Radar#Radar equation

With the radar equation ( or radar basic equation ) can be registered by the receiver performance in dependence of the transmission power, the distance and the characteristics of the reflecting object can be determined. Hence it can be estimated whether the circumstances the object in the receiver generates a sufficiently strong signal that can be detected. Due to the different reflection conditions at point targets ( air surveillance ) and by volume targets ( weather radar ) different radar equations are formulated for these two cases. In general, the radar equation is derived from the inverse square law and is like this only for unhindered radiations in free space.

General Overview

Apart from a few special cases, in radar applications, the ratio of distance to wavelength is so large that the transmitting antenna - regardless of their size - can be considered as a mathematical point. Therefore, the energy is distributed as a spherical wave to ever larger areas. For the determination of the reflected energy must therefore be distinguished:

• In a " pin point " (e.g., an airplane ), the absorption area is constant; therefore takes the received power from 1 / r ². Part of it is ( passive) reflected back to the radar device, the back-scattered energy back with 1 / r ² decreases; the receiving antenna is indeed also a point target. Overall, you have to multiply both factors and therefore it is a 1/r4-Zusammenhang.
• For very large scale objectives such as (not too distant ) clouds also increases the illuminated volume by a factor of r ². That is, the entire signal received by the cloud energy is constant. A certain fraction of it is reflected back and only applies to this back, the 1 / r ², depending on the energy, so that a total of only 1 / r ² relationship applies.

• With increasing distance of the clouds but they fill an ever smaller proportion of the beam, because a growing proportion of the transmitted energy no longer meets the cloud. Then none of the previous two points more; The result is in this case a transition from one portion to 1 / r ² - a portion 1/r4-Zusammenhang.

Radar equation is valid only for primary radar. A secondary radar does not use the passive reflection of radio waves. Rather, there is a bi-directional radio link. The received power is reduced as the distance to a 1 / r ² - dependence by the simple law of distance. When the transponder responds, its transmit power does not depend on the received power. Thus considered separately a 1 / r ² depending on the way back.

Radar equation for a point target

Point targets are called reflecting objects that do not complete the pulse volume of a radar completely, that is, that their geometric extent much smaller than the product of the velocity of propagation and transmission pulse length ( c0 · τ ), and much smaller than the width of the antenna pattern at the site of reflection are. These conditions are in airspace reconnaissance and target tracking radar for example.

Pr = received power Pt = transmitter power Gt = antenna gain of the transmitting antenna Gr = antenna gain of the receiving antenna λ = wavelength of the carrier frequency σ = effective reflecting surface ( RCS), σ0 = spherical stray reference area of ​​1 m2 Rt = distance transmitting antenna - reflective object

The equation assumes that the distance between the object and the transmitter is significantly larger than the wavelength of the radar. That is, the object must be in the far field of the transmitter are located. Further provided by the power ratio such that the duration of the transmit pulse corresponding to about the duration of the echo signal in the signal processing, ie that no pulse compression method is employed.

By rearranging the above equation is obtained after the removal of a form of radar equation, which is often used in practice to assess the operating performance of radar systems:

Here, the antenna gain in transmit and receive mode were combined to G2: that is possible when a monostatic radar antenna (Rt ≡ Rr) forms the same antenna pattern in the transmission torque, as during the reception time (Gt = Gr). The maximum range Rmax is then determined by the receiver sensitivity Pr_min. For practical application still various internal and external losses as Lges incorporated with.

Radar equation for a volume target

The radar equation for volume targets (read: for Weather Radar ) radar uses the same parameters and other contexts. The main difference, however, are the characteristic properties of the reflecting surface, which additionally change with increasing distance from the radar. At a rain each raindrop is much smaller than the wavelength of the radar device. Therefore, the effective reflecting surface of a raindrop is determined by the Rayleigh scattering:

With D as the raindrop diameter and ε as the dielectric constant. For the usual radar frequency bands L to X Water has a factor of | K | 2 = 0.93 and for ice, we have | K | 2 = 0.2.

With a volume target, the pulse volume is now completely filled by these reflective objects. The sum of the reflecting surface is called η with the temporary variable:

The Impusvolumen V increases by the divergence of the antenna beam with the distance to the radar:

φ = vertical opening angle of the antenna pattern θ = horizontal opening angle R = Distance to radar τ = transmission pulse duration c0 = speed of light

The internal parameters of the radar as well as partially free-space loss are combined for meteorological concerns in a factor C, which as:

Is used. This has already been taken into account that most weather radars use a symmetric diagram form θ with φ = φ · θ = and therefore is θ2. This leads to a highly simplified form of the radar equation for volume targets, as it is used in meteorology:

This equation can now be deduced from the measured received power directly to the reflectivity. This is a measure of the type and number of the reflecting objects, this conclusion is not yet clear: Many small water droplets give the same reflectivity as a few large. To resolve these ambiguities partially polarimetric radar is used and measured differential reflectivity.