Aerospace System & Avionics

EEE381BAEROSPACE

SYSTEMS & AVIONICS

RadarPart 2 – The radar range equation

Ref: Moir & Seabridge 2006, Chapter 3,4

Dr Ron Smith

EEE381B

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

EEE381B

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

EEE381B

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

EEE381B

1.2 UNITS OF THE EQUATION

4

min3

22

)4( S

GPR tMax

mW

mmWRofunits Max 4

22

EEE381B

2. DEVELOPING RADAR RANGE EQUATION

EEE381B

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,

EEE381B

2.2 POWER DENSITY AT TARGET [4]

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

24 R

GPRrangeatdensitypower t

EEE381B

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

EEE381B

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

EEE381B

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:

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 radar receive chain components except the antenna.

EEE381B

2.5.1 RELATIVE POWER RECEIVED RANGE

EEE381B

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

EEE381B

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.

EEE381B

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

EEE381B

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

EEE381B

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

EEE381B

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.

EEE381B

3.4.1 RECEIVER BANDWIDTH

EEE381B

3.4.2 SIGNAL-TO-NOISE

EEE381B

3.4.3 RECEIVER THRESHOLD

EEE381B

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.

EEE381B

4.1.1 RCS OF A METAL PLATE Large RCS, but

decreases rapidly as the incident angle deviates from the normal.

2

224

ba

EEE381B

4.1.2 RCS OF A METAL SPHERE Small RCS, but is

independent of incident angle.

2r

EEE381B

4.1.3 RCS OF A METAL CYLINDER RCS can be quite small

or fairly large depending on orientation.

endthefrom

viewedas

r

ra

,4

,2

2

43

2

EEE381B

4.1.4 RCS OF A TRIHEDRAL CORNER REFLECTOR The RCS of a trihedral

(corner) is both large and relatively independent of incident angle.

EEE381B

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.

EEE381B

5.1 HISTORY* OF STEALTH AIRCRAFT [1]

EEE381B

5.2 AIRCRAFT HIGH RCS AREAS [1]

EEE381B

5.3 LOW OBSERVABILITY DESIGN AREAS [1]

EEE381B

5.3.1 LOW OBSERVABILITY DESIGN EXAMPLE[1]

EEE381B

5.3.2 LOW OBSERVABILITY DESIGN EXAMPLE[1]

EEE381B

5.4 COMPARATIVE RCS [1]

EEE381B

6. IN-CLASS EXERCISES

EEE381B

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.

EEE381B

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?

EEE381B

6.3 RADAR RANGE EQUATION CALCULATION

EEE381B

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?

EEE381B

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"