Radar range equation is useful to know the range of the target We will get those modified forms of Radar range equation from the standard form of Radar range equation. Pd = 0.9; Pfa = 1e-6; NumPulses = 10; … Substitute, Equation 2 in Equation 3.$$P_{de}=\left (\frac{P_tG}{4\pi R^2}\right )\left (\frac{\sigma}{4\pi R^2}\right )\:\:\:\:\:Equation\:4$$$$P_r=\left (\frac{P_tG}{4\pi R^2}\right )\left (\frac{\sigma}{4\pi R^2}\right )A_e$$$$\Rightarrow P_r=\frac{P_tG\sigma A_e}{\left (4\pi\right )^2 R^4}$$$$\Rightarrow R^4=\frac{P_tG\sigma A_e}{\left (4\pi\right )^2 P_r}$$$$\Rightarrow R=\left [\frac{P_tG\sigma A_e}{\left (4\pi\right )^2 P_r}\right ]^{1/4}\:\:\:\:\:Equation\:6$$If the echo signal is having the power less than the power of the minimum detectable signal, then Radar cannot detect the target since it is beyond the maximum limit of the Radar's range.Therefore, we can say that the range of the target is said to be maximum range when the received echo signal is having the power equal to that of minimum detectable signal. Furthermore, the only purpose of EA is to prevent, delay, or confuse the radar … The amount of power, which is reflected back towards the Radar depends on its cross section. We will get the following equation, by substituting $R=R_{Max}$ and $P_r=S_{min}$ in Equation 6.$$R_{Max}=\left [\frac{P_tG\sigma A_e}{\left (4\pi\right )^2 S_{min}}\right ]^{1/4}\:\:\:\:\:Equation\:7$$We know the following relation between the Gain of directional Antenna, $G$ and effective aperture, $A_e$.$$G=\frac{4\pi A_e}{\lambda^2}\:\:\:\:\:Equation\:8$$$$R_{Max}=\left [ \frac{P_t\sigma A_e}{\left ( 4\pi \right )^2S_{min}}\left ( \frac{4\pi A_e}{\lambda^2} \right ) \right ]^{1/4}$$$$\Rightarrow R_{Max}=\left [\frac{P_tG\sigma {A_e}^2}{4\pi \lambda^2 S_{min}}\right ]^{1/4}\:\:\:\:\:Equation\:9$$We will get the following relation between effective aperture, $A_e$ and the Gain of directional Antenna, $G$ from Equation 8.$$A_e=\frac{G\lambda^2}{4\pi}\:\:\:\:\:Equation\:10$$$$R_{Max}=\left [\frac{P_tG\sigma}{\left (4\pi\right )^2 S_{min}}(\frac{G\lambda^2}{4\pi})\right ]^{1/4}$$$$\Rightarrow R_{Max}=\left [\frac{P_tG^2 \lambda^2 \sigma}{\left (4\pi\right )^2 S_{min}}\right ]^{1/4}\:\:\:\:\:Equation\:11$$In previous section, we got the standard and modified forms of the Radar range equation. For example, a target return echo in 98 microsecond after the time of transmitted pulse. In general, Radars use directional Antennas. This section derives the J/S ratio from the one-way range equation for J and the two-way range equation for S, and deals exclusively with active (trans mitting) Electronic Attack (EA) devices or systems. Now, let us discuss about the derivation of the standard form of Radar range equation.The standard form of Radar range equation is also called as simple form of Radar range equation. Now, let us solve a few problems by using those equations.$$R_{Max}=\left [\frac{P_tG \sigma A_e}{\left (4\pi \right )^2 S_{min}}\right ]^{1/4}$$$$R_{Max}=\left [\frac{ \left ( 250\times 10^3 \right )\left ( 4000 \right )\left ( 25 \right )\left ( 4 \right )}{\left ( 4\pi \right )^2 \left ( 10^{-12} \right )} \right ]^{1/4}$$Substitute, $C=3\times 10^8m/sec$ and $f=10GHZ$ in above equation.$$R_{Max}=\left [\frac{P_t \sigma {A_e}^2}{4\pi \lambda^2 S_{min}}\right ]^{1/4}$$$$R_{Max}=\left [ \frac{\left ( 400\times 10^3 \right )\left ( 30 \right )\left ( 5^2 \right )}{4\pi\left ( 0.003 \right )^2\left ( 10 \right )^{-10}} \right ]^{1/4}$$ Learn about that on Below is the equation for range in a two-way (round-trip) monostatic radar:The radar range equation can take many forms, in terms of energy, antenna diameter, receive noise figure, etc. This combination was often mentioned jocularly to “P–13”. Now, let us derive the standard form of Radar range equation.$$P_{di}=\frac{P_t}{4\pi R^2}\:\:\:\:\:Equation\:1$$The above power density is valid for an isotropic Antenna. RADAR RANGE EQUATION PARAMETER VALUE (MKS) VALUE (dB) 106 w 60 dBw 6309.6 w/w 38 dB 6309.6 w/w 38 dB 0.0375 m -14.26 dB(m) 3.98 m2 6 dBsm 60×103 m 47.78 dB(m) 4×10-21 w-s -204 dB(w-s) 2.5×106 Hz 64 dB(Hz) 6.31 w/w 8 dB 5.01 w/w 7 dB The radar range equation can take many forms, in terms of energy, antenna diameter, receive noise figure, etc. radar range equation represents the physical dependences of the transmit power, which is the wave propagation up to the receiving of the echo signals. Or you could quadruple the frequency (one fourth the wavelength), or double the radius of the aperture. t is the time in seconds between the original transmitted pulse and arrival of the echo from the target.

understanding the radar range equation we will devote considerable class time to it and to the things it impacts, like detection theory, matched filters and the ambiguity function. It often refers to stuff that should be on a compost pile...But wait, there are exceptions to the radar range equation! Use Albersheim's equation to determine the required SNR for the specified detection and false-alarm probabilities. One factor that is not covered in the "simple" radar range equation is atmospheric attenuation.

P rec = Power Received P t = Transmit Power In radar range, aperture area is the most important thing to consider! 2.2 BASIC RADAR RANGE EQUATION One form of the basic radar range equation is 2 3 4 4 0 S T T R N n P P G G SNR P R kT BF L (2-1…

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