This Radar Range Collection includes the fundamental mathematical pieces that are used to derive the Radar Range Equation. Each piece builds on fundamental geometry and fundamental physics to derive the calculation used in a radar system.
This collection will explain the derivation of the Radar Range Equation from these fundamental elements that form the complex mathematics behind a radar system.
The Radar Range Equation represents a model of the physical propagation of the transmitted power. The transmitted power is visualized as the wave propagation up to the receiving of the signals rebounding off a distant object. The power, PR, measured at the receiving antenna is given by the radar equation. PR is dependent on the transmitted power, PS, the slant range, R, and the reflecting characteristics of the target, which is characterized as the radar cross-section, σ).
At known thresholds of sensing, the radar equation determines the theoretically maximum range that could be calculated for a given radar set .
We start with the basic understanding that under ideal conditions electromagnetic energy will propagate outward. With an isotropic radiation source (emitting power in all directions equally) emitting constant power, the radiating power spreads out evenly in all directions. In other words, if you think of an imaginary sphere with the radiating antenna at its center, the same power will emanate from the antenna and will travel outward and pass through the imaginary sphere with no dissipation of the power.
The further the power travels the more the power density at any imaginary sphere decreases. Remember power density is the power per unit area. And since the sphere increases in size the greater is its radius, the larger is the total area over which the electromagnetic power spreads.
An Equation for the Antenna Gain as a Function of Wavelength computes an antenna's power density gain based on the inputs listed below. Antenna gain is created by directional radiation of the power. If the power of an antenna is is cause to be redistributed with more radiation being emitted in one direction, then an increase of the power density in the direction of the radiation results.
G=4⋅π⋅A⋅Kaλ2
An antenna's power gain or simply gain is a performance measure of the antenna which can be thought of as combining the antenna's directivity and electrical efficiency.
Range=4√PS⋅G2⋅λ2⋅σPE