1. Basic radar range equation 2. Developing the radar range equation 3. Design impacts 4. Receiver sensitivity 5. Radar cross-section 6.

Transcription

1 Radar The radar range equation Prof. N.V.S.N. Sarma 1

2 Outline 1. Basic radar range equation. Developing the radar range equation 3. Design impacts 4. Receiver sensitivity 5. Radar cross-section 6. Low observability 7. Exercises

3 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. R Max = 4 PG t 3 λ σ ( 4π ) S min 3

4 1.1 Components of the equation R max the maximum range of the radar P t average power of the transmitter G gain of the transmit/receive antenna λ wavelength of the operating frequency σ radar cross-section of the target S min minimum detectable signal power 4

5 1. Units of the equation R Max = 4 PG t 3 λ σ ( 4π ) S min W m m units of RMax = 4 = W m 5

6 . Developing radar range equation 6

7 .1 Transmitted power Recall from the previous lecture that the average transmitted power is a function of peak pulse power and the pulse duration: P t = P ave = P peak T p τ, where T = p 1 PRF 7

8 . Power density at target [4] Recall that power density decreases as a function of distance traveled: power density at range R = PG t 4πR 8

9 .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, σ: power density reflected PG t = 4πR σ 9

10 .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. power density received at antenna = PG σ π t 4πR 4 R 10

11 .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: power at receiver, P r = PG (4 t σ π ) R 4 A e = PG t (4 σλ 3 4 π ) R, recalling that A e = λ G 4 π * In this equation the receiver is assumed to be all radar receive chain components except the antenna. 11

12 .5.1 Relative power received α range 1

13 .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: for P r = S min, R max = 4 PG t (4 π) 3 λ σ S min 13

14 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. 14

15 3.1 Power, P t Increase in transmitter power yields 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%,

16 3. Time-on-target, τ/t p 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

17 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. Fora dish G α A p or α ( D/) andr max α G 4 or α D

18 3.4 Receiver sensitivity, S min 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 Simplistically, the smaller the radar pulse width, the larger the required receiver bandwidth and the larger the receiver noise floor. 18

19 3.4.1 Receiver bandwidth 19

20 3.4. Signal-to-noise 0

21 3.4.3 Receiver threshold 1

22 4. Radar cross-section, section, σ The radar cross-section of a target is a measure of its size as seen by a radar, expressed as an area, m. It is a complex function of the geometric crosssection 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.

23 4.1.1 RCS of a metal plate Large RCS, but decreases rapidly as the incident angle deviates from the normal. σ = 4 πa λ b 3

24 4.1. RCS of a metal sphere Small RCS, but is independent of incident angle. σ =πr 4

25 4.1.3 RCS of a metal cylinder RCS can be quite small or fairly large depending on orientation. σ = πra λ, as viewed σ = 4 3 π λ r 4, from the end 5

26 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 decades old. 6

27 5. Aircraft high RCS areas [1] 7

28 5.3 Low observability design areas [1] 8

29 5.4 Comparative RCS [1] 9

30 6. In-class exercises 30

31 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. 31

32 6. Quick response exercise # 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? 3

33 6.3 Radar range equation calculation 33

34 6.3 Radar range equation calculation A specific Air Search Radar has the following technical specifications: Operating frequency MHz Transmitter peak power kw PRF Hz, and pulse widths of 9 / 3 μsec Phased array antenna with a gain of 38.5 db For its published maximum range of 50 miles for a nominal target such as the F-18, what is the receiver chain sensitivity in dbm? 34

35 References 1) Moir & Seabridge, Military Avionics Systems, American Institute of Aeronautics & Astronautics, 006. [Sections.6 &.7] ) David Adamy, EW101 - A First Course in Electronic Warfare, Artech House, 000. [Chapters 3,4 & 6] 3) George W. Stimson, Introduction to Airborne Radar, Second Edition, SciTch Publishing, ) Principles of Radar Systems, student laboratory manual, , Lab- Volt (Quebec) Ltd, ) John C. Vaquer, US Navy Surface Officer Warfare School Documents, Combat Systems Engineering : Radar, 101/navy/docs/swos/cmd/fun1/1-1/sld001.htm 6) Mark A. Hicks, "Clip art licensed from the Clip Art Gallery on DiscoverySchool.com" 35