Basic radar theory pdf

An example of too small spacing is shown in this slide. Both targets produce a backscatter, but both signals have insignifi- Slide 13 cant time difference with each other. The radar signal processing cannot detect two targets therefore.

The next slide shows the wave propagation at two aims with distance of more than meters. For the angular measurement, the radar supposes the target is positioned in the Slide 16 direction of the axis of the main beam. This is another good reason to use a highly directive antenna. The half-power points of the antenna radiation pattern are normally specified as the limits of the antenna beam width for the purpose of defining angular reso- lution; two identical targets at the same distance are, therefore, resolved in angle if they are separat- ed by more than the antenna -3 dB beam width.

The spacing between two targets can be expressed as distance too. But then the spacing in azimuth SA depends on the range to the radar additionally.

With reference to the slide, two targets are situat- ed at the same range from the radar. The rectangular triangle refers to the half of the beamwidth and the half of the spacing.

Generally, resolution is defined as resolving power. Resolution is the minimum separation between two targets that the equip- ment radar is capable of distinguishing. Differences in Doppler shift make it possible to distinguish two targets, which are located inside the same resolution cell. The range and angular resolutions lead to the resolution cell. The meaning of this cell is very clear: unless one can rely on Slide 17 eventual different Doppler shifts it is impossible to distinguish two targets which are located inside the same resolution cell.

The target resolution of a radar set is its ability to distinguish between targets that are very close in either range or bearing. Weapons-control radar, which requires great precision, should be able to distinguish between targets that are only some meters apart. Search radar is usually less precise and only distinguishes between targets that are hundreds of meters or even a nautical mile apart. Resolu- tion is usually divided into two categories; range resolution and bearing resolution.

The meaning of this cell is very clear: unless one can rely on eventual different Doppler shifts it is impossible to distinguish two targets which are located inside the same resolution cell. Resolution should not be confused with accuracy. Nevertheless, in most radar projects, a first guess for the accuracy figure one standard deviation will be half the value of the corresponding resolu- tion. When the radar is realized, the accuracy is frequently better than the first guessed because: e. If the transmitted pulse is a perfect rectangular one, the received pulse will look like a Gaussian curve because the receiver bandwidth is finite; in addition the noise will disrupt the Gaussian shape of the received pulse.

Hence it is obvious that the accuracy of this measurement is not really linked to the pulse width which defines the range resolution but rather on the receiver signal strength which is linked to the range.

Hence the range error should increase with the range. Radar Coverage Coverage is the volume defined in terms of range, azimuth, and elevation angle or altitude within a radar can provide useful information on the smallest aircraft of interest, in this case a small general aviation aircraft.

The coverage of a single radar set depends on geographical peculiarities, and the vertical an- tenna pattern. It looks like a flat cylinder with a radius of the maximum range generally in the slide shown as green with a Slide 18 gap in the middle: the cone of silence.

Low level coverage is determined by topographical considerations as well as radar performance. Local obstructions can have a significant impact on radar coverage and very often determine the required height of the radar antenna. For airport radars, it is customary to specify the low coverage at range intervals from the radar site. In the case of en route radars, the low coverage is usually more generalized, for example, ft throughout the coverage volume.

However, these demands can be surprisingly difficult to achieve in mountainous areas. Careful analysis of the operational requirement is required, particularly, in the specific directions where low cover is operationally important.

High level coverage requirements are usually easier to achieve for both en route and approach ra- dars. Typical figures are ft for an en Route radar and ft for an approach radar.

Ground movement radars are usually required to provide coverage to an altitude of ft in order to display missed approaches, helicopter operations etc.

Of more significance is the required back angle coverage, which can be more difficult to achieve. This can be significant for both approach and en route radars.

Traffic over-flying an airport or en-route radar can be lost in the overhead gap or cone of silence for a significant period depending on the back angle and the height of the aircraft. It is always appropri- ate to consider traffic routings relative to the radar overhead gap when considering the radar site and the back angle requirements. Aircraft flying close to the overhead gap fly an apparent circular path around the radar head due to slant range considerations.

Back angle figures of between 30 and 40 degrees are typical for modern antenna designs. At the frequen- cies normally used for radar, radio waves usually travel in a straight line. The waves may be obstructed by weather or shad- owing, and interference may come from other aircraft or from reflections from ground objects. This figure still disregards the influence of the refraction of Slide 19 electromagnetic waves in the earth atmosphere.

Refraction A phenomenon called refraction occurs when radar waves pass through media with different indices of refraction. In a vacuum, radio waves travel in straight lines. The speed of wave propagation differs from c if the medium of propagation is matter. This velocity difference is not significant in air, but can have large effects for radars. When a ray, the path of propagation of an electromagnetic wave, passes from a material having a smaller index of refraction to a material having a larger index of refraction, the ray is bent upwards.

If the ray goes from a material having a larger index of refraction to a material with a smaller index of refraction, the ray is bent downwards.

The index of refraction of the atmosphere is not constant and depends on temperature, air pressure, and humidity. The temperature, partial pressure of the dry air, and the water vapor content normally decrease with increasing altitude; therefore, the index of refraction normally decreases with altitude.

Since the velocity of propagation is inversely proportional to the index of refraction, radio waves move slightly more rapidly in the upper atmosphere than they do near the surface of the earth.

The result is a downward bending of the rays towards the Earth. Since the rays are not straight, as in a vacuum, this effect can introduce error in elevation angle measurements. In the presence of standard refraction, the curvature of the rays is less than the curvature of the earth. This extends the radar line of sight beyond the geometrical horizon. To simplify radar calculations, refracted rays are often replotted as straight-line propagation for a fictitious earth having a larger radius than the actual earth.

The smaller values are more likely to exist in cold, dry climates or at high altitudes, whereas larger values occur in tropical climates. From trigo- nometry, one can determine the radar horizon range, the maximum distance that radar can detect targets. The range is given by where requiv is the effective radius and haim and hantenna are the heights of the transmitter and target respectively.

The effective Earth radius for line of sight varies with carrier frequency! The required service availability is a crucial factor in determin- ing the system design. For most ATC applications, total radar failure is not an acceptable situation. On the other hand, the provision of dual sensors to meet a single operational require- ment is not always easy to justify. Significantly reduced availability requirements can be placed on individual sensors if alternative coverage can be provided by an adjacent facility on the network.

In the context of en route radar services, the distribution of radar stations can usually be arranged to provide overlapping cover. A failure of an individual radar station can be tolerated because adjacent stations provide adequate coverage.

The situation becomes more difficult where low cover requirements are more demanding, for example, at airports. In these circumstances and subject to the availability of a networked alter- native, the users may be able to tolerate the reduction in low coverage for a limited period. Finally, in the circumstances where both primary and secondary services are available, it may be possible to continue operations in the absence of one of the services usually primary radar.

The feasibility of this approach is likely to govern the level of system redundancy. Turning to the configuration of individual sensors, a simple, but costly solution is to provide two independent single channel sensors.

These facilities are normally geographically closely sited but not so close that they obstruct one another in order to provide near identical coverage. This config- uration is likely to meet the most demanding of availability requirements.

An alternative, more cost effective solution is to provide a single sensor with dual electronics. In this case, the antenna and turning gear represent a common mode failure item, but with careful design, very high availability can be achieved. In the exceptional circumstance of failure or planned maintenance, an alternative service from the radar network can be used albeit with restricted low coverage.

There are clearly many permutations of these configurations, which are relevant to specific opera- tional circumstances, and it is important that they are fully discussed with the end users. In some primary radar configurations, both channels of a dual channel primary radar system are used to provide the optimum day to day service.

Loss of one channel, does not result in a service failure, but may cause some reduction in performance. These reductions in performance need to be calibrated i.

Operational time is sometimes referred to as uptime, and non-operational time is sometimes called down- time. Mean time between failures MTBF is the predicted elapsed Slide 22 time between inherent failures of a system during operation. MTBF can be calculated as the arithmetic mean average time between failures of a system.

The MTBF is typically part of a model that assumes the failed system is immediately repaired zero elapsed time , as a part of a renewal process. This is in contrast to the mean time to failure MTTF , which measures average time between failures with the modeling assumption that the failed system is not repaired.

Mean time to repair MTTR is a basic measure of the maintainability of repairable items. It rep- resents the average time required to repair a failed component or device. Bestsellers Editors' Picks All Ebooks. Explore Audiobooks. Bestsellers Editors' Picks All audiobooks. Explore Magazines. Editors' Picks All magazines. Explore Podcasts All podcasts.

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That three-day program consists of a mixture of lectures, demonstrations, laboratory sessions, and tours. Online Publication. Robert O'Donnell. LL Introduction to Radar Systems.