aerospace system & avionics
DESCRIPTION
By Ron SmithTRANSCRIPT
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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
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min3
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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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* 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:
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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.
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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.
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4.1.2 RCS OF A METAL SPHERE Small RCS, but is
independent of incident angle.
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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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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"