CN114966239B - Quasi-far field measuring method based on separable excitation coefficient variables - Google Patents

Quasi-far field measuring method based on separable excitation coefficient variables Download PDF

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CN114966239B
CN114966239B CN202210902679.8A CN202210902679A CN114966239B CN 114966239 B CN114966239 B CN 114966239B CN 202210902679 A CN202210902679 A CN 202210902679A CN 114966239 B CN114966239 B CN 114966239B
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CN114966239A (en
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栗曦
张鹏
韩伟
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Shaanxi Shibei Communication Technology Co ltd
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Abstract

The invention discloses a quasi-far field measuring method based on separable excitation coefficient variables, which comprises the following steps: the method comprises the following steps: determining the quasi-far field distance of the antenna to be measured, and step two: and (3) extracting the amplitude and the phase of the quasi-far field position of the antenna, and performing the third step: obtaining a far field directional diagram function of the one-dimensional linear array, and the fourth step: obtaining a far-field directional pattern function of the two-dimensional antenna array, and performing the following steps: an amplitude and phase pattern and gain are obtained. The one-dimensional antenna array quasi-far field measurement method based on cylindrical wave expansion is suitable for measuring antennas with large one-dimensional electrical size and small another-dimensional electrical size, is suitable for measuring two-dimensional antenna arrays, increases the universality of a quasi-far field extrapolation algorithm, obtains an antenna far field directional diagram accurately, measures in a quasi-far field range of an antenna to be measured, and avoids the problems of large test distance and low near field measurement efficiency required by far field measurement, so that the antenna test efficiency is remarkably improved.

Description

Quasi-far field measuring method based on separable excitation coefficient variables
Technical Field
The invention belongs to the technical field of antenna measurement, and particularly relates to a separable quasi-far field measurement method based on an excitation coefficient variable.
Background
The existing antenna far-field measurement needs to meet the far-field measurement distance, the conventional darkroom environment cannot meet the far-field measurement requirement of a large-caliber antenna, if a near-field measurement method is adopted, the required time is long, the efficiency is low, and in order to realize rapid measurement in a short distance, a one-dimensional antenna array quasi far-field measurement method based on cylindrical wave expansion is provided in the prior art, the method is suitable for measuring an antenna with a large one-dimensional electrical size and a small other-dimensional electrical size, only the measurement distance needs to meet the far-field condition of the small size of the antenna to be measured, therefore, the measurement distance is at the quasi far-field position of the large size, only information on one section can be obtained through single measurement, the measurement is named as quasi far-field measurement, the existing quasi far-field measurement method is only suitable for measuring one-dimensional antenna arrays, but is difficult to be suitable for measuring two-dimensional antenna arrays, and the quasi far-field measurement efficiency is not high.
Disclosure of Invention
The invention aims to provide a quasi-far-field measuring method based on separable excitation coefficient variables, which solves the problems in the prior art.
In order to achieve the purpose, the invention provides the following technical scheme: the quasi-far field measurement method based on separable excitation coefficient variables comprises the following steps:
the method comprises the following steps: determining the quasi-far field distance of the antenna to be measured;
step two: extracting the amplitude and the phase at the quasi-far field position of the antenna;
step three: obtaining a far field directional diagram function of the one-dimensional linear array, which specifically comprises the following steps:
electric field of observation point located on plane under cylindrical coordinate system:
Figure 920370DEST_PATH_IMAGE001
equation 1
Wherein,
Figure 371074DEST_PATH_IMAGE002
is shown at
Figure 769694DEST_PATH_IMAGE003
The electric field at the observation point on the plane,
Figure 291942DEST_PATH_IMAGE004
are all variables in a standard coordinate system under a spherical coordinate system,
Figure 944772DEST_PATH_IMAGE005
in order to be able to set the integer number,
Figure 831956DEST_PATH_IMAGE006
，
Figure 452293DEST_PATH_IMAGE007
the setting is 2-10, and the device is,
Figure 512653DEST_PATH_IMAGE008
to encompass the minimum cylinder radius of the antenna,jis a unit of an imaginary number, and is,kas the number of free-space waves,
Figure 19989DEST_PATH_IMAGE009
in a standard coordinate system
Figure 999447DEST_PATH_IMAGE010
The direction unit vector of the direction unit vector,
Figure 869531DEST_PATH_IMAGE011
in a standard coordinate system
Figure 61478DEST_PATH_IMAGE012
The direction unit vector of the direction unit vector,
Figure 688899DEST_PATH_IMAGE013
and
Figure 370417DEST_PATH_IMAGE014
is the coefficient of the cylindrical wave expansion,
Figure 184920DEST_PATH_IMAGE015
is composed of
Figure 180558DEST_PATH_IMAGE016
To the second type of Hankel function, at
Figure 193644DEST_PATH_IMAGE003
General form of the electric field of an observation point on a plane, its arbitrary linearly polarized electric field component
Figure 265637DEST_PATH_IMAGE017
Can be expressed as follows:
Figure 347862DEST_PATH_IMAGE018
equation 2
Wherein
Figure 960240DEST_PATH_IMAGE019
Represents the cylindrical wave expansion coefficient (of equation 1)A n OrB n ) Defined in the antenna under testρ = ρ 0 An electric field ofE m ，eAt the bottom of the index, the electric field at the observation point can be expressed as:
Figure 827833DEST_PATH_IMAGE020
equation 3
Then, inverting the above equation can result in:
Figure 601885DEST_PATH_IMAGE021
equation 4
Since the observation point is located in the far field, combining the properties of the Hankel function:
Figure 905828DEST_PATH_IMAGE022
equation 5
Bringing the above intoρ = ρ 0 In the expression of the electric field component of (a), it can be found that:
Figure 259580DEST_PATH_IMAGE023
equation 6
Removing the constant irrelevant to the angle in the above formula to obtain the far field directional diagram function of the antenna to be measured
Figure 699788DEST_PATH_IMAGE024
Comprises the following steps:
Figure 441479DEST_PATH_IMAGE025
equation 7
Step four: obtaining a far-field directional pattern function of the two-dimensional antenna array, specifically:
the excitation coefficient for each cell can be expressed as:
Figure 717871DEST_PATH_IMAGE026
equation 8
Wherein,Mis a value of the number of column-wise antenna elements,Nis a quantity value of a row-wise antenna element if the array antenna hasM×NA plurality of antenna units, each of which has a plurality of antenna elements,
Figure 265527DEST_PATH_IMAGE027
Figure 91401DEST_PATH_IMAGE028
Figure 941676DEST_PATH_IMAGE029
Figure 361156DEST_PATH_IMAGE030
the excitation coefficients are normalized for the columns of the two-dimensional antenna array,
Figure 571558DEST_PATH_IMAGE031
Figure 268249DEST_PATH_IMAGE032
Figure 679639DEST_PATH_IMAGE029
Figure 711049DEST_PATH_IMAGE033
for the row normalization excitation coefficient of the two-dimensional antenna array, a two-dimensional antenna array directional diagram can be obtained according to the directional diagram product theorem and the superposition theorem
Figure 600507DEST_PATH_IMAGE034
Comprises the following steps:
Figure 417285DEST_PATH_IMAGE035
equation 9
Wherein,
Figure 468418DEST_PATH_IMAGE036
are variables in a standard coordinate system under spherical coordinates,
Figure 987124DEST_PATH_IMAGE037
the distance between each unit in the direction isd x ，
Figure 290060DEST_PATH_IMAGE038
The distance between the direction units isd y ，I MN Is prepared from (a)M , N) The excitation coefficients of the location elements, m being the column-wise antenna element integer number, n being the row-wise antenna element integer number,
Figure 679453DEST_PATH_IMAGE039
for the excitation coefficients of the (m, n) -th element, the continued simplification can result in:
Figure 432645DEST_PATH_IMAGE040
equation 10
Then
Figure 189380DEST_PATH_IMAGE041
Equation 11
In the formula,
Figure 420641DEST_PATH_IMAGE042
normalizing the excitation coefficient for the mth column of the two-dimensional antenna array;
Figure 930120DEST_PATH_IMAGE043
equation 12
In the formula,
Figure 452282DEST_PATH_IMAGE044
normalizing the excitation coefficient for the nth row of the two-dimensional antenna array;
therefore, the number of the first and second electrodes is increased,
Figure 820946DEST_PATH_IMAGE045
can be expressed as
Figure 714953DEST_PATH_IMAGE046
Equation 13
Wherein,
Figure 829671DEST_PATH_IMAGE047
and
Figure 924666DEST_PATH_IMAGE048
directional diagram functions of the column direction one-dimensional linear array and the row direction one-dimensional linear array are respectively calculated by using the formula in the step three;
step five: obtaining an amplitude directional diagram, a phase directional diagram and a gain, specifically:
amplitude directional diagram
Figure 639681DEST_PATH_IMAGE049
Comprises the following steps:
Figure 212744DEST_PATH_IMAGE050
equation 14
Wherein, (ii) (dB) Is in amplitude units;
phase directional diagram
Figure 713127DEST_PATH_IMAGE051
Comprises the following steps:
Figure 838078DEST_PATH_IMAGE052
equation 15
Wherein angle () is a phase taking function inρ = ρ 0 An electric field ofE m The electric field can be expressed as:
Figure 650176DEST_PATH_IMAGE053
equation 16
At the same time, is located atρ = ρ 0 Electric field ofE m Can also be expressed as:
Figure 495772DEST_PATH_IMAGE054
equation 17
By the above two formulae, it is possible to obtain:
Figure 788345DEST_PATH_IMAGE055
equation 18
If the observation point is located in the far field region, the electric field can be written as:
Figure 553038DEST_PATH_IMAGE056
equation 19
The directional pattern function of the far field region
Figure 993378DEST_PATH_IMAGE057
Can be expressed as:
Figure 501720DEST_PATH_IMAGE058
equation 20
Gain compensation of antenna under test between quasi-far field and far field
Figure 711115DEST_PATH_IMAGE059
The calculation is as follows:
Figure 53235DEST_PATH_IMAGE060
equation 21
Wherein,
Figure 230138DEST_PATH_IMAGE061
a far-field pattern function is represented,
Figure 558483DEST_PATH_IMAGE062
representing a quasi-far-field pattern function.
Preferably, in the first step, the quasi-far-field distance measurement satisfies the far-field distance of the antenna unit, the distance between the antenna to be measured and the test probe is calculated, and the antenna is placed on the turntable at the distance.
Preferably, in the second step, the control computer is used to control a test probe with known characteristics and consistent with the working frequency of the antenna to be tested, and the amplitude and phase on a certain surface at the quasi-far-field position of the antenna are corresponded, and the amplitude and phase information obtained by the test is stored in the test file of the control computer.
Compared with the prior art, the invention has the beneficial effects that:
the universality of a quasi far-field extrapolation algorithm is increased: the quasi-far field measurement method of the one-dimensional antenna array based on the cylindrical wave expansion is suitable for measuring the antenna with large one-dimensional electrical size and small other-dimensional electrical size, is suitable for measuring the two-dimensional antenna array, increases the universality of a quasi-far field extrapolation algorithm, and obtains an antenna far field pattern accurately;
the antenna test efficiency is obviously improved: the antenna test system is used for measuring in the quasi-far field range of the antenna to be tested, so that the problems of large test distance and low near field measurement efficiency required by far field measurement are solved, and the antenna test efficiency is remarkably improved.
The measurement distance is significantly reduced: the distance between the antenna to be tested and the probe only needs to meet the quasi-far field condition, the test distance is obviously reduced, and the cost of darkroom construction is greatly saved.
The reconstructed far-field directional diagram has high precision: by combining the quasi-far-field measurement method based on separable excitation coefficient variables, the finally obtained far-field directional pattern of the antenna to be measured is high in accuracy, and far-field data can be efficiently reconstructed through an algorithm.
Drawings
FIG. 1 is a schematic diagram of a quasi-far field antenna test of the present invention;
FIG. 2 is a schematic view of the (r, φ, z) coordinate system of the present invention;
FIG. 3 is a simplified model diagram of an array antenna of the present invention;
FIG. 4 is a simplified model diagram of an antenna under test according to the present invention;
FIG. 5 is a schematic flow chart of a quasi-far-field measurement method according to the present invention;
fig. 6 is a schematic diagram comparing a reconstructed amplitude pattern with a theoretically calculated amplitude pattern.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
The invention discloses a quasi-far field measuring method based on separable excitation coefficient variables, which relates to an antenna to be tested arranged on a rotary table, a control computer, a test probe and a test instrument in an antenna measuring system in the measuring process, wherein the characteristics of all the test probes are known before testing, and the method comprises the following steps:
the method comprises the following steps: determining the quasi-far field distance of the antenna to be measured: the method is suitable for measuring a two-dimensional antenna array, the quasi-far-field distance can be measured only when the quasi-far-field distance meets the far-field distance of the antenna unit, the distance between the antenna to be measured and the test probe is calculated, the antenna is placed on the turntable at the distance, referring to fig. 1, the distance between the antenna to be measured and the test probe placed on the turntable is the quasi-far-field distance of the antenna to be measured, and the antenna to be measured and the test probe are required to have consistent working frequency, same height and polarization matching before testing.
Step two: the amplitude and phase on a certain surface at the quasi-far field position of the antenna are extracted: and controlling a test probe with the same working frequency and known characteristics with the antenna to be tested by using a control computer, corresponding to the amplitude and the phase on the quasi-far-field surface of the antenna, and storing the amplitude and phase information in a test file of the control computer.
Step three: obtaining a far field directional diagram function of the one-dimensional linear array: according to the amplitude and the phase of a radiation field of an antenna to be detected, a one-dimensional antenna array quasi-far-field extrapolation algorithm based on cylindrical wave expansion firstly deduces the relation between a measured value and a coefficient on a certain tangent plane observation point, carries out fast Fourier transform calculation on the measured value to obtain the coefficient, combines the property of a Hankel function, and can extrapolate a far-field directional diagram function of a one-dimensional linear array by carrying out inverse Fourier transform on the coefficient, specifically:
referring to FIGS. 2 and 3, the cylindrical coordinate system is located at
Figure 12598DEST_PATH_IMAGE003
Electric field of observation point on plane:
Figure 650252DEST_PATH_IMAGE063
equation 1
Wherein,
Figure 189818DEST_PATH_IMAGE002
representing the electric field at an observation point lying on a plane,
Figure 587433DEST_PATH_IMAGE004
are all variables in a standard coordinate system under a spherical coordinate system,
Figure 896054DEST_PATH_IMAGE005
in order to be able to set the integer number,
Figure 970189DEST_PATH_IMAGE006
，
Figure 731472DEST_PATH_IMAGE007
the setting is 2-10, and the device is,
Figure 932777DEST_PATH_IMAGE008
to encompass the minimum cylinder radius of the antenna,jis the unit of an imaginary number,kis a function of the wave number in free space,
Figure 954960DEST_PATH_IMAGE009
in a standard coordinate system
Figure 75363DEST_PATH_IMAGE010
The direction unit vector of the direction unit vector,
Figure 464887DEST_PATH_IMAGE011
in a standard coordinate system
Figure 63359DEST_PATH_IMAGE012
The direction unit vector of the direction unit vector,
Figure 940048DEST_PATH_IMAGE013
and
Figure 372297DEST_PATH_IMAGE014
is the coefficient of expansion of the cylindrical wave,
Figure 373751DEST_PATH_IMAGE015
is composed of
Figure 775914DEST_PATH_IMAGE016
To the second type of Hankel function, at
Figure 38268DEST_PATH_IMAGE003
General form of the electric field of an observation point on a plane, its arbitrary linearly polarized electric field component
Figure 766052DEST_PATH_IMAGE017
Can be expressed as follows:
Figure 599010DEST_PATH_IMAGE018
equation 2
Wherein
Figure 70443DEST_PATH_IMAGE019
Representing cylinderWave expansion coefficient (of equation 1)A n OrB n ) Defined in the antenna under testρ = ρ 0 An electric field ofE m ，eTo the bottom of the exponent, the electric field at the observation point can be expressed as:
Figure 187303DEST_PATH_IMAGE064
equation 3
By inverting the above equation, we can obtain:
Figure 820410DEST_PATH_IMAGE021
equation 4
Since the observation point is located in the far field, combining the properties of the Hankel function:
Figure 406243DEST_PATH_IMAGE022
equation 5
Bringing the above intoρ = ρ 0 In the expression of the electric field component, it can be found that:
Figure 415788DEST_PATH_IMAGE023
equation 6
Removing the constant irrelevant to the angle in the above formula to obtain the far field directional diagram function of the antenna to be measured
Figure 387155DEST_PATH_IMAGE024
Comprises the following steps:
Figure 456742DEST_PATH_IMAGE065
equation 7
Step four: obtaining a far field directional diagram function of the two-dimensional antenna array: according to the characteristic that the two-dimensional antenna array has separable variables of the excitation coefficient, a far field pattern function of the two-dimensional antenna array is obtained through calculation through a far field pattern function of the one-dimensional linear array, and specifically:
although the physical size of a common two-dimensional antenna array does not satisfy the conditions of large one-dimensional size and small one-dimensional size, the antenna has the characteristic of separable variables of excitation coefficients, namely the excitation coefficient of each unit can be expressed as:
Figure 264292DEST_PATH_IMAGE026
equation 8
Wherein,Mis a value of the number of column-wise antenna elements,Nis a quantity value of a row-wise antenna element if the array antenna hasM×NAn antenna unit, wherein,I MN is prepared from (a)m , n) The excitation coefficient of the location unit is,
Figure 77527DEST_PATH_IMAGE027
Figure 168980DEST_PATH_IMAGE028
Figure 143889DEST_PATH_IMAGE029
Figure 704315DEST_PATH_IMAGE030
the excitation coefficients are normalized for the columns of the two-dimensional antenna array,
Figure 55662DEST_PATH_IMAGE031
Figure 1621DEST_PATH_IMAGE032
Figure 147431DEST_PATH_IMAGE029
Figure 941293DEST_PATH_IMAGE033
for the row normalization excitation coefficient of the two-dimensional antenna array, the two-dimensional antenna array can be obtained according to the directional diagram product theorem and the superposition theoremDirectional diagram
Figure 955385DEST_PATH_IMAGE034
Comprises the following steps:
Figure 896796DEST_PATH_IMAGE066
equation 9
Wherein,
Figure 479087DEST_PATH_IMAGE036
are variables in a standard coordinate system under spherical coordinates,
Figure 748526DEST_PATH_IMAGE037
the distance between the units in the direction isd x ，
Figure 441675DEST_PATH_IMAGE038
The distance between the direction units isd y ，I MN Is prepared fromM , N) The excitation coefficients of the location elements, m being the column-wise antenna element integer number, n being the row-wise antenna element integer number,
Figure 362227DEST_PATH_IMAGE039
for the excitation coefficients of the (m, n) -th element, the continued simplification can result in:
Figure 115419DEST_PATH_IMAGE040
equation 10
Then
Figure 606574DEST_PATH_IMAGE041
Equation 11
In the formula,
Figure 103415DEST_PATH_IMAGE042
normalizing laser for mth column of two-dimensional antenna arrayAn excitation coefficient;
Figure 612894DEST_PATH_IMAGE043
equation 12
In the formula,
Figure 412353DEST_PATH_IMAGE044
normalizing the excitation coefficient for the nth row of the two-dimensional antenna array;
therefore, the temperature of the molten metal is controlled,
Figure 781018DEST_PATH_IMAGE045
can be expressed as
Figure 81549DEST_PATH_IMAGE046
Equation 13
Wherein,
Figure 711114DEST_PATH_IMAGE047
and
Figure 806109DEST_PATH_IMAGE048
directional diagram functions of the column direction one-dimensional linear array and the row direction one-dimensional linear array are respectively calculated by using the formula in the step three;
step five: calculating to obtain an amplitude directional diagram, a phase directional diagram and gain of the antenna to be measured: according to the far field directional diagram function of the antenna to be measured, taking the absolute value of the far field directional diagram function of the antenna to be measured to obtain the amplitude directional diagram of the antenna to be measured, taking the angle of the far field directional diagram function of the antenna to be measured to obtain the phase directional diagram of the antenna to be measured, calculating to obtain the gain compensation of the antenna to be measured between a quasi far field and a far field, and completing the quasi far field measurement of the antenna, specifically:
amplitude directional diagram
Figure 271856DEST_PATH_IMAGE049
Comprises the following steps:
Figure 110499DEST_PATH_IMAGE050
equation 14
Wherein, (ii) (dB) Is in amplitude units;
phase directional diagram
Figure 860149DEST_PATH_IMAGE051
Comprises the following steps:
Figure 126046DEST_PATH_IMAGE052
equation 15
Wherein angle () is a phase taking function inρ = ρ 0 An electric field ofE m The electric field can be expressed as:
Figure 79089DEST_PATH_IMAGE067
equation 16
At the same time, is located atρ = ρ 0 Electric field ofE m Can also be expressed as:
Figure 455844DEST_PATH_IMAGE054
equation 17
By the above two formulae, it is possible to obtain:
Figure 60001DEST_PATH_IMAGE055
equation 18
If the observation point is located in the far field region, the electric field can be written as:
Figure 496798DEST_PATH_IMAGE056
equation 19
The directional pattern function of the far field region
Figure 937138DEST_PATH_IMAGE057
Can be expressed as:
Figure 117584DEST_PATH_IMAGE058
equation 20
Gain compensation of antenna under test between quasi-far field and far field
Figure 107405DEST_PATH_IMAGE059
The calculation is as follows:
Figure 715104DEST_PATH_IMAGE060
equation 21
Wherein,
Figure 377161DEST_PATH_IMAGE061
a far-field pattern function is represented,
Figure 361297DEST_PATH_IMAGE062
representing a quasi-far-field pattern function.
The invention provides an integral technical scheme of a quasi-far field measuring method based on separable excitation coefficient variables, which is used for improving the testing efficiency, is suitable for measuring a two-dimensional antenna array and has the characteristic of separable excitation coefficient variables.
The quasi-far field measurement method based on separable excitation coefficient variables, which is provided by the invention, expands the antenna to be measured applicable to quasi-far field measurement from a one-dimensional antenna array to a two-dimensional antenna array, does not influence the precision and accuracy of reconstructing a far field pattern, and calculates the far field pattern of the antenna to be measured quickly, efficiently and accurately by a fast Fourier transform method.
The two-dimensional antenna array has the characteristic of separable excitation coefficient variables, is applied to the quasi-far-field measurement of an actual antenna, improves the universality of a quasi-far-field extrapolation algorithm, does not influence the precision of a far-field directional diagram, can obviously improve the testing efficiency of the quasi-far field of the antenna, and saves the cost of microwave darkroom construction.
The invention has the advantages that: the method improves the universality of a quasi-far-field extrapolation algorithm, is suitable for the quasi-far-field measurement of a two-dimensional antenna array, obviously reduces the test distance of the antenna to be tested, does not influence the accuracy of a far-field pattern, and improves the efficiency of the quasi-far-field test.
The following is a simulation measurement based on the separable quasi-far field measurement method of the excitation coefficient variable disclosed by the invention:
simulation conditions and contents:
the antenna to be tested shown in fig. 4 is an array antenna, the frequency of the antenna to be tested is 3 GHz, the array antenna is arranged along two directions, each unit consists of two half-wave oscillators and consists of Ne antenna units, the distance between the y-axis antenna units is dy, the array amplitude distribution is Taylor distribution of-30 dB, and the detailed parameters of the antenna to be tested are shown in table 1.
Table 1: detailed parameters of the antenna to be measured
Parameter(s) Means of Value taking
Ne Number of array antenna elements 10*10
dy Unit pitch in y-axis direction 0.5λ
dx Unit pitch in x-axis direction 0.5λ
In a simulation experiment, the quasi-far-field test distance is selected to be 2 meters, the sampling interval is 1 degree, and the number of sampling points is 361 points.
Simulation results and analysis
Fig. 6 is a schematic diagram comparing the amplitude directional diagram reconstructed by the present invention with the amplitude directional diagram obtained by theoretical calculation, in which the abscissa represents angle change, the ordinate represents the amplitude value of the antenna at different angles, the solid line represents the amplitude directional diagram of the antenna obtained by theoretical calculation, and the dotted line represents the amplitude directional diagram reconstructed by the present invention, and refer to fig. 6 that the amplitude directional diagram reconstructed by the present invention matches with the amplitude directional diagram obtained by theoretical calculation.
In short, the quasi-far field measurement method based on separable excitation coefficient variables solves the problem of quasi-far field measurement of a two-dimensional antenna array, determines the test distance of an antenna to be tested according to the quasi-far field measurement condition of the antenna, extracts the amplitude and the phase on a certain surface at the quasi-far field position of the antenna, firstly calculates the far field directional diagram function of a one-dimensional linear array, obtains the far field directional diagram function of the two-dimensional antenna array based on the far field directional diagram function, realizes the quasi-far field measurement of the two-dimensional antenna array, provides the quasi-far field measurement mode of the two-dimensional antenna array by combining the characteristic that the two-dimensional antenna array has separable variables of the excitation coefficients, reconstructs the far field directional diagram of the antenna to be tested efficiently and accurately, and remarkably improves the test efficiency.

Claims (3)

1. The quasi-far-field measurement method based on separable excitation coefficient variables is characterized by comprising the following steps of:
the method comprises the following steps: determining the quasi-far field distance of the antenna to be measured;
step two: extracting the amplitude and the phase at the quasi-far field position of the antenna;
step three: obtaining a far field directional diagram function of the one-dimensional linear array, which specifically comprises the following steps:
electric field of observation point located on plane under cylindrical coordinate system:
Figure 3877DEST_PATH_IMAGE001
equation 1
Wherein,
Figure 907111DEST_PATH_IMAGE002
is shown lying on a plane
Figure 446677DEST_PATH_IMAGE003
The electric field of the observation point of (a),
Figure 434089DEST_PATH_IMAGE004
are all variables in a standard coordinate system under a spherical coordinate system,
Figure 742711DEST_PATH_IMAGE005
in order to be able to set the integer number,
Figure 957792DEST_PATH_IMAGE006
，
Figure 109287DEST_PATH_IMAGE007
the setting is 2-10, and the device is,
Figure 169647DEST_PATH_IMAGE008
to encompass the minimum cylinder radius of the antenna,jis the unit of an imaginary number,kas the number of free-space waves,
Figure 208142DEST_PATH_IMAGE009
in a standard coordinate system
Figure 594123DEST_PATH_IMAGE010
The direction unit vector of the direction unit vector,
Figure 967336DEST_PATH_IMAGE011
in a standard coordinate system
Figure 831387DEST_PATH_IMAGE012
The direction unit vector of the direction unit vector,
Figure 255546DEST_PATH_IMAGE013
and
Figure 546850DEST_PATH_IMAGE014
is the coefficient of expansion of the cylindrical wave,
Figure 407359DEST_PATH_IMAGE015
is composed of
Figure 75100DEST_PATH_IMAGE016
To the second type of Hankel function, at
Figure 88187DEST_PATH_IMAGE003
General form of the electric field of an observation point on a plane, its arbitrary linearly polarized electric field component
Figure 550392DEST_PATH_IMAGE017
Can be expressed as follows:
Figure 39142DEST_PATH_IMAGE018
equation 2
Wherein
Figure 369630DEST_PATH_IMAGE019
Represents the cylindrical wave expansion coefficient (of equation 1)A n OrB n ) Defined in the antenna under testρ = ρ 0 An electric field ofE m ，eTo the bottom of the exponent, the electric field at the observation point can be expressed as:
Figure 361856DEST_PATH_IMAGE020
equation 3
Then, inverting the above equation can result in:
Figure 135908DEST_PATH_IMAGE021
equation 4
Since the observation point is located in the far field, combining the properties of the Hankel function:
Figure 846376DEST_PATH_IMAGE022
equation 5
Bringing the above intoρ = ρ 0 In the expression of the electric field component, it can be found that:
Figure 714974DEST_PATH_IMAGE023
equation 6
Removing the constant irrelevant to the angle in the above formula to obtain the far field directional diagram function of the antenna to be measured
Figure 827287DEST_PATH_IMAGE024
Comprises the following steps:
Figure 506661DEST_PATH_IMAGE025
equation 7
Step four: obtaining a far-field directional pattern function of the two-dimensional antenna array, specifically:
the excitation coefficient for each cell can be expressed as:
Figure 704424DEST_PATH_IMAGE026
equation 8
Wherein,Mis a value of the number of column-wise antenna elements,Nis a quantity value of a row-wise antenna element if the array antenna hasM×NA plurality of antenna units, each of which has a plurality of antenna elements,
Figure 376714DEST_PATH_IMAGE027
Figure 609112DEST_PATH_IMAGE028
Figure 724967DEST_PATH_IMAGE029
Figure 144447DEST_PATH_IMAGE030
the excitation coefficients are normalized for the columns of the two-dimensional antenna array,
Figure 620428DEST_PATH_IMAGE031
Figure 441753DEST_PATH_IMAGE032
Figure 728509DEST_PATH_IMAGE029
Figure 900864DEST_PATH_IMAGE033
for the row normalization excitation coefficient of the two-dimensional antenna array, a two-dimensional antenna array directional diagram can be obtained according to the directional diagram product theorem and the superposition theorem
Figure 790323DEST_PATH_IMAGE034
Comprises the following steps:
Figure 856368DEST_PATH_IMAGE035
publicFormula 9
Wherein,
Figure 438659DEST_PATH_IMAGE036
are variables in a standard coordinate system under spherical coordinates,
Figure 708098DEST_PATH_IMAGE037
the distance between each unit in the direction isd x ，
Figure 666826DEST_PATH_IMAGE038
The distance between the direction units isd y ，I MN Is prepared fromM , N) The excitation coefficients of the location elements, m being the column-wise antenna element integer number, n being the row-wise antenna element integer number,
Figure 321799DEST_PATH_IMAGE039
for the excitation coefficients of the (m, n) -th element, the continued simplification can result in:
Figure 74991DEST_PATH_IMAGE040
equation 10
Then
Figure 831725DEST_PATH_IMAGE041
Equation 11
In the formula,
Figure 328566DEST_PATH_IMAGE042
normalizing the excitation coefficient for the mth column of the two-dimensional antenna array;
Figure 103624DEST_PATH_IMAGE043
equation 12
In the formula,
Figure 762138DEST_PATH_IMAGE044
normalizing the excitation coefficient for the nth row of the two-dimensional antenna array;
therefore, the temperature of the molten metal is controlled,
Figure 396382DEST_PATH_IMAGE045
can be expressed as
Figure 306700DEST_PATH_IMAGE046
Equation 13
Wherein,
Figure 77210DEST_PATH_IMAGE047
and
Figure 31260DEST_PATH_IMAGE048
directional diagram functions of the column direction one-dimensional linear array and the row direction one-dimensional linear array are respectively calculated by using the formula in the step three;
step five: obtaining an amplitude directional diagram, a phase directional diagram and a gain, specifically:
amplitude directional diagram
Figure 887220DEST_PATH_IMAGE049
Comprises the following steps:
Figure 866809DEST_PATH_IMAGE050
equation 14
Wherein, (ii) (dB) Is in amplitude units;
phase direction diagram function
Figure 226246DEST_PATH_IMAGE051
Comprises the following steps:
Figure 616776DEST_PATH_IMAGE052
publicFormula 15
Wherein angle () is a phase taking function inρ = ρ 0 An electric field ofE m The electric field can be expressed as:
Figure 960033DEST_PATH_IMAGE053
equation 16
At the same time, is located atρ = ρ 0 Electric field ofE m Can also be expressed as:
Figure 602366DEST_PATH_IMAGE054
equation 17
By the above two formulae, it is possible to obtain:
Figure 957256DEST_PATH_IMAGE055
equation 18
If the observation point is located in the far field region, the electric field can be written as:
Figure 394053DEST_PATH_IMAGE056
equation 19
Directional pattern function of far field region
Figure 83660DEST_PATH_IMAGE057
Can be expressed as:
Figure 529685DEST_PATH_IMAGE058
equation 20
Gain compensation of antenna under test between quasi-far field and far field
Figure 739081DEST_PATH_IMAGE059
The calculation is as follows:
Figure 346780DEST_PATH_IMAGE060
equation 21
Wherein,
Figure 523683DEST_PATH_IMAGE061
a far-field pattern function is represented,
Figure 242240DEST_PATH_IMAGE062
representing a quasi-far-field pattern function.
2. The quasi-far-field measurement method based on separable excitation coefficient variables according to claim 1, characterized in that: in the first step, the quasi-far-field distance measurement meets the far-field distance of the antenna unit, the distance between the antenna to be measured and the test probe is calculated, and the antenna is placed on the turntable at the distance.
3. The quasi-far-field measurement method based on separable excitation coefficient variables according to claim 1, characterized in that: in the second step, a control computer is used for controlling a test probe which is consistent with the working frequency of the antenna to be tested and has known characteristics, the amplitude and the phase position of the test probe on a certain surface at the quasi-far-field position of the antenna are corresponded, and the amplitude and the phase position information obtained by the test are stored in a test file of the control computer.
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