Lectures Radar2 Hocvien

8/2/2019 Lectures Radar2 Hocvien

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PART I- RADAR

B- Radar Range Equation


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2/2011 Radar range equation - 2

Outline

1. Basic radar range equation

2. Developing the radar range equation

3. Design impacts4. Receiver sensitivity

5. Radar cross-section

Exercises


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1. Basic radar range equation

There are many different versions of theradar range equation.

We will use, and fully derive, the onepresented below.

4

min

3

22

)4( SGPR tMax


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1.1 Components of the equation

Rmax the maximum range of the radar

Pt average power of the transmitter

G gain of the transmit/receive antenna

wavelength of the operating frequency

radar cross-section of the target Smin minimum detectable signal power


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1.2 Units of the equation

4

min

3

22

)4( S

GPR tMax

mW

mmWRofunits Max 4

22


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2. Developing radar range equation


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2.1 Transmitted power

Recall from the previous lecture that theaverage transmitted power is a function of

peak pulse power and the pulse duration:

PRFTwhere

T

PPP p

p

peak

avet

1,


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2.2 Power density at target

Recall that power density decreases as afunction of distance traveled:

24 R

GPRrangeatdensitypower t


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2.3 Reflected power

The amount of powerreflected back from a

target is a function ofthe power density at thetarget and the targets

radar cross-section, :

2

4 R

GPreflecteddensitypower t


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2.4 Power density of echo at antenna

The power density of the returned signal, echo,again spreads as it travels back towards the

radar receive antenna.

22

44 RR

GPantennaatreceiveddensitypower t


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2.5 Power of echo at receiver*

The antenna captures only a portion of theechoed power density as a function of the

receive antennas effective aperture:

4

,)4()4(

,

2

43

22

42

GAthatrecalling

R

GPA

R

GPPreceiveratpower

e

te

tr

* In this equation the receiver is assumed to be all radarreceive chain components except the antenna.


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2.5.1 Relative power received range


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2.6 Minimum detectable signal power

Therefore a radar system is capable ofdetecting targets as long as the received echo

power is greater than or equal to the minimumdetectable signal power of the receive chain:

4

min

3

22

maxmin)4(

,S

GPRSPfor tr


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3. Radar design impacts

A careful study of the radar range equationprovides further insight as to the effect of severalradar design decisions.

In general the equation tells us that for a radarto have a long range, the transmitter must behigh power, the antenna must be large and havehigh gain, and the receiver must be verysensitive.


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3.1 Power, Pt

Increases in transmitter power yield asurprisingly small increase in radar range,

since range increases by the inverse fourthpower.

For example, a doubling of transmitter peak powerresults increases radar range by only 19%,

19.124


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3.2 Time-on-target, /Tp

The average power transmitted can also beincreased by increasing the pulse duty cycle,

sometimes referred to as the time-on-target. A combined doubling of the pulse width and

doubling of the transmitter peak power will givea fourfold increase in average transmitted

power, and ~41% increase in radar range.

41.144


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3.3 Gain, G

Antenna gain is a major consideration in thedesign of the radar system.

For a parabolic dish, doubling the antenna size(diameter) will yield a fourfold increase in gain and a

doubling of radar range.

4 44 2

max

2

)2/(

DorGRand

DorAGdishaFor p


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3.4 Receiver sensitivity, Smin

Similar to that of transmitter power, increases inreceiver sensitivity yield relatively smallincreases in radar range.

Only 19% range increase for a halving of sensitivity,and at the expense of false alarms.

Receiver design is a complex subject: OK

Simplistically, the smaller the radar pulse width,the larger the required receiver bandwidth andthe larger the receiver noise floor.


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3.4.1 Receiver bandwidth


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3.4.2 Signal-to-noise


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3.4.3 Receiver threshold


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4. Radar cross-section,

The radar cross-section of a target is a measureof its size as seen by a radar, expressed as anarea, m2.

It is a complex function of the geometric cross-section of the target at the incident angle of theradar signal, as well as the directivity andreflectivity of the target.

The RCS is a characteristic of the target, not theradar.


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4.1.1 RCS of a metal plate

Large RCS, butdecreases rapidly as theincident angle deviates

from the normal.

2

224

ba


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4.1.2 RCS of a metal sphere

Small RCS, but isindependent of incidentangle.

2r


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4.1.3 RCS of a metal cylinder

RCS can be quite smallor fairly large dependingon orientation.

endthefrom

viewedas

r

ra

,4

,2

2

43

2


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4.1.4 RCS of a trihedral corner reflector

The RCS of a trihedral(corner) is both large andrelatively independent of

incident angle.


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Exercises

Think carefully about the derivation of the radar rangeequation just presented. Is there a potentially significant losscomponent missing?

Hint: recall the simple link equation from your very earlylectures.

(Atmospheric loss is not accounted for in this version of theradar range equation. It rather complicates this simpleestimate)


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Radar range equation calculation

The US Navy AN/SPS-48 Air Search Radar is amedium-range, three-dimensional (height, range, andbearing) air search radar.

Published technical specifications include: Operating frequency 2900-3100 MHz

Transmitter peak power 60-2200 kW

PRF 161-1366 Hz, and pulse widths of 9 / 3 sec

Phased array antenna with a gain of 38.5 dB

For its published maximum range of 250 miles for anominal target such as the F-18, what is the receiverchain sensitivity in bBm?

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