pulsed radar (ii) radar equation
TRANSCRIPT
RADIOLOCATION J. Mateu - J. Berenguer
RADIOLOCATION
Pulsed Radar (II)Radar Equation
Jordi Mateu- Jordi Berenguer
RADIOLOCATION J. Mateu - J. Berenguer
Pulsed Radar
1. Introduction to Radar Systems2. Radar Equation (Simplified)3. Signal Detection with noise4. False Alarm and detection probability5. Pulse integration6. Radar Block diagram7. RADAR Antennas8. Matched Filter9. Radar Cross Section (RCS)10. Other considerations of Radar Systems
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar Equation
Transmitted signal
Echo signalRADAR
TARGET
1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET
4- Part of the signal (3) is reflected in the RADAR direction5- Part of the signal (4) is captured by the antenna
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar Equation
1- Generate the signal2- Transmit the signal in the direction of the TARGET
Single point radiating (IsotropicAntenna, which radiates the same intensity of radiation in all directions)
The density power (W/m2) at R:
24 RPt
ฯ
The density power (W/m2) at R:
22 44 REIRPG
RPt
ฯฯ=
Antenna G gain [unitless], measures the capacity of the antenna to focus the energy in only one direction.
EIRP: Equivalent isotropic radiated power๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ = ๐ธ๐ธ๐ก๐ก ยท ๐บ๐บ
Emitter
Receiver
Isotropicantenna
Pt
Circulator
Emitter
Receiver
Circulator
Secondary or side antenna lobes
Main antenna lobe(maximum antenna gain)
G
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar Equation
1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET4- Part of the signal (3) is reflected in the RADAR direction
R GR
Pt24ฯ
ฯRADAR CROSS SECTION
(RCS)[units of area m2]
ฯฯ
GR
Pt24
ฯฯ
GR
Pt24
Amount of power reflected to the RADAR direction
Transmitted Power: ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ = ๐ธ๐ธ๐ก๐ก ๏ฟฝ ๐บ๐บ
Emitter
Receiver
Circulator
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar Equation
1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET4- Part of the signal (3) is reflected in the RADAR direction5- Part of the signal (4) is captured by the antenna
R GR
Pt24ฯ
ฯฯ
GR
Pt2422 4
14 R
GR
Pt
ฯฯ
ฯ
( ) 4222 441
4 RGP
RG
RP tt
ฯฯ
ฯฯ
ฯโ โ
= Power density (W/m2) of the reflected signal that reaches the antenna
Transmitted Power: ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ = ๐ธ๐ธ๐ก๐ก ๏ฟฝ ๐บ๐บ
Emitter
Receiver
Circulator
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar Equation
1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET4- Part of the signal (3) is reflected in the RADAR direction5- Part of the signal (4) is captured by the antenna
R
22 41
4 RG
RPt
ฯฯ
ฯ
Pr
Aeff (m2): capacity of the antenna to capture the energy, related with G through the equation:
๐บ๐บ๐ด๐ด๐๐๐๐๐๐
=4๐๐ฮป2
Being ฮป the wavelength of the electromagnetic wave
( ) ( ) 42
2
43
22
4222 44444 RAP
RGP
RAGP
RA
GR
PP effttefftefftr ฯฮป
ฯฯฯฮป
ฯฯ
ฯฯ
ฯ====
Pt
Received power at the antenna output:๐ธ๐ธ๐๐ = P๐๐ ๏ฟฝ ๐ด๐ด๐๐๐๐๐๐
Where P๐๐ is the power spectral density in (W/m2) which reaches the antenna surface.
Emitter
Receiver
Circulator
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar Equation
RG
RPt
24ฯ
ฯฯ
GR
Pt24
22 41
4 RG
RPt
ฯฯ
ฯ
efft A
RG
RP
22 41
4 ฯฯ
ฯ
22 44 RA
GR
PP efftr ฯ
ฯฯ
โ โ =
1 2
3,45
SUMMARY
Direct way
Reflected way
Effect of the target
Transmitted Power: ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ๐ธ = ๐ธ๐ธ๐ก๐ก ๏ฟฝ ๐บ๐บ
Emitter
Receiver
Circulator
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar EquationSUMMARY
22 44 RA
GR
PP efftr ฯ
ฯฯ
=TARGET /
NO TARGET
We miss the effect of the receiver
RADIOLOCATION J. Mateu - J. Berenguer
Primary Surveillance RADAR: Radar EquationSUMMARY & Conclusion
We assume the transmitter and receiver are co-located
Simplified Radar Equation:
( ) ( ) 42
2
43
22
4222 44444 RAP
RGP
RAGP
RA
GR
PP effttefftefftr ฯฮป
ฯฯฯฮป
ฯฯ
ฯฯ
ฯ====
The range of the target to the Radar is obtained as:
๐ธ๐ธ4 =๐ธ๐ธ๐ก๐ก๐บ๐บ๐๐๐ด๐ด๐๐๐๐๐๐
4๐๐ 2๐ธ๐ธ๐๐
And the maximum range of the Radar is obtained when the received power equals the minimum detectable signal Smin,that is, Pr=Smin, then:
๐น๐น๐๐๐๐๐๐๐๐ =๐ท๐ท๐๐๐ฎ๐ฎ๐๐๐จ๐จ๐๐๐๐๐๐๐๐๐ ๐ ๐๐๐บ๐บ๐๐๐๐๐๐
RADIOLOCATION J. Mateu - J. Berenguer
Conclusion (I)
โข Primary Radar is a non cooperative
โข Primary Radar sees all traffic !!
โข Primary Radar is very simple in principle. But involves many technologies and is very challenging.
โข Complementary to other surveillance techniques (SSR)
โข Power received is inversely proportional to the fourth power of range.
โ Highly directive (High Gain, large Aeff) antennaโ Powerful transmitterโ Hypersensitive receiverโ Advanced Signal processor
RADIOLOCATION J. Mateu - J. Berenguer
Conclusion (II)
โข The radar energy will be attenuated with the fourth power of the distance.
โข For primary radar the transmitted power must be sufficient, allowing for attenuation, for the radar to detect an echo from an aircraft at maximum range.
โข The higher the PRF (together with beam width and scanning rate) the more โhitsโ on a target and hence the stronger and more recognisable will be the return.
โข The PRF is, however, a compromise as it must be low enough to accommodate the required maximum unambiguous range.
โข Thus the pulse length will affect the minimum range of a primary radar system.
RADIOLOCATION J. Mateu - J. Berenguer
Questionsโข 1. Could you reproduce the Radar equation for a
Bistatic Radar