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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 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. 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**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: EEE381B**2.2 Power density at target [4]**• Recall that power density decreases as a function of distance traveled: 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, : 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. 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: * In this equation the receiver is assumed to be all radar receive chain components except the antenna. 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: 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%, 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. 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. 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. EEE381B**4.1.2 RCS of a metal sphere**• Small RCS, but is independent of incident angle. EEE381B**4.1.3 RCS of a metal cylinder**• RCS can be quite small or fairly large depending on orientation. EEE381B**The RCS of a trihedral (corner) is both large and relatively**independent of incident angle. 4.1.4 RCS of a trihedral corner reflector 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**5.2 Aircraft high RCS areas [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**• 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**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" EEE381B