The basic principle of operation of primary radar is simple to understand. However, the theory can be quite complex. An understanding
of the theory is essential in order to be able to specify and operate primary radar systems correctly. The implementation and operation of primary radars systems involve a wide range of disciplines such as building works, heavy mechanical and electrical engineering, high power microwave engineering, and advanced high speed signal and data processing techniques. Some laws of nature have a greater importance here.
Radar measurement of range, or distance, is made possible because of the properties of radiated electromagnetic energy.
1. Reflection of electromagnetic waves
The electromagnetic waves are reflected if they meet an electrically leading surface. If these reflected waves are received again at the place of their origin, then that means an obstacle is in the propagation direction.
2. Electromagnetic energy travels through air at a constant speed, at approximately the speed of light,
o 300,000 kilometers per second or
o 186,000 statute miles per second or
o 162,000 nautical miles per second.
o This constant speed allows the determination of the distance between the reflecting objects (airplanes, ships or cars) and the radar site by measuring the running time of the transmitted pulses.
3. This energy normally travels through space in a straight line, and will vary only slightly because of atmospheric and weather conditions. By using of special radar antennas this energy can be focused into a desired direction. Thus the direction (in azimuth and elevation of the reflecting objects can be measured.
4. (The effects atmosphere and weather have on the transmitted energy will be discussed later; however, for this discussion on determining range and direction, these effects will be temporarily ignored.)
Radar Basic Principles
The following shows the operating principle of a primary radar set. The radar antenna illuminates the target with a microwave signal, which is then reflected and picked up by a receiving device. The electrical signal picked up by the receiving antenna is called echo or return. The radar signal is generated by a powerful transmitter and received by a highly sensitive receiver.
All targets produce a diffuse reflection i.e. it is reflected in a wide number of directions. The reflected signal is also called scattering. Backscatter is the term given to reflections in the opposite direction to the incident rays.
Radar signals can be displayed on the traditional plan position indicator (PPI) or other more advanced radar display systems. A PPI has a rotating vector with the radar at the origin, which indicates the pointing direction of the antenna and hence the bearing of targets.
The radar transmitter produces the short duration high-power rf pulses of energy that are into space by the antenna.
The duplexer alternately switches the antenna between the transmitter and receiver so that only one antenna need be used. This switching is necessary because the high-power pulses of the transmitter would destroy the receiver if energy were allowed to enter the receiver.
The receivers amplify and demodulate the received RF-signals. The receiver provides video signals on the output.
The Antenna transfers the transmitter energy to signals in space with the required distribution and efficiency. This process is applied in an identical way on reception.
The indicator should present to the observer a continuous, easily understandable, graphic picture of the relative position of radar targets.
The electronic principle on which radar operates is very similar to the principle of sound-wave reflection. If you shout in the direction of a sound-reflecting object (like a rocky canyon or cave), you will hear an echo. If you know the speed of sound in air, you can then estimate the distance and general direction of the object. The time required for an echo to return can be roughly converted to distance if the speed of sound is known.
Radar uses electromagnetic energy pulses in much the same way, as shown in 1. The radio-frequency (rf) energy is transmitted to and reflected from the reflecting object. A small portion of the reflected energy returns to the radar set. This returned energy is called an ECHO, just as it is in sound terminology. Radar sets use the echo to determine the direction and distance of the reflecting object.
Radar is an acronym for
RAdio (Aim)* Detecting And Ranging
Modern radar can extract widely more information from a target's echo signal than its range. But the calculating of the range by measuring the delay time is one of its most important functions.
The distance is determined from the running time of the high-frequency transmitted signal and the propagation c0. The actual range of a target from the radar is known as slant range. Slant range is the line of sight distance between the radar and the object illuminated. While ground range is the horizontal distance between the emitter and its target and its calculation requires knowledge of the target's elevation. Since the waves travel to a target and back, the round trip time is dividing by two in order to obtain the time the wave took to reach the target. Therefore the following formula arises for the slant range:
c0 = speed of light = 3·108m/s
t = measured running time [s]
R = slant range antenna - aim [m]
The distances are expressed in kilometers or nautical miles (1 NM = 1.852 km).
Derivation of the equation
Range is the distance from the radar site to the target measured along the line of sight.
prinziple of radar
1: radar principle
The factor of two in the equation comes from the observation that the radar pulse must travel to the target and back before detection, or twice the range.
Where c0= 3·108 m/s, is the speed of light at which all electromagnetic waves propagate.
If the respective running time t is known, then the distance R between a target and the radar set can be calculated by using this equation.
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.
Radar units usually work with very high frequencies. Reasons for this are:
* quasi-optically propagation of these waves.
* High resolution (the smaller the wavelength, the smaller the objects the radar is able to detect).
* Higher the frequency, smaller the antenna size at the same gain.
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 your own ship or aircraft and is referred to as the relative bearing.)
The antennas of most radar systems are designed to radiate energy in a one-directional lobe or beam that can be moved in bearing simply by moving the antenna. As you can see in the 2, the shape of the beam is such that the echo signal strength varies in amplitude as the antenna beam moves across the target. In actual practice, search radar antennas move continuously; the point of maximum echo, determined by the detection circuitry or visually by the operator, is when the beam points direct at the target. Weapons-control and guidance radar systems are positioned to the point of maximum signal return and maintained at that position either manually or by automatic tracking circuits.
In order to have an exact determination of the bearing angle, a survey of the north direction is necessary. Therefore, older radar sets must expensively be surveyed either with a compass or with help of known trigonometrically points. More modern radar sets take on this task and with help of the GPS satellites determine the northdirection independently.
Transfer of Bearing Information
The rapid and accurate transmission of the bearing information between the turntable with the mounted antenna and the scopes can be carried out for
* servo systems and
* counting of azimuth change pulses.
Servo systems are used in older radar antennas and missile launchers and works with help of devices like synchro torque transmitters and synchro torque receivers. In newer radar units we find a system of Azimuth-Change-Pulses (ACP). In every rotation of the antenna a coder sends many pulses, these are then counted in the scopes.
Newer radar units work completely without or with a partial mechanical motion. These radars employ electronic phase scanning in bearing and/or in elevation (phased-array-antenna).
Simple triangular relation between elevation and 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) in the following formulae and s. The altitude can be calculated with the values of distanceR and elevation angleε.
sin α =
The values of distanceR and elevation angleε we insert in the equation:
H = R · sin ε
The altitude cannot be so simply calculated on a flying airplane, while refraction is caused when electromagnetic waves cross airlayers at different density and the earth's surface has a bend.. Both factors are compensated for with an integrated altitude calculation by extensive formulae.
One can take the mathematical rule for the calculation from 2. A triangle arises between the points: center of the earth, the radar site and the position of the aircraft. The sides of this triangle are described by the cosine theorem and therefore by the equation:
R2 = re2 + (re + H)2 - 2re(re + H) · cos α
(re is the earth radius here).
Under the assumption that the earth is a sphere, the section of the circumference of the earth can be calculated with help of a simple ratio from the complete circumference of the earth from the angle α:
360° · Rtopogr. = α · 2π re
This segment of the circumference of the earth can be considered an approximation of the actual topographical range (here though still without considering refraction).
Example given: The measured slant range is 30km (20NM), the altitude is 1000m (3000ft) and the earth radius is 6370km. Then the calculated difference between the slant range and the topographical range is -19m!
In practice, however, the propagation of electromagnetic waves is also subject to a refraction, this means, the transmitted beam of the radar unit isn't a straight side of this triangle but this side is also bent and it depends on:
* the transmitted wavelength,
* the barometric pressure,
* the air temperature and
* the atmospheric humidity.
The earth radius can be multiplied with a factor for an approximation of the influence of the refraction. An equivalent earth radius of 4/3·re≈8500km is often used and can additionally modified by a manual input of a correction factor to consider temporarily changed weather conditions or changed barometric pressure.
E.G. the following equation is used to calculate the height into the height finder PRW-16 meaning at this:
1. height without including the earth's radius
2. term including the earth's equivalent radius (about 8500 km)
3. term including the refraction into the atmosphere
4. term including the refraction's temperature.
The Radar Equation
The radar equation represents the physical dependences of the transmit power, that is the wave propagation up to the receiving of the echo-signals. Furthermore one can assess the performance of the radar with the radar equation.
Influence of the Earth's Surface
An extended, but less frequent used form of the radar equation considers additional terms, like the Earth's surface but does not classify receiver sensitivity and atmospheric absorption.
In this equation, in addition to the already well-known quantities are:
= Loss factor in place of Lges.
= Effective reflection surface in place of σ
= Pulse length
= Boltzmann's constant
= absolute temperatur in K
= Noise of the receiver
= Clarity factor of the display terminal
= Reflected beam angle
= Break-even factor
= Distance of the absorbing medium
Radar Reflections from Flat Ground
The trigonometric representation shows the influence of the Earth's surface. The Earth plane surrounding a radar antenna has a significant impact on the vertical polar diagram.
The combination of the direct and re-reflected ground echo changes the transmitting and receiving patterns of the antenna. This is substantial in the VHF range and decreases with increasing frequency. For the detection of targets at low heights, a reflection at the Earth's surface is necessary. This is possible only if the ripples of the area within the first Fresnel zone do not exceed the value 0.001R (i.e.: Within a radius of 1000m no obstacle may be larger than 1m!).
Specialized Radars at lower (VHF-) frequency band make use of the reflections at the Earth's surface and lobing to maximize cover at low levels. At higher frequencies these reflections are more disturbing. The following picture shows the lobe structure caused by ground reflections. Normally this is highly undesirable as it introduces intermittent cover as aircraft fly through the lobes. The technique has been used in ATC ground mounted radars to extend the range but is only successful at low frequencies where the broad lobe structure permits adequate cover at higher elevations.
Free space vertical pattern diagram
Effect of ground reflections
“Gray, my dear friend, is every theory”: here it is the idealized cosecant squared- diagram!
The radar equation in practice
Not every transmitting vacuum tube is equally good. Minimal production tolerances can influence the obtainable transmit power and therefore also the theoretical attainable range.
Remember: the most important feature of this equation is the fourth-root dependence!
Other then the transmit power we assume all other factors are constant.
Calling all of them the coefficient k, so the maximum range equation becomes:
We can explain how such deviations change the maximum range values: if e.g. the transmitted power of the russian Radar “Spoon Rest” is permited to fluctuate from 160kW to 250 kW, will the maximum range values be correct for distances between 250 to 270km?
From the relationship shown, we can state that 250km(160kW)·1,118=279.5km(250kW) so the maximum range value would be correct between 250 and 270 km!
In practice results were reached between 180 kW and 240 kW since the transmitted power of the planar vacuum tube was frequency dependent.
The inversion of this argument is also permissible: if the transmit power is reduced by 1/16 (e.g. failure into one of sixteen transmitter modules), then the change on the maximum range of the radar station is negligible in the practice <2%.
Sensitivity of the Receiver
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 of the maximum range.
For every receiver there is a certain receiving power as of which the receiver can work at all. This smallest workable received power is frequently often called MDS - Minimum Discernible Signal in radar technology. Typical radar values of the MDS echo lie in the range of -104 dBm to -110 dBm.
The antenna gain is squared under the 4th root (Remember: the same antenna is used during transmission and reception).
If one quadruples the antenna gain, it will double the maximum range.
Here is a concrete example from VHF- radar technology: Sometimes the P-12 (yagi antennae array: G=69) was mounted at the antenna of the P-14 (same frequency, parabolic dish antenna: G=900). This combination was often mentioned jocularly to “P-13”. 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 mis-adjustment of the antenna give away half of what is invested. Nevertheless: 1.6 times the maximum range isn't degraded either. But there are more disturbances now: too many ambiguous targets (overreaches).
In order to overcome some of the target size fluctuations many radars use two or more different illumination frequencies. Frequency diversity typically uses two transmitters operating in tandem to illuminate the target with two separate frequencies like shown in the picture.
The received signals can be separately processed in order to maintain coherence. In addition to the 3dB gain in performance achieved by using two transmitters in parallel, the use of two separate frequencies improves the radar performance by (typically) 2.8dBs.
The synchronizer supplies the synchronizing signals that time the transmitted pulses, the indicator, and other associated circuits.
The oscillator tube of the transmitter is keyed by a high-power dc pulse of energy generated by this separate unit called the Modulator.
The radar transmitter produces the short duration high-power rf pulses of energy that are radiated into space by the antenna.
A commutator is actually a time controlled switch. The word comes from Latin and means „collecting bar” or „call handling”. Either the commutator works passively (all incoming RF pulses on the three input jacks will be conduct to the output jack) or actively (the RF input pulses are switched to the output time controlled by separate gate pulses like shown in the .)
Since very high frequencies must be switched very fast, the commutator uses a wiring technology like the one used by the duplexer.
The duplexer alternately switches the antenna between the transmitter and receiver so that only one antenna is used. This switching is necessary because the high-power pulses of the transmitter would destroy the receiver if energy was allowed to enter the receiver.
The antenna transfers the transmitter energy to signals in space with the required distribution and efficiency. This process is identical during reception.
The frequency selector is a frequency-separating filter. It separates the received echo-signals into the receivers depending on the frequency.
The receivers amlify and demodulate the received RF-signals. The receiver provides videosignals on the output.
At the transmitter, pulse f1 is delayed by a predetermined time with respect to pulse f2. To undo this delay on the receiving path (The pulse f1 won't dwell faster, even if we want it!), the pulse f2 must be delayed exactly with the same time delay. Now the signal processor can process both signals simultaneously. Notice, that the first pulse transmitted is shown on the oscilloscope as the first pulse as well, i.e. on the left side of the screen!
The single signals are processed in parallel in separate channels at a multiple frequency radar unit. These signals arethen accumulated and compared with a threshold value. Several processing procedures are used:
* linear addition of the amplitudes of all channels (maximum range at low jamming immunity);
* multiplication of the amplitudes of all channels (maximum jamming immunity, but at the lowest value of the maximum range);
* addition of the squares of the amplitudes of all channels (optimal procedure!);
* linear addition of the amplitudes of several channels followed by a multiplication of the partial sums (This procedure is drawn in the upper functional block diagram.);
* Multiplication of the amplitudes of several channels followed by addition of the partial results.
High effectiveness is reached when using one of the mentioned processing procedures.
But which procedure to use to which radar unit is usually highly classified.
The indicator should present to the observer a continuous, easily understandable, graphic picture of the relative position of radar targets.
1. Simultaneous transmission of several pulses at different carrier frequency in the simplest form can be made with several transmitters and receivers working simultaneously.
2. Succession following radiation of several signals the carrier frequency can be changed by changing the frequency:
o of each pulse after the other (frequency agility),
o within the duration of a single pulse (frequency diversity) and
o after several pulses (possible at higher pulse repetition frequencies only).
Combinations of several methods are also used.
For example the ATC-radar ASR-910 uses multiple frequencies, transmitting two pulses closely following the other (frequency diversity), and the RRP-117 air defense radar is also equipped with two frequency carriers and an additional pulse compression. (Since the spectra of the transmitted frequencies cover themselves in the pulse compression, other rules have to be considered.)
The delayed radiation of several signals has advantages opposite to the simultaneous radiation of several signals:
* different transmitted signals don't influence each other,
* more favorable energy conditions arise from the delay, therefore there is no need of using different transmitters and
* a simple construction of the transmitters and the antenna systems.
The work with two transmitters of different frequencies (E.g.: ASR-910) is often looked at falsely only for reasons of the redundancy. („However, if a transmitter fails, I still have the other transmitter!”) The projected maximum range of the radar unit is then reduced to 70%¹. This fact is usually noticed by the flight checker, however, the cause is usually checked somewhere else.
¹) fourth root from the losses of 3dB (decreased Tx-power) plus 2 to 2,5dB increasing of the fluctuations loss
Radar Equation of a Frequency Diversity Radar
The radar equation we have developed is independent of the modulation scheme and in general can be used with each radar unit. In practice, some other variation of the radar equation will be more convenient for system analysis.
The following equation is valid:
Lf (ne) = Lf (1)·exp 1/ ne
ne = Number of the statistically independent samples
The number of the statistically independent samples is a result of the diversity-bandwidth Δf (this is the frequency spacing between the transmitted pulses) and the correlation-frequency fc of the target.
Therefore:By putting aside the power doubling achieved with two transmitters at constant frequencies, the maximum range through frequency diversity mode can never be better due losses caused by fluctuation.
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. Radio navigation performance accuracy is usually presented as a statistical measure of system error and is specified as:
1. Predictable: The accuracy of a position in relation to the geographic or geodetic co-ordinates of the earth.
2. Repeatable: The accuracy in which a user can return to a position whose co-ordinates have been measured at a previous time with the same navigation system.
3. Relative: The accuracy which a user can determine one position relative to another (by neglegting all possible errors).
Some results of radar units are indicated in the following table as example:
accuracy in bearing
accuracy in range
accuracy in height
< 20 m
< 50 m
340 m (at 185 km)
< 44.4 m
< 60 m
< 25 m