Course project

SPbSUT them. Bonch-Bruevich

Department of Radio Systems and Signal Processing

Course project by discipline

"Radio engineering systems", on the topic:

"Effective scattering area"

Completed:

Student of group RT-91

Krotov R.E.

Accepted by: Professor of the Department of ROS Gurevich V.E.

Task issued: 10/30/13

Protection period: 12/11/13

Introduction, etc.

Block diagram of the radar

Radar schematic diagram

Theory of the device

Conclusion

Bibliography

Effective scattering area

(EPR; eng. Radar Cross-Section, RCS; in some sources - effective scattering surface, effective scattering diameter,effective reflective area, EOP) in radar - the area of ​​some fictitious flat surface located normal to the direction of the incident plane wave and which is an ideal and isotropic re-emitter, which, being placed at the target location, creates at the radar station antenna the same power flux density as the real target ...

Example of a monostatic EPR diagram (B-26 Invader)

EPR is a quantitative measure of an object's ability to scatter an electromagnetic wave. Along with the energy potential of the transceiver path and the KU of the radar antennas, the EPR of the object is included in the equation of the radar range and determines the range at which an object can be detected by radar... An increased RCS value means a greater radar signature of an object, a decrease in RCS makes detection more difficult (stealth technology).

The EPR of a particular object depends on its shape, size, material from which it is made, on its orientation (perspective) in relation to the antennas of the transmitting and receiving positions of the radar (including the polarization of electromagnetic waves), and on the wavelength of the probing radio signal. RCS is determined in the conditions of the far zone of the scatterer, receiving and transmitting radar antennas.

Since the EPR is a formally introduced parameter, its value does not coincide either with the value of the total surface area of ​​the diffuser, or with the value of its cross-sectional area (eng. Cross-Section). Calculation of EPR is one of the problems of applied electrodynamics, which is solved analytically with varying degrees of approximation (only for a limited range of simple bodies, for example, a conducting sphere, cylinder, thin rectangular plate, etc.) or by numerical methods. EPR measurement (control) is carried out on landfills 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 ones - the EPR is usually normalized to the square of the wavelength of the probing radio signal. RCS of extended cylindrical objects is normalized to their length (linear RCS, RCS per unit length). The RCS of objects distributed in the volume (for example, a rain cloud) is normalized to the volume of the radar resolution element (RCS / cubic meter). EPR of surface targets (as a rule, of 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 sounding radio signal) - the ratio of the radio emission power of an equivalent isotropic source (which creates at the observation point the same radio power flux density as the irradiated scatterer) to the power flux density (W / m2) of the sounding radio emission at the point where the scatterer is located.

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 EPR determined in this way is called bistatic EPR (two-position EPR, eng. bistatic RCS).

Backscatter plot(DOR, monostatic EPR, single-position EPR, eng. 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 a special case of it - monostatic EPR, that is, DOR (they mix the concepts of EPR and DOR) due to the low prevalence of bistatic (multi-position) radars (in comparison with traditional monostatic radars equipped with a single receiving and transmitting antenna). Nevertheless, one should distinguish between RCS (θ, φ; θ 0, φ 0) and RCS (θ, φ) = RCS (θ, φ; θ 0 = θ, φ 0 = φ), where θ, φ is the direction to scattered field registration point; 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 origin of which is aligned with the scatterer).

In the general case, for a probing electromagnetic wave with a nonharmonic time dependence (broadband in the spatio-temporal sense, a probing signal) effective scattering area- the ratio of the energy of the equivalent isotropic source to the energy flux density (J / sq. m.) of the probing radio emission at the point where the scatterer is located.

EPR calculation

Consider the reflection of a wave incident on an isotropically reflecting surface with an area equal to the EPR. 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 emitted power

Or, using the field strengths of the incident wave and the reflected wave:

Receiver input power:

,

where is the effective antenna area.

It is possible to determine the power flux of the incident wave through the radiated power and the directivity of the antenna. D for a given direction of radiation.

Where .

Thus,

. (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 value of the received signal power.

RCS of the target does not depend on the intensity of the emitted wave, or 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 the distance between the radar and the target changes, the ratio changes in inverse proportion 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 the ratio at a given distance to the target ...

,

where k is the wavenumber.

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:

,
,

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 reflecting planes. Radiation entering the corner reflector is reflected in the strictly opposite direction.

Triangular

If a corner reflector with triangular edges is used, then the EPR

Dipole reflector

Dipole reflectors are used to create passive interference with radar operation.

The EPR value of a dipole reflector generally depends on the observation angle, however, the EPR for all angles:

Dipole reflectors are used to mask air targets and terrain, as well as passive radar beacons.

The sector of reflection of the dipole reflector is ~ 70 °

The simplest volumetric distributed target is dipole reflectors, which are dropped in large numbers from an aircraft or fired by special projectiles, scattered in the air and form a cloud of reflectors. They are used to generate passive interference in a wide frequency range and simultaneously against many RTS.

Dipole reflectors are passive half-wave vibrators with a geometric length close to half the wavelength of the irradiating radar (l ≈ 0.47λ). They are made from metallized paper, aluminum foil, metallized fiberglass and other materials.

EPR clouds from n dipole reflectors is determined by the product of the RCS of individual reflectors in the cloud:

σ = n σ do,

where: σ do- EPR of one dipole reflector.

With linear polarization of the incident electromagnetic wave, the maximum EPR value of a single dipole reflector is observed when its geometric axis coincides with the vector E electric field strength of the wave. Then:

σ do max = 0.86λ 2

If the dipole reflector is oriented perpendicular to the vector E irradiating electromagnetic wave, then σ do = 0.

Due to the turbulence of the atmosphere and the difference in the aerodynamic properties of the dipole reflectors, they are oriented arbitrarily in the cloud. Therefore, in the calculations, the average value of the RCS of a single dipole reflector is used.

σ do sr = 1/5 σ do max = 0.17λ 2,

where: λ - the wavelength of the irradiating radar.

Hence, it follows that the simultaneous suppression of RTS operating at different frequencies is possible only when using dipole reflectors of different lengths.

The simplest point targets are corner reflectors. With relatively small geometric dimensions, they have a significant RCS in a wide wavelength range, which makes it possible to effectively simulate various point targets.

Corner reflector consists of rigidly connected mutually perpendicular planes. The simplest corner reflector is a dihedral or triangular angle (Figure 3.3, a, b).

Figure 3.3. The principle of operation of the corner reflector:

a - dihedral; b - triangular.

The triangular corner reflector has the property of specular reflection towards the radar when irradiated within an angle of 45 0, which ensures the preservation of a large RCS within this angle. To expand the scattering diagram, corner reflectors are used, consisting of four or eight corners. The DR of a triangular reflector is shown in Figure 3.4.

Figure 3.4. Scatter diagram of a triangular reflector.

In practice, triangular corner reflectors are used that have a triangular, rectangular or sectorial shape (Figure 3.5, a, b, c).

Figure 3.5. Corner reflectors: a - with triangular edges (θ 0.5 ≈ 60 0);

b - with sector edges; v - with square edges (θ 0.5 ≈ 35 0).

For objects of simple geometric shape, analytical expressions can be obtained to determine their RCS. Since the power flux density is directly proportional to the square of the electric field strength, the target EPR formula can be represented as

σ = 4πD 2 E 2 2 / E 2 1

Attitude E 2 / E 1 included in this expression can be found on the basis of Huygens' principle. This method consists in the fact that each point on the surface of the irradiated object is considered as a source of a secondary spherical wave. Then, summing up the action of secondary spherical waves at the location of the radar, one can find the strength of the resulting electric field of the secondary radiation. Calculation formulas for determining the RCS of some simple targets are given in Table 3.1.

Table 3.1. EPR of some simple targets.

It is customary to distinguish between specular, diffuse and resonant reflections. If the linear dimensions of the reflecting surface are much larger than the wavelength, and the surface itself is smooth, then specular reflection occurs. In this case, the angle of incidence of the radio beam is equal to the angle of reflection, and the secondary radiation wave does not return to the radar (except for the case of normal incidence).

If the linear dimensions of the object surface are large in comparison with the wavelength, and the surface itself is rough, then diffuse reflection takes place. At the same time, due to the different orientation of the surface elements, electromagnetic waves are scattered in different directions, including in the direction to the radar. Resonant reflection is observed when the linear dimensions of the reflecting objects or their elements are equal to an odd number of half-waves. In contrast to diffuse reflection, secondary resonance radiation usually has a high intensity and pronounced directivity, depending on the design and orientation of the element causing the reflection.

In cases where the wavelength is large compared to the linear dimensions of the target, the incident wave bends around the target and the intensity of the reflected wave is negligible.

From the point of view of signal formation during reflection, the objects of radar observation are usually divided into small-sized and distributed in space or on the surface.

Small-sized objects include objects whose dimensions are much smaller than the dimensions of the radar resolution element in terms of range and angular coordinates. In some cases, small-sized objects have the simplest geometric configuration. Their reflective properties can be easily determined theoretically and predicted for each specific relative position of the target and radar in question. In real life, targets of the simplest type are quite rare. More often you have to deal with objects of complex configuration, which consist of a number of rigidly interconnected simple reflective elements. Examples of targets with complex configurations include aircraft, ships, various structures, etc.

Other targets are a collection of individual objects distributed in a certain area of ​​space, significantly larger than the radar resolution element. Depending on the nature of this distribution, there are volumetric-distributed (for example, a rain cloud) and surface-distributed (land surface, etc.) targets. The signal reflected from such a target is the result of the interference of reflector signals distributed within the bin.

For a fixed relative position of the radar and reflecting objects, the amplitude and phase of the reflected wave have a well-defined value. Therefore, in principle, for each specific case, the resulting total reflected signal can be determined. However, in the process of radar observation, the relative position of the targets and the radar usually changes, which leads to random fluctuations in the intensity and phase of the resulting reflected signals.

Effective target scattering area (EPR).

The calculation of the radar observation range requires a quantitative characterization of the intensity of the reflected wave. The power of the reflected signal at the input of the station receiver depends on a number of factors and, above all, on the reflective properties of the target. Typically, radar targets are characterized by an effective scattering area. The effective scattering area of ​​the target in the case when the radar antenna emits and receives electromagnetic waves of the same polarization is understood to be the value of σc that satisfies the equality σcP1 = 4πK2P2, where P1 is the power flux density of the forward wave of a given polarization at the target location; P2 is the power flux density of the wave of a given polarization reflected from the target at the radar antenna; R is the distance from the radar to the target. The RCS value can be directly calculated by the formula

σcP1 = 4πR2P2 / P1

As follows from the above formula, σc has the dimension of area. Therefore, it can be conventionally considered as a certain area equivalent to a target with an area σc, which, by isotropically scattering all the wave power incident on it from the radar, creates at the receiving point the same power flux density P2 as the real target.

If the target EPR is set, then with known values ​​of P1 and R, the power flux density of the reflected wave P can be calculated, and then, having determined the power of the received signal, the range of the radar station can be estimated.

The effective scattering area σc does not depend on the intensity of the emitted wave, or on the distance between the station and the target. Indeed, any increase in P1 leads to a proportional increase in P2 and their ratio in the formula does not change. When the distance between the radar and the target changes, the P2 / P1 ratio changes in inverse proportion to R2 and the value of σc remains unchanged.

Complex and group goals

Consideration of the simplest reflectors is not difficult. Most real-world radar targets are complex combinations of different types of reflectors. In the process of radar observation of such targets, they deal with a signal that is the result of the interference of several signals reflected from individual elements of the target.

When a complex object is irradiated (for example, an airplane, ship, tank, etc.), the nature of the reflections from its individual elements strongly depends on their orientation. In some positions, certain parts of the aircraft or ship can give very strong signals, while in other positions the intensity of the reflected signals can drop to zero. In addition, when the position of the object relative to the radar changes, the phase relationships between the signals reflected from various elements change. This results in fluctuations in the resulting signal.

There may be other reasons for changes in the intensity of the reflected signals. Thus, a change in conductivity between individual elements of the aircraft can be observed, one of the reasons for which is vibration caused by the operation of the engine. With a change in conductivity, the distribution of currents induced on the surface of the aircraft and the intensity of the reflected signals change. In propeller driven and turboprop aircraft, an additional source of change in the intensity of reflections is the rotation of the propeller.

Fig 2.1. Dependence of the RCS of the target on the angle.

In the process of radar observation, the relative position of the aircraft (ship) and the radar station is constantly changing. This results in fluctuations of the reflected signals and the corresponding changes in the RCS. The distribution laws of the probabilities of the target's effective scattering area and the nature of changes in this quantity over time are usually determined experimentally. For this, the intensity of the reflected signals is recorded and, after processing the record, the statistical characteristics of the signals and EPR are found.

As many studies have shown, the exponential distribution law is valid with sufficient accuracy for the fluctuations of σt aircraft

EPR has the dimension of area, but is not a geometric area, but is an energy characteristic, that is, it determines the value of the received signal power.

RCS of the target does not depend on the intensity of the emitted wave, or 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 the distance between the radar and the target changes, the ratio ρ 2 / ρ 1 changes in inverse proportion to R and the RCS value remains unchanged.

EPR of common point targets

For most point targets, RCS information can be found in radar reference books.

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 ...

,

where k is the wavenumber.

1) If the object is small, then the distance and field of the incident wave can be considered unchanged. 2) Distance R can be considered as the sum of the distance to the target and the distance within the target:

,
,
,
,

Flat plate

A flat surface is a special case of a curved convex surface.

Corner reflector

The principle of operation of the corner reflector

The 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 edges is used, then the EPR

Application of corner reflectors

Corner reflectors are used

• as decoys
• as radio contrast landmarks
• when conducting experiments with strong directional radiation

Dipole reflector

Dipole reflectors are used to create passive interference with radar operation.

The EPR value of a dipole reflector generally depends on the observation angle, however, the EPR for all angles:

Dipole reflectors are used to mask air targets and terrain, as well as passive radar beacons.

The sector of reflection of the dipole reflector is ~ 70 °

EPR of complex targets

EPR of complex real objects is measured on special installations, or polygons, where the conditions of the far irradiation zone are attainable.

#	Target type	σ c
1	Aviation
1.1	Fighter aircraft	3-12
1.2	Stealth fighter	0,3-0,4
1.3	Front-line bomber	7-10
1.4	Heavy bomber	13-20
1.4.1	B-52 bomber	100
1.4	Transport plane	40-70
2	Ships
2.1	Submarine surfaced	30-150
2.2	The submarine's deckhouse on the surface	1-2
2.3	Small craft	50-200
2.4	Medium ships	²
2.5	Large 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	ALСM 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	Dove	0,01
6.15	House sparrow	0,0008

Effective target scattering area (RCS)

The calculation of the radar observation range requires a quantitative characterization of the intensity of the reflected wave. The power of the reflected signal at the input of the station receiver depends on a number of factors and, above all, on the reflective properties of the target. Typically, radar targets are characterized by an effective scattering area. Under the effective scattering area of ​​the target in the case when the radar antenna emits and receives electromagnetic waves of the same polarization, we mean the value у q, which satisfies the equality у Ц П 1 = 4рК 2 П 2, where П 1 is the power flux density of the forward wave of the given polarization at the point where the target is located; P 2 is the power flux density of the wave of a given polarization reflected from the target at the radar antenna; R is the distance from the radar to the target. The RCS value can be directly calculated by the formula

u c P 1 = 4рR 2 P 2 / P 1

As follows from the above formula, y q has the dimension of area. Therefore, it can be conventionally considered as a certain area equivalent to the target of a normal radio beam with an area y q, which, isotropically dissipating all the wave power incident on it from the radar, creates at the receiving point the same power flux density P2 as the real target.

If the target EPR is set, then with known values ​​of P 1 and R, the power flux density of the reflected wave P can be calculated, and then, having determined the power of the received signal, the range of the radar station can be estimated.

The effective scattering area y ^ does not depend on the intensity of the emitted wave or on the distance between the station and the target. Indeed, any increase in P 1 leads to a proportional increase in P 2 and their ratio in the formula does not change. When the distance between the radar and the target changes, the ratio P 2 / P 1 changes in inverse proportion to R 2, and the value of у remains unchanged.

Complex and group goals

Consideration of the simplest reflectors is not difficult. Most real-world radar targets are complex combinations of different types of reflectors. In the process of radar observation of such targets, they deal with a signal that is the result of the interference of several signals reflected from individual elements of the target.

When a complex object is irradiated (for example, an airplane, ship, tank, etc.), the nature of the reflections from its individual elements strongly depends on their orientation. In some positions, certain parts of the aircraft or ship can give very strong signals, while in other positions the intensity of the reflected signals can drop to zero. In addition, when the position of the object relative to the radar changes, the phase relationships between the signals reflected from various elements change. This results in fluctuations in the resulting signal.

There may be other reasons for changes in the intensity of the reflected signals. Thus, a change in conductivity between individual elements of the aircraft can be observed, one of the reasons for which is vibration caused by the operation of the engine. With a change in conductivity, the distribution of currents induced on the surface of the aircraft and the intensity of the reflected signals change. In propeller driven and turboprop aircraft, an additional source of change in the intensity of reflections is the rotation of the propeller.

Fig 2.1.

In the process of radar observation, the relative position of the aircraft (ship) and the radar station is constantly changing. This results in fluctuations of the reflected signals and the corresponding changes in the RCS. The distribution laws of the probabilities of the target's effective scattering area and the nature of changes in this quantity over time are usually determined experimentally. For this, the intensity of the reflected signals is recorded and, after processing the record, the statistical characteristics of the signals and EPR are found.

As many studies have shown, the exponential distribution law is valid with sufficient accuracy for fluctuations in q aircraft

W (y q) = (1 /<у ц >) exp (- y c /<у ц >).

where<у ц >- average value of RCS.

The return radiation patterns of ships have a finer lobe structure than those of airplanes, due to the significantly larger size and complex structures of the ships. The reflective elements of the ship are many and varied, so the ship can also be viewed as a group of elements, the reflections of which have random phases.

Experimental studies show that the ship's RCS fluctuations are also approximately described by an exponential distribution law.

Data on the laws of distribution of signal amplitudes or EPR are necessary to calculate the radar range and substantiate the signal processing technique. Information about the correlation function and the fluctuation spectrum is also important in determining the accuracy of coordinate measurements.

In a practical assessment of the range of a radar station, first of all, the average value of the RCS is usually used<у ц >This value can be obtained by averaging the values<у ц >for different directions of incidence of the incident wave. The table shows the average values ​​of the RCS of various real targets, obtained as a result of generalizing a large number of measurements at waves of the centimeter range. Using these values, it is possible to calculate the average values ​​of the detection range of various targets.