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 transmit-receive 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 (angle) 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 diffuser 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:

,

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 .

In this way,

. (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 ...

,

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:

,
,

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°

The simplest volumetrically distributed targets are chaff, which are dropped in large numbers from an aircraft or fired by special projectiles, disperse in the air and form a cloud of reflectors. They are used to set up passive interference in a wide frequency range and simultaneously against many RTS.

Chaff 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 chaff reflectors is determined by the product of the RCS of individual reflectors located 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 value of the RCS of a single dipole reflector is observed when its geometric axis coincides with the vector E strength of the electric field of the wave. Then:

σ do max = 0.86λ 2

If the chaff 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 dipole reflectors, they orient themselves randomly in the cloud. Therefore, the average value of the RCS of a single dipole reflector is used in calculations.

σ do sr = 1/5 σ do max = 0.17λ 2,

where: λ - wavelength of the irradiating radar.

It follows that the simultaneous suppression of RTS operating at different frequencies is possible only when using chaff of different lengths.

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

Corner reflector consists of rigidly interconnected mutually perpendicular planes. The simplest corner reflector is a dihedral or trihedral angle (Fig. 3.3, a, b).

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

a - dihedral; b - trihedral.

The trihedral 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 trihedral reflector is shown in Fig. 3.4.

Fig.3.4. Scattering diagram of a trihedral reflector.

In practice, triangular corner reflectors are used, having a triangular, rectangular or sector shape (Fig. 3.5, a, b, c).

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

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

For objects of a 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 EPR formula of the target can be represented as

σ \u003d 4πD 2 E 2 2 / E 2 1

Attitude E 2 / E 1, included in this expression, can be found on the basis of the Huygens principle. This method consists in 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 station, 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 a 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 in the case of normal incidence).

If the linear dimensions of the surface of the object are large compared to the wavelength, and the surface itself is rough, then diffuse reflection takes place. In this case, due to the different orientation of the surface elements, electromagnetic waves are scattered in different directions, including in the direction of 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. Unlike diffuse reflection, secondary resonant radiation usually has a high intensity and a pronounced directionality, depending on the design and orientation of the reflecting element.

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

From the point of view of signal formation upon reflection, 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 location of the target in question and the radar. In real conditions, goals 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. Aircraft, ships, various structures, etc. can serve as examples of targets of complex configuration.

Other targets are a collection of individual objects distributed in a certain area of ​​space, much larger than the resolution element of the radar. Depending on the nature of this distribution, volume-distributed (for example, a rain cloud) and surface-distributed (land surface, etc.) targets are distinguished. The signal reflected from such a target is the result of the interference of reflector signals distributed within the resolution 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, the resulting total reflected signal can be determined for each specific case. However, during radar surveillance, the relative positions of the targets and the radar usually change, resulting in random fluctuations in the intensity and phase of the resulting echoes.

Effective target scattering area (ESR).

The calculation of the range of radar observation requires a quantitative characteristic 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 reflecting 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 radiates and receives electromagnetic waves of the same polarization, it is understood the value σt, which satisfies the equation σtP1=4πK2P2, where P1 is the power flux density of the direct wave of this polarization at the target location; P2 is the power flux density of a 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 formula above, σц has the dimension of area. Therefore, it can be conditionally considered as a certain area equivalent to the target, normal to the radio beam, with area σц, which, 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 RCS of the target is given, then with known values ​​of P1 and R, it is possible to calculate the power flux density of the reflected wave P, and then, having determined the power of the received signal, estimate the range of the radar station.

The effective scattering area σc does not depend on the intensity of the emitted wave, nor 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 changing the distance between the radar and the target, the ratio P2/P1 changes inversely proportional to R2 and the value of σc remains unchanged.

Complex and group goals

Consideration of the simplest reflectors does not cause difficulties. Most real radar targets are a complex combination of different types of reflectors. In the process of radar observation of such targets, one deals 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 aircraft, a ship, a 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 may produce very intense signals, and in other positions, the intensity of the reflected signals may 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.

Other reasons for changes in the intensity of the reflected signals are also possible. Thus, there may be a change in conductivity between the individual elements of the aircraft, one of the causes of which are vibrations caused by the operation of the engine. When the conductivity changes, the distributions of the currents induced on the aircraft surface and the intensity of the reflected signals change. For propeller 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 mutual position of the aircraft (ship) and the radar is constantly changing. The result of this is the fluctuations of the reflected signals and the corresponding changes in the EPR. The laws of probability distribution of the effective scattering area of ​​the target and the nature of changes in this value over time are usually determined experimentally. To do 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 shown by many studies, the exponential distribution law is valid with sufficient accuracy for the fluctuation σc of aircraft

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 ...

,

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:

,
,
,
,

flat plate

A flat surface is a special case of a curved 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	Person	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

Effective area of ​​dispersion of the target (EPR)

The calculation of the range of radar observation requires a quantitative characteristic 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 reflecting 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 radiates and receives electromagnetic waves of the same polarization, is understood the value of y c, satisfying the equality y c P 1 =4pK 2 P 2, where P 1 is the power flux density of the direct wave of this polarization at the location of the target; P 2 -- power flux density reflected from the target wave of a given polarization at the radar antenna; R is the distance from the radar to the target. The RCS value can be directly calculated by the formula

at c P 1 \u003d 4pR 2 P 2 / P 1

As follows from the formula above, u has the dimension of area. Therefore, it can be conditionally considered as some area equivalent to the target, normal to the radio beam, with area y u, which, isotropically scattering all the wave power incident on it from the radar, creates at the receiving point the same power flux density P 2 as the real target.

If the RCS of the target is given, then with known values ​​of P 1 and R, it is possible to calculate the power flux density of the reflected wave P, and then, having determined the power of the received signal, estimate the range of the radar station.

The effective scattering area y u does not depend on the intensity of the emitted wave, nor 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 changing the distance between the radar and the target, the ratio P 2 /P 1 changes inversely proportional to R 2 and the value of y c remains unchanged.

Complex and group goals

Consideration of the simplest reflectors does not cause difficulties. Most real radar targets are a complex combination of different types of reflectors. In the process of radar observation of such targets, one deals 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 aircraft, a ship, a 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 may produce very intense signals, and in other positions, the intensity of the reflected signals may 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.

Other reasons for changes in the intensity of the reflected signals are also possible. Thus, there may be a change in conductivity between the individual elements of the aircraft, one of the causes of which are vibrations caused by the operation of the engine. When the conductivity changes, the distributions of the currents induced on the aircraft surface and the intensity of the reflected signals change. For propeller 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 mutual position of the aircraft (ship) and the radar is constantly changing. The result of this is the fluctuations of the reflected signals and the corresponding changes in the EPR. The laws of probability distribution of the effective scattering area of ​​the target and the nature of changes in this value over time are usually determined experimentally. To do 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

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

where<у ц >- the average value of the RCS.

The return radiation diagrams of ships have a finer lobe structure than aircraft diagrams, which is explained by the significantly larger size and complex design of the ships. The reflective elements of a ship are numerous and varied, so the ship can also be considered as a group of elements whose reflections have random phases.

Experimental studies show that fluctuations in the EPR of a ship 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 range of the radar and substantiate the method of signal processing. Information about the correlation function and 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 irradiating wave. The table shows the average RCS values ​​of various real targets, obtained as a result of summarizing a large number of measurements at centimeter wavelengths. Using these values, it is possible to calculate the average values ​​of the detection range of various targets.