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## EEE381B Aerospace Systems & Avionics

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### EEE381BAerospace 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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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
- 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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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 target’s 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 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

- 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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4.1.3 RCS of a metal cylinder

- RCS can be quite small or fairly large depending on orientation.

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The RCS of a trihedral (corner) is both large and relatively independent of incident angle.4.1.4 RCS of a trihedral corner reflector

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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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5.4 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

- 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/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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