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Derive an expression for RADAR range. Discuss effect of RADAR cross section in the range determination.

Mumbai University > Electronics and telecommunication > Sem 7 > Microwave and Radar Engineering

Marks: 10 Marks

Year: May 2016

RADAR consists of the transmitting and receiving antenna. Sometimes the receiving and transmitting antenna are the same.

Let the transmitter power Pt is radiated by an isotropic antenna and the power density at distance R from the radar is

W=Pt4πR2 W=Pt4πR2 Since radar uses a very directive antenna the power density at R with the directive antenna is

=GPt4πR2=GPt4πR2 where G is gain of the antenna

This power is intercepted by the target at distance R and is scattered in all the direction. Some part of the scattered power reaches to the radar and is dependent on the radar cross section of the target.

The power density at radar then is given as =GPt/4πR^2.σ/4πR^2 where σ is radar cross section.

The radar antenna captures a portion of echo energy incident on it.The power received by the antenna depends on the effective area of the antenna, Pr=\dfrac{GP_t}{4πR^2}.\dfrac{σ}{4πR^2}.A_e The maximum range of radar Rmax is the distance beyond which the target cannot be detected.R_{\max}=\bigg[\dfrac{P_t GA_e σ}{(4π)^2 S_{\min}}\bigg]^\dfrac{1}{4}whereSmin=Pr-received power at radar.

Equation R_{\max}$ is directly proportional to the radar cross section, so to increase the radar range larger cross section is required. But the radar cross section is an uncertain figure and the above equation is not an efficient equation to calculate the range of radar.


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RADAR consists of the transmitting and receiving antenna. Sometimes the receiving and transmitting antenna are the same.

Let the transmitter power Pt is radiated by an isotropic antenna and the power density at distance R from the radar is

$$W=\dfrac{P_t}{4πR^2}$$

Since radar uses a very directive antenna the power density at R with the directive antenna is

$=\dfrac{GP_t}{4πR^2}$ where G is gain of the antenna

This power is intercepted by the target at distance R and is scattered in all the direction. Some part of the scattered power reaches to the radar and is dependent on the radar cross section of the target.

The power density at radar then is given as

$=\dfrac{GP_t}{4πR^2 }.\dfrac{σ}{4πR^2} where σ is radar cross section The radar antenna captures a portion of echo energy incident on it. The power received by the antenna depends on the effective area of the antenna, $Pr=\dfrac{GP_t}{4πR^2}.\dfrac{σ}{4πR^2}.A_e$ The maximum range of radar Rmax is the distance beyond which the target cannot be detected. $R_{\max}=\bigg[\dfrac{P_t GA_e σ}{(4π)^2 S_{\min}}\bigg]^\dfrac{1}{4}$ where Smin=Pr received power at radar. Equation $R_{\max}$ is directly proportional to the radar cross section, so to increase the radar range larger cross section is required. But the radar cross section is an uncertain figure and the above equation is not an efficient equation to calculate the range of radar.

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