The radar range equation is the
most fundamental formula for radar operation. As its name implies, it gives the
possible maximum range of a radar, as determined by the following factors:
- Electrical noise. This is a function of environmental
noise, which tends to be unpredictable, and the noise inherent in the
electronic systems of the receiver. A radar pulse echo return must be
above the noise threshold for a target to be detected.
- Transmitter power. As mentioned, this is a function of
pulse power and PRF, as well as antenna gain.
- Receiver gain. This is a function of the receiver
antenna gain and the sensitivity of the receiver electronics.
- Attenuation due to range. The power of a radar beam
will fall off with the square of distance. Since the radar must pick up
the return echo of the transmit pulse, which also falls off by the square
of distance, that means that the strength of a return pulse falls off by
the fourth power of the distance to the target.
- Target "radar cross section (RCS)". The RCS
of a target is effectively its reflectivity to radar. RCS varies with the
material being illuminated, for example metal surfaces tend to be more
reflective than plastic surfaces, and with the physical configuration of
the surfaces. A smooth surface tends to be less reflective than a jagged
rough surface. The RCS of a target tends to be highly variable, depending
on the viewing angle of the target. An aircraft that is very bright to
radar from one angle may be almost invisible from another, and its radar
return may change drastically as it flies around.
- Atmospheric attenuation. This is the trickiest of all
the factors to estimate, since it can vary wildly given different
atmospheric conditions. It is usually just given as a flat constant, since
it is hard to do much better in practice.
This gives a simplified version of
the radar range equation:
power * gain * RCS
----------------------- > noise
attenuation * range^4
There are many variations of this
equation, usually providing greater detail or modified to demonstrate the
capabilities of different radar configurations. The basic idea is simple: the
capability of a radar to detect a target is directly proportional to its
transmit power, its receiver gain, and the RCS of a target; and inversely
proportional to the atmospheric attenuation and the fourth power of the range.
