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EEE381B Aerospace Systems & Avionics Radar Part 2 – The radar range equation Ref: Moir & Seabridge 2006, Chapter 3,4 Dr Ron Smith Outline Basic radar range equation Developing the radar range equation Design impacts Receiver sensitivity Radar cross-section Low observability Exercises

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eee381b aerospace systems avionics

EEE381BAerospace Systems & Avionics

Radar

Part 2 – The radar range equation

Ref: Moir & Seabridge 2006, Chapter 3,4

Dr Ron Smith

outline
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
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
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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2 1 transmitted power
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
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
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, :

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2 4 power density of echo at antenna
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
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:

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

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2 6 minimum detectable signal power
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
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 p t
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 t p
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 g ain g
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 s min
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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4 radar cross section
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
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
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
4.1.3 RCS of a metal cylinder
  • RCS can be quite small or fairly large depending on orientation.

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5 low observability
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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6 1 quick response exercise 1
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
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 calculation38
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
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/swos/cmd/fun12/12-1/sld001.htm
  • Mark A. Hicks, "Clip art licensed from the Clip Art Gallery on DiscoverySchool.com"

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