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Radar principle

Direction determination (bearing)

The angular determination of the target is determined by the directivity of the antenna. Directivity, sometimes known as the directive gain, is the ability of the antenna to concentrate the transmitted energy in a particular direction. An antenna with high directivity is also called a directive antenna. By measuring the direction in which the antenna is pointing when the echo is received, both the azimuth and elevation angles from the radar to the object or target can be determined. The accuracy of angular measurement is determined by the directivity, which is a function of the size of the antenna.

Direction determination (bearing)

The true bearing (referenced to true north) of a radar target is the angle between true north and a line pointed directly at the target. This angle is measured in the horizontal plane and in a clockwise direction from true north. (The bearing angle to the radar target may also be measured in a clockwise direction from the centerline of aircraft and is referred to as the relative bearing.

Height

The height of a target over the earth's surface is called height or altitude. This is denominated by the letter H (like: Height). The altitude can be calculated with the values of distanceR and elevation angleε.

The Radar equation

PS - transmitted power [W] ; G - antenna gain: λ – wavelength [m]; σ – radar cross section [m2]; PEmin - smallest received power

The smallest received power that can be detected by the radar is called PEmin. Smaller powers than PEmin aren't usable since they are lost in the noise of the receiver. The minimum power is detected at the maximum range Rmax as seen

from the equation.

Influencesonthemaximumrange:

fluctuation losses; atmospheric losses; influence of Earth’s surface; radar reflections from flat ground

Radar cross section

The size and ability of a target to reflect radar energy can be summarized into a single term, σ, known as the radar cross-section, which has units of m².

The target radar cross sectional area depends on: •the airplane’s physical geometry and exterior features, •the direction of the illuminating radar,

•the radar transmitters frequency, •the used material types.

The experimental radar cross section of aircraft at 3 GHz frequency as a function of azimuth angle

Noise

Noise is characterized by its statistical properties. Noise that contains all frequencies with equal amplitudes is called „white” noise. The sources of noise arise from inside and outside a circuit

Frequency dependence of the relation noise temperature (noise power )

Accuracy versus Resolution

Accuracy is the degree of conformance between the estimated or measured position and/or the velocity of a platform at a given time and its true position or velocity (not confused with resolution).

The target resolution of a radar is its ability to distinguish between targets that are very close in either range or bearing. Resolution is usually divided into two categories: range resolution and bearing resolution.

The stated value of required accuracy represents the uncertainty of the reported value with respect to the true value and indicates the interval in which the true value lies with a stated probability. The recommended probability level is 95 per cent, which corresponds to 2 standard deviations of the mean for a normal (Gaussian) distribution of the variable. The assumption that all known correction are taken into account implies that the errors in the reported values will have a mean value (or bias) close to zero.

Dwell time and Hits per scan

The time that an antenna beam spend on a target is called dwell time. The dwell time depends predominantly on

TD=(ΘAZ *60)/(360 * n) in [seconds],

ΘAZ - the beam width; n - the turn speed of the antenna (rotations per minute).

The value “hits per scan” m says how many echo signals per single target during every antenna swing are received

m = TD/PRT,

PRT - pulse repetition time.