CN109670140A - A kind of array antenna Electrical Analysis method based on array element feature mode - Google Patents
A kind of array antenna Electrical Analysis method based on array element feature mode Download PDFInfo
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Abstract
The invention discloses a kind of the array antenna Electrical Analysis method based on array element feature mode, the determination including array element radiation mode；The calculating of mode excitation coefficient of the array element in battle array under environment；The calculating of array antenna far-field pattern；Array antenna excitation port network parameter solves.The present invention strictly considers the mutual coupling effect between array element, can Accurate Analysis array antenna electrical property.Mentioned method can be used for disclosing the essence of the mutual coupling effect between array element, and the analysis and design for array antenna have important engineering significance.
Description
Technical field
The invention belongs to antenna technical fields, and in particular to a kind of array antenna electrical property based on array element feature mode point
Analysis method can be used for instructing the array antenna Electrical Analysis in real work.
Background technique
Array antenna is developed so far over one hundred year history, is easily achieved multi-beam since it has, wave beam agile and ultralow
The advantages that minor lobe, has been widely used in communication and radar system.In Practical Project, due to the presence of mutual coupling effect, radiation is single
Performance of the member in array environment and free space are inconsistent.As a result, mutual coupling effect will significantly affect array day
Radiation, scattering and the port attribute of line reduce the electrical property of antenna and increase design difficulty.Therefore, radiating element is furtherd investigate
Between mutual coupling effect the mechanism of action for array antenna Accurate Analysis and design it is most important.
In general, there are two main classes for the strategy of Accurate Analysis array antenna electrical property.One is by entire array antenna
It is considered as a system, algebra side is constructed using numerical method (such as moment method) according to electromagnetic field governing equation and corresponding boundary condition
Cheng Jinhang solves analysis.Such methods can Accurate Analysis antenna electrical property and be widely used.Another kind of research strategy is intended to
Electromagnetic coupling relationship between radiating element is probed into, and then that establishes array electrical property and isolated radiating element electromagnetic signature is associated with mould
Type.Obviously, compared with direct solving method, this research strategy explicitly provides the pass of the function between element characteristics and array characteristics
System, is conducive to the design of array antenna.Many scientific research personnel have been based on second of strategy and have carried out correlative study abundant.Example
Such as, the correlation model between active cell directional diagram and isolated radiating element directional diagram is established based on matrix ports scattering parameter,
Relationship in quantitative description radiating element battle array between radiation characteristic and its radiation feature in free space.But this method is only
Suitable for the radiating element of minimum scatter antenna type, such as short electric dipole, short magnetic dipole etc..Minimum can be used in radiating element
Scatter antenna it is approximate under the premise of, antenna pattern in mutual impedance and unit battle array can be provided between unit based on isolated unit feature
Calculating formula.
Summary of the invention
In view of the above-mentioned problems, the invention proposes a kind of array antenna Electrical Analysis sides based on array element feature mode
Method, this method consider the mutual coupling effect between array element, can Accurate Analysis array antenna radiation, scattering and port network parameters,
It is of great significance to the array antenna electrical property prediction in Practical Project.
The present invention is realized by following technical proposals.
A kind of array antenna Electrical Analysis method based on array element feature mode, includes the following steps:
(1) determine that its feature mode information, feature mode information include characteristic value, mode current according to array element geometric parameter
And mode electric field；
(2) according to array antenna geometric parameter and activation profile, building coupling equilibrium equation solves and obtains array element in array
Mode excitation coefficient in environment；
(3) pattern weight coefficient of each array element in the case where considering mutual coupling effect is determined, and then according to obtained pattern weight system
Several and array element mode electric field determines array far field direction of an electric field figure；
(4) it calculates and obtains array stimulating port network parameters, including impedance and scattering parameter.
Further, it in the step (1), determines array element feature mode information, carries out in accordance with the following steps:
(1a) constructs generalized eigenvalue equation according to improved Electric Field Integral Equation, solves and obtains m-th of array element a rank characteristic valueMode currentAnd mode electric field
(1b) determines array element surface total current J according to step (1a) array element character modules information obtainedm；
(1c) determines array element global radiation electric field E according to step (1a) array element character modules information obtainedm。
Further, in the step (2), mode excitation coefficient of each array element in array environment is determined, according to following step
It is rapid to carry out:
(2a) determines the equilibrium equation that mode excitation coefficient of the array element m in battle array under environment is met；
(2b) repeats step (2a), obtains the equilibrium equation that all order modes of array element m are met；
(2c) repeats step (2b) to array elements all in array, can be obtained the mould of the stringent each array element for considering mutual coupling effect
The coupling equilibrium equation that formula drive factor is met；
The coupling equilibrium equation established in (2d) solution procedure (2c), can be obtained the mode of each array element in array environment
Drive factor V.
Further, it in the step (3), determines the far field direction of an electric field figure of array antenna, carries out in accordance with the following steps:
(3a) determines the pattern weight FACTOR P of array element according to the array element mode excitation coefficient obtained in step (3)；
The far field pattern function of (3b) array antenna is represented by the linear combination of each array element mode electric field.
Further, it in the step (4), determines the excitation port network parameter of array antenna, carries out in accordance with the following steps:
The mode weighting coefficient matrix P for the array antenna array element that (4a) is obtained according to step (3a), determines antenna feed point
Locate the functional relation between total current and mode excitation coefficient；
The initial mode drive factor V of (4b) array antenna array element0The letter met with radiating element port driving voltage
Number relationship；
(4c) can determine array antenna impedance parameter Z by Ohm's law；
(4d) can get the scattering parameter S of array stimulating port by microwave network theory.
The technology of the present invention compared with prior art, has the following characteristics that
1. in Practical Project, there is important engineering significance to the Accurate Analysis of array antenna electrical property.The invention proposes
A kind of array antenna Electrical Analysis method based on array element feature mode constructs battle array from isolated array element radiation feature
Correlation model between first radiation feature and array antenna global radiation feature proposes a kind of ginseng for characterizing mutual coupling
Number --- mode coupling constant has great importance to the array antennas design and analysis for considering mutual coupling effect.
2. the present invention strictly considers the mutual coupling effect between array element compared with traditional array antenna electric performance analysis method,
It can Accurate Analysis array antenna electrical property.Also, mentioned method can be used for disclosing the essence of the mutual coupling effect between array element, i.e. mode coupling
It closes.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the array antenna Electrical Analysis method based on array element feature mode of the present invention；
Fig. 2 is butterfly antenna geometric graph；
Fig. 3 is 6 × 6 butterfly array antennas；
Fig. 4 is binary butterfly battle array S side by side12Parameter is with array element spacing change curve；
Fig. 5 is compared using the present invention and Simulation on Vertical Via Interconnect result φ=0 ° surface radiation directional diagram；
Fig. 6 is compared using the present invention and Simulation on Vertical Via Interconnect result φ=90 ° surface radiation directional diagram；
Fig. 7 is compared using the present invention and Simulation on Vertical Via Interconnect result φ=0 ° area scattering directional diagram；
Fig. 8 is compared using the present invention and Simulation on Vertical Via Interconnect result φ=90 ° area scattering directional diagram.
Specific embodiment
The invention will be described in further detail with reference to the accompanying drawings and examples, but is not intended as doing invention any limit
The foundation of system.
Referring to Fig.1, the present invention is a kind of array antenna Electrical Analysis method based on array element feature mode, specific steps
It is as follows:
Step 1, array element character modules information is determined
According to array element geometric parameter, solves and obtain its character modules information, include the following steps:
(1a) constructs generalized eigenvalue equation according to improved Electric Field Integral Equation, solves and obtains m-th of array element a rank characteristic valueMode currentAnd mode electric field
(1b) determines the surface total current J of array element m according to step (1a) array element character modules information obtainedm:
In formula, j is imaginary unit；NmNumber is truncated for the mode of array element m；For mode excitation coefficient, and meet
In formula,To be incident on array element m surface SmOn electric field；
(1c) determines array element global radiation electric field according to step (1a) array element character modules information obtained
Step 2, array element mode excitation coefficient is determined
According to the array element character modules information determined in step 1, it is contemplated that array geometry parameter and activation profile situation, really
Determine mode excitation coefficient of the array element in array environment, includes the following steps:
(2a) determines mode excitation coefficient of the array element m in battle array under environment:
In formula, M is array element sum, NnNumber is truncated for the mode of array element n,The respectively b rank feature of array element n
Value, mode excitation coefficient,For the initial mode drive factor of array element m a rank, it can be calculated and be obtained by following formula:
For mode coupling constant, it can be calculated and be obtained by following formula:
In formula,For the b rank mode electric field of array element n.
(2b) repeats step (2a), obtains the equilibrium equation that all order modes of array element m are met, as follows:
In formula
In formula, subscript T is transposition operation, and operator diag is generated to input diagonal matrix of the parameter as diagonal entry, Vm、
VnMode excitation coefficient array respectively in the battle array of array element m and array element n,For the initial mode drive factor array of the array element,
CmnIt is array element n to the Mode Coupling matrix of array element m, ΛnFor the diagonal matrix about array element n characteristic value；
(2c) repeats step (2b) to array elements all in array, can be obtained the mould of the stringent each array element for considering mutual coupling effect
The coupling equilibrium equation that formula drive factor is met:
V=V0+CΛV
In formula
Λ=diag (Λn)
In formula, V is the array of mode excitation coefficient composition in each array element battle array of array antenna, V0For at the beginning of each array element of array antenna
The array of beginning mode excitation coefficient composition, C are Mode Coupling matrix, and Λ is about each array element characteristic value of array antenna to angular moment
Battle array；
The coupling equilibrium equation established in (2d) solution procedure (2c), can be obtained the mode of each array element in array environment
Drive factor V:
V=(U-C Λ)-1V0
In formula, U is unit matrix.
Step 3, array antenna far field direction of an electric field figure is solved
According to mode excitation coefficient of each array element obtained in step 2 in array environment, the far field of array antenna is determined
Direction of an electric field figure, includes the following steps:
(3a) determines that the pattern weight coefficient of array element is as follows according to the array element mode excitation coefficient obtained in step (3):
P=Λ V=Λ (U-C Λ)-1V0
In formula, Λ is the diagonal matrix about each array element characteristic value of array antenna, and V is mode in each array element battle array of array antenna
The array of drive factor composition, U are unit matrix, and C is Mode Coupling matrix, V0For the initial mode excitation of each array element of array antenna
The array of coefficient composition；
The far field pattern function of (3b) array antenna is represented by each array element mode electric field linear combination, and calculating formula is such as
Under:
F (θ, φ)=Π P=Π Λ (U-C Λ)-1V0
In formula
In formula, P is the array of each array element mode weighting coefficient composition of array antenna, and Λ is special about each array element of array antenna
The diagonal matrix of value indicative, V are the array of mode excitation coefficient composition in each array element battle array of array antenna, and U is unit matrix, and C is mould
Formula coupling matrix, V0For the array of the initial mode drive factor composition of each array element of array antenna, k is Electromagnetic Wave Propagation constant, For a rank mode far field of array element m, rmFor the position vector of array element m.
Step 4, array antenna excitation port network parameter is solved
By the functional relation between building array antenna excitation port voltage, electric current and array pattern, array day is obtained
Line excitation port network parameter, comprising the following steps:
The mode weighting coefficient matrix P for the array antenna array element that (4a) is obtained according to step (3a), determines antenna feed point
Locate the functional relation between total current and array antenna mode excitation coefficient column:
In formula, B is the matrix of mode current intensity composition at each array element feeding point of array antenna, and P is each battle array of array antenna
The array of meta schema weighting coefficient composition, iportFor each array element excitation port electric current array of array antenna,For the port of array element n
Electric current,For rank mode current intensity each at array element n feeding point composition matrix,For the b of n-th of array element
Current strength of the rank mode in excitation port；
The initial mode drive factor V of (4b) array antenna array element0Meet such as ShiShimonoseki with radiating element port driving voltage
System:
In formula,For radiating element n port voltage；
(4c) can determine array antenna impedance parameter by Ohm's law:
Z=[B Λ (U-C Λ)-1BT]-1
In formula, B is the matrix of mode current intensity composition at each array element feeding point of array antenna, and Λ is about array antenna
The diagonal matrix of each array element characteristic value, U are unit matrix, and C is Mode Coupling matrix；
(4d) can get the scattering parameter of array stimulating port by microwave network theory:
S=(Z-Z0)(Z+Z0)-1
In formula, Z is array antenna port Impedance parameter, Z0For the diagonal matrix being made of transmission line impedance parameter.
Advantages of the present invention can be further described by emulation case below.
1. simulation parameter
It is analysis case, knot with the butterfly radiating element of center operating frequency f=2GHz and its array antenna formed
Structure size is as shown in Figures 2 and 3.For radiating field analysis, using Chebyshev's activation profile of -20dB minor level,
For scattering field analysis, using unit amplitude, incidence angle θ0=30 °, φ0=45 ° of linear polarization plane electric fields are used as
Radio field.
2. emulation content and result
Fig. 4 gives the frequency response curve of the port scattering parameter of binary juxtaposed array, Fig. 5 and Fig. 6 give φ=
The normalization far-field pattern curve in 0 ° of face and φ=90 ° face, Fig. 7 and Fig. 8 give single station in φ=0 ° face and φ=90 ° face
Radar Cross Section curve.There it can be seen that can the radiation of Accurate Analysis array antenna, scattering and port net using the present invention
Network parameter, it is consistent with traditional moment Method Analysis result, demonstrate the validity of the method for the present invention.
The invention is not limited to above-mentioned case study on implementation, on the basis of technical solution disclosed by the invention, this field
According to disclosed technology contents, some of which technical characteristic can be made technical staff by not needing creative labor
Some replacements and deformation, these replacements and deformation are within the scope of the invention.
Claims (5)
1. a kind of array antenna Electrical Analysis method based on array element feature mode, which comprises the steps of:
(1) its feature mode information is determined according to array element geometric parameter；
(2) according to array antenna geometric parameter and activation profile, building coupling equilibrium equation solves and obtains array element in array environment
In mode excitation coefficient；
(3) determine pattern weight coefficient of each array element in the case where considering mutual coupling effect, so according to obtained pattern weight coefficient and
Array element mode electric field determines array far field direction of an electric field figure；
(4) it calculates and obtains array stimulating port network parameters, including impedance and scattering parameter.
2. a kind of array antenna Electrical Analysis method based on array element feature mode according to claim 1, feature
It is, in the step (1), determines array element feature mode information, carries out in accordance with the following steps:
(1a) constructs generalized eigenvalue equation according to improved Electric Field Integral Equation, solves and obtains m-th of array element a rank characteristic valueMould
Formula electric currentAnd mode electric field
(1b) determines array element surface total current J according to step (1a) array element character modules information obtainedm:
In formula, j is imaginary unit；NmNumber is truncated for the mode of array element m；For mode excitation coefficient, and meet
In formula,To be incident on array element m surface SmOn electric field；
(1c) determines array element global radiation electric field E according to step (1a) array element character modules information obtainedm:
3. a kind of array antenna Electrical Analysis method based on array element feature mode according to claim 1, feature
It is, in the step (2), determines mode excitation coefficient of each array element in array environment, carries out in accordance with the following steps:
(2a) determines mode excitation coefficient of the array element m in battle array under environmentThe equilibrium equation met；
In formula, M is array element sum, NnNumber is truncated for the mode of array element n,Vb nRespectively the b rank characteristic value of array element n, mould
Formula drive factor,For the initial mode drive factor of array element m a rank；For mode coupling constant；
(2b) repeats step (2a), and it is as follows to obtain the equilibrium equation that all order modes of array element m are met:
In formula
In formula, subscript T is transposition operation, and operator diag is generated to input diagonal matrix of the parameter as diagonal entry, Vm、VnPoint
Not Wei mode excitation coefficient array in the battle array of array element m and array element n,For the initial mode drive factor array of the array element, CmnFor
Mode Coupling matrix of the array element n to array element m, ΛnFor the diagonal matrix about array element n characteristic value；
(2c) repeats step (2b) to array elements all in array, and the mode that can be obtained the stringent each array element for considering mutual coupling effect swashs
Encourage the coupling equilibrium equation that coefficient is met:
V=V0+CΛV
In formula
Λ=diag (Λn)
In formula, V is the array of mode excitation coefficient composition in each array element battle array of array antenna, V0For each array element introductory die of array antenna
The array of formula drive factor composition, C are Mode Coupling matrix, and Λ is the diagonal matrix about each array element characteristic value of array antenna；
The coupling equilibrium equation established in (2d) solution procedure (2c), can be obtained the mode excitation of each array element in array environment
Coefficient V:
V=(U-C Λ)-1V0
In formula, U is unit matrix.
4. a kind of array antenna Electrical Analysis method based on array element feature mode according to claim 1, feature
It is, in the step (3), determines the far field direction of an electric field figure of array antenna, carries out in accordance with the following steps:
(3a) determines the following P of pattern weight coefficient of array element according to the array element mode excitation coefficient obtained in step (3):
P=Λ V=Λ (U-C Λ)-1V0
In formula, Λ is the diagonal matrix about each array element characteristic value of array antenna, and V is mode excitation in each array element battle array of array antenna
The array of coefficient composition, U are unit matrix, and C is Mode Coupling matrix, V0For the initial mode drive factor of each array element of array antenna
The array of composition；
Far field pattern function F (θ, φ) of (3b) array antenna is represented by the linear combination of each array element mode electric field, meter
Formula is as follows:
F (θ, φ)=Π P=Π Λ (U-C Λ)-1V0
In formula, Π is the array of array antenna each array element mode far field composition, and (θ, φ) is viewing angle, and P is each battle array of array antenna
The array of meta schema weighting coefficient composition, Λ are the diagonal matrix about each array element characteristic value of array antenna, and V is that array antenna is each
The array that mode excitation coefficient forms in array element battle array, U are unit matrix, and C is Mode Coupling matrix, V0For each array element of array antenna
The array of initial mode drive factor composition.
5. a kind of array antenna Electrical Analysis method based on array element feature mode according to claim 4, feature
It is, in the step (4), determines the excitation port network parameter of array antenna, carries out in accordance with the following steps:
The mode weighting coefficient matrix P for the array antenna array element that (4a) is obtained according to step (3a), determines total at antenna feed point
Functional relation between electric current and array antenna mode excitation coefficient column:
In formula, B is the matrix of mode current intensity composition at each array element feeding point of array antenna, and P is each array element mould of array antenna
The array of formula weighting coefficient composition, iportFor each array element excitation port electric current array of array antenna,For the port electricity of array element n
Stream,For rank mode current intensity each at array element n feeding point composition matrix,For the b rank of n-th of array element
Current strength of the mode in excitation port；
The initial mode drive factor V of (4b) array antenna array element0It is closed with the function that radiating element port driving voltage is met
System:
In formula,For radiating element n port voltage；
(4c) can determine array antenna impedance parameter Z by Ohm's law:
Z=[B Λ (U-C Λ)-1BT]-1
In formula, B is the matrix of mode current intensity composition at each array element feeding point of array antenna, and Λ is about each battle array of array antenna
The diagonal matrix of first characteristic value, U are unit matrix, and C is Mode Coupling matrix；
(4d) can get the scattering parameter S of array stimulating port by microwave network theory:
S=(Z-Z0)(Z+Z0)-1
In formula, Z is array antenna port Impedance parameter, Z0For the diagonal matrix being made of transmission line impedance parameter.
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