Effective scattering area of an aircraft AN 2. Method for measuring the effective scattering area of ground objects by a radar with a synthesized antenna aperture. The physical meaning of epr
where S=ab; x = . (7.8)
The dependence of the RCS on the irradiation angle is called the target scatterplot. A flat sheet has a scatterplot described by a function of the form (sinx/x)2.
At large ratios of the sheet size to the wavelength, the scattering diagram will be very sharp, i.e., with an increase in α, the RCS value of the sheet changes sharply in accordance with the function σc, decreasing in some directions to zero.
For a number of applications, it is desirable to maintain a high RCS value over a wide range of irradiation angles. This is necessary, for example, when using reflectors as passive radio beacons. This property has a corner reflector.
EPR corner reflector. The corner reflector consists of three mutually perpendicular metal sheets, it has the property of reflecting radio waves in the direction of the irradiating radar, which is explained by the triple reflection from the walls of the reflector that the wave experiences if the irradiation direction is near the symmetry axis (within the solid angle of 45 °) of the corner reflector. Formula for calculating the RCS of a corner reflector:
At a=1 m and λi=10 cm, the EPR of the corner reflector σуo = 419 m2. Thus, the RCS of a corner reflector is somewhat smaller than the RCS of a flat plate with dimensions a = b = l m. However, the corner reflector retains a large RCS value in a fairly wide sector, while the RCS of the plate decreases sharply with slight deviations of the irradiation direction from the normal.
Biconical reflectors, made up of two identical metal cones, are also used as passive radar beacons at sea. If the angle between the generatrices of the cones is 90°, then the beam, after double reflection from the surface of the cones, is directed towards the radar, which ensures a large RCS value. The advantage of a biconical reflector is a uniform scattering pattern in a plane perpendicular to its axis.
EPR ball. To determine the RCS of a large (radius compared to λu) ball with a perfectly conducting smooth surface, formula (5.3) can be used. σsh =4π rsh2 (7.10)
Thus, the RCS of a ball is equal to its cross-sectional area, regardless of the wavelength and direction of irradiation:
Due to this property, a large ball with a well-conducting surface is used as a reference for experimental measurement of the RCS of real objects by comparing the intensity of the reflected signals. When the ratio of the ball radius to the wavelength decreases to the values rsh /λi ≤2, the function σsh/π rsh2 has a number of resonant maxima and minima, i.e., the ball begins to behave like a vibrator. With a ball diameter close to λi/2, the RCS of the ball is four times the area of its cross section. For a small ball rsh ≤λ and /(2π) the EPR is determined by the Rayleigh diffraction formula
σsh =4.4 104 rsh6 / λi4 (7.11)
and is characterized by a strong dependence on the wavelength of the irradiating radio waves. This case occurs, for example, when radio waves are reflected from raindrops and fog. Taking into account the value of the dielectric constant of water (ε = 80), the EPR of raindrops σk =306 dk6 / λi4 where dk is the diameter of the drops.
7.3. Effective Scattering Area of Objects
Often in practice it is necessary to determine the resulting reflected signal created by several objects or a plurality of elementary reflectors distributed on the surface or in the volume irradiated by the radar probing signals. So, on the screen of an indicator of an aircraft radar for surveying the earth's surface, an image is created by modulating the CRT beam in brightness by signals reflected from the corresponding sections of the Earth's surface or the resolved volume involved in the formation of the resulting signal at the receiver input. For a pulsed radar with a probing pulse duration τu, a bottom width in the horizontal and vertical planes at a distance D>> τand s/2, the resolved volume V0 will be equal to the volume of a cylinder with a height h= τand c/2 and a base area s=pab V0 =h s.
If a unit volume of space contains n1 randomly located reflectors with the same RCS equal to σC, then the average statistical value of the RCS of all reflectors in the resolved volume is σc = σc n V0. (7.12)
In the case of rain, σt is the RCS of the raindrop multiplied by the number of vibrators per unit volume n1 and is related to the rain intensity I (mm/h). To simplify calculations, you can use the specific RCS per unit volume σc = σc n1 (m-1), which can be calculated using the formulas
σо =6 10-14 I1.6 λi-4 (for rain); (7.13)
σо =6 10-13 I2 λi-4 (for snow). (7.14)
When calculating the reflected signals from a cloud of dipole reflectors (metallized tapes), the specific RCS is also used, which, with an arbitrary orientation in space of dipoles of length λi/2
σvo =0.11 λi2 n1. /m2/. (7.15)
Random fluctuations in the RCS of targets caused by changes in the mutual position of the radar and the target, and in the case of group and distributed targets - and changes in the relative position of elementary reflectors, lead to fluctuations in the reflected signals. The statistical properties of signals and EPR of targets can be quite fully described by the PV and the spectrum (correlation function) of fluctuations.
It is known that the RCS of a set of elementary reflectors is described by an exponential distribution law. The spectral characteristics of signals reflected by complex and distributed objects consisting of many reflectors are determined by the relative speed of the target and the radar, the mutual displacement of elementary reflectors, and the change in the composition of reflectors (their number and RCS) during scanning (moving) of the DND. In the case of complex targets (ship, aircraft, etc.), the resulting reflected signal is formed by summing the reflections from individual surface areas (mainly “shiny” points), which can be considered elementary reflectors. At a high relative speed of movement of the radar and the target, the width of the spectrum of the reflected signal can be considered equal to the difference in the Doppler frequency increments for the extreme elements of the target. So, if the angular width of the target is θts, and the heading angle of its middle (the angle between the relative velocity vector V and the direction to the target) is equal to α, then the width of the reflected signal spectrum at small θts is ∆F=2Vθts sin α /λi. (7.16)
Knowing the width of the spectrum, one can also calculate the signal correlation time τ = l/∆F, which characterizes the fluctuation rate. From formula (7.16) it follows that the fluctuation speed is related to the relative speed of movement, course and size of the target, which can be used to identify the type of target by the nature of the fluctuation of the reflected signal. The width of the spectrum also depends on the angular displacements of elementary reflectors relative to the center of mass of the target. Thus, when the aircraft yaws and rolls, frequencies up to hundreds of hertz appear in the spectrum of signal fluctuations.
Fluctuations in the phase front of the reflected wave lead to errors in determining the bearing of the target. Such fluctuations are inevitable in the radar direction finding of complex objects, the position of the center of reflection of which is constantly changing due to the mutual movement of the radar and the target, changes in the angle of elementary reflectors and their composition. Experience shows that the root-mean-square error of the deviation of the angle of arrival of the radar signal of a real target with a visible linear dimension dc at a distance D from the radar σα=dc/4D. (7.17)
Fluctuations in the phase front of the reflected wave are called target angular noise. Their spectrum for real purposes lies in the low frequency region from 0 to 5 Hz and has a width of about fractions of a hertz. The fluctuation spectrum must be known when designing a radar with automatic target tracking in angular coordinates. Statistical characteristics of the EPR of targets and reflected signals are necessary when calculating the range of a radar, the accuracy of measuring coordinates, and also when designing a radar signal processing device. Approximate calculations are carried out with the exponential law of distribution of the RCS of targets. When assessing the range of the radar, the average value of the RCS of the target is used, which is obtained by averaging the RCS values for different directions of target exposure. In table. 7.1 shows the average RCS values for real objects /2/. Table 7.1
EPR for real objects of radar surveillance
In practice, sometimes there is a need to artificially increase or decrease the RCS of real objects. So, to facilitate the search for rescue boats and rafts, corner reflectors are installed on them, which sharply increase the range of radar detection. In other cases, in order to reduce the detectability of missiles, aircraft and ships, they seek to reduce their RCS by a rational choice of surface configuration and the use of protective coatings that reduce the reflection of radio waves.
To avoid detection by enemy radars, modern fighters, ships and missiles must have the smallest effective scattering area (ESR). Scientists and engineers who develop such subtle objects, using computational electrodynamics techniques, optimize the EPR and scattering effects of arbitrary objects when using radar. The object under consideration scatters electromagnetic waves incident on it in all directions, and part of the energy returned to the source of electromagnetic waves in the process of the so-called. backscattering, forms a kind of "echo" of the object. RCS is just a measure of the intensity of the radar echo signal.
In practice, a reference conducting sphere is used as an object for calibrating radars. A similar statement of the problem is used to verify the numerical calculation of the EPR, since the solution to this classical problem of electrodynamics was obtained by Gustav Mie back in 1908.
In this note, we will describe how to perform such a reference calculation using an efficient 2D axisymmetric formulation, and also briefly note the general principles for solving a wide class of scattering problems in COMSOL Multiphysics ® .
Fig.1. Distribution of the electric field (its norm) and the time-averaged energy flux (arrows) around a perfectly conducting sphere in free space.
Scattering on a conductive sphere: size matters
In a three-dimensional setting, even with the use of perfectly matched layers (Perfectly Matched Layers - PML), which effectively limit the computational domain and simulate open boundaries, and symmetry conditions, the calculation with a detailed frequency/wavelength resolution can take quite a long time.
Fortunately, if the object is axisymmetric and scatters waves isotropically, a full 3d analysis is not required. To analyze the propagation of electromagnetic waves and the resonant behavior of an object, it is sufficient to perform a calculation for its cross section in a two-dimensional axisymmetric formulation under certain conditions.
Two-dimensional axisymmetric model of the microwave process: an inside view
Let's assume that our sphere is metallic and has a high conductivity. For this problem, the surface of the sphere is set as a perfect electrical conductor (PEC), and its interior is excluded from the computational domain. The region around it is defined as a vacuum with appropriate material properties, and the outermost layer uses a spherical type PML used to absorb all outgoing waves and prevent reflection from the boundaries of the computational domain.
Modeling of metal objects in wave electromagnetic problems
For the numerical solution of electrodynamics problems in the frequency domain, there are several techniques for efficient modeling of metal objects. The illustration below shows techniques and guidelines for using Transition boundary condition (TBC), Impedance boundary condition (IBC), and Perfect Electric Conductor (PEC) conditions.
Rice. 3. Axisymmetric Geometry and Defining a Left Circularly Polarized Background Electromagnetic Field in the COMSOL Multiphysics ® GUI.
In the computational domain (except for PML), the excitation of the background field with left circular polarization directed in the negative direction of the z axis is set (Fig. 3). Note that only the first azimuth mode is calculated.
By default, for microwave problems, COMSOL Multiphysics ® automatically generates a free triangular (or tetrahedral for 3D problems) mesh under the maximum frequency specified for the study in the frequency domain (Frequency Domain study), which in this example is 200 MHz. To ensure sufficient resolution of wave processes in the model, the maximum grid element size is set to 0.2 wavelength. In other words, the spatial resolution is given as five second order elements per wavelength. In perfectly matched layers, the mesh is built by pulling in the direction of absorption, which ensures maximum efficiency of the PML.
Because the number of degrees of freedom in the model is very small (compared to the three-dimensional setting), then its calculation takes only a few seconds. At the output, the user can obtain and visualize the distribution of the electric field around the sphere (in the near zone), which is the sum of the background and scattered fields.
For this problem, the most interesting characteristics relate to the far-field region. To obtain them in the model, you need to activate the Far-Field Calculation condition on the outer boundary of the computational domain (in this case, on the inner boundary of the PML), which allows you to calculate the fields in the far zone outside the computational domain at any point based on the Stratton-Chu integral relations. Activation adds an additional variable - the field amplitude in the far zone, on the basis of which, in post-processing, the software calculates engineering variables that comply with IEEE standards: effective isotropically radiated power, gain (so-called Gain, including taking into account input mismatch), coefficient directional action and EPR.
From the polar graph, a specialist can determine the direction of the field in the far zone in a certain plane, and the three-dimensional radiation pattern in the far zone allows you to study the stray field in more detail (Fig. 4).
Rice. 4. 3D far-field visualization based on a 2D axisymmetric model in COMSOL Multiphysics ® .
Recovery of a solution for a three-dimensional problem
The results for the "reduced" model in the axisymmetric formulation relate to the process of irradiation of a conducting sphere by a background field with circular polarization. In the original 3d problem, the characteristics of the stray field are studied for the case of a linearly polarized plane wave. How to get around this difference?
By definition, linear polarization can be obtained by adding right and left circular polarization. The 2D axisymmetric model with the above settings (Fig. 2) corresponds to the first azimuthal mode (m = 1) of the background field with left circular polarization. The solution for the negative azimuthal mode with right-hand circular polarization can be easily derived from the already solved problem, using the symmetry properties and performing simple algebraic transformations.
By conducting just one 2D analysis and mirroring the results already in post-processing, you can extract all the necessary data, while significantly saving computing resources (Fig. 5).
Rice. 5. Comparison of the scan of the effective scattering area (on a logarithmic scale) in terms of scattering angles for a full three-dimensional calculation and the proposed two-dimensional axisymmetric model.
The 1D graph (Fig. 5) with the EPR comparison demonstrates an acceptable fit between the 3D and 2D axisymmetric models. A slight discrepancy is observed only in the region of forward and backward scattering, near the axis of rotation.
In addition, visualization of the obtained two-dimensional results in three-dimensional space will require the transformation of the coordinate system from cylindrical to Cartesian. On fig. Figure 6 shows a 3D visualization of the results for a 2D axisymmetric model.
Rice. 6. Three-dimensional representation of the obtained results based on a two-dimensional calculation.
Spiraling arrows indicate the background field with circular polarization. The graph in a horizontal section represents the distribution of the radial component of the background field (the wave process is displayed using plane deformations). The norm of the total electric field is constructed on the surface of the sphere. Another arrow diagram shows a superposition of two circular polarizations, which is equivalent to a linearly polarized background field in three dimensions.
Conclusion
In the process of modern development in the field of radiophysics and microwave technology for engineers, effective modeling techniques that reduce resource consumption and time costs are indispensable, regardless of the numerical analysis method used.
To maintain integrity and recreate all relevant physical effects when simulating a real component with a large electrical size, it is possible to simplify the numerical calculation process without loss of accuracy by solving the problem in a two-dimensional axisymmetric formulation. When modeling and analyzing axisymmetric objects such as scattering spheres and disks, conical horn and parabolic antennas, calculations for the cross section of the device are several orders of magnitude faster than using a full 3D model.
Fundamentals of Antenna Modeling in COMSOL Multiphysics
Wave scattering is one of the most fundamental phenomena in physics, because It is in the form of scattered electromagnetic or acoustic waves that we receive a huge amount of information about the world around us. The full-wave formulations available in the RF and Wave Optics modules, as well as in the Acoustics module, allow these phenomena to be modeled in detail using the finite element method. In this webinar, we will discuss established practices for solving scattering problems in COMSOL, including the use of Background Field formulations, Far-Field Calculation functionality, broadband calculations using new technologies based on the discontinuous Galerkin method ( dG-FEM), as well as simulation of antennas and sensors in the signal reception mode.
At the end of the webinar, we will discuss the available templates and examples in the COMSOL Models and Applications Library, as well as answer questions from the user on this topic.
You can also request a demo of COMSOL in the comments or on our website.
Final GIF:
To accurately determine the secondary electromagnetic field at the location of the radar receiver, it is necessary to solve the problem of electromagnetic wave reflection from location objects, which, as a rule, have a complex configuration. It is not always possible to solve this problem with sufficient accuracy, therefore, it is necessary to find such a characteristic of the reflecting properties of an object that would make it possible to relatively easily determine the intensity of the secondary electromagnetic field at the reception point.
Schematically, the interaction of the location station with the object is shown in Fig. 2.2.
Fig.2.2. Interaction of the radar with a reflecting object
The transmitting device creates a power flux density P1 at the reflecting object. The reflected electromagnetic wave creates a power flux density P2 at the location of the receiving antenna of the location system.
It is necessary to find a value that rationally connects the flows P1 and P2. The effective scattering area (ESR) - Se was chosen as such a value.
The effective scattering area can be considered as the area of the area located perpendicular to the electromagnetic wave incident on it, which, with isotropic dispersion of all the power incident on it, creates at the location of the radar receiver the same power flux density P2 as the real reflecting object. The Se value is also called the “effective surface”, “secondary radiation effective surface”, or “effective reflecting surface”.
The value of Se can be determined from the relation Se P1=4p R2 P2 ,
Se=4pR2P2,/P1 (2.1)
The effective scattering area can be expressed in terms of the electric and magnetic field strengths (E1 and H1) of the direct wave at the location of the object and in terms of the electric and magnetic field strengths (E2, and H2) of the reflected wave at the location of the radar.
Se \u003d 4p R2 E2 2 / E1 2 \u003d 4p R2H2 2 / H1 2.
As follows from formula (2.1), Se has the dimension of area. If the linear and angular dimensions of the object are smaller than the dimensions of the resolving volume of the radar in terms of range and angular coordinates, the value of the effective scattering area does not depend on the distance to the reflecting object. However, as can be seen from Fig.2.2., the value of the RCS depends on the orientation of the object relative to the transmitter and receiver of the location system, Se=Se(q). In the general case, with an arbitrary orientation of an object in space, the RCS depends on three angles: the viewing angles of the reflecting object in space a and b, and the roll angle of the object e: Se = Se (a, b, e).
For real reflecting objects, the dependence of the effective scattering area on the irradiation angles is determined experimentally. So, if you turn the reflecting object relative to the direction to the transceiver, you can remove the diagram of the reverse secondary radiation Se(q). For the majority of aerodynamic objects (aircraft) the diagram of the return secondary radiation is strongly indented; the range of change in the effective scattering area is large and reaches 30 - 35 decibels.
For reflectors of the simplest configuration, the effective reflective area can be calculated theoretically. Such reflectors, in particular, include: a linear half-wave vibrator, a metal plate, metal and dielectric corner reflectors.
The effective scattering area of a half-wave vibrator depends on the length of the electromagnetic wave incident on it and the angle q between the normal to the vibrator and the direction to the location station
Se=0.86l2 cos4q.
The maximum RCS of the half-wave vibrator is Sem=0.86l2, which significantly exceeds its geometric area.
The effective scattering area Se of the radar reflecting volume filled with half-wave vibrators can be determined by the formula
Se = n Ses, (2.2)
where n is the number of vibrators in the resolution volume,
Ses=0.17l2 - the average value of the RCS of a half-wave vibrator, provided that the angle q changes equiprobably from 0 to p /2.
The backscattering pattern of a metal plate has a petal character. The width of the lobes decreases with increasing ratio of the plate edge length to the wavelength. The EPR of the plate is directly proportional to its area S and, with a normal incidence of an electromagnetic wave on the plate, is equal to
The effective scattering area of the ball depends on the ratio of the ball diameter dw to the wavelength. For a metal ball
Se=690 dsh6/l4 at dsh<< l ,
Se \u003d p (dsh / 2) 2 with dsh \u003e l.
To create powerful reflected signals, metal corner reflectors are widely used, which consist of three triangular or three square plates connected at an angle p / 2. The advantage of corner reflectors is the ability to intensively reflect electromagnetic waves coming from different directions. EPR of a corner reflector with square edges
for triangular reflector
where l is the length of the reflector rib.
The effective scattering area of an elongated spheroid when it is irradiated along the longitudinal axis is determined by the formula
where a is the major semiaxis, b is the minor semiaxis of the spheroid.
The most common surface-distributed objects are areas of the earth's surface. The conditions for irradiating the radar of the earth's surface are shown in fig. 2.3, a.
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Rice. 2.3. To the determination of the effective scattering area of volumetric (a) and surface (b) objects
The effective scattering area of such objects is determined by the area of the earth's surface, reflections from individual elements of which arrive at the radar receiving antenna at the same time. The area of the element depends on the width of the main maximum of the antenna pattern in two planes - q and y, the angle of inclination j of the main maximum, counted from the horizontal, the duration of the probing pulse, the scattering coefficient g. Such a reflective area can be represented as a rectangle spaced from the radar at a distance R
Provided that ct /2cosj< y R / sinj, стороны прямоугольника равны RDq (Dq -ширина диаграммы направленности) и ct /2cosj , площадь отражающей площадки S = R(Dq) ct /2cosj . Соответствующая S перпендикулярная линии визирования площадка S0=S sinj .
Knowing S0 and g, one can determine Se.
Se=(g R(Dq) c t) tgj /2. (2.3)
As follows from formula (2.3), the RCS of surface-distributed objects, in contrast to the RCS of point objects, depends on the range.
The effective scattering area Se can be expressed in terms of the height H of the radar above the surface
S e \u003d g HDq st / 2 cos (j) .
The effective scattering area of spatially distributed objects, consisting of a large number of homogeneous reflectors distributed with a uniform density n0 in space and having an average reflective surface Ses, can be determined using formula (2.2).
S e \u003d no S es V,
where V is the reflecting volume, determined by the resolution of the radar in terms of range, angular coordinates and the size of the space filled with reflectors. Formation of a signal from a cloud of reflectors is shown in Fig. 2.3, b.
In the case when the cloud of distributed reflectors completely covers the conical beam of the radiation pattern, and the distance R to the resolving volume is much greater than the range resolution ct/2, the reflecting volume is a cylinder with a height сt/2 and a base pR2(Dq)2/4, where Dq is the width of the main maximum of the radiation pattern at the level of 0.5. For these conditions, the reflecting volume is V=pR2(Dq)ct/8, and the EPR of a spatially distributed object is determined by the formula
S e \u003d S es n0 p R2 (Dq) 2ct / 8. (2.4).
When the beam is incompletely filled, the diameter of the reflecting volume is equal to the transverse linear dimensions L o of the object, and the effective scattering area is determined by the formula
Se=Ses n0p L0 2c /8 (2.5)
As follows from formulas (2.4) and (2.5), with volumetrically distributed objects that completely cover the main maximum of the radar station antenna pattern, the RCS is directly proportional to the square of the distance to the reflecting volume. If the object does not block the main beam of the diagram, the RCS does not depend on the distance between the radar and the reflecting volume.
For long-range radar stations, aerodynamic objects are point or concentrated, the RCS of which does not depend on the range. For systems of near location, such objects are linearly extended, in which the area of the irradiated surface grows linearly with increasing range. Therefore, the effective scattering area increases with an increase in the distance R between the radar and a linearly extended object and with an increase in the width of the antenna pattern. In the case when the reflecting properties of an object are constant along its length, Se grows in direct proportion to R.
Statistical characteristics of reflected signals
Distribution law of signal amplitudes reflected from an object
Most reflected signals in systems are random processes. Therefore, to evaluate the operation of the system, it is necessary to know not only the average values of the energy parameters of the signal, but also the laws of distribution of amplitudes and powers, as well as spectral and correlation characteristics. The necessary data can be obtained on the basis of experimental and theoretical studies.
For systems of near location, the following statistical models of objects can be selected:
1. a set of a large number of reflective elements with the same reflective properties with a given total average value of the reflective surface S e;
2. a set of elements according to the first model and one (dominant) element with a stable effective reflective surface S0, exceeding the reflective surface of one element.
The amplitude distribution laws found for the first model are a special case of the distribution law for the second model at S0 =0. Therefore, the second model is considered first.
The amplitude of the signal reflected from the object according to model 2 can be represented as
u cos(w0t-j)=u0 cos(w0t-j0)+ uS cos(w0t-jS) (2.6)
where uS cos (w0t-jS)=S ui cos(w0t-ji).
The process of adding oscillations can be traced in Fig. 2.4, where the signals u , u0 and uS are shown in vector form.
Segments x, x0, as well as y and y0 are projections of signal amplitudes u and u0 on mutually perpendicular axes.
Rice. 2.4. Vector diagram of the signal reflected from the object
In accordance with the central limit theorem, the projections x and y obey the normal probability distribution, and their joint two-dimensional probability density is equal to the product of one-dimensional probability densities,
where D = Dx = Dy is the dispersion of the orthogonal components x and y.
It is easy to pass from the two-dimensional law w(x, y) to the two-dimensional law w(u,j). According to the rules of probability theory, the two-dimensional distribution density of amplitudes and phases
To determine the law of distribution of amplitudes of the reflected signal w(u), it is necessary to integrate the two-dimensional distribution law w(u,j) over the region of all possible values of j.
where I0 (u,u0/2D) is the zero-order Bessel function of the first kind,
Thus, the distribution law of the amplitudes of the reflected signal, which is called the generalized Rayleigh distribution law, has been obtained. If u0=0, which corresponds to the first model, the distribution law of the amplitudes goes into the Rayleigh distribution law,
The distribution laws of the amplitudes normalized with respect to D1/2 for the two models at different values of the amplitude of the stable component u0 are shown in Figs. 2.5. As u0/D1/2 increases, the amplitude distribution law approaches the normal one.
The distribution law of the effective reflective surface
Considering that the signal amplitudes u are proportional to the power, it is possible to find the distribution laws for the power of signals reflected from objects using the obtained amplitude distribution laws. The average power of the resulting signal, allocated to a load of 1 ohm,
where D=m1(xk2)=m1(yk2)=m1(uS2/2)=så2/2.
The effective reflecting surface of an object is proportional to the signal power, therefore, to determine the distribution law of the effective reflecting surface according to the found amplitude distribution law (2.7), we can use the following formula
w(Se)=w(u)çdu/dSeç. (2.8)
As a result of substitution (2.7) into (2.8), the distribution law of the reflecting surface is reduced to the form:
Fig.2.5 Signal amplitude distribution density (а) (at uo/so=0 - curve 1; uo/so=1 - curve 2; uo/so=3 - curve 3; uo/so=6 - curve 4).
and effective reflecting surface (b) (at Se0 /Seå= 0 - curve 1; at Se0 /Seå= 1 - curve 2; at Se0 /Seå=3 - curve 3 and at Se0 /Seå = 20 - curve 4).
course project
SPbGUT im. Bonch-Bruevich
Department of Radio Systems and Signal Processing
Course project by discipline
"Radio systems", on the topic:
"Effective Scattering Area"
Completed:
Student of the RT-91 group
Krotov R.E.
Received by: professor of the department of ROS Gurevich V.E.
Quest issued: 10/30/13
Protection period: 12/11/13
Introduction and so on
Structural diagram of the radar
Schematic diagram of the radar
Theory of device operation
Conclusion
Bibliography
Effective scattering area
(EPR; eng. Radar Cross Section.RCS; in some sources effective scattering surface, effective scattering cross section,effective reflective area, EOP) in radar - the area of some fictitious flat surface located normally to the direction of the incident plane wave and being an ideal and isotropic re-radiator, which, when placed at the target location, creates the same power flux density at the radar station antenna as the real target .
Example of a monostatic EPR diagram (B-26 Invader)
RCS is a quantitative measure of the property of an object to scatter an electromagnetic wave. Along with the energy potential of the transceiver path and the CG of the radar antennas, the EPR of the object is included in the radar range equation and determines the range at which an object can be detected by radar. An increased RCS value means a greater radar visibility of an object, a decrease in RCS makes it difficult to detect (stealth technology).
The EPR of a particular object depends on its shape, size, material from which it is made, on its orientation (view) in relation to the antennas of the transmitting and receiving positions of the radar (including the polarization of electromagnetic waves), on the wavelength of the probing radio signal. The RCS is determined in the conditions of the far zone of the scatterer, the receiving and transmitting antennas of the radar.
Since RCS is a formally introduced parameter, its value does not coincide with either the value of the total surface area of the scatterer or the value of its cross-sectional area (eng. Cross section). Calculation of EPR is one of the problems of applied electrodynamics, which is solved with varying degrees of approximation analytically (only for a limited range of simple-shaped bodies, for example, a conducting sphere, cylinder, thin rectangular plate, etc.) or numerical methods. Measurement (control) of RCS is carried out at test sites and in radio frequency anechoic chambers using real objects and their scale models.
EPR has the dimension of area and is usually indicated in sq.m. or dBq.m.. For objects of a simple form - test - EPR is usually normalized to the square of the wavelength of the probing radio signal. EPR of extended cylindrical objects is normalized to their length (linear EPR, EPR per unit length). The EPR of objects distributed in the volume (for example, a rain cloud) is normalized to the volume of the radar resolution element (EPR / m3). The RCS of surface targets (as a rule, a section of the earth's surface) is normalized to the area of the radar resolution element (EPR / sq. M.). In other words, the RCS of distributed objects depends on the linear dimensions of a particular resolution element of a particular radar, which depend on the distance between the radar and the object.
EPR can be defined as follows (the definition is equivalent to that given at the beginning of the article):
Effective scattering area(for a harmonic probing radio signal) - the ratio of the radio emission power of an equivalent isotropic source (creating the same radio emission power flux density at the observation point as the irradiated scatterer) to the power flux density (W/sq.m.) of the probing radio emission at the location of the scatterer.
The RCS depends on the direction from the scatterer to the source of the probing radio signal and the direction to the observation point. Since these directions may not coincide (in the general case, the source of the probing signal and the point of registration of the scattered field are separated in space), then the RCS determined in this way is called bistatic EPR (two-position EPR, English bistatic RCS).
Backscatter diagram(DOR, monostatic EPR, single position EPR, English monostatic RCS, back-scattering RCS) is the RCS value when the directions from the scatterer to the source of the probing signal and to the observation point coincide. EPR is often understood as its special case - monostatic EPR, that is, DOR (the concepts of EPR and DOR are mixed) due to the low prevalence of bistatic (multi-position) radars (compared to traditional monostatic radars equipped with a single transceiver antenna). However, one should distinguish between EPR(θ, φ; θ 0, φ 0) and DOR(θ, φ) = EPR(θ, φ; θ 0 =θ, φ 0 =φ), where θ, φ is the direction to point of registration of the scattered field; θ 0 , φ 0 - direction to the source of the probing wave (θ, φ, θ 0 , φ 0 - angles of the spherical coordinate system, the beginning of which is aligned with the diffuser).
In the general case, for a probing electromagnetic wave with a non-harmonic time dependence (broadband probing signal in the space-time sense) effective scattering area is the ratio of the energy of an equivalent isotropic source to the energy flux density (J/sq.m.) of probing radio emission at the location of the scatterer.
EPR calculation
Consider the reflection of a wave incident on an isotropically reflecting surface with an area equal to the RCS. The power reflected from such a target is the product of the RCS and the density of the incident power flux:
where is the RCS of the target, is the power flux density of the incident wave of a given polarization at the target location, is the power reflected by the target.
On the other hand, the isotropically radiated power
Or, using the field strengths of the incident wave and the reflected wave:
Receiver input power:
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,where is the effective area of the antenna.
It is possible to determine the power flux of the incident wave in terms of the radiated power and the directivity of the antenna D for a given direction of radiation.
Where 
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In this way,
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(9)The physical meaning of epr
EPR has the dimension of area [ m²], but is not a geometric area(!), but is an energy characteristic, that is, it determines the magnitude of the power of the received signal.
The RCS of the target does not depend on the intensity of the emitted wave, nor on the distance between the station and the target. Any increase leads to a proportional increase and their ratio in the formula does not change. When changing the distance between the radar and the target, the ratio changes inversely and the RCS value remains unchanged.
EPR of common point targets
convex surface
Field from the entire surface S is determined by the integral It is necessary to determine E 2 and attitude at a given distance to the target ...
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,where k- wave number.
1) If the object is small, then the distance and field of the incident wave can be considered unchanged.
2) Distance R can be thought of as the sum of the distance to the target and the distance within the target:
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,flat plate
A flat surface is a special case of a curved convex surface.
Corner reflector
Corner reflector- a device in the form of a rectangular tetrahedron with mutually perpendicular reflective planes. The radiation that enters the corner reflector is reflected in the strictly opposite direction.
Triangular
If a corner reflector with triangular faces is used, then the EPR
chaff
Chaffs are used to create passive interference with the operation of the radar.
The value of the RCS of a dipole reflector generally depends on the observation angle, however, the RCS for all angles:
Chaffs are used to mask aerial targets and terrain, as well as passive radar beacons.
The reflection sector of the chaff is ~70°
EPR has the dimensions of the area, but is not a geometric area, but is an energy characteristic, that is, it determines the magnitude of the power of the received signal.
The RCS of the target does not depend on the intensity of the emitted wave, nor on the distance between the station and the target. Any increase in ρ 1 leads to a proportional increase in ρ 2 and their ratio in the formula does not change. When changing the distance between the radar and the target, the ratio ρ 2 / ρ 1 changes inversely proportional to R and the EPR value remains unchanged.
EPR of common point targets
For most point targets, information about the EPR can be found in radar manuals.
convex surface
The field from the entire surface S is determined by the integral It is necessary to determine E 2 and the ratio at a given distance to the target ...
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where k is the wave number.
1) If the object is small, then the distance and field of the incident wave can be considered unchanged. 2) The distance R can be considered as the sum of the distance to the target and the distance within the target:
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flat plate
A flat surface is a special case of a curvilinear convex surface.
Corner reflector
The principle of operation of the corner reflector
Corner reflector consists of three perpendicular surfaces. Unlike a plate, a corner reflector gives good reflection over a wide range of angles.
Triangular
If a corner reflector with triangular faces is used, then the EPR
Application of corner reflectors
Corner reflectors are applied
- as decoys
- like radio contrast landmarks
- when conducting experiments with strong directional radiation
chaff
Chaffs are used to create passive interference with the operation of the radar.
The value of the RCS of a dipole reflector generally depends on the observation angle, however, the RCS for all angles:
Chaffs are used to mask air targets and terrain, as well as passive radar beacons.
The reflection sector of the chaff is ~70°
EPR of complex targets
RCS of complex real objects are measured at special installations, or ranges, where the conditions of the far irradiation zone are achievable.
| # | Target Type | σ c |
|---|---|---|
| 1 | Aviation | |
| 1.1 | Fighter aircraft | 3-12 |
| 1.2 | stealth fighter | 0,3-0,4 |
| 1.3 | frontline bomber | 7-10 |
| 1.4 | Heavy bomber | 13-20 |
| 1.4.1 | B-52 bomber | 100 |
| 1.4 | Transport aircraft | 40-70 |
| 2 | ships | |
| 2.1 | Submarine on the surface | 30-150 |
| 2.2 | Cutting a submarine on the surface | 1-2 |
| 2.3 | small craft | 50-200 |
| 2.4 | medium ships | ² |
| 2.5 | big ships | > 10² |
| 2.6 | Cruiser | ~12 000 14 000 |
| 3 | Ground targets | |
| 3.1 | Automobile | 3-10 |
| 3.2 | Tank T-90 | 29 |
| 4 | Ammunition | |
| 4.1 | ALSM cruise missile | 0,07-0,8 |
| 4.2 | The warhead of an operational-tactical missile | 0,15-1,6 |
| 4.3 | ballistic missile warhead | 0,03-0,05 |
| 5 | Other purposes | |
| 5.1 | Human | 0,8-1 |
| 6 | Birds | |
| 6.1 | Rook | 0,0048 |
| 6.2 | mute swan | 0,0228 |
| 6.3 | Cormorant | 0,0092 |
| 6.4 | red kite | 0,0248 |
| 6.5 | Mallard | 0,0214 |
| 6.6 | Grey goose | 0,0225 |
| 6.7 | Hoodie | 0,0047 |
| 6.8 | field sparrow | 0,0008 |
| 6.9 | common starling | 0,0023 |
| 6.10 | black-headed gull | 0,0052 |
| 6.11 | White stork | 0,0287 |
| 6.12 | Lapwing | 0,0054 |
| 6.13 | Turkey vulture | 0,025 |
| 6.14 | rock dove | 0,01 |
| 6.15 | house sparrow | 0,0008 |