (i is more than or equal to 1 and less than or equal to M) linear array antenna and the central node of the radiation unit of the ith linear array antenna from the M linear array antennas, and calculating the electrical property of the ith linear array antenna after deformation in an airborne environment by using a linear array antenna electric coupling model;
(4) decomposing the electrical property of the ith deformed linear array antenna into the electrical property change items of an ideal linear array and the electrical property change items of the linear array caused by structural deformation, wherein the electrical property change items of the linear array are composed of excitation current of the electrical property of the ideal linear array and antenna space phase errors caused by structural deformation;
(5) fast Fourier Transform (FFT) is respectively carried out on the ideal linear array electrical property and the linear array electrical property change items to obtain the amplitude and the phase adjustment quantity of the excitation current for compensating the antenna space phase error;
(6) judging whether the adjustment quantity of the excitation current amplitude and the phase of all the M linear array antennas is calculated, if so, obtaining the adjustment quantity of the excitation current amplitude and the phase of the M linear array antennas, otherwise, extracting the next linear array antenna, and repeating the steps (3) to (6);
(7) bringing the obtained M linear array antennas, namely the adjustment quantity of the excitation current amplitude and the phase of all the area array antennas, into an area array antenna electromechanical coupling model, and calculating the electrical property of the deformed area array antenna;
(8) judging whether the electrical property of the compensated deformed array antenna meets the index requirement, if so, indicating that the excitation current amplitude and the phase adjustment quantity with the optimal electrical property of the compensated deformed array antenna are obtained, so that the area array antenna achieves the optimal working performance in the service environment; otherwise, modifying the structural parameters of the area array antenna, and repeating the steps (1) to (7) until the requirements are met.
In the step (1), the geometric model parameters of the area array antenna comprise the position distribution, the number, the size and the unit interval of the radiation units of the area array antenna, and the size parameters of the T/R assembly, the cold plate and the reinforcing ribs; the material properties of the area array antenna comprise density rho, elastic modulus E and Poisson ratio mu; the electromagnetic working parameters of the area array antenna comprise the central working frequency f of the area array antenna, the amplitude and the phase of the exciting current.
In the step (2), calculating the structural deformation of the area array antenna, establishing a finite element model of the area array antenna structure according to the structural parameters and the material properties of the area array antenna, determining the constraint conditions of the finite element model of the area array antenna according to the actual installation of the area array antenna, loading an airborne random vibration power spectrum, and calculating the position offset of the central node of the area array antenna radiation unit in the x, y and z directions.
In the step (3), the electric performance of the ith deformed linear array antenna calculated by using the linear array antenna electric coupling model is realized by the following formula:
wherein d is the spacing between the radiating elements, IinIs the exciting current of ideal linear array electrical property of the nth radiating element in the ith linear array antenna,wherein A isinIn order to excite the amplitude of the current,is the excitation current phase, k is the wave constant, j is the imaginary unit; k is 2 pi/lambda, lambda is the working wavelength of the planar antenna, theta is the pitch angle of the linear antenna, and delta yinAnd Δ zinPosition errors in y-direction and z-direction, Δ y, generated by the nth radiation element in the ith linear arrayi0And Δ zi0The position errors of the 0 th radiation unit, namely the initial radiation unit in the ith linear array in the y direction and the z direction respectively.
In the step (4), the electrical property of the ith deformed linear array antenna is decomposed into the electrical property change items of the ideal linear array and the linear array electrical property change items caused by the structural deformation, and the process is carried out according to the following steps:
when the structural deformation of the linear array antenna radiation unit is not more than 0.06 lambda/pi cos (lambda/2 d), according to the exponential function propertyDecomposing an array factor directional diagram of the deformed linear array antenna:
wherein,the electrical property change items caused by the deformation of the i linear array antenna structures are represented; f. ofia(theta) represents the ideal electrical performance of the ith linear array antenna.
In order to carry out subsequent fast Fourier transform on the ideal electrical property and electrical property change items of the linear array, u is used for expressing sin theta, and f is used for expressing sin thetaia(theta) and fiae(θ) is expressed as:
in the step (5), the ideal linear array electrical property and the electrical property variation item of the ith deformed linear array antenna are respectively subjected to FFT (fast Fourier transform) conversion according to the following steps:
(5a) excitation current I for ideal linear array electrical property of ith deformed linear array antennainPerforming FFT:
wherein, αimM represents the serial number of the current signal after fast Fourier transform;
in the main beam direction of ideal linear array antennaIn the above, the excitation current I of the antenna electrical property and the ideal linear array electrical property is establishedinFourier transform relation between the first and the second, ideal linear array electrical property f of the ith deformed linear array antennaia(u) performing an FFT:
wherein u ═ sin θ;representing the spatial phase generated by the linear array antenna radiation unit in an ideal state;indicating the main beam pointing direction of the linear array antenna;
(5b) disturbance term f for linear array antenna electrical propertyiae(theta), establishing a Fourier series expression, adopting FFT to βim＝FFT[kIin(Δyin-Δyi0)]，γim＝FFT[kIin(Δzin-Δzi0)]Since the discrete Fourier transform satisfies the linear superposition, fiaeThe Fourier series form of (θ) can be expressed as:
the influence of the structural deformation on the direction u is converted into the main beam pointing direction u of the linear array antennamThe adjustment amount of the excitation current is calculated in the direction of the main beam of the line array antenna, and the formula F is shown in the specificationiae(u) becomes:
in this case, the antenna array factor directional diagram f with structural error existsiasThe Fourier series form of (theta) is
(5c) Fourier series F of factor directional diagram of deformed linear array antennaias(u) performing FFT inverse transformation to obtain an array factor directional diagram of the deformed linear array antenna, wherein the array factor directional diagram is as follows:
wherein,the excitation current which indicates that the ith deformed linear array antenna contains the structural error is usually adjusted to compensate the influence of the structural deformation on the electrical performance of the linear array;
(5d) main beam pointing at linear array antennaAnd calculating the adjustment quantity of the amplitude and the phase of the excitation current. In main beam direction umAbove, an excitation current I containing a structural errorinsComprises the following steps:
the current and the exciting current I of the ideal linear array electrical propertyinThe relationship is as follows:
wherein,representing an amplitude disturbance coefficient caused by a structural error in the excitation current of the deformed area array antenna;representing phase disturbance caused by structural errors in exciting current of the deformed area array antenna, wherein Im represents an imaginary part of an imaginary number;
(5e) exciting current amplitude disturbance coefficient delta A caused by linear array antenna structure deformationnAnd phase perturbationAnd correcting to compensate the influence of the structural deformation on the electrical performance of the linear array antenna. Amplitude coefficient adjustment quantity delta A of induced excitation currentinc＝-ΔAinAmount of phase adjustment of excitation currentThe adjusted excitation current becomes:
using adjusted excitation current IincReplacing a deformed linear array antenna array factor fiasExcitation current I of ideal linear array electrical properties in (theta)inAnd the electrical property of the compensated deformed linear array antenna is as follows:
in the formula,an amplitude coefficient adjustment amount representing the excitation current;indicating the amount of adjustment of the phase of the excitation current.
In the step (6), whether the adjustment quantities of the excitation current amplitude and the phase have been calculated for all the linear array antennas is judged, if yes, the adjustment quantities of the excitation current amplitude and the phase of the area array unit are obtained, if not, the next linear array antenna is extracted, and the steps (3) to (6) are repeated.
In the step (7), the obtained M linear array antennas, that is, the adjustment amounts of the excitation current amplitude and the phase of all the area array antennas are brought into an area array antenna electromechanical coupling model, where the model is:
in the step (7), the electrical property of the compensated deformed linear array antenna is calculated to obtain the electrical property parameters of the antenna, such as antenna gain, side lobe level, beam pointing and the like. Judging whether the electrical property of the compensated deformed array antenna meets the index requirement, if so, indicating that the excitation current amplitude and the phase adjustment quantity with the optimal electrical property of the compensated deformed array antenna are obtained, so that the area array antenna achieves the optimal working performance in the service environment; otherwise, modifying the structural parameters of the area array antenna, including enhancing the structural rigidity of the antenna, modifying the constraint position of the area array antenna, and the like, and repeating the steps (1) to (8) until the requirements are met.
In the step (8), modifying the structural parameters of the area array antenna, including enhancing the structural rigidity of the area array antenna and modifying the constraint position of the area array antenna.
The antenna electric coupling model and the Fourier transform are based on the antenna electric coupling model, the influence of environmental load on the electric performance of the serving area array antenna can be compensated, the electric performance of the antenna is improved, the structural complexity and the structural weight of the antenna are not increased, the problem of the electric performance deterioration of the array antenna caused by the serving environmental load can be solved, when the area array antenna is in a serving process, the electric performance of the deformed area array antenna can be compensated, the normal work of the antenna is ensured, and the structural complexity and the structural weight of the antenna are not increased. Meanwhile, the compensated deformed area array antenna has strong anti-interference capability to a working environment, and when the environmental load changes in a small range, the deformed area array antenna can be ensured to have good electrical property without additionally adjusting the area array antenna. Therefore, the method provides important technical guarantee for improving the electrical performance of the antenna, and is particularly suitable for large-scale area array antennas.
Compared with the prior art, the invention has the following characteristics:
1. according to the invention, the structural deformation of the area array antenna under the actual airborne environment is analyzed, and the adjustment quantity of the excitation current amplitude and the phase of the area array antenna is solved by combining fast Fourier transform based on the coupling relation between the structural deformation and the electrical property, so that the compensation of the electrical property of the deformed area array antenna is realized under the condition of not increasing the structural complexity and the structural weight of the antenna, and the influence of the environmental load of the antenna on the electrical property under the actual working condition is effectively reduced;
2. the compensated deformed area array antenna has strong anti-interference capability to a working environment, and when the environmental load changes in a small range, the deformed area array antenna can be ensured to have good electrical property without additionally adjusting the area array antenna. Therefore, the method provided by the invention can be used for compensating the electrical property of the area array antenna in the service process, and provides an important technical guarantee for improving the electrical property of the antenna.
Drawings
FIG. 1 is an electrical performance compensation method of a deformed area array antenna based on electromechanical coupling and Fourier transform;
FIG. 2 is a schematic diagram of an arrangement of radiating elements of an area array antenna;
FIG. 3 is a diagram of the spatial geometry of viewpoint P relative to coordinate system xyz;
FIG. 4 is a schematic diagram of a geometric model of an area array antenna;
FIG. 5 is a schematic diagram of a finite element model of an area array antenna in ANSYS software;
FIG. 6 is an on-board random vibration acceleration power spectrum;
FIG. 7 is a random vibration deformation cloud diagram of an area array antenna;
FIG. 8 is a graph comparing far field patterns of an ideal and deformed rear array antenna;
fig. 9 is a comparison graph of the far field patterns of the ideal and compensated area array antenna.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the invention relates to a deformed area array antenna electrical property compensation method based on electromechanical coupling and fourier transform, which comprises the following specific steps:
step 1, determining geometric model parameters, material attributes and electromagnetic working parameters of an area array antenna
1.1, determining a geometric model of the area array antenna structure according to the structural parameters of the array surface shape, the caliber size, the type, the number and the arrangement of radiation units in the array and an antenna frame of the area array antenna;
1.2. and determining the material properties of a cold plate, a T/R assembly, a reinforcing rib and a radiating unit in the area array antenna system, wherein the material properties comprise density rho, elastic modulus E and Poisson ratio mu.
1.3. And determining the electromagnetic working parameters of the area array antenna, wherein the electromagnetic working parameters comprise the central working frequency f of the antenna and the amplitude and the phase of the excitation current.
Step 2, obtaining the array surface deformation amount through finite element analysis
2.1 constructing a structural finite element model in ANSYS according to geometric model parameters and material properties of the area array antenna, wherein the unit types of the cold plate, the T/R assembly and the reinforcing rib are SOLID units SOLID92, and the unit type of the radiation unit is a surface unit SHELL 63. The cold plate and the reinforcing rib, the cold plate and the T/R assembly, the T/R assembly and the radiation unit, and the radiation unit and the reinforcing rib are connected with each other, and no relative displacement exists.
2.2 according to the installation mode of the antenna, applying constraint to the area array antenna, applying airborne random vibration acceleration power spectrum to the finite element model of the area array antenna structure, calculating to obtain the random vibration deformation of the array surface, extracting the position offset of the radiation unit caused by the vibration deformation, and the nth radiation unitThe amount of positional displacement in the x, y, z directions is (Δ x)0,Δy0,Δz0)······(ΔxN-1,ΔyN-1,ΔzN-1) Wherein (Δ x)n,Δyn,Δzn) N ∈ (0, N-1), N is a natural number between 0 and N-1, and represents the number of N radiating elements in the area array antenna.
Step 3, calculating the electrical property of the linear array antenna by using the electric coupling model
Extracting the ith linear array antenna from the M linear array antennas, using a linear array antenna electric coupling model, and calculating the electrical property of the ith deformed linear array antenna as follows:
wherein d is the spacing between the radiating elements, IinIs the exciting current of ideal linear array electrical property of the nth radiating element in the ith linear array antenna,wherein A isinIn order to excite the amplitude of the current,k is a wave constant, k is 2 pi/lambda, lambda is the working wavelength of the planar array antenna, theta is the pitch angle of the linear array antenna, and delta y is the phase of the exciting currentinAnd Δ zinPosition errors in y-direction and z-direction, Δ y, generated by the nth radiation element in the ith linear arrayi0And Δ zi0The position errors of the 0 th radiation unit, namely the initial radiation unit in the ith linear array in the y direction and the z direction respectively.
Step 4, decomposing the electrical property of the ith deformed linear array antenna
When the structural deformation of the linear array antenna radiation unit is not more than 0.06 lambda/pi cos (lambda/2 d), decomposing an array factor directional diagram of the ith deformed linear array antenna:
wherein,the electrical property change items caused by the deformation of the i linear array antenna structures are represented; f. ofia(theta) represents the ideal electrical performance of the ith linear array antenna.
Step 5, respectively carrying out FFT (fast Fourier transform) on the ideal electrical property and the electrical property change items of the ith linear array
(5a) Excitation current I in ideal linear array electrical property of ith deformed linear array antennainPerforming FFT:
wherein, αimM represents the serial number of the current signal after fast Fourier transform for the Fourier series of the excitation current.
In the main beam direction of ideal linear array antennaEstablishing Fourier transform relation between the electrical property of the antenna and the exciting current of the electrical property of the ideal linear array, and establishing the electrical property f of the ideal linear array of the ith deformed linear array antennaia(u) performing an FFT:
wherein u ═ sin θ;representing the spatial phase generated by the linear array antenna radiation unit in an ideal state;indicating the main beam pointing direction of the linear array antenna;
(5b) disturbance term f for linear array antenna electrical propertyiae(theta), establishing a Fourier series expression, adopting FFT to βim＝FFT[kIin(Δyin-Δyi0)]，γim＝FFT[kIin(Δzin-Δzi0)]Since the discrete Fourier transform satisfies the linear superposition, fiaeThe Fourier series form of (θ) can be expressed as:
the influence of the structural deformation on the direction u is converted into the main beam pointing direction u of the linear array antennamThe adjustment amount of the excitation current is calculated in the direction of the main beam of the line array antenna, and the formula F is shown in the specificationiae(u) becomes:
in this case, the antenna array factor directional diagram f with structural error existsiasThe Fourier series form of (θ) is:
(5c) fourier series F of factor directional diagram of deformed linear array antennaias(u) performing FFT inverse transformation to obtain an array factor directional diagram of the deformed linear array antenna, wherein the array factor directional diagram is as follows:
wherein,the excitation current representing the structure error contained in the ith deformed linear array antenna can be adjusted to compensate the influence of the structure deformation on the linear array electrical performance.
(5d) Main beam pointing at linear array antennaAnd calculating the adjustment quantity of the amplitude and the phase of the excitation current. In main beam direction umAbove, an excitation current I containing a structural errorinsComprises the following steps:
the current and the exciting current I of the ideal linear array electrical propertyinThe relationship is as follows:
wherein,
representing an amplitude disturbance coefficient caused by a structural error in the excitation current of the deformed area array antenna;representing phase disturbance caused by structural errors in exciting current of the deformed area array antenna, wherein Im represents an imaginary part of an imaginary number;
(5e) exciting current amplitude disturbance coefficient delta A caused by linear array antenna structure deformationnAnd phase perturbationAnd correcting to compensate the influence of the structural deformation on the electrical performance of the linear array antenna. Introduction ofAmplitude coefficient adjustment amount Δ a of excitation currentinc＝-ΔAinAmount of phase adjustment of excitation currentThe adjusted excitation current becomes:
using adjusted excitation current IincReplacing a deformed linear array antenna array factor fiasExcitation current I of ideal linear array electrical property in (theta)inAnd the electrical property of the compensated deformed linear array antenna is as follows:
in the formula,an amplitude coefficient adjustment amount representing the excitation current;indicating the amount of adjustment of the phase of the excitation current.
Step 6, judging whether all linear array antennas are compensated
And (4) judging whether the adjustment quantity of the excitation current amplitude and the phase is calculated for all the linear array antennas, if so, obtaining the adjustment quantity of the excitation current amplitude and the phase of the area array unit, if not, extracting the next linear array antenna, and repeating the steps (3) to (6).
Step 7, calculating the electromechanical coupling of the area array antenna
The obtained adjustment quantities of the excitation current amplitude and the phase of the M linear array antenna units, namely all the area array antenna units are brought into an area array antenna electromechanical coupling model, and the model is as follows:
step 8, judging whether the compensated deformed area array antenna meets the design requirements
And calculating the electrical property of the compensated deformed linear array antenna to obtain antenna electrical property parameters including antenna gain, side lobe level, beam pointing and the like. Judging whether the electrical property of the compensated deformed array antenna meets the index requirement, if so, indicating that the excitation current amplitude and the phase adjustment quantity with the optimal electrical property of the compensated deformed array antenna are obtained, so that the area array antenna achieves the optimal working performance in the service environment; otherwise, modifying the structural parameters of the area array antenna, including enhancing the structural rigidity of the antenna, modifying the constraint position of the area array antenna, and the like, and repeating the steps (1) to (8) until the requirements are met.
The advantages of the invention can be further illustrated by simulation experiments:
determining area array antenna parameters
In this example, taking a rectangular area array antenna as an example, as shown in fig. 2, the central operating frequency is f equal to 10Ghz (wavelength λ equal to 30mm), the radiation elements are arranged in an xoy plane in an equidistant rectangular grid, and M equal to 12 and N equal to 12 are taken, and a total of 144 radiation elements constitute an active phased array antenna array; dx＝0.5λ＝15mm，dy0.5 λ 15 mm. The spatial geometry of the viewpoint P with respect to the coordinate system xyz is shown in fig. 3. Specific parameters of the material properties of the area array antenna are shown in table 1.
TABLE 1 Material Properties of area array antennas
Secondly, calculating the compensation exciting current
1. Finite element analysis to obtain array surface deformation
1.1 the geometric structure model of the area array antenna is built in ANSYS according to the geometric model size of the area array antenna, as shown in figure 4. The unit type of the cold plate, the T/R assembly and the reinforcing ribs is SOLID unit SOLID92, the unit type of the radiation unit is plane unit SHELL63, and the structural finite element model of the area array antenna is obtained by meshing the geometric model of the area array antenna according to the set material properties and the unit types and is shown in figure 5. Wherein, the cold plate and the reinforcing rib, the cold plate and the T/R assembly, the T/R assembly and the radiation unit, and the reinforcing rib and the radiation unit are connected with each other without relative displacement.
1.2 according to the constraint conditions of the finite element model of the area array antenna structure and a given random vibration acceleration power spectrum (as shown in figure 6), calculating the random vibration deformation of the area array antenna through ANSYS software to obtain a deformation cloud chart (as shown in figure 7) of the area array antenna structure, and respectively extracting the position offset (delta x) of the center of a radiation unit in the three directions of x, y and z in the finite element model of the area array antenna structure under the vibration loadn,Δyn,Δzn) Wherein N ∈ (0, N-1).
2. Antenna electrical performance calculation by linear array antenna electric coupling model
Dividing the area array antenna into 12 linear array antennas, extracting the ith (i is more than or equal to 1 and less than or equal to 12) linear array antenna, and calculating the electrical property of the ith deformed linear array antenna by using a linear array antenna electrical coupling model:
wherein d is the spacing between the radiating elements, IinFor the exciting current of the nth radiating element in the ith linear array antenna,wherein A isinIn order to excite the amplitude of the current,k is a wave constant, k is 2 pi/lambda, lambda is the working wavelength of the planar array antenna, theta is the pitch angle of the linear array antenna, and delta y is the phase of the exciting currentinAnd Δ zinPosition errors in y-direction and z-direction, Δ y, generated by the nth radiation element in the ith linear arrayi0And Δ zi0The position errors of the 0 th radiation unit, namely the initial radiation unit in the ith linear array in the y direction and the z direction respectively.
3. Decompose ith deformation linear array antenna electrical property
Decomposing an array factor directional diagram of the ith deformed linear array antenna:
wherein,the electrical property change items caused by the deformation of the i linear array antenna structures are represented; f. ofia(theta) represents the ideal electrical performance of the ith linear array antenna. A comparison of the ideal and deformed array antenna far field patterns is shown in fig. 8.
4. Method for calculating excitation current amplitude and phase compensation quantity of deformed linear array antenna by using FFT (fast Fourier transform)
Respectively carrying out FFT (fast Fourier transform) on ideal electrical property and electrical property change items of the ith linear array, and calculating excitation current compensation quantity of the deformed linear array antenna, wherein the FFT comprises the following specific steps:
4.1 excitation current I in ideal electrical property of ith linear arrayinPerforming FFT:
wherein, αimFor Fourier series of excitation current, m represents fast FourierThe serial number of the current signal after the inner leaf transformation.
In the main beam direction of ideal linear array antennaAnd establishing a Fourier transform relation between the electrical property of the antenna and the excitation current, and establishing the ideal electrical property f of the ith linear array antennaia(u) performing an FFT:
wherein u ═ sin θ;representing the spatial phase generated by the linear array antenna radiation unit in an ideal state;indicating the main beam pointing direction of the linear array antenna.
4.2 Electrical Performance perturbation term f for line array antennaiae(theta), establishing a Fourier series expression, adopting FFT to βim＝FFT[kIin(Δyin-Δyi0)]，γim＝FFT[kIin(Δzin-Δzi0)]Since the discrete Fourier transform satisfies the linear superposition, fiaeThe Fourier series form of (θ) can be expressed as:
in this case, the antenna array factor directional diagram f with structural error existsiasThe Fourier series form of (θ) is:
4.3 Fourier series F of factor directional diagram of deformed linear array antennaias(u) performing FFT inverse transformation to obtain an array factor directional diagram of the deformed linear array antenna, wherein the array factor directional diagram is as follows:
wherein,the excitation current representing the structure error contained in the ith deformed linear array antenna can be adjusted to compensate the influence of the structure deformation on the linear array electrical performance.
4.4 Main Beam pointing at Linear array antennaAnd calculating the adjustment quantity of the amplitude and the phase of the excitation current. In main beam direction umAbove, an excitation current I containing a structural errorinsComprises the following steps:
the current and the exciting current I of the linear array antenna under the ideal stateinThe relationship is as follows:
wherein,
representing an amplitude disturbance coefficient caused by a structural error in the excitation current of the deformed area array antenna;the phase disturbance caused by the structural error in the excitation current of the deformed area array antenna is shown.
4.5 exciting current amplitude disturbance coefficient delta A caused by linear array antenna structure deformationnAnd phase perturbationAnd correcting to compensate the influence of the structural deformation on the electrical performance of the linear array antenna. Amplitude coefficient adjustment quantity delta A of induced excitation currentinc＝-ΔAinAmount of phase adjustment of excitation currentThe adjusted excitation current becomes:
using adjusted excitation current IincReplacing a deformed linear array antenna array factor fiasExcitation current I in (theta)inAnd the electrical property of the compensated deformed linear array antenna is as follows:
in the formula,an amplitude coefficient adjustment amount representing the excitation current;indicating the amount of adjustment of the phase of the excitation current.
5. Judging whether all linear array antennas have been compensated
And judging whether the adjustment quantity of the excitation current amplitude and the phase of all the linear array antennas is calculated, if so, obtaining the adjustment quantity of the excitation current amplitude and the phase of the area array unit, if not, extracting the next linear array antenna, and repeating the step 2 to the step 4.
6. Electromechanical coupling calculation antenna electrical property of area array antenna
The obtained adjustment quantities of the excitation current amplitude and the phase of the 12 linear array antenna units, namely all the area array antenna units are substituted into an area array antenna electromechanical coupling model, and the model is as follows:
third, simulation results and analysis
As can be seen from the above, the structural deformation of the area array antenna causes the antenna gain to decrease, the side lobe level to increase, and the beam pointing to be deviated, resulting in the deterioration of the antenna performance. The obtained compensation excitation current is substituted into a directional diagram function of the deformed area array antenna to obtain a compensated directional diagram function of the area array antenna, and an ideal area array antenna directional diagram and the compensated directional diagram of the area array antenna are drawn in the same coordinate system, as shown in fig. 9. As can be seen from fig. 9, the compensated antenna pattern function is very close to the antenna pattern function in an ideal situation, and the compensation effect is good. Table 2 shows the electrical performance parameters of the array antenna under the ideal condition, the vibration deformation condition, and three different compensated states, including gain, side lobe level, and beam pointing, respectively.
TABLE 2 Electrical parameters of ideal, deformed and compensated area array antenna
The data in table 2 show that when the area array antenna is affected by random vibration, the antenna gain is reduced, the side lobe level is raised, and the beam pointing deviation is caused, the electrical performance of the antenna is compensated by adopting the compensation method, the gain loss of the compensated antenna is reduced from 1.08dB to 0.058dB, the gain loss is reduced by one order of magnitude, and the index requirement that the gain loss is less than 0.5dB in the engineering is met; the level of the side lobe is reduced to-29.45 dB from-26.08 dB, and the level of the side lobe is obviously improved; the beam pointing deviation is changed from 0.1 degrees to 0 degrees, and the beam directivity is more accurate. In the embodiment, the electrical property compensation method of the deformed area array antenna based on electromechanical coupling and Fourier transform is adopted, the compensation effect on the electrical property of the antenna is good, and the compensated electrical property of the antenna meets the index requirement, so that the method can be applied to the actual service work of the electrical property of the antenna.
Claims (8)
1. The electrical property compensation method of the deformed area array antenna based on electromechanical coupling and Fourier transform is characterized by comprising the following steps:
(1) determining geometric model parameters and material attributes of the area array antenna and simultaneously determining working parameters of the area array antenna according to structural parameters of the area array antenna with M rows and N columns, namely M linear array antennas;
(2) establishing a finite element model of the area array antenna structure according to the geometric model parameters and the material attributes of the area array antenna; determining constraint conditions of an antenna finite element model according to the installation form of the area array antenna; applying airborne random vibration power spectrum to the finite element model of the area array antenna, calculating the structural deformation of the area array antenna, and extracting the position offset of the central node of the radiation unit of the area array antenna in the x, y and z directions;
(3) extracting the position offset of the ith linear array antenna in the M linear array antennas and the central node of the radiation unit of the ith linear array antenna, wherein i is more than or equal to 1 and less than or equal to M; calculating the electrical property of the ith linear array antenna after deformation in an airborne environment by using a linear array antenna electric coupling model;
(4) decomposing the electrical property of the ith deformed linear array antenna into the electrical property of an ideal linear array and the electrical property change item of the linear array caused by the structural deformation, wherein the electrical property change item of the linear array is the excitation current I of the electrical property of the ideal linear arrayinAnd the antenna space phase error caused by structural deformation;
(5) respectively carrying out fast Fourier transform on the change items of the electrical property of the ideal linear array and the electrical property of the linear array to obtain the amplitude of the excitation current and the adjustment quantity of the phase for compensating the spatial phase error of the antenna;
the method specifically comprises the following steps:
(5a) exciting current I for ideal linear array electrical property of ith deformed linear array antennainExpressed in the form of a Fourier series;
establishing an excitation current I between the electrical property of the antenna and the electrical property of the ideal linear array in the main beam direction of the ideal linear array antennainFourier transform relation between the first and the second, ideal linear array electrical property f of the ith deformed linear array antennaia(u) performing fast Fourier transform to obtain Fourier series expression Fia(u)；
(5b) Disturbance term f for linear array antenna electrical propertyiae(u) establishing a Fourier series expression F thereofiae(u); the influence of the structural deformation on the direction u is converted into the main beam pointing direction u of the linear array antennamThe adjustment amount of the excitation current is calculated in the pointing direction of the main beam of the linear array antenna, and at the moment, the Fourier series F of the ideal electrical performance of the linear array antenna is calculatedia(u) and Fourier series F of electrical property disturbance termsiae(u) superposing to obtain an antenna array factor directional diagram f with structural errorsiasFourier series form F of (u)ias(u)；
(5c) Fourier series F of factor directional diagram of deformed linear array antennaias(u) performing inverse fast Fourier transform to obtain an array factor directional diagram of the deformed linear array antenna, wherein the excitation current I in the directional diagraminsNamely, the deformed linear array antenna contains the excitation current of the structure error, and the influence of the structure deformation on the linear array electrical property can be compensated by adjusting the current;
(5d) calculating the adjustment amount of the amplitude and phase of the excitation current according to the excitation current I containing the structure errorinsExcitation current I having electrical properties equivalent to ideal linear arrayinObtaining the amplitude disturbance coefficient delta A caused by the structure error in the exciting current of the deformed linear array antennainAnd phase perturbation due to structural errors
(5e) Exciting current amplitude disturbance coefficient delta A caused by linear array antenna structure deformationinAnd phase perturbationCorrecting to compensate the influence of structural deformation on the electrical performance of the linear array antenna; amplitude coefficient adjustment quantity delta A of induced excitation currentinc＝-ΔAinAmount of phase adjustment of excitation currentThe adjusted excitation current I is obtainedinc；
Using adjusted excitation current IincReplacing a deformed linear array antenna array factor fiasExcitation current I of ideal linear array electrical property in (theta)inThe electrical performance of the compensated deformed linear array antenna can be obtained;
(6) judging whether the adjustment quantity of the excitation current amplitude and the phase of all the M linear array antennas is calculated, if so, obtaining the adjustment quantity of the excitation current amplitude and the phase of the M linear array antennas, otherwise, extracting the next linear array antenna, and repeating the steps (3) to (6);
(7) bringing the obtained adjustment quantities of the excitation current amplitude and the phase of the M linear array antennas, namely all the area array antennas, into an area array antenna electromechanical coupling model, and calculating the electrical property of the deformed area array antenna;
(8) judging whether the electrical property of the compensated deformed array antenna meets the index requirement, if so, indicating that the excitation current amplitude and the phase adjustment quantity with the optimal electrical property of the compensated deformed array antenna are obtained, so that the area array antenna achieves the optimal working performance in the service environment; otherwise, modifying the structural parameters of the area array antenna, and repeating the steps (1) to (7) until the requirements are met.
2. The electromechanical coupling and fourier transform-based electrical performance compensation method for the deformed area array antenna, according to claim 1, wherein in the step (1), the geometric model parameters of the area array antenna comprise position distribution, number, size and unit spacing of radiating units of the area array antenna, and size parameters of a T/R assembly, a cold plate and a reinforcing rib; the material properties of the area array antenna comprise density rho, elastic modulus E and Poisson ratio mu; the electromagnetic working parameters of the area array antenna comprise the central working frequency f of the area array antenna, the amplitude and the phase of the exciting current.
3. The method for compensating the electrical property of the deformed planar array antenna based on the electromechanical coupling and the Fourier transform as claimed in claim 1, wherein in the step (3), the electrical property f of the ith deformed linear array antenna is calculated by adopting a linear array antenna electromechanical coupling modelias(θ) is achieved by:
<mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mi>exp</mi> <mo>{</mo> <mi>j</mi> <mi>k</mi> <mo>&lsqb;</mo> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&theta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&theta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&theta;</mi> <mo>&rsqb;</mo> <mo>}</mo> </mrow>
in the formula, d is the distance between the radiation units; i isinIs the exciting current of ideal linear array electrical property of the nth radiating element in the ith linear array antenna,wherein A isinIn order to excite the amplitude of the current,is the excitation current phase; j is an imaginary unit; k is a wave constant, k is 2 pi/lambda, and lambda is the working wavelength of the area array antenna; theta is the pitch angle of the linear array antenna; Δ yinAnd Δ zinPosition errors along the y direction and the z direction generated by the nth radiation unit in the ith linear array respectively; Δ yi0And Δ zi0The position errors of the 0 th radiation unit, namely the initial radiation unit in the ith linear array in the y direction and the z direction respectively.
4. The electromechanical coupling and fourier transform-based electrical property compensation method for the deformed planar array antenna according to claim 1, wherein in the step (4), the electrical property of the ith deformed linear array antenna is decomposed into an ideal linear array electrical property and a linear array electrical property change item caused by structural deformation, and specifically:
when the structural deformation of the linear array antenna radiation unit is not more than 0.06 lambda/pi cos (lambda/2 d), decomposing an array factor directional diagram of the deformed linear array antenna:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mi>exp</mi> <mo>{</mo> <mi>j</mi> <mi>k</mi> <mo>&lsqb;</mo> <mi>n</mi> <mi>d</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&theta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&theta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&theta;</mi> <mo>&rsqb;</mo> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&ap;</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>k</mi> <mi>n</mi> <mi>d</mi> <mi>sin</mi> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>{</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> <mi>k</mi> <mo>&lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&theta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&theta;</mi> <mo>&rsqb;</mo> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>e</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
wherein,representing an electrical property change item caused by the deformation of the ith linear array antenna structure; f. ofia(theta) represents the ideal electrical performance of the ith linear array antenna;
in order to carry out subsequent fast Fourier transform on the ideal electrical property and electrical property change items of the linear array, u is used for expressing sin theta, and f is used for expressing sin thetaia(theta) and fiae(θ) is expressed as:
<mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>k</mi> <mi>n</mi> <mi>d</mi> <mi>u</mi> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>e</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>j</mi> <mi>k</mi> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>&lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;y</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>u</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;z</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>u</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&rsqb;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>k</mi> <mi>n</mi> <mi>d</mi> <mi>u</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
5. the electromechanical coupling and fourier transform-based electrical property compensation method for the deformed planar array antenna according to claim 1, wherein in the step (5), fast fourier transform is performed on the ideal linear array electrical property and the linear array electrical property variation item of the ith deformed linear array antenna, specifically:
(5a) exciting current I for ideal linear array electrical property of ith deformed linear array antennainExpressed in the form of a fourier series:
<mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>.</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>n</mi> <mi>m</mi> </mrow> </msup> <mo>,</mo> <mn>0</mn> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow>
wherein, αimThe series number of the current signals in the Fourier series is m;
in the main beam direction of ideal linear array antennaIn the above, the excitation current I of the antenna electrical property and the ideal linear array electrical property is establishedinFourier transform relation between the first and the second, ideal linear array electrical property f of the ith deformed linear array antennaia(u) performing a fast fourier transform:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>a</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>.</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mi>k</mi> <mi>n</mi> <mi>d</mi> <mfrac> <mrow> <mi>m</mi> <mi>&lambda;</mi> </mrow> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </mfrac> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>.</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mn>0</mn> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow>
wherein,representing the spatial phase generated by the linear array antenna radiation unit in an ideal state;indicating the main beam pointing direction of the linear array antenna;
(5b) disturbance term f for linear array antenna electrical propertyiae(u) establishing a Fourier series expression thereof, using fast Fourier transform to βim＝FFT[kIin(Δyin-Δyi0)]，γim＝FFT[kIin(Δzin-Δzi0)]Since the discrete Fourier transform satisfies the linear superposition, fiae(u) is expressed in the form of a Fourier series as:
<mrow> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>e</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>j</mi> <mi>N</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>(</mo> <mrow> <mi>u</mi> <mo>&CenterDot;</mo> <msub> <mi>&beta;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>u</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&CenterDot;</mo> <msub> <mi>&gamma;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> <mo>)</mo> <mo>&CenterDot;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> </mrow>
the influence of the structural deformation on the direction u is converted into the main beam pointing direction u of the linear array antennamThe adjustment amount of the excitation current is calculated in the direction of the main beam of the line array antenna, and the formula F is shown in the specificationiae(u) becomes:
<mrow> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>e</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>j</mi> <mi>N</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>(</mo> <mrow> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>&CenterDot;</mo> <msub> <mi>&beta;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <msub> <mi>u</mi> <mi>m</mi> </msub> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&CenterDot;</mo> <msub> <mi>&gamma;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> <mo>)</mo> <mo>&CenterDot;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> </mrow>
in this case, the antenna array factor directional diagram f with structural error existsias(u) has the form of a Fourier series:
<mrow> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>a</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>e</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>&lsqb;</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>+</mo> <mi>j</mi> <mrow> <mo>(</mo> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>&CenterDot;</mo> <msub> <mi>&beta;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <msub> <mi>u</mi> <mi>m</mi> </msub> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&CenterDot;</mo> <msub> <mi>&gamma;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>&CenterDot;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>3
(5c) fourier series F of factor directional diagram of deformed linear array antennaias(u) intoAnd (3) performing fast Fourier inverse transformation to obtain an array factor directional diagram of the deformed linear array antenna, wherein the array factor directional diagram is as follows:
<mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>s</mi> </mrow> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mi>j</mi> <mi>k</mi> <mi>n</mi> <mi>d</mi> <mi>u</mi> <mo>)</mo> </mrow> </mrow>
wherein,the excitation current which contains the structure error in the ith deformed linear array antenna is represented, and the influence of the structure deformation on the linear array electrical property can be compensated by adjusting the excitation current;
(5d) calculating the amplitude and phase of the excitation current, including the structure error of the excitation current IinsComprises the following steps:
<mrow> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>FFT</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&lsqb;</mo> <msub> <mi>&alpha;</mi> <mi>m</mi> </msub> <mo>+</mo> <mi>j</mi> <mrow> <mo>(</mo> <msub> <mi>u</mi> <mi>m</mi> </msub> <mo>&CenterDot;</mo> <msub> <mi>&beta;</mi> <mi>m</mi> </msub> <mo>+</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <msub> <mi>u</mi> <mi>m</mi> </msub> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&CenterDot;</mo> <msub> <mi>&gamma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>
the current and the exciting current I of the ideal linear array electrical propertyinThe relationship is as follows:
wherein,representing an amplitude disturbance coefficient caused by structural errors in the excitation current of the deformed linear array antenna, wherein Re represents a real part of an imaginary number;representing phase disturbance caused by structural errors in excitation current of the deformed linear array antenna, wherein Im represents an imaginary part of an imaginary number;
(5e) exciting current amplitude disturbance coefficient delta A caused by linear array antenna structure deformationinAnd phase perturbationCorrecting to compensate the influence of structural deformation on the electrical performance of the linear array antenna; amplitude coefficient adjustment quantity delta A of induced excitation currentinc＝-ΔAinAmount of phase adjustment of excitation currentThe adjusted excitation current becomes:
using adjusted excitation current IincReplacing a deformed linear array antenna array factor fiasExcitation current I of ideal linear array electrical property in (theta)inAnd the electrical property of the compensated deformed linear array antenna is as follows:
in the formula,a system adjustment quantity representing the amplitude of the excitation current;indicating the amount of adjustment of the phase of the excitation current.
6. The electrical property compensation method for the deformed area array antenna based on the electromechanical coupling and the fourier transform as claimed in claim 1, wherein in the step (7), the obtained adjustment quantities of the excitation current amplitude and the phase of the M linear array antennas, that is, all the area array antennas, are substituted into an area array antenna electrical coupling model, which is:
7. the method for compensating the electrical property of the deformed planar array antenna based on the electromechanical coupling and the fourier transform as claimed in claim 1, wherein in the step (7), the electrical property of the deformed linear array antenna after compensation is calculated to obtain parameters including antenna gain, side lobe level and beam pointing antenna electrical property.
8. The electrical property compensation method for the deformed area array antenna based on the electromechanical coupling and the fourier transform as claimed in claim 1, wherein in the step (8), the structural parameters of the area array antenna are modified, including enhancing the structural rigidity of the area array antenna and modifying the constraint position of the area array antenna.
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