CN101252223A - Method for determining flatness of flat plate slotted antenna array face - Google Patents

Abstract

The invention discloses a method for determing the planeness of a planar slot antenna array surface, mainly aiming at resolving the problem that the prior method does not take the interferences of the deformation error and the manufacturing error on the planeness of the array surface in actual operating conditions into consideration. Based on the antenna structural mechanics analysis and a functional relation expression between the deformation error and the manufacturing error of the planeness of the constructed array surface and a directional diagram of a far field of an electromagnetic field, the method of the invention analyzes the inference of the deformation error of the planeness of the array surface caused by the structural stress on the electrical property, and simultaneously analyzes the interference of the manufacturing error of the planeness of the array surface caused by the structural stress on the electrical property; depending on the analytic interferences of errors on the electrical property, the ratios of the deformation error and the manufacturing error are reasonably assigned by an optimized process, so as to realize the relatively accurate determination of the planeness of the planar slot antenna array surface. The method can be used for directing the processing, manufacturing and structural design of the planeness of the planar slot antenna array surface, thereby improving the whole performance of the planar slot antenna.

Description

Method for determining flatness of flat plate slotted antenna array face

Technical field

The invention belongs to antenna technical field, specifically relate under the constraints of electrical performance indexes, provide definite method of reasonable antenna array flatness, can be used for design Planar Slot Antenna.

Background technology

The front flatness is to weigh one of important technology performance index of estimating the Planar Slot Antenna quality, and it not only directly influences the aperture efficiency of antenna, also influences the main lobe width and the minor level of antenna pattern.Because the level of manufacturing process and the operational environment of antenna all can cause the flatness of antenna array and change, and the variation of flatness will directly influence the electrical property of antenna.Usually can determine its surface accuracy by antenna surface is measured, and then extrapolate the influence relation of surface accuracy antenna electric performance.Surface accuracy requires relevant with operating frequency usually, operating frequency is high more, and just tight more to the requirement of surface accuracy, generally requiring surface accuracy is 1/16～1/32 of operation wavelength, but for the surface accuracy of Planar Slot Antenna, promptly the front flatness determines also there is not the ripe method of a cover so far.

At present, definite method of the most frequently used at home and abroad front flatness has following several:

(1) the reflecting surface error of reflector antenna is to the influence of antenna gain, generally acknowledged Shandong is (Ruze) formula (Ruze J now, Amenna Tolerance Theory-A Review, proceeding of ieee, 1966) proper, Shandong formula now is to adopt statistical method to provide relation between its surface accuracy and the gain loss at reflector antenna.Because Shandong formula now provides at reflector antenna, and what adopt is the method for statistics, and what therefore be applied to flatness of flat plate slotted antenna array face determines to exist improper part.

(2) the front TOLERANCE ANALYSIS theory of array antenna, belonging to a period of time site error influences electrical property, be to consider as desirable point source, adopt the method for statistics to analyze the influence situation of the site error in a period of time, thereby provide determining the flatness on plane, a period of time place to electrical property by a period of time.This method is reported in " modern radar " 1996 the 18th phases " TOLERANCE ANALYSIS of ultralow secondary lobe array antenna " to some extent.This method is not owing to consider the characteristic of slit battle array, and same what adopt is the analytical method of statistics, thereby can not reflect the information of front flatness comprehensively.

In addition, above-mentioned two kinds of methods are not owing to combine with the antenna actual condition, having ignored the influence to electrical property of the distortion inaccuracy of front flatness in actual condition and foozle, is not again at Planar Slot Antenna simultaneously, thus facial plane degree poised for battle determine very inaccuracy.

The content of invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art, a kind of method for determining flatness of flat plate slotted antenna array face is provided, to realize flatness of flat plate slotted antenna array face being determined the more accurately overall performance of raising Planar Slot Antenna.

Realize that technical scheme of the present invention is, based on the antenna structure mechanical analysis, functional relation according to front flatness distortion inaccuracy and foozle and far-field pattern, analyze Planar Slot Antenna front distortion inaccuracy and foozle influence relation to far-field pattern, adopt the method for optimizing to distribute the proportion of distortion inaccuracy and foozle, can determine the front flatness of Planar Slot Antenna, detailed process is as follows:

A. the Planar Slot Antenna structure is carried out mechanical analysis, and obtains Planar Slot Antenna displacement structure information { δ } by stiffness equations:

{δ}＝[K] ^-1{p} (1)

In the formula, [K] is the stiffness matrix of Planar Slot Antenna structure, and { P} is for acting on the structural load vector of Planar Slot Antenna;

B. from described displacement information { δ }, extract the distortion inaccuracy Δ f (x of front flatness _p, y _p);

C. utilize the distortion inaccuracy Δ f (x of front flatness _p, y _p), the functional relation of structure front flatness distortion inaccuracy and far-field pattern:

$E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}{e}^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}---\left(11\right)$

In the formula, E _Total(θ φ) is Planar Slot Antenna front far-field pattern, f _p(l _p, w _p, V _p, θ φ) is the far-field pattern expression formula of Planar Slot Antenna front slit p, θ, φ are respectively the horizontal angle and the angle of pitch of Planar Slot Antenna front far zone field, l _p, w _p, V _pBe respectively long, the wide and driving voltage of seam of seam of slit p, k is a propagation constant, x _p, y _pPosition coordinates for slit p;

D. by the methods analyst distortion inaccuracy of statistics and the functional relation of far-field pattern, make up the function expression of front flatness foozle and far-field pattern:

$\stackrel{\‾}{E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})}=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}\exp (-\frac{{\mathrm{\σ}}^2}{2}{\left(k\cos \mathrm{\θ}\right)}^2)---\left(15\right)$

In the formula, σ is the root-mean-square value of front flatness foozle;

E. calculate the functional relation of front flatness distortion inaccuracy and far-field pattern and the function expression of foozle and far-field pattern respectively, obtain distortion inaccuracy and foozle Different Effects relation Planar Slot Antenna front far-field pattern;

F. according to distortion inaccuracy and foozle Different Effects relation, adopt the method for optimizing to distribute the proportion of distortion inaccuracy and foozle, can determine the front flatness of Planar Slot Antenna Planar Slot Antenna front far-field pattern.

The present invention is owing to adopt the functional relation of flatness of flat plate slotted antenna array face distortion inaccuracy and foozle and far-field pattern, analyze front flatness distortion inaccuracy and foozle influence relation to electrical property, and then reasonably distribute the proportion of front flatness distortion inaccuracy and foozle, can determine the front flatness of Planar Slot Antenna better.

L-G simulation test proves, can provide more rational front flatness error partition density with method of the present invention, improves the front flatness of Planar Slot Antenna and determines precision.

Description of drawings

Fig. 1 is the structure chart of Planar Slot Antenna;

Fig. 2 is the flow chart that the present invention determines flatness of flat plate slotted antenna array face;

Fig. 3 is the crack coordinate graph of a relation of Planar Slot Antenna;

Fig. 4 is the malformation condition diagram of Planar Slot Antenna;

Fig. 5 is the standing-wave line array antenna schematic diagram that the present invention uses;

Fig. 6 is the distortion front power radiation pattern of Fig. 5 when distortion cycle n=4;

Fig. 7 is that Fig. 5 is at the power radiation pattern that exists under the foozle situation.

Followingly the present invention is described in further detail with reference to accompanying drawing.

Embodiment

With reference to Fig. 1, the version of Planar Slot Antenna is usually by radiating guide with coupled waveguide is two-layer constitutes, by centroclinal seam of broadside and radiating guide coupling, this centroclinal seam is a coupling slot to coupled waveguide, is distributed between coupled waveguide and the radiating guide as driving source.The longitudinal joint of face width limit, radiating guide upper strata disalignment carries out radiation, and this longitudinal joint is a radiating slot, is distributed in aspect on the radiating guide.Radiating guide is vertical mutually with coupled waveguide, can be coupled with many radiating guides to realize a coupled waveguide.The present invention mainly is in order to provide method for determining flatness of flat plate slotted antenna array face, and therefore main research is front upper half-space electromagnetic radiation at the radiating slot place, will not relate to the problem of waveguide inside here.Because there is front flatness problem in Planar Slot Antenna, originally the radiating slot position changes, and brings the radiating slot space phase to change, and then influences the external electromagnetic field distribution, causes the Planar Slot Antenna electrical property to reduce.Therefore, emphasis consideration of the present invention is: how rationally to determine the front flatness, to guarantee the Planar Slot Antenna electrical performance indexes.

With reference to Fig. 2, the present invention determines flatness of flat plate slotted antenna array face, be to consider that flatness of flat plate slotted antenna array face comprises on the basis of distortion inaccuracy and two kinds of factors of foozle, make up the functional relation of front flatness distortion inaccuracy and foozle and far-field pattern, analyze Planar Slot Antenna front distortion inaccuracy and foozle influence relation to far-field pattern, and adopt the method for optimizing to distribute the proportion of distortion inaccuracy and foozle, can determine the front flatness of Planar Slot Antenna, concrete steps are as follows:

The first step: provide Planar Slot Antenna displacement structure information { δ }

The application structure analysis software ANSYS is carried out mechanical analysis to the Planar Slot Antenna structure, sets up the geometrical model of Planar Slot Antenna structure, and the imposed load vector obtains the displacement information { δ } of Planar Slot Antenna structure by stiffness equations:

{δ}＝[K] ^-1{p} (1)

In the formula, [K] is the stiffness matrix of Planar Slot Antenna structure, and { P} is for acting on the structural load vector of Planar Slot Antenna;

Second step: from described displacement information { δ }, extract the distortion inaccuracy Δ f (x of front flatness _p, y _p)

Owing to contain distortion inaccuracy Δ f (x in the displacement information { δ } except that the front flatness _p, y _p) in addition other displacement information, thereby can extract the distortion inaccuracy information Δ f (x of front flatness by a kind of self-built extraction matrix [A] _p, y _p), that is:

Δf(x _p，y _p)＝[A]{δ} ；(2)

The 3rd step: the distortion inaccuracy Δ f (x that utilizes the front flatness _p, y _p), make up the functional relation of front flatness distortion inaccuracy and far-field pattern according to the following procedure:

1. provide the functional relation of the single slit of Planar Slot Antenna front far-field pattern

The Electric Field Distribution of setting each slit is identical, and cross stream component is only arranged, and the width in each slit identical be w _p=w, crack coordinate relation as shown in Figure 3, the electric field strength E of p seam _p(y) be:

$E_p\left(y\right)=\frac{V_p}{w}\cos \left(\frac{\mathrm{\πy}}{{2l}_p}\right)---\left(3\right)$

In the formula, l _p, w _p, V _pBe respectively long, the wide and driving voltage of seam of seam of slit p, y is the y direction value of rectangular coordinate;

Determine electric field strength E _p(y) after, the far-field pattern in the slit that it is corresponding can be by opening the far-field pattern f of the rectangular aperture antenna on unlimited conductive plane _p(θ φ) is expressed as:

$f_p(\mathrm{\θ},\mathrm{\φ})=E_{\mathrm{\θ}}{\hat{a}}_{\mathrm{\θ}}+E_{\mathrm{\φ}}{\hat{a}}_{\mathrm{\φ}}---\left(4\right)$

$E_{\mathrm{\θ}}=-V_p{l}_p\cos \mathrm{\φ}\frac{\cos \left({\mathrm{kl}}_p\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}{{\left({\mathrm{kl}}_p\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}^2-{\left(\frac{\mathrm{\π}}{2}\right)}^2}---\left(5\right)$

$E_{\mathrm{\φ}}=V_p{l}_p\sin \mathrm{\φ}\cos \mathrm{\θ}\frac{\cos \left({\mathrm{kl}}_p\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}{{\left({\mathrm{kl}}_p\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}^2-{\left(\frac{\mathrm{\π}}{2}\right)}^2}---\left(6\right)$

In the formula, θ, φ are respectively the horizontal angle and the angle of pitch of Planar Slot Antenna front far zone field,

Be horizontal angle and pitching angle theta, the unit vector on the φ direction, E _θ, E _φFor

Electric field component on the direction, k are propagation constant,

Be the far-field pattern f in the single slit of Planar Slot Antenna front _p(θ φ) is:

$f_p(\mathrm{\θ},\mathrm{\φ})=V_p{l}_p\frac{\cos \left({\mathrm{kl}}_n\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}{{\left({\mathrm{kl}}_n\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}^2-{\left(\frac{\mathrm{\π}}{2}\right)}^2}(\sin \mathrm{\φ}\cos \mathrm{\θ}{\hat{a}}_{\mathrm{\φ}}-\cos \mathrm{\φ}{\hat{a}}_{\mathrm{\θ}})=f_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ});---\left(7\right)$

2. the functional relation of single slit far-field pattern is sued for peace, obtain the far-field pattern function E in all slits of Planar Slot Antenna front _Total(θ, φ) relational expression is:

$E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})\frac{e^{-\mathrm{jk}{r}_p}}{r_p}\≈\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})\frac{e^{-\mathrm{jkr}}}{r}{e}^{\mathrm{jk}(r-r_p)}---\left(8\right)$

In the formula: r _pBe the distance of slit p central point to point of observation, r is the distance of seam face reference point to point of observation;

3. the z that extracts the front flatness is to distortion inaccuracy z _p

By as shown in Figure 4 mechanical analysis deformation pattern as can be known, distortion inaccuracy mainly is perpendicular to the distortion of front direction, promptly the flatness distortion inaccuracy of front mainly be the z of radiating slot to distortion inaccuracy, therefore the front flatness distortion inaccuracy that extracts is that z is to distortion inaccuracy z _pFor:

z _p＝Δf(x _p，y _p) ；(9)

By z to distortion inaccuracy z _pObtain stitching the face reference point to the slit central point apart from r-r _p

Because z is to distortion inaccuracy z _pExistence, bring the front slit to change to the path length difference of point of observation, seam face reference point to the slit central point apart from r-r _pFor:

In the formula,

Be respectively x, y, the unit vector on the z direction; x _p, y _pPosition coordinates for slit p;

5. with (10) formula substitution (8) formula, obtain front flatness distortion inaccuracy and the far-field pattern function expression is:

$E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]+\mathrm{jk}{z}_p\cos \mathrm{\θ}};---\left(11\right)$

$=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}{e}^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}$

The 4th step:, make up the function expression of front flatness foozle and far-field pattern according to the following procedure by the methods analyst distortion inaccuracy of statistics and the functional relation of far-field pattern:

1. be poised for battle functional relation (11) formula of facial plane degree distortion inaccuracy and far-field pattern and carry out the average processing, promptly

$\stackrel{\‾}{E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})}=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}\stackrel{\‾}{e^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}}---\left(12\right)$

2. with the average item on (12) formula equation the right

Carry out following processing

(1) sets the site error Δ f (x in each slit _p, y _p) be independent of each other, and satisfy all refer to be 0, variance is σ ²Normal distribution, i.e. position error delta f (x _p, y _p) probability distributing density function f (Δ f (x _p, y _p)) be:

$f\left(\mathrm{\Δf}(x_p,y_p)\right)=\frac{1}{\mathrm{\σ}\sqrt{2\mathrm{\π}}}\exp (-\frac{{\mathrm{\Δf}}^2(x_p,y_p)}{{2\mathrm{\σ}}^2})---\left(13\right)$

(2) according to site error Δ f (x _p, y _p) probability distributing density function f (Δ f (x _p, y _p)), with the average item on (12) formula equation the right

Processing obtains:

$\stackrel{\‾}{e^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}}={\∫}_{-\∞}^{+\∞}{e}^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}f\left(\mathrm{\Δf}(x_p,y_p)\right)d\left(\mathrm{\Δf}(x_p,y_p)\right)=\exp (-\frac{{\mathrm{\σ}}^2}{2}{\left(k\cos \mathrm{\θ}\right)}^2)---\left(14\right)$

3. with (14) formula substitution (12) formula, the function expression that obtains front flatness foozle and far-field pattern is:

$\stackrel{\‾}{E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})}=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}\exp (-\frac{{\mathrm{\σ}}^2}{2}{\left(k\cos \mathrm{\θ}\right)}^2);---\left(15\right)$

The 5th step: calculate the functional relation of front flatness distortion inaccuracy and far-field pattern and the function expression of foozle and far-field pattern respectively, obtain distortion inaccuracy and foozle Different Effects relation to Planar Slot Antenna front far-field pattern;

The 6th step: according to distortion inaccuracy and foozle Different Effects relation, adopt the method for optimizing to distribute the proportion of distortion inaccuracy and foozle, can determine the front flatness of Planar Slot Antenna to Planar Slot Antenna front far-field pattern.

Advantage of the present invention can further specify by following emulation:

One. simulated conditions

1. the standing-wave line array antenna to 16 slits shown in Figure 5 carries out determining of front flatness.The parameter of this antenna is: design frequency: 10GHz, waveguide dimensions: 22.86*10.16*1mm ³, stitch wide: w=1.6mm.Table 1 provides excitation amplitude, side-play amount and the resonance length of this each array element of antenna that draws by Taylor's synthesis.

Table 1

Sequence number	The excitation amplitude	Side-play amount x (mm)	Resonance length 21 (mm)	Sequence number	The excitation amplitude	Side-play amount x (mm)	Resonance length 21 (mm)
								1	0.3652	1.40	14.47	9	1.0000	2.35	14.42
2	0.4419	1.54	14.55	10	0.9523	2.29	14.42
								3	0.5602	1.74	14.42	11	0.8750	2.19	14.43
4	0.6801	1.92	14.35	12	0.7841	2.07	14.46
								5	0.7841	2.07	14.46	13	0.6801	1.92	14.35
6	0.8750	2.19	14.43	14	0.5602	1.74	14.42
								7	0.9523	2.29	14.42	15	0.4419	1.54	14.55
8	1.0000	2.35	14.42	16	0.3652	1.40	14.47

2. the distorted pattern of supposing this linear array antenna is:

z _p＝σcos(2πny/8λ _g) (16)

In the formula, σ is the amplitude of distortion, and n is the distortion cycle, λ _gBe guide wavelength.

Two. simulation process

Be poised for battle the functional relation of facial plane degree distortion inaccuracy and far-field pattern by the MATLAB programming and analyze, provide the front flatness in σ=0, λ/10, λ/30, the power radiation pattern of the H face under λ/50 situations, as shown in Figure 6.The power radiation pattern of distortion front utilized the functional relation of front flatness foozle and far-field pattern that Fig. 6 is analyzed when Fig. 6 was distortion cycle n=4, had provided root-mean-square value σ=0 respectively, λ/10, λ/30, the power radiation pattern under λ/50 situations, as shown in Figure 7.

Three. simulation result

Can draw following emulation conclusion by Fig. 6 and Fig. 7:

1) directive gain of antenna loss increases along with the increase of flatness tolerance, this tolerance mainly shows as foozle and distortion inaccuracy, but under the situation of same root-mean-square value, the influence of foozle will be higher than distortion inaccuracy, so gain loss will mainly be subjected to the influence of foozle.

2) for the standing-wave line array antenna, the cyclomorphosis of front flatness, very little to the influence of main lobe, mainly be that secondary lobe is exerted an influence, and along with the raising of flatness amplitude, the influence of secondary lobe is increased, and under the identical situation of cyclomorphosis, be the same to the impact position of secondary lobe.

3) front flatness distortion inaccuracy does not almost have the influence of main lobe, mainly is to influence minor level.Along with root mean square increase, the level of secondary lobe will progressively improve, and does not widen the width of main lobe; And front flatness foozle almost can be ignored minor level influence.

Therefore for an actual antennas structure, at known front flatness distortion inaccuracy and foozle after the influence relation to electrical property, can be according to the demand of actual antennas to electrical performance indexes, the obtain an equitable breakdown proportion of front flatness foozle and distortion inaccuracy of the method for adopt optimizing, reaching the electrical performance indexes optimum, thereby determine the front flatness of Planar Slot Antenna.For example,, then need reduce the distortion inaccuracy of Planar Slot Antenna, can improve the rigidity and the intensity of antenna structure the demanding antenna of minor level; To the strict antenna that gains, then need in the process of making, to reduce the foozle of front flatness as far as possible, improve the processing and manufacturing precision of antenna surface.

Claims (3)

1. method for determining flatness of flat plate slotted antenna array face comprises following process:

A. the Planar Slot Antenna structure is carried out mechanical analysis, and obtains Planar Slot Antenna displacement structure information { δ } by stiffness equations:

{δ}＝[K] ^-1{p} (1)

In the formula, [K] is the stiffness matrix of Planar Slot Antenna structure, and { P} is for acting on the structural load vector of Planar Slot Antenna;

B. from described displacement information { δ }, extract the distortion inaccuracy Δ f (x of front flatness _p, y _p);

C. utilize the distortion inaccuracy Δ f (x of front flatness _p, y _p), the functional relation of structure front flatness distortion inaccuracy and far-field pattern:

$E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}{e}^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}---\left(11\right)$

In the formula, E _Total(θ φ) is Planar Slot Antenna front far-field pattern, f _p(l _p, w _p, V _p, θ φ) is the far-field pattern expression formula of Planar Slot Antenna front slit p, θ, φ are respectively the horizontal angle and the angle of pitch of Planar Slot Antenna front far zone field, l _p, w _p, V _pBe respectively long, the wide and driving voltage of seam of seam of slit p, k is a propagation constant, x _p, y _pPosition coordinates for slit p;

D. by the methods analyst distortion inaccuracy of statistics and the functional relation of far-field pattern, make up the function expression of front flatness foozle and far-field pattern:

$\stackrel{\‾}{E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})}=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}\exp (-\frac{{\mathrm{\σ}}^2}{2}{\left(k\cos \mathrm{\θ}\right)}^2)---\left(15\right)$

In the formula, σ is the root-mean-square value of front flatness foozle;

E. calculate the functional relation of front flatness distortion inaccuracy and far-field pattern and the function expression of foozle and far-field pattern respectively, obtain distortion inaccuracy and foozle Different Effects relation Planar Slot Antenna front far-field pattern;

F. according to distortion inaccuracy and foozle Different Effects relation, adopt the method for optimizing to distribute the proportion of distortion inaccuracy and foozle, can determine the front flatness of Planar Slot Antenna Planar Slot Antenna front far-field pattern.

2. method for determining flatness of flat plate slotted antenna array face according to claim 1 is characterized in that the functional relation of the described structure front of step C flatness distortion inaccuracy and far-field pattern carrying out according to the following procedure:

C1. provide the functional relation of the single slit of Planar Slot Antenna front far-field pattern:

$f_p(\mathrm{\θ},\mathrm{\φ})=V_p{l}_p\frac{\cos \left({\mathrm{kl}}_n\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}{{\left({\mathrm{kl}}_n\sin \mathrm{\φ}\sin \mathrm{\θ}\right)}^2-{\left(\frac{\mathrm{\π}}{2}\right)}^2}(\sin \mathrm{\φ}\cos \mathrm{\θ}{\hat{a}}_{\mathrm{\φ}}-\cos \mathrm{\φ}{\hat{a}}_{\mathrm{\θ}})=f_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})---\left(7\right)$

In the formula,

Be respectively horizontal angle and pitching angle theta, the unit vector on the φ direction;

C2. the functional relation of single slit far-field pattern is sued for peace, the far-field pattern functional relation that obtains all slits of Planar Slot Antenna front is:

$E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})\frac{e^{-\mathrm{jk}{r}_p}}{r_p}\≈\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})\frac{e^{-\mathrm{jkr}}}{r}{e}^{\mathrm{jk}(r-r_p)}---\left(8\right)$

In the formula, r _pBe the distance of slit p central point to point of observation, r is the distance of seam face reference point to point of observation;

C3. the z that extracts the front flatness is to distortion inaccuracy: z _p=Δ f (x _p, y _p);

C4. by z to distortion inaccuracy obtain stitching the face reference point to slit p central point apart from r-r _pFor:

In the formula,

Be respectively x, y, the unit vector on the z direction;

C5. with (10) formula substitution (8) formula, obtain front flatness distortion inaccuracy and the far-field pattern function expression is:

$E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]+\mathrm{jk}{z}_p\cos \mathrm{\θ}}.---\left(11\right)$

$=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}{e}^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}$

3. method for determining flatness of flat plate slotted antenna array face according to claim 1 is characterized in that the function expression of described structure foozle of step D and far-field pattern carrying out according to the following procedure:

The functional relation of D1. being poised for battle facial plane degree distortion inaccuracy and far-field pattern carries out average to be handled, promptly

$\stackrel{\‾}{E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})}=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}\stackrel{\‾}{e^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}};---\left(12\right)$

D2. set the site error Δ f (x in each slit _p, y _p) be independent of each other, and satisfy all refer to be 0, variance is σ ²Normal distribution, then with the average item on (12) formula equation the right

Processing list is shown:

$\stackrel{\‾}{e^{\mathrm{jk\Δf}(x_p,y_p)\cos \mathrm{\θ}}}=\exp (-\frac{{\mathrm{\σ}}^2}{2}{\left(k\cos \mathrm{\θ}\right)}^2);---\left(14\right)$

D3. with (14) formula substitution (12) formula, the function expression that obtains front flatness foozle and far-field pattern is:

$\stackrel{\‾}{E_{\mathrm{total}}(\mathrm{\θ},\mathrm{\φ})}=\underset{p}{\mathrm{\Σ}}{f}_p(l_p,w_p,V_p,\mathrm{\θ},\mathrm{\φ})e^{\mathrm{jk}\sin \mathrm{\θ}[x_p\cos \mathrm{\φ}+y_p\sin \mathrm{\φ}]}\exp (-\frac{{\mathrm{\σ}}^2}{2}{\left(k\cos \mathrm{\θ}\right)}^2).---\left(15\right)$

Images