radar range). 2.2 BASIC RADAR RANGE EQUATION One form of the basic radar range equation is 2 … System Toolbox™ by the functions: This example shows how to compute the required peak transmit power using the radar equation. Radar Detector Range Radar has a range loss inversely proportional to range to the 4th power (1/R 4).Radio communications range losses are inversely proportional to range squared (one-way path is 1/R 2).Signal power received (by a radar detector), where Gdet is detector antenna gain, can be expressed as shown below. TWO-WAY RADAR EQUATION (MONOSTATIC) Peak power at the radar receiver input is: On reducing the above equation to log form we have: 10log P r = 10log P t + 10log G t + 10log G r + 10log F - 20log f - 40log R - 30log 4 B + 20log c or in simplified terms: 10log P r = 10log P t + 10log G t + 10log G r + G F - 2 "1 (in dB) electromagnetic waves propagate under ideal conditions without disturbing influences. Where: P. av = average power Ω = solid angle searched t. s = scan time for Ω Α e = antenna area. Note that if you increase the frequency or antenna area, the change in gain means it takes more beams to search a given volume. The table has been taken from rfcafe for explanation purpose. t. s . The gain of an antenna is:From the equation it is easy to see that in order to double range, you must increase power by 16 times (12 dB!) Enter 40 dB for the antenna Gain.. Set the Wavelength to 3 cm.. Set the SNR detection threshold parameter to 10 dB.. This effect is called 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. A fine-grained lobing structure is often filled in by irregularities in the ground plane. So, the power density $P_{de}$ of echo signal at Radar can be mathematically represented as −$$P_{de}=P_{dd}\left (\frac{\sigma}{4\pi R^2}\right )\:\:\:\:\:Equation\:3$$ Range Multiplier: Range x Range Multiplier = New Range i.e., for a 12 dB sensitivity decrease 500 miles x 0.5 = 250 miles. The appropriate parameters are given in Table 2 in “dB units” and MKS units. Whether the input power is increased from 1 watt to 100 watts or from 1,000 watts to 100,000 watts, the amount of increase is still 20 decibels. To model the noise term, assume the thermal From the one way range equation Section 4-3: 10log (Pr1 or J) = 10log Pj + 10log Gja + 10log Gr - 1 (in dB) [6] From the two way range equation … Use the function Assume that the minimum detectable SNR at the receiver of a monostatic radar operating at 1 GHz is 13 dB. 4 . destruction pattern resulting from the ground reflections breaks down. by:The product of the effective noise temperature and the receiver noise factor is 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.
Effects of Sensitivity Decrease.