CC BY
7
Y^K 621.396
Investigation of the Field Scattered by Phased Equidistant Arrays Based on Asymptotic Methods of Electrodynamics
Sidorchuk 0. L.1, Fryz S. P.\ Havrylko Y. V?, Sobolenko S. 0.\ Fedorova N. V.3
1S. Korolev Military Institute, Zhitomir, Ukraine 2 National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine telecommunication Technologies, State University of Telecommunications, Kyiv
E-mail: sidorchuk_ o&ukr.ncl■
It is suggested that, the asymptotic method of saddle point, be used for solution of integral elect.rodynamic equations of the electromagnetic field scattered by phased equidistant, antenna arrays. This makes it. possible to study the regularities of the re-radiat.ed field in two arbitrary planes. The obtained expressions will contribute to design of new antenna systems, which will reduce electromagnetic field scattering. This will as well improve the electromagnetic compatibility of electronic equipment, installed in the same or in adjacent, objects equipped with antenna systems. The research results can be used to design algorithms for detection, recognition and identification of radar targets.
Key words: phased antenna arrays, study of electromagnetic field, asymptotic methods, effective scattering surface
DOI: 10.20535/RADAP. 2020.80.14-22
Introduction
The study of electromagnetic field scattering characteristics (re-radiation) caused by air and ground objects is important for radio detection and navigation. Sometimes it means "radar visibility"of the objects.
The antenna systems of air and ground objects are the largest contributors to their radar visibility.
They are the main sources of follow-up radiation or re-radiation of electromagnetic waves from the probing radar stations (RS). This phenomenon increases radar visibility of such objects in addition to negative impact on electromagnetic compatibility of radio electronic devices installed therein.
According to a number of sources fl 5]. the contribution of antenna systems can be up to 98% of the total effective scattering surface (ESS) of the objects.
This is especially true of aperture antennas and phased antenna arrays (PAA) of RS [5 7].
1 Analysis of recent research and publications
Analysis of the causes and regularities of PAA scattering proves complexity of its elimination. Special design and application of special coatings that reduce the level of reflected signal from the objects are not always acceptable for their antenna systems.
Typically, snch improvements result in degradation of other main characteristics of antenna systems gain, directional operation, etc. Therefore there is a need to optimize them according to the "efficiency visibility"characteristic [4 7].
Unfortunately, it is not always appropriate.
The problem is that each radio system is a source of radiation and any antenna scatters more than half of the incident energy [5].
Moreover, if the antenna system does not scatter any energy, it and does not receive it. It means that it is impossible to avoid snch scattering (re-radiation) completely, but the scattering can be significantly reduced [2 5].
So it is essential to study the electromagnetic field and scattered PAA in order to develop methods reducing it.
The scattering properties of any objects are usually described by effective surfaces (widths, areas) the scattering is to be described by integral (ctj) differential (aa) surfaces and the scattering matrix (M) [ ].
When studying scattering or wave re-radiation. PAA antenna system waves shall be considered a group of radiators, which represent an ensemble of shiny-spots.
In this case, the problem of finding integral and differential scattering surfaces is reduced to the calculation of ESS group of radiators, with surface current
brought upon each arid electromagnetic field strength amplitudes excitation [5 7].
The complex strength amplitude Er of the electromagnetic field scattered by the reflector, which is at a distance R from the observation point shall be calculated according to expression [7]:
Er —
En
JkR
(1)
where En is a complex wave strength amplitude on the n reflector; a1 is ESS for one radiator; k = 2n/\ is wave number; A is wave length.
On the basis of the superposition principle for a linear equidistant array from N radiators [ , ], the re-radiated signal at the receiving end shall be created by the interference of the signals reflected from all the radiators located along y axis (fig. ).
The complex field strength amplitude Ety, for a linear equidistant PAA with N emitters in [ ] shall be calculated according to the expression proposed in [7]:
Erv, —
N
E
Ei.
JkR
(2)
where Ein is a complex strength amplitude for the wave falling on n radiator; an is ESS of n radiator; Rn is a distance from observation point to n radiator.
x
M-1
,, m=1 n=l
+ Em,n (t ,0) + -ATg{pm,n)
(3)
where an (<p, 0) is a back scattering diagram for n radiator; pm,n is a reflection coefRcient; ARm,n (<p, 0) is a travel path deviation for a plane equidistant antenna array; Fm,n (t, 0) is a phase distribution of the incident signal function of the spatial and temporal aperture coordinates; M is a number of radiators along axis x] N is a number of radiators along axis y.
The study of the causes and regularities of secondary emission show that the main parameters of the system "PAA probing RS"that affect the level of the reflected signal, are the angles Of ,<p. They characterize the aspect of PAA re-radiation.
The re-radiated signal level is influenced by a complex of PAA characteristics: orientation diagram f (Of, p), number of radiators along axis y M and along axis x N , the dist^ce between them dx mid dy and the electromagnetic waves travel path deviation.
A possibility to reduce ESS of the antenna system by means of effective phase distribution of the incident signal Fm,n (t, f, 0)
clS ct function of spatial and temporal PAA aperture coordinates was considered in
[71-
f (9,<p), dx, dy, M,N are a priori known design characteristics of PAA class. They are practically unchanged during the service life of RS [7].
Angles 0,<f vary depending on PAA spatial position relative to the probing RS and PAA operating mode [7].
Consequently, we can reduce ESS of an equidistant PAA by changing design properties of all radiators, or by changing distances between them proportionally
d>xi dy.
For this purpose, we must study the amplitudes in the waveguide aperture of n radiator (Fig. ).
Fig. 1. Parameters of equidistant rectangular PAA for calculation of the scattered field at an incidence angle Of for a plane electromagnetic wave normally polarized to the incidence plane
The expression for back scattering (<f, Of) (of an integral single-position ESS) for a rectangular PAA shown in Fig. 1. shall be as follows [7]:
(V, Of )= an (tfi,0) x / M N
X E E IP
| cos (kARm,n (<p, 0)) +
Fig. 2. Waveguide characteristics nsed for calculation of the scattered field with incident normally polarized wave
The amplitudes of the field, which is excited on a linear equidistant array (Fig. 3) were considered in [10].
However, the final expressions concerned determination of the amplitudes, excited during aperture of snch array only if the incident wave is normally polarized to the incidence plane.
In other free sources [7.9.11]. the excited amplitudes and re-radiation field expressions are simplified and rather approximate. They do not allow to study the total field scattered from PAA with necessary accuracy in the case it is exposed to the wave normally polarized to the incidence plane at an angle Of from arbitrarily-selected f in order to reduce it.
Efn — E+n + Ef n,
(4)
where E+n is the strength of radiator field n= 1; Ejn is the strength of field n = -l.
In this case, the total field scattered by the linear radiator array shall be:
( ^ )
EfP — Ef 0 Efn,
(5)
where Ef 0 is the strength of the field, which is formed by the central radiator.
In order to determine Ef 0 it is necessary to investigate the wave amplitude in the aperture.
Let an independent source be placed inside the central radiator in the transmission mode (see Fig. 1) and form a field, which shall be marked Ef 0, Hf 0 inside and outside.
Inside the horn snch a field shall be usually considered eigenfunction and marked -mn. However, due to the fact that index is already in nse, we shall propose a
field with a unit amplitude as E±r
■H
±mxmv
It is
reflected from the aperture with a reflection coefficient
P+
mxm„ •
Ëp o — (Ë-mœmy Hp o = (H—m^my
+ P+ma
+ P+mxmy ,
(6)
Fig. 3. Characteristics of horn-type radiator line nsed for calculation of the scattered field with incident plane electromagnetic wave normally polarized to the incidence plane
Against this background, the purpose of the article is to study the field re-radiated by a linear equidistant PAA, which is formed by an incident wave normally-polarized to the incidence plane at an angle <p, and to determine causes and regularities of this phenomenon in order to reduce it.
2 Presentation of the basic material
Let the electromagnetic wave Ef, Hf which is formed by external currents distributed with density j mid m be incident to the PAA aperture consisting from n horn-type radiator linear arrays (see Fig. ).
It is important to find a field scattered by snch antenna.
Solution. We shall number the radiators from the center to the edges so that the central one is a zero one, while the extreme radiators are (N — 1)/2 as shown in (see Fig. 1). The total number of the elements in the array shall be odd and equal to N.
The strength of the field Efn, formed by a pair of radiators symmetrically located about the center shall be written as
where (—mx, my) is the number of standing semi-waves, which fall on the sides of the cross-section and extend from the neck to aperture; (+mx, my) is the number of standing semi- waves propagating from the aperture to the neck.
Consequently, on the surface of the antenna aperture Sf from the inner side, a full field can be presented by an eigenfnnction expansion [9,10]:
E ^ ] C±mxmy {E+mœmy + P—mœmy E—mœmy^
H 'y ] C±mxmy {H+mxmy + P—mœmy H+m^m^
(7)
where A±m^my are eigenfunction amplitudes; E+m^my, H+mxmy are eigenfunctions, which spread from the aperture to the neck; E-mxmy, H-m^my are eigenfunctions spreading from the neck to the aperture;
p—mxmv - coefficient of eigenfunction reflection from internal inhomogeneities in the horn.
In order to study the field Epp scattered by-aperture of one or n-th radiator of the antenna, we shall nse asymptotic methods with application of Lorentz lemma.
In order we could determine snch a field, it is necessary to implement strict boundary conditions, i.e. continuity and tangential components of the total field E mid H to aperture S p.
Let's place coordinate origin in the center of the array (2 = 0) (see Fig. ).
For this case we have:
[Ef (z — 0) + EPp (z — 0) (Hf (z — 0) + HPp (z — 0)
E (z — 0)
H (z — 0)) ,
(8)
where Ef, Hf are the strengths of electric and magnetic fields incident on the aperture and excited by currents beyond the horn; E, H are the strengths of the electric and magnetic fields from the aperture (4).
y
rn^rri
T
T
A component of the field Epp scattered throughout the space may be presented as a continuous spectrum of plane waves [9]:
Epp = ±jj&(kx,ky) e-i(k*x+kyy+k*z)dkxdky,
— TO
(9)
where A (kx,ky) is a spectral function of the complex amplitudes of plane waves: k^j ^^ fag are projections of the wave vector to the axes x,y,z, which are connected by formula k2 = k"2 + k^ + k2z.
After we ping (4) and (C) into (5). we get:
EfT + 11 (kx, ky) e—i(k-x+k«y)dkxdky
Let's ping (10) into (7)
Epp =
epp 4-k2
TO /■
u №
C+v E+VT (1 + p—v) •
— \Sp)
• ei{kxx+kv y) — (z = 0)ei{kxx+kv y)
dxdy
• e—i{kxX+ky y+k* z)dkxdky. (14)
The magnetic components of the scattered field can be obtained from the Maxwell's equations:
(1+ P+v),
v=\
(10)
J { (I tip) - Hp) } dV
v
E, Hp
Ep, H
,dS,
Hpp = — rotE.
up
(15)
where C+u is an amplitude of the excited wave.
A similar expression will be used for H field components.
Let's multiply both sides of the equation (7) by ei(kxx+kvy) anj integrate them over x mid y on the aperture surface Sp.
We shall write the Lorentz lemma [9] for the volume limited by an infinitely distant from the antenna surface and a bounded surface Sp (see Fig. ) as:
In order to calculate the scattered field according to [5] we shall apply the cross-section method. We must take into consideration that in addition to the waves excited in the aperture and reflected from the internal inhomogeneities. there are so-called "parasite"waves.
The field scattered by n-th radiator shall be written
as:
(ID
and then complete the integration from EpT to infinite limits provided EpT (z = 0) = 0 beyond the surface Sp. If we use the relation obtained in [9]:
e —
00 ( TO
//I// [E [A+nE+n(1+ p—„)]ei(k*x+ky y)
-TO ^ si
• EUT(z = 0)ei(k*x+kyy) dxdy^j
e-i(kxx+ky y+kz z)dkxdky, (16)
AT (kx, ky) = 412 11 x
AT (kx, ky) e-i(k*x+kyy)dkxdky
x ei{kxx+kyv)dxdy, (12)
we shall have:
AT (kx, ky) = -JJ EUt (z = 0) ei(k*x+kyy)dxdy+
(Sp )
p p TO
+ E C+-(1+ P+-) ¿(k*x+kyv)dxdy. (13)
(Sp)
v=1
where Sp is the aperture integration surface of n-th radiator (see Fig. ) from the inner side; ep is a unit electromagnetic field strength vector; A+n is a spectral function of the complex amplitudes of the plane waves excited at the aperture; E+n is the strength vector of the electromagnetic field incident on the n-th radiator; kx, ky, kz are the projections of the wave vector on axes x, y, z; EVT (z = 0) is the strength vector of the electromagnetic field after taking into account the boundary conditions and integration ad infinitum beyond the surface Sp; p—n the internal inhomogeneities reflection coefficient of the n-th radiator.
For the case of normal polarization of the wave in the plane of incidence, after plugging eigenfnnctions [9] into ( ) and their integration over x, y the tangential
x
component of the field EppT will be:
EPpr = -
bp sin ( ^ )
TO / \
s£^ (?)
The method of saddle point (steepest descent) is one of snch asymptotic methods. It gives us an adequate accuracy and has a wide application for the study of different wave phenomena: acoustic, electromagnetic, etc [10].
In order to apply the above method, we shall present the expression (15) in a spherical coordinate system:
sin2 (^) cos (- ¿cos2 () sin (x = r sin 0 cos f, y = r sin 0 sin f, z = r cos f.
; T2 + ______...... .
+ E0ap
fe) - (ky)2
sin (Or (ky — k sin Of )) 1 Of-(ky — k sin Of) J
• e{-i{ k*x+kvy+kzz))dkxdky, ^
where «^d bp are the dimensions of the rectangular aperture of the n-th horn radiator (see Fig. ).
We have to decide on the most effective or appropriate method studying the field EppT in order to solve the problem.
Generally, the theory of wave propagation suggests a limited number of problems that allow exact solution. In those few cases where strict relations are known, they are quite complicated and do not allow to reveal physical nature or canse of the process regularities even with the help of advanced software packages.
We can understand the attention to the approximate methods of the wave theory, particularly asymptotic methods [10.11] in recent years.
They are still relevant. In order we could apply the above methods, we shall rewrite (14) as:
1
where
1x1 (kx) = bp (^sin 2
2 / kxbp
Ixi (ky) = 2 £ —C*t (1 + PHn)~ f-n {k
y
n=1
1 _ f apky
rnr
— Eoap-
sin ((ky — ksin 0n))
Of- (ky — k sin 0n)
We get the following dependence:
EpPT = J Ixi (kx )exp(—ikxr sin 0 cos y) dkxx
— TO
TO
x/ Ix. (ky )eM—Hky sin sin * + ^ cos 0))dky .
— TO
(21)
Using the method of saddle point, we solve the equation (21):
EPPr « cos TJ^^ exp (^o) 42
2-k cos z
exp
x (k sin W0 cos zo) ..
r | f (¿o)| x Ix1 (k sin z0) k cos z0 exp (i<pm)
rk (—i sin 0 cos <p sin z0 + cos z0f (Wo))
.
EPpr = 4^2 J Ixi(kx)exp(—ikxx)dkx
— TO TO
x 1x2 (ky) exp( —i(ky y + kz z))dky, (18)
In order we could identify the physical nature of the phenomenon, let us consider a field scattered in some planes.
Usually we use a plane <p = 3^/2 and p = -k. In the plane f = 3-k/2 we have:
(19)
sin <p = —1; cos <p = 0; W0 = —0;
zo = 0; f (Wo) = — i; f'' (Wo) = i;
fo = 4; <fm = 4; f'' (zo) = i
(23)
E1
rpr |^=
k cos 0 / / -K ^ » -exp —i[kr--1 1 x
2nr pV V 2 J
x Ixi (kx = 0) 1x2 (ky = — k sin 0) . (24)
In the plane <p = n we get: (20) sin ip = 0; cos p = —1; Wo = 0;
The functions Ix1 (kx) mid Ix2 (ky) under the integrals in the expression (15) depend upon several parameters characterizing the system.
In this case, it will be the method of asymptotic evaluations helping us both take the integral and obtain the explicit dependence from the parameters specified in arbitrary planes of the incident wave.
f (Wo) = — i cos Oi; zo = — 0; f'' (Wo) = i cos 0;
<fo = 4; = 4; f'' (zo) = i
44
k cos 0 ( ( -K \\ -exp —i[kr--x
2-nr F V V 2JJ
x Ixi (kx = — k sin 0) 1x2 (ky = 0) . (26)
E,
rpr
2
2
The expression (22) shall be as follows for a linear equidistant antenna array:
EPpr —
f
bp sln( ^)
fax bp
to / \ 2
]T i-)2C^my X (l+Pomy) exp(—inkydy) mv=i \ ap /
• 2 / \ i ■ 2 i n \ • i kv av\
ln (~2) S{— 1 COs2i-2~) Sln{"V")
№)2 - k2 — Eq exp (indy (k sln Qn — ky))
sln ((ky — k sln #n))
-f (ky — k sln 0n) X exp (—i (kxx + kyy + kzz)) dkxdky, (27)
where C^my has been obtained in [ , ].
In contrast to the existing approaches, the expression (27) allows to calculate a field both for linear and equidistant rectangular PA A.
The expression (27) differs from (21) because it takes into account the number of n radiator and the distance between them dy.
The difference is also in use of (27) for more accurate expression for the amplitude C^ and additional multipliers exp(—inkydy) and exp (indy (k sin On — ky)).
HL_ AEpap (l+cos(0n)) w
°On —--n-X
(n^Y
^sln ^if^) cos ^ ^¡T- sln
(l + \ll — (£T) (i — P2^n){l — (& sln 0n)2) j (cos (sln (^ sln 0n)
H
+
— (Y) (1 — P^)^ — ( ^ sln On)2)
(28)
Fig. 4 shows the maximum amplitude superposition's for the most common modes of electromagnetic
to
field strength ^ —2C^Qm for a linear equidistant
my = 1
PAA depending on the changing coefficient of reflection Pvmy (27) from the internal heterogeneities of each radiator.
The simulation was performed for Pvmy — 0,8 Curve 1 and for pQm — 0,6 - Curve 2.
0 30" 60" 90" 120" 150" 180"
Fig. 4. Maximum amplitudes of the electromagnetic
field
Fig. 4 demonstrates that an improvement of adjustment in the antenna path shall result in an increase in the maximum amplitude of the signal in the transmission mode.
Fig. 5 shows the normalized maximum amplitudes of the waves excited at the aperture of the linear equidistant PAA depending on the side-scan remote sensing angle 6f with spedfied y: for incident normally-polarized wave C(Curves 1,2,3,4,5) and if the incidence plane and the plane of polarization of the
waves coincide C_
\h
(lines 6,7).
0,8 0,6 0,4 0,2 cm, cm, (B / m) pi =0,95 P. = ,9 t
cZ\ /
A p01, = 0 /
K = 0, / .
V Pi'., 0,3 ef
360°
Fig. 5. Dependence of the maximum normalized wave amplitude from the side-scan remote sensing angle resulting from reflection coefficient changes
The studies were carried out for different values of the reflection coefficients.
The wave amplitudes (lines 1,2,3) in Fig. 5 are almost identical with the sensing angle wave amplitudes in a polar coordinate system (lines 1,2,3) in Fig. 6, which were obtained using a simplified expression.
We can check the reliability of the obtained mathematical expressions using asymptotic methods for solution of integral equations.
To reveal the causes and regularities of re-radiation from the aperture of the equidistant PAA for the specified arbitrarily selected y provided a normal polarization of the incident wave in the incident plane, we shall
x
mxm
y
0
use again the asymptotic method of saddle point in the plane ¡p = 3/2-k mv\ ¡p = -k.
Thus, the field scattered in the plane ¡p = 3/2-k shall
be:
E
L H
kbp sin 9 / / -k\ .
exp i—tikr — — ) ) x
CAR i )
fcAlAeA
180
Pp {<e= ¥ ) 2^r V " V"' 2 <| — E0ap exp (indyk (sin 9 + sin 9f)) x
sin ^(sin 9 + sin 6n) j
^ (sin 9 + sin 0n)
TO
+ 2 ^ —CHtny (1 + P—Orny) exp (—ikndy sine) x
210
330
my = 1
• 2 i \ / kav
cos (^ sin 0) + ¿cos2 (sin (^ sin 6)
1
sin
\myn J
(32)
Fig. 6. How the wave amplitude depends from the side-scan remote sensing angle in a polar coordinate system
After we take an integral (16) the field scattered by the antenna array shall be as follows in the plane ¡p = 3/2^'.p = -n/2
In the plane p = n we get: EpH(.=) = ^exp (—*(kr — |)) x
x IX1 (kx = — k sin 0) Ix2 (ky =0), (33)
where
Ix1 (kx = — k sin 0)
PL H__
^pP (v= ^ ) = 2^r
k cos 9 ( / .
exp 1 ykr — — ) ) x
bp sin ^ ^br sin
k bv • n sin 9
(34)
x 4i (kx = 0) IX2 (ky = — k sin 9), (29) Ix2 (ky = 0) = 2 ^ —G+L-^ (l + pH0m J x
where
• 2 lny n
sin --Eoa,p- ka
2 P ^ sin 9
sin ^ sin
( kxbp\
sin -- .
\ 2 J ( kxbp
T i-l kxbp\ 1
1x1 = bp sin 1 -^
exp (ikndy sin Of).
' (30)
(35)
Ix 1 (0) = bp, if kx = 0.
Taking into account (33), (34) the expression for the scattered field in the plane ¡p = -k shall be:
IX2 (ky = — k sin 0) = — 2 V CHL-" (1 + P—omy)
/ •
^—i kndy sin 6
2 (^f-) cos( ^ sin 0)
1
sin 0
+
+
2 /m^ \ i kar. • /A
«cos2 (—) sin ( sin 0 I
1 — ( sin 0
P L H
kbp cos 0 2-nr
^ (sin 0 + sin 0n)
exp ^—i [kr — ^^ x
sin ^ ^br sin
k bv • n ~2T sin 0
H ^sin2 ^
y ! 2
^ ^ + PH0m^ si
in ^ sin 0 j
sin ^Ot sin 0
— Eoap-kO^ . 0
-¡fi- sin 0
exp(ikndy sin 9f). (36)
2
^o • eind»k (sin6+sin6n) • si^^ (sin9 + sin0n)) Conclusion
The application of asymptotic methods of electrodynamics allows us to determine the field
0
2
2
2
y
2
scattered from the horn aperture in the case of normal polarization of the incident wave to the plane of incidence, and in the case of coincidence of the plane of incidence and wave polarization.
The electromagnetic field scattered by phased equidistant RS antenna arrays can be reduced by application of asymptotic methods for solution of integral equations as evidenced from the simulation according to the obtained expressions.
We have proved that in order to determine the scattered field it is advisable to apply the method of saddle point.
The wave amplitude diag rams as functions of the side-scan remote sensing angle shown in Figure 4, 5. C demonstrate that an improvement of adjustment in the antenna path shall result in an increase in the maximum amplitude of the signal in the transmission mode. According to the antenna reciprocity principle, snch adjustment will improve absorption of the top type waves at the aperture of an individual radiator or an equidistant antenna array.
This will reduce the voltage standing wave ratio and the side lobe level.
Consequently, the probing RS will receive a reduced re-radiated signal, which will improve reconnaissance protection of PAA [1.9].
The above expressions (6) for an individual radiator and (16) for an equidistant antenna array-have computational, practical, and methodological valne. Their consistent development and physical interpretation will allow us to estimate their use in the study of the scattered (re-radiated field) for PAA and other antenna systems with pyramidal horns used as exciters.
The results obtained apply both to the development of electrodynamics theory and to the improvement of calculation methods [12 16]. They can be applied in the development of algorithms for detection and recognition of radar targets.
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Застосування асимптотичних метод!в для дослщження електромагштного поля, розсияного еквщистантними ан-тенними ретштками
СиОорчук О. Л., Фриз С. П., Гаврилки 6. В., Соболенка С. О., Федорова Н. В.
Вудь-яка антенна система е джерелом вторинного випромшюванпя, оскшьки розс!юе не менше половини падаючо! на не! еперги, що вплнвае на рад!олокац!йпу пом!тн!сть всього об'екта, на якому вони встановлеш.
Це означав, що такого розаювання (перевипромшю-вання) антеною, у тому чпсл! фазированою антенною реппткою, усунути неможлпво, проте його можна сутте-во зменшити.
Запропоновано використання асимптотичного методу перевалу для розв'язання штегральнпх електроди-нам!чних р!внянь електромагштного поля, розс!яного фазованими екв!дистантними антенними репптками. Це дозволяв досл!дити законом!рност! иеревииромшенного поля в двох дов!льних площинах.
Результата моделювання амшнтуд хвил!, як функцш кута зондування св!дчать, що покращення узгодження в антенному тракт! призведе до зб!лынення максимально! амшптуди сигналу в режим! передач!. В!дпов!дно до принципу оберненост! антен таке узгодження покра-щить поглинапня вищих тишв хвиль, що паводяться на розкрив! одиночного вииромшювача або екв!дистантно! антенно! репптки. Це дозволить зменшити коеф!ц!ент стоячо! хвил! за напругою та р!вень б!чних пелюсток.
Отриман! вирази стануть у нагод! шд час проекту-вання пових аптепних систем, конструктивн! особли-вост! яких сприятимуть зменшенню розс!ювання в!д них електромагштного поля. Так! дп також дозволять покращити електромагштну сум!сн!сть радюелектрон-пих засоб!в, що встановлеш на одному, або на сус!дн!х об'ектах, до складу яких входять антенн! системи.
Результата досл!джень може бути використано у процес! розробки алгоритм!в виявлення, розшзнавання та !дентиф!каци рад!олокац!йних об'ект!в.
Ключовг слова: фазоваш антенн! репптки, досл!-дження електромагштного поля, асимптотичш методп, ефектпвна поверхпя розс!юваппя
Применение асимптотических методов для исследования электромагнитного поля, рассеянного эквидистантными антенными решетками
Сидорчук О. Л., Фриз С. П., Гаврилко Е. В., Соболенке С. А., Федорова Н. В.
Апертурные антенны и фазированные антенные решетки вносят наибольший вклад в радиолокационную заметность воздушных и наземных объектов и могут составлять до 98% их общей эффективной рассеивающей поверхности. Известно, что любая антенная система является источником вторичного излучения, поскольку она рассеивает по меньшей мере половину падающей на нее энергии. Это означает, что такого рассеяния (переизлучения) антенной или фазированной антенной решеткой полностью избежать невозможно, но его можно существенно уменьшить.
Реализация известных способов устранения переизлучения (рассеяния) приводит к ухудшению других
основных характеристик антенных систем - коэффициентов усиления, направленного действия и так далее. На уровень переизлучаемого сигнала также влияет множество характеристик самой антенной решетки: диаграмма направленности, количество излучателей, расстояние между ними и разница в распространении электромагнитных волн. Таким образом, исследование электромагнитного поля, рассеянного фазированной антенной решеткой, и выяснение причин и закономерностей такого явления, с целью его снижения, является весьма актуальной задачей.
Для исследования поля, рассеянного одиночным или те-м антенным излучателем, был применен асимптотический метод с использованием леммы Лоренца и точных граничных условий - непрерывности тангенциальных составляющих полного поля Е и Н к раскрыву рупора Яр. Используемый для этого математический аппарат позволяет рассчитывать поле не только для линейной, но и для прямоугольной эквидистантной фазированной антенной решетки. Его особенностью является учет количества облучателей и расстояния между ними.
Для решения интегральных электродинамических уравнений электромагнитного поля, рассеянного фазированными антенными решетками, используется асимптотический метод седловой точки (перевала). Это позволяет исследовать закономерности переизлученного поля в двух произвольных плоскостях.
Выражения, приведенные для одного излучателя и эквидистантной антенной решетки, имеют не только расчетно-практичное, но и методическое значение. Их последовательный вывод и физическая интерпретация позволят оценить пределы их использования при изучении рассеянного (переизлученного поля) не только фазированных антенных решеток, но и других антенных систем, содержащих рупора пирамидальной формы.
Диаграммы амплитуд волн, построенные как функции угла зондирования, показывают, что улучшение согласования в антенном тракте приведет к увеличению максимальной амплитуды сигнала в режиме передачи. В соответствии с принципом взаимности антенн такое согласование улучшит поглощение волн высших типов в апертуре отдельного излучателя или эквидистантной антенной решетки. Что, в свою очередь, уменьшит коэффициент стоячей волны по напряжению и уровень боковых лепестков.
Выведенные математические выражения будут полезны при проектировании новых антенных систем, особенности конструкции которых помогут уменьшить рассеивание электромагнитного поля от них. Такие действия также улучшат электромагнитную совместимость радиоэлектронных устройств, установленных на одном или соседних объектах, содержащих антенные системы.
Полученные результаты могут быть применены при разработке алгоритмов обнаружения и идентификации радиолокационных целей.
Ключевые слова: фазированные антенные решетки, исследование электромагнитного поля, асимптотические методы, эффективная поверхность рассеяния
