EEE381B Aerospace Systems

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EEE381BAerospace Systems Avionics

• Radar
• Part 2 The radar range equation
• Ref Moir Seabridge 2006, Chapter 3,4

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Outline

• Basic radar range equation
• Developing the radar range equation
• Design impacts
• Receiver sensitivity
• Radar cross-section
• Low observability
• 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.

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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
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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

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2.2 Power density at target 4

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

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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 targets radar cross-section, ?

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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.

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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
  antennas effective aperture

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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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,

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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.

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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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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 example1
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5.3.2 Low observability design example1
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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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References

• Moir Seabridge, Military Avionics Systems,
  American Institute of Aeronautics Astronautics,
  2006. Sections 2.6 2.7
• David Adamy, EW101 - A First Course in Electronic
  Warfare, Artech House, 2000. Chapters 3,4 6
• George W. Stimson, Introduction to Airborne
  Radar, Second Edition, SciTch Publishing, 1998.
• Principles of Radar Systems, student laboratory
  manual, 38542-00, Lab-Volt (Quebec) Ltd, 2006.
• John C. Vaquer, US Navy Surface Officer Warfare
  School Documents, Combat Systems Engineering
  Radar, http//www.fas.org/man/dod-101/navy/docs/sw
  os/cmd/fun12/12-1/sld001.htm
• Mark A. Hicks, "Clip art licensed from the Clip
  Art Gallery on DiscoverySchool.com"