Download - Lecture Set4 Radars

8/11/2019 Lecture Set4 Radars

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Kyu/ET422 Draft Lecture Notes-Radar 2014

RADAR AND SENSOR SYSTEMS

Basic principle of operation

Radar measurement of range, or distance, is made possible because of the properties of radiatedelectromagnetic energy:

This energy normally travels through space in a straight line, at a constant speed, and will

vary only slightly because of atmospheric and weather conditions.

Electromagnetic energy travels through air at approximately the speed of light,

300,000 kilometers per second or

186,000 statute miles per second or

162,000 nautical miles per second.

Reflection of electromagnetic waves

The electromagnetic waves are reflected if they meet an electrically leading surface. If thesereflected waves are received again at the place of their origin, then that means an obstacle is in

the propagation direction.

These principles can basically be implemented in a radar system, and allow the determination of

the distance, the direction and the height of the reflecting object

The radio-frequency (RF) energy emitted by the radar system is transmitted to and reflected from

the reflecting object. A small portion of the reflected energy returns to the radar set. This

returned energy is called an ECHO, just as it is in sound terminology. Radar sets use the echo to

determine the direction and distance of the reflecting object.

The word radar is a contraction of RAdio Detecting And Ranging.

As implied by this contraction, radars are used to detect the presence of an aim (as object of

detection) and to determine its location. The contraction implies that the quantity measured is

range. While this is correct, modern radars are also used to measure range and angle.

Although radar cannot reorganize the color of the object and resolve the detailed features of the

target like the human eye, it can see through darkness, fog and rain, and over a much longer

range. It can also measure the range, direction, and velocity of the target.Basic radar consists of a transmitter, a receiver, and a transmitting and receiving antenna. A very

small portion of the transmitted energy is intercepted and reflected by the target. A part of the

reflection is reradiated back to the radar (this is called back-reradiation), as shown in Fig. 7.1.The back-reradiation is received by the radar, amplified, and processed. The range to the target isfound from the time it takes for the transmitted signal to travel to the target and back. The

direction or angular position of the target is determined by the arrival angle of the returned

signal. A directive antenna with a narrow beamwidth is generally used to find the direction.The relative motion of the target can be determined from the doppler shift in the carrier

frequency of the returned signal.


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Although the basic concept is fairly simple, the actual implementation of radar could be

complicated in order to obtain the information in a complex environment. A sophisticated radar

is required to search, detect, and track multiple targets in a hostile environment; to identify thetarget from land and sea clutter; and to discern the target from its size and shape. To search and

track targets would require mechanical or electronic scanning of the antenna beam. For

mechanical scanning, a motor or gimbal can be used, but the speed is slow. Phased arrays can beused for electronic scanning, which has the advantages of fast speed and a stationary antenna

Fig 1 Radar and back-radiation

Radar can be classified according to locations of deployment, operating functions, applications,

and waveforms.

1. Locations: airborne, ground-based, ship or marine, space-based, missile or smart weapon, etc.2. Functions: search, track, search and track

3. Applications: traffic control, weather, terrain avoidance, collision avoidance, navigation, air

defense, remote sensing, imaging or mapping, surveillance, reconnaissance, missile or weaponguidance, weapon fuses, distance measurement (e.g., altimeter), intruder detection, speed

measurement (police radar), etc.

4. Waveforms: pulsed, pulse compression, continuous wave (CW), frequency modulatedContinuous wave (FMCW)

Radar can also be classified as monostatic radar or bistatic radar. Monostatic radar uses a single

antenna serving as a transmitting and receiving antenna. The transmitting and receiving signalsare separated by a duplexer. Bistatic radar uses a separate transmitting and receiving antenna to

improve the isolation between transmitter and receiver. Most radar systems are monostatic types.

RADAR EQUATIONThe radar equation gives the range in terms of the characteristics of the transmitter, receiver,

antenna, target, and environment. It is a basic equation for understanding radar operation.

Consider a simple system configuration, as shown in Fig 2. The radar consists of a transmitter, areceiver, and an antenna for transmitting and receiving. A duplexer is used to separate thetransmitting and receiving signals. A circulator is shown in fig 2 used as a duplexer. A switch


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can also be used, since transmitting and receiving are operating at different times. The target

could be an aircraft, missile, satellite, ship, tank, car, person, mountain, iceberg, cloud, wind,

raindrop, and so on. Different targets will have different radar cross sections s. The parameterPt is the transmitted power and Pr is the received power. For a pulse radar, Pt is the peak pulse

power. For a CW radar, it is the average power. Since the same antenna is used for transmitting

and receiving, we have

t rG G G gain of antenna

e et er A A A effective area of the antenna

Basic Radar system

Note that,

2

4t etG A

et tA A

Where is the free space wavelength, is the antenna efficiency and tA is the antenna aperture

size

Let us first assume that there is no misalignment (which means the maximum of the antennabeam is aimed at the target), no polarization mismatch, no loss in the atmosphere, and no

impedance mismatch at the antenna feed. Later, a loss term will be incorporated to account for

the above losses. The target is assumed to be located in the far-field region of the antennaThe power density (in watts per square meter) at the target location from an isotropic antenna is

given by

24

tp

power densityR


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For a radar using a directive antenna with a gain of Gt , the power density at the target location

should be increased by Gt times. We have

Power density at target location from a directive antenna =24

tt

pG

R

The measure of the amount of incident power intercepted by the target and reradiated back in the

direction of the radar is denoted by the radar cross section , where is in square meters andis defined as

arg

power backscaterred at theradar

powerdesnity at the t et

Therefore, the backscattered power at the target location is

Power backscattered to radar (W) =2

4

t tp G

R

Power density backscattered by target and returned to radar location=2 24 4

t tp G

R R

The radar receiving antenna captures only a small portion of this backscattered power. The

captured receiving power is given by;

Pr = returned power captured by radar(w)=2 24 4

t tef

p GA

R R

Where2

4

ref

GA

There fore2

2 24 4 4

t t rr

p G Gp

R R

But for monostatic Radar,r t

G G 2 2

2 24 4 4

tr

p Gp R R

This is the Radar Equation

If the minimum allowable signal power is Smin, then we have the maximum allowable range

when the received signal is Smin.Let Pr= Smin

Then

1

42 2

max 3

min4

tp GR RS

The maximum radar range Rmax is the distance beyond which the required signal is too smallfor the required system

Radar Cross section

The RCS of a target is the effective area defined as the ratio of backscattered power to theincident power density. The larger the RCS, the higher the power backscattered to the radar.

The RCS depends on the actual size of the target, the shape of the target, the materials of the

target, the frequency and polarization of the incident wave, and the incident and reflected anglesrelative to the target. The RCS can be considered as the effective area of the target. It does not

necessarily have a simple relationship to the


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physical area, but the larger the target size, the larger the cross section is likely to be.

PULSE RADARA pulse radar transmits a train of rectangular pulses, each pulse consisting of a short burst of

microwave signals, as shown in Fig below

. The pulse has a width t and a pulse repetition period Tp =1/fp , where fp is the pulse repetition

frequency (PRF) or pulse repetition rate.The transmitting pulse hits the target and returns to the radar at some time tR later depending on

the distance, where tR is the round-trip time of a pulsed microwave signal. The target range can

be determined by


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where c is the speed of light. To avoid range ambiguities, the maximum tR should be less than

Tp. The maximum range without ambiguity requires

The average power is related to the peak power by

where Pt is the peak pulse power.

A matched filter is normally designed to maximize the output peak signal to average noise power

ratio. The ideal matched-filter receiver cannot always be exactly realized in practice but can beapproximated with practical receiver circuits. For optimal performance, the pulse width is

designed such that

1B Where B is the bandwidth

7.6 CONTINUOUS-WAVE OR DOPPLER RADARContinuous-wave or doppler radar is a simple type of radar. It can be used to detect a moving

target and determine the velocity of the target. It is well known in acoustics and optics that if

there is a relative movement between the source (oscillator) and the observer, an apparent shift in

frequency will result. The phenomenon is called the doppler effect, and the frequency shift is thedoppler shift. Doppler shift is the basis of CW or doppler radar.

Consider that a radar transmitter has a frequency f0 and the relative target velocity is vr. If R is

the distance from the radar to the target, the total number of wavelengths contained in the two-

way round trip between the target and radar is 02 /R

The total angular excursion or phase made by the electromagnetic wave during its transit to

and from the target is

0

22

R

If the target is in relative motion with the radar, R and are continuously changing. The change

in with respect to time gives a frequency shift d . The doppler angular frequency shift d is

given by


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0 0

4 42d d r

d dRf v

dt dt

There fore

where f0 is the transmitting signal frequency, c is the speed of light, and vr is the relativevelocity of the target. Since vr is normally much smaller than c, fd is very small unless f0 is at a

high (microwave) frequency. The received signal frequency is 0 df f . The plus sign is for an

approaching target and the minus sign for a recedingtarget.

For a target that is not directly moving toward or away from a radar as shown in Fig below, the

relative velocity vr may be written as

cosrv v

where v is the target speed and is the angle between the target trajectory and the line joiningthe target and radar. It can be seen that

Therefore, the Doppler shift is zero when the trajectory is perpendicular to the radar line of sight.


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Doppler or CW radar block diagram.

Exercise

A police radar operating at 10.5 GHz is used to track a cars speed. If a car is moving at a speedof 100 km/h and is directly aproaching the police radar, what is the doppler shift frequency in

hertz?Continuous-wave radar is relatively simple as compared to pulse radar, since no pulsemodulation is needed

Extra content

The following figure shows the operating principle of primary radar. The radar antenna

illuminates the target with a microwave signal, which is then reflected and picked up by a

receiving device. The electrical signal picked up by the receiving antenna is called echo or

return. The radar signal is generated by a powerful transmitter and received by a highly sensitivereceiver.

Block diagram of a primary radar with the signal flow

Signal Routing

The radar transmitter produces short duration high-power RF- pulses of energy.


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The duplexer alternately switches the antenna between the transmitter and receiver so that

only one antenna need be used. This switching is necessary because the high-power pulses

of the transmitter would destroy the receiver if energy were allowed to enter the receiver.

The antenna transfers the transmitter energy to signals in space with the required

distribution and efficiency. This process is applied in an identical way on reception.

The transmitted pulses are radiated into space by the antenna as an electromagnetic wave.

This wave travels in a straight line with a constant velocity and will be reflected by an aim.

The antenna receives the back scattered echo signals.

During reception the duplexer lead the weakly echo signals to the receiver.

The hypersensitive receiver amplifies and demodulates the received RF-signals. The

receiver provides video signals on the output.

The indicator should present to the observer a continuous, easily understandable, graphicpicture of the relative position of radar targets.

All targets produce a diffuse reflection i.e. it is reflected in a wide number of directions. The

reflected signal is also called scattering. Backscatter is the term given to reflections in the

opposite direction to the incident rays. Radar signals can be displayed on the traditional plan

position indicator (PPI) or other more advanced radar display systems. A PPI has a rotating

vector with the radar at the origin, which indicates the pointing direction of the antenna and

hence the bearing of targets. It shows a map-like picture of the area covered by the radar beam.

Signal Timing

Most functions of a radar set are time-dependent. Time synchronization between the transmitter

and receiver of a radar set is required for range measurement. Radar systems radiate each pulse

during transmit time (or Pulse Width ), wait for returning echoes during listening or rest time,

and then radiate the next pulse, as shown in figure below

A so called synchronizer coordinates the timing for range determination and supplies the

synchronizing signals for the radar. It sent simultaneously signals to the transmitter, which sends

a new pulse, and to the indicator, and other associated circuits.


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The time between the beginning of one pulse and the start of the next pulse is called pulse-

repetition time (PRT) and is equal to the reciprocal of PRF as follows:

The Pulse Repetition Frequency (PRF) of the radar system is the number of pulses that are

transmitted per second. The frequency of pulse transmission affects the maximum range that can

be displayed .

Ranging

The distance of the aim is determined from the running time of the high-frequency transmitted

signal and the propagation speed c0. The actual range of a target from the radar is known as slant

range. Slant range is the line of sight distance between the radar and the object illuminated.

While ground range is the horizontal distance between the emitter and its target and itscalculation requires knowledge of the target's elevation. Since the waves travel to a target and

back, the round trip time is divided by two in order to obtain the time the wave took to reach the

target. Therefore the following formula arises for the slant range


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If the respective running time tdelay is known, then the distanceRbetween a target and the radar

set can be calculated by using this equation

Maximum Unambiguous Range

A problem with pulsed radars and range measurement is how to unambiguously determine the

range to the target if the target returns a strong echo. This problem arises because of the fact that

pulsed radars typically transmit a sequence of pulses. The radar receiver measures the time

between the leading edges of the last transmitting pulse and the echo pulse. It is possible that an

echo will be received from a long range target after the transmission of a second transmitting

pulse.

In this case, the radar will determine the wrong time interval and therefore the wrong range. The

measurement process assumes that the pulse is associated with the second transmitted pulse and

declares a much reduced range for the target. This is called range ambiguity and occurs where

there are strong targets at a range in excess of the pulse repetition time. The pulse repetition time

defines a maximum unambiguous range. To increase the value of the unambiguous range, it is

necessary to increase the PRT, this means: to reduce the PRF. Echo signals arriving after the

reception time are placed either into the


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o transmit time where they remain unconsidered since the radar equipment isn't ready to

receive during this time, or

o into the following reception time where they lead to measuring failures (ambiguous

returns).

The maximum unambiguous range for given radar system can be determined by using the

formula:

The pulse repetition time (PRT) of the radar is important when determining the maximum rangebecause target return-times that exceed the PRT of the radar system appear at incorrect locations

(ranges) on the radar screen. Returns that appear at these incorrect ranges are referred as

ambiguous returns or second time around (second-sweep) echoes. The pulse width in this

equation indicates that the complete echo impulse must be received.

Radar Parameters

Elevation AngleThe elevation angle is the angle between the horizontal plane and the line of sight, measured in

the vertical plane.

Height

The height of a target over the earth's surface is called height or altitude.

Accuracy

Accuracy is the degree of conformance between the estimated or measured position and/or the

velocity of a platform at a given time and its true position or velocity

Radar Resolution

The target resolution of radar is its ability to distinguish between targets that are very close ineither range or bearing. Weapons-control radar, which requires great precision, should be able to

distinguish between targets that are only yards apart. Search radar is usually less precise and only

distinguishes between targets that are hundreds of yards or even miles apart. Radar resolution is

usually divided into two categories; range resolution and angular (bearing) resolution.


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Angular Resolution

Angular resolution is the minimum angular separation at which two equal targets at the same

range can be separated.

Range Resolution

Range resolution is the ability of a radar system to distinguish between two or more targets onthe same bearing but at different ranges. The degree of range resolution depends on the width of

the transmitted pulse, the types and sizes of targets, and the efficiency of the receiver and

indicator.

Therefore, the theoretical range resolution of a radar system can be calculated from the following

formula:

Theoretical Maximum Radar Range equation

The radar equation represents the physical dependences of the transmit power, that is the wave

propagation up to the receiving of the echo-signals. Furthermore one can assess the performance

of the radar with the radar equation.

The received energy is an extremely small part of the transmitted energy

The radar equation relates the important parameters affecting the received signal of radar. Now

we assess what kinds of factors are expressed in this radar equation.

Ptx is the peak power transmitted by the radar. This is a known value of the radar. It is important t

directly related to the transmitted power.

Prx is the power returned to the radar from a target. This is an unknown value of the radar,

but it is one that is directly calculated. To detect a target, this power must be greater

than the minimum detectable signal of the receiver.


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Antenna Gain

The antenna gain of the radar is a known value. This is a measure of the antenna's ability to focus

outgoing energy into the directed beam.

int

int

Maximum radiation ensity

G Average radiation ensity

Antenna gain describes the degree to which an antenna concentrates electromagnetic energy in a

narrow angular beam. The two parameters associated with the gain of an antenna are the

directive gain and directivity. The gain of an antenna serves as a figure of merit relative to an

isotropic source with the directivity of an isotropic antenna being equal to 1. The power received

from a given target is directly related to the square of the antenna gain, while the antenna is used

both for transmitting and receiving.

Antenna Aperture

Remember: the same antenna is used during transmission and reception. In case of transmission

the whole energy will be processed by the antenna. In case of receiving, the antenna has got the

same gain, but the antenna receives a part of the incoming energy only. But as a second effect is

that of the antenna's aperture, which describes how well an antenna can pick up power from an

incoming electromagnetic wave. As a receiver, antenna aperture can be visualized as the area of

a circle constructed broadside to incoming radiation where all radiation passing within the circle

is delivered by the antenna to a matched load. Thus incoming power density (watts per square

meter) aperture (square meters) = available power from antenna (watts). Antenna gain isdirectly proportional to aperture. An isotropic antenna has an aperture of / 4. An antenna with

a gain of G has an aperture of G / 4.

Radar Cross Section

The size and ability of a target to reflect radar energy can be summarized into a single term, t,

known as the radar cross-section RCS, which has units of m. If absolutely all of the incident


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radar energy on the target were reflected equally in all directions, then the radar cross section

would be equal to the target's cross-sectional area as seen by the transmitter. In practice, some

energy is absorbed and the reflected energy is not distributed equally in all directions. Therefore,

the radar cross-section is quite difficult to estimate and is normally determined by measurement.

The target radar cross sectional area depends of:

o the airplanes physical geometry and exterior features,

o the direction of the illuminating radar,

o the radar transmitters frequency,

o used material types of the reflecting surface.

Free-space Path Loss

R is the target range of the term in the equation. This value can be calculated by measuring the

time it takes the signal to return. The range is important since the power obtaining a reflecting

object is inversely related to the square of its range from the radar.

Free-space path loss is the loss in signal strength of an electromagnetic wave that would result

from a line-of-sight path through free space, with no obstacles nearby to cause reflection or

diffraction. The power loss is proportional to the square of the distance between the radars

transmitter and the reflecting obstacle.


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