radar equation2

8/3/2019 Radar Equation2

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RADAR EQUATION

Assigned By: Sir Irfan

Presented By: SADIQ

ABID

Peak Power of RADAR & SNR



Goal Derive the radar equation

The radar equation provides a relationship between the

received power, the characteristics of the target, andcharacteristics of the radar itself.

Steps in deriving the radar equation:

1) Determine the radiated power per unit area (the power flux

density) incident on the target2) Determine the power flux density scattered back toward the

radar (the radar cross section)

3) Determine the amount of power collected by the antenna

(the antenna effective area).



24 RPP t

isotropic

So power flux density ( P, watts/m 2) at a distance R from an

isotropic antenna is:

(1)

Consider an isotropic antenna that transmits radiation equally

in all directions

Where Pt is the transmitted power



24 R

GP

Pt

inc

Since in Radar we used directed antenna to transmit power in

particular direction.So gain(G) is multiplied with Power density .

So from (1)

(2)



24 R

GP p t

inc

(3)

Some typical values:

Gain = 10,000 (40 db)Transmitted Power = 100,000 Watts

Target is at 100 km range

Incident Power Flux Density = 8 x 10-3 Watts/m2



Radar cross section: Radar cross sectional area of a target(σ)

determines density back to the Radar.

So re radiated power density back to Radar is:

Aereradiated .Pr

The echo signal which is captured by the Radar is:

24.

RisnP

(4)

(5)



So put equation (2) and equation (3) in (4) We get:

4216Pr

R

AeGPt

(6)

Where:

Pt=transmitted power

Pr=received power

G=gain of AntennaAe=antenna effective aperture

σ=cross sectional of the target



2:Peak Power of RADAR & SNR



A continuous-wave radar transmission may be easily figured because the

transmitter operates continuously.

However pulsed radar transmitters are switched on and off to provide range

timing information with each pulse.

The amount of energy in this waveform is important because maximum range

is directly related to transmitter output power.

Introduction



Pave = (Ppeak )Duty Cycle

Pave= Ppeak.(τ /T)

Where:

τ=pulse width in (μ) seconds

T=pulse repetition interval in (m) second



SNR…….???



Internal Noise:

It is generated by all electronic components and appears as random

variations superimposed on the desired echo signal.

The lower the power of the echo signal, the more difficult it is to separate it

from the noise.

Noise figure:It is a measure of the noise produced by a receiver compared to an ideal

receiver, and this needs to be minimized.

Noise



In modern radar systems, due to the high performance of their receivers,

the internal noise is typically about equal to or lower than the externalscene noise.

External Noise: due to environmental effects natural thermal radiation

of the background scene surrounding the target of interest.

flicker noise: which is a random fluctuation in an electrical signal it

occurs due to ions bombarment and diffusion in a materials.It depends on 1/f and much lower than thermal noise when the

frequency is high.

Noise



signal-to-noise ratio(SNR): SNR is defined as the ratio of a signal power

to the noise power within the desired signal.

SNR compares the level of a desired signal (such as targets) to the level

of background noise.

Higher SNR, the better it is in isolating actual targets from the

surrounding noise signals.

SNR



3: Pulse Integration



A pulse integrator is a improvement technique to address

gains in probability of detection by using multiple transmit

pulses.

This gain will be achieved by inserted in receiving path radarsignal processor adding radar returns (thus the word

integrator) from different successive pulse periods.

Pulse Integration



Depending on location of the pulse integrator in the signal

processing chain this process is referred to as:coherent integration

non-coherent integration

Pulse Integration



With coherent integration we insert a coherent integrator, or signal

processor, between the matched filter and amplitude detector as

shown in Figure 1.

The signal processor samples the return from each transmit pulse at

a spacing equal to the range resolution of the radar set and adds thereturns from N pulses. After it accumulates the N pulse sum it

performs the amplitude detection and threshold check.

Coherent Integration



The Non-Coherent Integrator is placed after the amplitude or

square law detector as shown in Figure 2.

The name non-coherent integration derives from the fact that,

since the signal has undergone amplitude or square law

detection, the phase information is lost.

The non-coherent integrator operates in the same fashion as the

coherent integrator in that it sums the returns from N pulses

before performing the threshold check

Non-coherent Integration



In older radars the pulse integration was implemented via the

persistence on displays plus the integrating capability of a humanoperator.

Non-coherent Integration



4: Power aperture product



Partial performance of phased array radar relies on its power-aperture product

( z).

which is the product of the average radiated power and the effective arrayaperture area.

Power aperture product

AePeve Z ).(



It can be seen that when the target goes away from the reciver the improvements

factor becomes better.

Improvements is due to auto correlation function



Thanks

radar equation2

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