Dec 21, 2015

By Ron Smith

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EEE381BAEROSPACE

SYSTEMS & AVIONICS

RadarPart 2 – The radar range equation

Ref: Moir & Seabridge 2006, Chapter 3,4

Dr Ron Smith

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OUTLINE1. Basic radar range equation2. Developing the radar range equation3. Design impacts4. Receiver sensitivity5. Radar cross-section6. Low observability7. Exercises

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1. BASIC RADAR RANGE EQUATION

There are many different versions of the radar range equation.

We will use, and fully derive, the one presented below.

4

min3

22

)4( S

GPR 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 λ – 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

min3

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

the average transmitted power is a function of peak pulse power and the pulse duration:

PRFTwhere

T

PPP p

p

peakavet

1,

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2.2 POWER DENSITY AT TARGET [4]

Recall that power density decreases as a function of distance traveled:

24 R

GPRrangeatdensitypower t

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2.3 REFLECTED POWER

The amount of power reflected back from a target is a function of the power density at the target and the target’s radar cross-section, :

24 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 the echoed power density as a function of the receive antenna’s effective aperture:

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,

2

43

22

42

GAthatrecalling

R

GPA

R

GPPreceiveratpower

e

te

tr

* In this equation the receiver is assumed to be all radar receive 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 of

detecting targets as long as the received echo power is greater than or equal to the minimum detectable signal power of the receive chain:

4

min3

22

maxmin )4(,

S

GPRSPfor t

r

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3. RADAR DESIGN IMPACTS

A careful study of the radar range equation provides further insight as to the effect of several radar design decisions.

In general the equation tells us that for a radar to have a long range, the transmitter must be high power, the antenna must be large and have high gain, and the receiver must be very sensitive.

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3.1 POWER, PT

Increases in transmitter power yield a surprisingly small increase in radar range, since range increases by the inverse fourth power.For example, a doubling of transmitter peak

power results increases radar range by only 19%,

19.124

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3.2 TIME-ON-TARGET, /TP

The average power transmitted can also be increased 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 give a 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

the design 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 2max

2)2/(

DorGRand

DorAGdishaFor p

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3.4 RECEIVER SENSITIVITY, SMIN

Similar to that of transmitter power, increases in receiver sensitivity yield relatively small increases 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 beyond the

scope of this course, see §3.5.3. Simplistically, the smaller the radar pulse width,

the larger the required receiver bandwidth and the 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 measure of its size as seen by a radar, expressed as an area, m2.

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

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

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4.1.1 RCS OF A METAL PLATE Large RCS, but

decreases rapidly as the incident angle deviates from the normal.

2

224

ba

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4.1.2 RCS OF A METAL SPHERE Small RCS, but is

independent of incident angle.

2r

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4.1.3 RCS OF A METAL CYLINDER RCS can be quite small

or fairly large depending on orientation.

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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 and relatively independent of incident angle.

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5. LOW OBSERVABILITY From the previous discussion on the

radar cross-section of targets, it should be obvious that determining the radar cross-section of an airplane is a complicated task.

The art of designing an aircraft to specifically have a low RCS is known as low observability, or more commonly known as “stealth”.

Stealth is a relatively new technology,even full RCS prediction is only 2 decades

old.

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5.1 HISTORY* OF STEALTH AIRCRAFT [1]

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5.2 AIRCRAFT HIGH RCS AREAS [1]

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5.3 LOW OBSERVABILITY DESIGN AREAS [1]

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5.3.1 LOW OBSERVABILITY DESIGN EXAMPLE[1]

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5.3.2 LOW OBSERVABILITY DESIGN EXAMPLE[1]

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5.4 COMPARATIVE RCS [1]

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6. IN-CLASS EXERCISES

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6.1 QUICK RESPONSE EXERCISE # 1 Think carefully about the derivation of

the radar range equation just presented. Is there a potentially significant loss component missing?Hint: recall the simple link equation from

your very early lectures.

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6.2 QUICK RESPONSE EXERCISE # 2 Why have designers of stealth aircraft

sought to blend the physical transitions / features of the aircraft?

Will reduction in your aircraft RCS alone make you invisible to the enemy?How else might they find you?

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6.3 RADAR RANGE EQUATION CALCULATION

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6.3 RADAR RANGE EQUATION CALCULATION The US Navy AN/SPS-48 Air Search Radar is

a medium-range, three-dimensional (height, range, and bearing) 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 μsec Phased array antenna with a gain of 38.5 dB

For its published maximum range of 250 miles for a nominal target such as the F-18, what is the receiver chain sensitivity in bBm?

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REFERENCES1) Moir & Seabridge, Military Avionics Systems, American Institute

of Aeronautics & Astronautics, 2006. [Sections 2.6 & 2.7]2) David Adamy, EW101 - A First Course in Electronic Warfare,

Artech House, 2000. [Chapters 3,4 & 6]3) George W. Stimson, Introduction to Airborne Radar, Second

Edition, SciTch Publishing, 1998.4) Principles of Radar Systems, student laboratory manual, 38542-

00, Lab-Volt (Quebec) Ltd, 2006.5) John C. Vaquer, US Navy Surface Officer Warfare School

Documents, Combat Systems Engineering : Radar, http://www.fas.org/man/dod-101/navy/docs/swos/cmd/fun12/12-1/sld001.htm

6) Mark A. Hicks, "Clip art licensed from the Clip Art Gallery on DiscoverySchool.com"

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