Radars

Institute of Engineering Studies (IES,Bangalore)

Radars Materials

RADARS The word radar is an acronym which was coined in 1942 by US Navy for Radio detection and ranging. In general consist of a T x , Ry, display and antenna. Block diagram is as shown below.

Radar cross section

Tx Duplexer

Indicator

T /Rx

Rx

x

Target (moving/fixed)

Functions of duplexer are 1. To isolate T x , and Ry, during Transmission Transmission and reception. r eception. 2. To protect Rx, from high power T xer 3. To help use a single T x / Ry antenna.

General Requirements for any Radar system: system: 1. Duplexer should be automatic 2. Txer should remain silent during echo period 3. Txed Pulse should be quite powerful to counter the attenuation. 4. The Rxed,pulse being weak, the Rx, should be extremely sensitive and at the same time immune to noise (clutter) signals should have necessary amplification etc. 5. Radar antenna should be highly directive and have large gain so that it can radiate strong signal and Rxeve weak signal. 6. Pulse repetition frequency (PRF) of Radar should be high compared to target scanning period. PRF PRF = dut c cle cle/ ulse ulse width idth i.e., small duty cycle provides necessary time required for the pulse to go to the target, get reflected and provided echo pulse.

Average power

Range = Pt X duty cycle Range = Pt X PRF X duty cycle

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Radars Materials

Radar Range Equation It relates the range of radar to the characteristics of Tx , R x, antenna target and environment

R

I

Watts/

Power density at distance R from an isotropic isotropic source =

Power density at distance from directive antenna of power given G= The total power intercepted intercept ed by target having area

watts. ( σ) watts.

Area of target as a s seen by radar (Radar cross section) Power density of echo signal at radar station is = Rx antenna captures

σ=

=

watts/

a portion of echo power. If Ae → effective area of R x antenna then

watts Maximum Radar Range (R max): Is the distance beyond which the target cannot be detected. It occurs when R xed echo signal power P r Just = min detectable signal (S min) i.e., when P r = S min R= Rmax

But G=

2



Radars Materials

∴

Factors effecting Radar range 1. In case radar range to be doubled we have to increase Tx power 16 times since R max of Pt

1/4

We also know that R max α√x or Rmax α√f ⇒ increase in frequency range. But for parabolic reflector beam

width = λ/D. if ↑beam width ↓ which reduces tracking range. 2. S min (or Pr min) set limit on R x sensitivity i.e, noise figure of radar R x is a factors that is to be considered for obtaining larger range R max .

→

SNR;

→o/p

SNR ;

G→

.

But

=G

Noise figur e F=

F= 1+

Gain

⇒∆N = (F-1) GNi i/p Noise power Noise equivalent power generated by R x Ni = KT o B

Bottom max const

Rx B .w temperature

∴ ∆ N= (F-1) (F -1) G K

If ∆ N > S min its not possible to detect target So,

For parabolic reflector Ae =

∴

Maximum umambiguous range:

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Radars Materials

The range beyond which targets appear as second time around echoes is called max umambgious range.

Runamiguous =

T= TR= But

Runamiguous =

= C/2Prf

Doppler effect When target is moving relative to radar it will result in apparent shif t shif t in carrier frequency of R xed signal.

R→distance between target and radar, total no. of

wave lengths=

Total phase shift ∅=2π.

If target is in motion both R &

ϕ changes,

Doppler angler freeq width =

2πfd = =

Doppler frequency shift f d=

⟶ relative velocity of target w.r.t radar

.

υ → speed of target θ→ angle by target trajectory and line joining radar

CW Doppler radar:

Txer

generates oscillations oscillations of frequency ‘f 0 ’, a portion of this radiated ra diated energy intercepted by target and re

radiated energy is collected by R x . If target in motion with velocity V r Rxed Signal will be frequency by

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Radars Materials

amount fd. The purpose of using beat fr equency amplifier amplifier is to eliminate echoes from stationary targets and amplify Doppler echoes. This radar can be used to measure speeds of objects and can able to detect moving objects. But in practical it is limited by fact that several objects at a given bearing tend to confuse. Also range discrimination achieved by introducing very constantly complex circuitry further limited by max power it transmits. It is not capable of indicating range and can show only velocity.

MRI Radar: When it is desired to remove clutter due to stationary objects, MTI ra dar is employed. It compares a set of Rxed echoes with those R xed during the previous sweep and cancelling out those whose phase has remained unchanged. Moving targets will give change of phase. Here for comparison delay line with delay T= 1/PRF can be used.

Blind speeds:

If target has uniform velocity, the successive sweeps will have Doppler phase shifts of exactly 2π and target appears stationary and gives wrong radar indication. The speed corresponding to thus condition is called blind speed.

Variable Prf will solve blind speed problem.

FMCW Radar : (Air borne Altimeter) The T xed Signal in CW radar is not modulated. Therefore it can provide neither range nor sense which particular cycle of oscillations is being received at any instant

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Brand Name

Range

L

1-2

S

2-4

C

4-8

X

8-12.5

Ku

12.5-18.0

K

18-26.5

Ka

26.5-40.0

Radars Materials

Problems: 1. Calculate max range of radar which operate at 3 cm with peak power of 600kw, if its antenna is 5mr2 min detectable signal is 10 13 w and radar cross section is 20m2 ANS:

λ = 3cm,

In nautical mile = 1.853 km

-14

2. A 10GHz Radar has the following characteristics Pt = 250kw, G= 2500, S min = 10

w

, σ = 2m2 ; Rmax =?

2

Ae= 10m ANS:

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Radars Materials

3. A marine radar is operating at 20 GHz has maximum range of 50 km with antenna gain of 4000. If transmitter power has 250kw and minimum detectable signal of 10 -11 w. Determine cross section of target that radar can sight? f=10GHz, Rmax= 50 km, G= 4000, P t= 250K, Smin= 10-11, σ = ? ANS:

=

σ=

=

3. A guided missile tracking radar has following specifications. P t = 400kw, Prf= 1500PPs Pulse

width = 0.8μsec. Determine (a) Runambgious (b) Duty cycle (c) Average power (d) B.W. of Radar. ANS: a.

Runamb =

=

b. Duty cycle =

c.

Range =

d.

B.w =η/tw η= 1⇒ η= 1.4 ⇒

5. Military radar operate a 5GHz with 2.5 Mw power o/p if antenna diameter is 5m, R x B.w = 1.6 MHz 2

and has 12dB noise figure what is R max For 1m target?

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Radars Materials

ANS: Pt = 2.5 x 106 w, D= 5 m, σ = 1m2, B= 1.6 x 10 6 Hz ; For 12dB= 15.85 λ=c/f =

0.06m

= 48

6. A civilian Radar has maximum maximum range of 30 kms. kms. Determine maximum maxi mum range with an equivalent echoing area of 50 times and effect of doubling T x Power on range. ANS: Rmax = 30 km Maximum range with equivalent echoing area of 50 times R max = 30 (50)1/4 = 80 kms. Range would be increased if P t is doubled by factor = 4√2 = 1.19 7. What is the duty cycle of radar with Pw of 3μs

and PRT of 6 ms? ms?

ANS: Duty cycle =

= 0.5 milli

8. Calculate average power when peak power= 1 kw, Pw= 3µs and rest time= 1997µs . ANS: Average power = Peak power x duty cycle Duty cycle =

= 0.5 milli

Average power = 1 K x 0.5 milli = 0.5

ω

9. Calculate S min which has IF Bandwidth of 1.5MHz noise Fig if 9 dB. ANS: F= Smin = K

8

= 1.38 x



Radars Materials

Smin = 4.17 x

10. A low power short range radar is solid state throughout, including includ ing a low low noise RF amp which gives an overall noise figure of 4.77dB. If antenna diameter is 1m. If B.W. B. W. is 500 KHz, operating frequency frequency 8 GHz and supposed to detect targets of 5m 2 area of maximum distance 12 km. what must be peak transmitted power? ANS: F= 10 0.477 = 3

,

D= 1m

B= 500K

f= 8 GHz

11. Calculate maximum range of deep spa ce radar operating a 25 GHz and using peak pulse power of 2

25Mw. The antenna diameter is 64m, target cross section 1m and noise figure is 1.1. Further more the R x B.w. is 5 KHz (because low prf) ANS:

λ = c/f =

12. An MTJ radar operate a 5GHz with prf of 800 ps. Calculate lowest three blind speeds. ANS:

λ = Vc/f = 0.6m Repeat for n= 2, 3 also. 13. With a CW C W transmit transmit frequency of 5GHz, calculate Doppler frequency seen by stationary radar when target radial velocity is 100km/h

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Radars Materials

ANS:

λ=

10


Radars

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