Table 1. Table 2. Effects of Sensitivity Increase. Table 3. Effects of Sensitivity Decrease. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged. Note the similarity of Figure 1 to Figure 3 in Section Transmitted power, transmitting and receiving antenna gains, and the one-way free space loss are the same as those described in Section The physical arrangement of the elements is different, of course, but otherwise the only difference is the addition of the equivalent gain of the target RCS factor.

RCS area is not the same as physical area. The table of values for K 1 is again presented here for completeness. The constant, K 1in the table includes a range and frequency unit conversion factor. While it's understood that RCS is the antenna aperture area equivalent to an isotropically radiated target return signal, the target gain factor represents a gain, as shown in the equivalent circuit of Figure 1.

This value of K2 plus K2 for other area units and frequency multiplier values are summarized in the adjoining table. Because the factors are given in dB form, they are more convenient to use and allow calculation without a calculator when the factors are read from a chart or nomograph.

Most radars are monostatic. That is, the radar transmitting and receiving antennas are literally the same antenna.

There are some radars that are considered "monostatic" but have separate transmitting and receiving antennas that are colocated. Figure 2 is the visualization of the path losses occurring with the two-way radar equation. Note: to avoid having to include additional terms, always combine any transmission line loss with antenna gain. Losses due to antenna polarization and atmospheric absorption also need to be included. Figure 2. The maximum radar range R max is the distance beyond which the target can no longer be detected and correctly processed.

It occurs when the received echo signal just equals S min. For pulse signals these equations assume the radar pulse is square.

If not, there is less power since Pt is actually the average power within the pulse width of the radar signal. Equations [17] and [19] relate the maximum detection range to S minthe minimum signal which can be detected and processed the receiver sensitivity.

The bandwidth B in equations [20] and [21] is directly related to S min.

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Thus a wider pulse width means a narrower receiver bandwidth which lowers S minassuming no integration. One cannot arbitrarily change the receiver bandwidth, since it has to match the transmitted signal. The "widest pulse width" occurs when the signal approaches a CW signal see Section A CW signal requires a very narrow bandwidth approximately Hz.

Therefore, receiver noise is very low and good sensitivity results see Section If the radar pulse is narrow, the receiver filter bandwidth must be increased for a match see Sectioni.

This increases receiver noise and decreases sensitivity. Note that a PRF increase may limit the maximum range due to the creation of overlapping return echoes see Section There are also other factors that limit the maximum practical detection range.

With a scanning radar, there is loss if the receiver integration time exceeds the radar's time on target.Radar cross-section RCS is a measure of how detectable an object is by radar. A larger RCS indicates that an object is more easily detected. An object reflects a limited amount of radar energy back to the source. The factors that influence this include:. While important in detecting targets, strength of emitter and distance are not factors that affect the calculation of an RCS because RCS is a property of the target's reflectivity.

Radar cross-section is used to detect airplanes in a wide variation of ranges. For example, a stealth aircraft which is designed to have low detectability will have design features that give it a low RCS such as absorbent paint, flat surfaces, surfaces specifically angled to reflect the signal somewhere other than towards the sourceas opposed to a passenger airliner that will have a high RCS bare metal, rounded surfaces effectively guaranteed to reflect some signal back to the source, lots of bumps like the engines, antennas, etc.

RCS is integral to the development of radar stealth technologyparticularly in applications involving aircraft and ballistic missiles.

In some cases, it is of interest to look at an area on the ground that includes many objects. Informally, the RCS of an object is the cross-sectional area of a perfectly reflecting sphere that would produce the same strength reflection as would the object in question. Bigger sizes of this imaginary sphere would produce stronger reflections. Thus, RCS is an abstraction: The radar cross-sectional area of an object does not necessarily bear a direct relationship with the physical cross-sectional area of that object but depends upon other factors.

Somewhat less informally, the RCS of a radar target is an effective area that intercepts the transmitted radar power and then scatters that power isotropically back to the radar receiver.

More precisely, the RCS of a radar target is the hypothetical area required to intercept the transmitted power density at the target such that if the total intercepted power were re-radiated isotropically, the power density actually observed at the receiver is produced. The scattering of incident radar power by a radar target is never isotropic even for a spherical targetand the RCS is a hypothetical area. However, RCS is an extremely valuable concept because it is a property of the target alone and may be measured or calculated.

Thus, RCS allows the performance of a radar system with a given target to be analysed independent of the radar and engagement parameters.

In general, RCS is a strong function of the orientation of the radar and target, or, for the bistatic radar transmitter and receiver not co-locateda function of the transmitter-target and receiver-target orientations. A target's RCS depends on its size, reflectivity of its surface, and the directivity of the radar reflection caused by the target's geometric shape. As a rule, the larger an object, the stronger its radar reflection and thus the greater its RCS. Also, radar of one band may not even detect certain size objects.

Materials such as metal are strongly radar reflective and tend to produce strong signals. Wood and cloth such as portions of planes and balloons used to be commonly made or plastic and fibreglass are less reflective or indeed transparent to radar making them suitable for radomes.

Even a very thin layer of metal can make an object strongly radar reflective. Chaff is often made from metallised plastic or glass in a similar manner to metallised foils on food stuffs with microscopically thin layers of metal.

Also, some devices are designed to be Radar active, such as radar antennas and this will increase RCS. The SR Blackbird and other planes were painted with a special " iron ball paint " that consisted of small metallic-coated balls. Radar energy received is converted to heat rather than being reflected.

The surfaces of the FA are designed to be flat and very angled. This has the effect that radar will be incident at a large angle to the normal ray that will then bounce off at a similarly high reflected angle; it is forward-scattered. The edges are sharp to prevent there being rounded surfaces. Rounded surfaces will often have some portion of the surface normal to the radar source.

As any ray incident along the normal will reflect back along the normal, this will make for a strong reflected signal. From the side, a fighter plane will present a much larger area than the same plane when viewed from the front. All other factors being equal, the plane will have a stronger signal from the side than from the front so the orientation between the Radar station and the target is important.

The relief of a surface could contain indentations that act as corner reflectors which would increase RCS from many orientations.

This could arise from open bomb-baysengine intakes, ordnance pylons, joints between constructed sections, etc. Also, it can be impractical to coat these surfaces with radar-absorbent materials. This does not equal geometric area. A perfectly conducting sphere of projected cross sectional area 1 m 2 i.Radar is a detection system that uses radio waves to determine the range, angle, or velocity of objects.

It can be used to detect aircraftshipsspacecraftguided missilesmotor vehiclesweather formationsand terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antennaa receiving antenna often the same antenna is used for transmitting and receiving and a receiver and processor to determine properties of the object s. Radio waves pulsed or continuous from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.

Radar was developed secretly for military use by several nations in the period before and during World War II. A key development was the cavity magnetron in the United Kingdomwhich allowed the creation of relatively small systems with sub-meter resolution. The modern uses of radar are highly diverse, including air and terrestrial traffic control, radar astronomyair-defense systemsantimissile systemsmarine radars to locate landmarks and other ships, aircraft anticollision systems, ocean surveillance systems, outer space surveillance and rendezvous systems, meteorological precipitation monitoring, altimetry and flight control systemsguided missile target locating systems, and ground-penetrating radar for geological observations.

High tech radar systems are associated with digital signal processingmachine learning and are capable of extracting useful information from very high noise levels.

## Radar Equation, 2-Way

Radar is a key technology that the self-driving systems are mainly designed to use, along with sonar and other sensors. Other systems similar to radar make use of other parts of the electromagnetic spectrum.

With the emergence of driverless vehicles, radar is expected to assist the automated platform to monitor its environment, thus preventing unwanted incidents.

As early asGerman physicist Heinrich Hertz showed that radio waves could be reflected from solid objects. InAlexander Popova physics instructor at the Imperial Russian Navy school in Kronstadtdeveloped an apparatus using a coherer tube for detecting distant lightning strikes.

The next year, he added a spark-gap transmitter. Inwhile testing this equipment for communicating between two ships in the Baltic Seahe took note of an interference beat caused by the passage of a third vessel. In his report, Popov wrote that this phenomenon might be used for detecting objects, but he did nothing more with this observation. Inhe demonstrated the feasibility of detecting a ship in dense fog, but not its distance from the transmitter.

He also obtained a British patent on September 23, [9] for a full radar system, that he called a telemobiloscope.

His system already used the classic antenna setup of horn antenna with parabolic reflector and was presented to German military officials in practical tests in Cologne and Rotterdam harbour but was rejected. InRobert Watson-Watt used radio technology to provide advance warning to airmen [11] and during the s went on to lead the U.

Through his lightning experiments, Watson-Watt became an expert on the use of radio direction finding before turning his inquiry to shortwave transmission. Requiring a suitable receiver for such studies, he told the "new boy" Arnold Frederic Wilkins to conduct an extensive review of available shortwave units. Wilkins would select a General Post Office model after noting its manual's description of a "fading" effect the common term for interference at the time when aircraft flew overhead.

Across the Atlantic inafter placing a transmitter and receiver on opposite sides of the Potomac RiverU. Navy researchers A.In the previous lecture, we have discussed the basics of radar and how radar is used for detection and location of an object in space.

But the question arises is there any limit which specifies the range up to which this detection is possible? So the answer to this question is yes, there exist some factors that decide the range of the radar.

And these factors combinely form the radar range equation. The radar range equation is used to evaluate the particular range up to which the object or target detection is possible. While designing a radar system, the radar range equation is an important aspect because it shows the range up to which the system can detect the target. In this section, we will derive the range equation for a radar system.

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So, let us proceed further and understand how the range of a radar is detected. Consider that the transmitting antenna is isotropic in nature thus it radiates the transmitted power in a uniform manner in all the directions. Then the power per unit area i.

It is the ratio of transmitted power by the antenna to the surface area of the imaginary sphere i. Here R denotes the radius of the sphere. Usually, radar systems use a directive antenna with narrow beamwidths that direct the radiated power in a single direction.

The antenna gain specifies the power density in the direction of the directive antenna to the power density in that particular direction by an isotropic antenna. Therefore, the power density by the directive antenna at the object is given by. We know the signal transmitted by the radar when intercepted by an object in space then the energy gets re-radiated in different directions.

And this leads to the reception of a part of transmitted signal i. Suppose P is the power incidenting on the object and is given by:. So, the reflected power density at the radar system is given by:. However, the power received by this antenna will be the product of power incidenting on the receiving antenna and the effective area of the antenna. This is given by:. More simply. The distance beyond which the object cannot be identified is defined as the highest range supported by the radar.

And this happens when received echo becomes equal to the minimum detectable signal S min.

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David Atlas: On one hand, the hybrid sky-surface wave radar equation is deduced.

Study on the detectability of the sky-surface wave hybrid radar. According to the radar equationafter signal processing and data processing, we compute statistical probability of radar to detect a target.

Reusable component model development approach for parallel and distributed simulation. According to the bistatic radar equationan attenuation factor [[alpha]. His topics include the development of the radar equationradar equations for clutter and jamming, beamshape loss, atmospheric effects, and loss factors in the radar equation.

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The book is divided into nine chapters, starting with the radar equation as a basis for all further discussions. Radar System Analysis and Modeling. Encyclopedia browser? Full browser?Radar Max Range is determined, ideally speaking, on the properties of the antenna only.

A signal at a certain frequency is transmitted, reflected, then hopefully, detected. Due to the three-dimensional propagation of radar waves, frequency hold the highest weight in determining range. Often, power consumption and range must be balanced for maximum usability. Place order in next. Antenna Downtilt and Coverage Calculator. Balanced Attenuator Calculator.

Bridged Tee Attenuator Calculator. Cascaded Noise Figure Calculator. Coaxial Cable Impedance Calculator. CRA Calculator. EIRP Calculator.

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Free Space Path Loss Calculator. Friis Transmission Calculator. IRA Calculator. Link Budget Calculator. Microstrip Calculator. Microstrip Patch Antenna Calculator. Noise Figure - Noise Temperature Calculator. N-Way Power Divider Calculator.

Pi Attenuator Calculator.Here are given some examples to demonstrate the consequences of changing selected parameters of Radar sets.

Not every transmitting vacuum tube is equally good. Minimal production tolerances can influence the obtainable transmit power and therefore also the theoretical attainable range. Other then the transmit power we assume all other factors are constant. Calling all of them the coefficient kso the maximum range equation becomes:.

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In order to double the range, the transmitted power would have to be increased by fold! We can explain how such deviations change the maximum range values: if e. While evaluating the minimal received power we follow a different procedure: It's also under the 4th root but in the denominator.

Well, a reduction of the minimal received power of the receiver gets an increase in the maximum range. For every receiver, there is a certain receiving power as of which the receiver can work at all.

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This smallest workable received power is frequently often called MDS - M inimum D iscernible S ignal in radar technology. The antenna gain is squared under the 4th root Remember: the same antenna is used during transmission and reception. In accordance with our radar equation the maximum range should increase:. Please note the fourth root was simplified against the square in the numerator and in the denominator at once.

It would be beautiful if the maximum range could be tripled so simply. But bigger antennas use much longer supply cables. Losses on the incoming feeding lines and losses due to the misadjustment of the antenna give away half of what is invested. Nevertheless: 1. But there are more disturbances now: too many ambiguous targets overreaches. The Radar Equation in Practice Here are given some examples to demonstrate the consequences of changing selected parameters of Radar sets.

Transmitted Power.