 Hello everyone, this is Dr. Rupali Shalke from Walchin Institute of Technology, Sholapur working as an associate professor in electronic department. In this video lecture, we are going to discuss on a radar range equation. Learning outcomes of this video lectures are after completion of the session students are able to derive the radar range equation and discuss some of the factors affecting the radar range equation. Now, the basic function of the radar is to determine the range of the target that is why let us see how this range of the target is derived. What is exactly a free space? A free space it is assumed that a target and the radar are being located into the free space means there is a no interruption or a no obstacles between the transmitter of the radar and the target. It is a empty space and it is totally a signals which have been transmitted from the transmitter are transmitted towards the target, the radar range equation relates the range of the radar to the characteristics of the transmitter, receiver, antenna, target and the environment or a we can call is a media through which the signals are transmitted. Let us consider some of the entities for the derivation. Let us consider if Pt is a power transmitted by the radar transmitter and the antenna used for them is a isotropic antenna and R is a distance between the transmitter and the target. Then the power density given by Pd at the distance R from the isotropic source is given by Pd is equal to the Pt divided by 4 pi R square that is nothing but a surface area of the spherical surface by the radius R and the power density is measured by watts per meter square. Radars are usually employs the direct to antenna to direct the transmitted power Pt into some particular direction means radars are usually using the direct to antennas. In such case the gain of the antenna is a measure to increase the power radiated in a direction of the target that is why in the equation of the power density at a distance R a direct to antenna gain is considered. If you see that the above equation is modified by considering the antenna gain. The target intercept the portion of the incident power and radiate it into the various direction. The major amount of the incident power is intercepted by the target and re-radiated back in the direction of the radar and this area is denoted by the radar cross section of the target which is given by the sigma and which is measured in unit is meter square. The power intercepted by the target having the areas sigma is given by P of t that is nothing but a total power is given by the transmitted power into the gain of the antenna into the cross section area divided by the 4 pi R square. The total power is measured into the watts where it multiplies by with the meter square as it is multiplied with the area the meter square is not considered in this equation. The cross section area of the target is nothing but a characteristics of a particular target means it depends on the target it is characteristics changes and it is used to measure its size and shape when the size depending upon the size and shape of the target this value of the sigma is changing. The power density at of the eco signals which are received at the radio radar station is given by P t into P of d is equal to P t g sigma upon 4 pi R square into 1 upon 4 pi R square. To receive the signals the signal the signals are going to travel the same distance that is why 1 upon 4 pi R square is again multiplied with the power density equation. The radar antenna captures the portion of this eco powers that is reflected power. If the reflected area of the receiving antenna is denoted by a then the effective area then the received power by the radar is given by P of R which is nothing but a received power to which that is a effective area of the antenna is multiplied. The maximum radar range equation which is denoted by R max is a distance behind which a target cannot be detected. It occurs when the received eco power is just equal to the minimum detectable signal that is why we indicate the received power as a minimum distance that is P R is equal to denoted by S mean and R is a maximum distance that is R max. This R max is a maximum distance where we are receiving the minimum detectable signal. When you substitute this values the P R will replace by S mean that is received power and R is replaced by R max which is a maximum range of the equation in the equation number 5. After substitution just rearranging this equation we will get the equation 7 which is nothing but a R max equation where which is going to be P T G sigma A is upon 4 pi square into the S mean the whole raise to 1 by 4. This is a maximum range equation for the radar. On the theory of antenna if we know that G gain of the antenna is given by 4 pi effective area divided by the lambda square where lambda is a frequency depends upon the frequency of the radar or aperture area or effective area is given by G into lambda square upon 4 pi. By substituting either G or A into the equation number 7 we will get R max alternative equations for the R max that is R max in terms of A that is effective area and R max in terms of gain of the antenna. These are the alternative equations for the radar range equations. Now what are the factors affecting this radar range equations? What could be the factors? By seeing the equation let us pause this video and just think on the what could be the factors? factors affecting the radar range equations this is the radar range equations that is same as we have seen the equation number 7 observed. It is observed that the radar range equation depends upon the transmitted power P T it depends upon the frequency on which G or A is depend that is frequency in terms of wavelength and cross section area of the target that is sigma and the minimum received signals that is S min. How they are affecting? If the radar range is to be double then we have to increase the transmitted power 16 times since R is inversely proportional to the P of T by 1 by 4 means we have to 16 times increase the transmitted power P T has to be increased 16 times. Now the second factor affecting that is a frequency we know that R max is directly proportional to the 1 upon square root of lambda or R max is directly proportional to the square root of the frequency. This implies that the as the frequency increases the range increases the this is a conflict to each other that is why as the directivity of the antenna is depends upon the wavelength. The third factor that is a target associated sectional area this factor involves a multi scattering process that are depend on the operating frequency and dimension geometry and orientation of the target as we are discussing the previous slide that area of cross section that is sigma of the target is varies which is used for determining the shape and size of the target as its value changes based on that this values are also changing the range of the target. The last affecting factor is the minimum received signal the factor set the limits on the gain of the receiver sensitivity. This factor limits the gain of the receiver sensitivity then this can be controlled by using the no adjusting the noise figure of the receiver which is given by R max is directly proportional to P of t. These are the few references through which we are considered the wave equations. Thank you.