[1.0] Basic Principles Of Radar
v1.0.0 / 1 of 2 / 01 feb 03 / greg goebel / public domain
* This chapter provides basic definitions and concepts in radar technology.
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[1.1] RADIO WAVE FREQUENCY & WAVELENGTH
[1.2] RADIO WAVE POLARIZATION, PHASE, INTERFERENCE, & PROPAGATION
[1.3] RADIO SYSTEM BASICS
[1.4] ANTENNA BASICS
[1.5] A SIMPLE PULSE RADAR SYSTEM
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[1.1] RADIO WAVE FREQUENCY & WAVELENGTH
* Radar is a variant of radio technology and shares many of the same basic
concepts. It is useful to discuss fundamental concepts of radio operation
to provide a basis for discussing fundamental concepts of radar operation.
Late in the 19th century, researchers discovered that if an alternating electric current were run through a wire or rod, it emitted an invisible form of radiation that could generate an alternating electric current in a separate wire or rod. This invisible radiation was quickly realized to be a form of "electromagnetic radiation", a disturbance of electric and magnetic fields that propagated through space.
Electromagnetic radiation is in the form of waves, conceptually similar to the waves set up by shaking a rope up and down, and propagating at a speed of 300,000,000 meters per second (186,000 miles per second). The waves could be generated at varying "frequencies", defined by the number of cyclical variations of the wave that passed through a plane every second. Frequencies were once measured in "cycles per second (CPS)", but now are universally defined in terms of "hertz (Hz)", after Heinrich Hertz, a pioneering radio researcher.
The frequencies of electromagnetic radiation are usually large numbers, and so it is useful to use "metric prefixes" as shorthand -- for example:
kilohertz (kHz): 1,000 hertz
megahertz (MHz): 1,000,000 hertz
gigahertz (GHz): 1,000,000,000 hertz
terahertz (THz): 1,000,000,000,000 hertz
The full range of frequencies of electromagnetic radiation is known as
the "electromagnetic spectrum". Radio waves only take up part
of this spectrum, generally involving kilohertz, megahertz, or gigahertz
radio emissions.
Above about 300 GHz, electromagnetic radiation moves into a region of
the spectrum known as "infrared"; and then with increasingly
higher frequencies into the region of visible light that we can see with
our eyes; and finally into energetic radiation defined as the "ultraviolet",
"X-ray", and (at the very highest frequencies) "gamma ray"
regions of the spectrum.
Put a little bit more simply, radio waves are the same thing as visible light, both being forms of electromagnetic radiation. The only difference is that radio waves have lower frequencies.
Incidentally, electromagnetic waves are entirely different from sound waves, which are mechanical disturbances propagating through the air, water, or a solid medium. The two kinds of waves can be confused because very low frequency electromagnetic waves are sometimes said to be at "audio" frequencies, and of course electromagnetic waves can be used to transmit audio waves, as turning on a household radio shows.
* This document focuses only on radio waves. Sometimes it is easier to talk about radio waves in terms of their "wavelength" in meters instead of their frequency. There is a simple relationship between the wavelength and frequency of a wave:
wavelength = wave_propagation_speed / frequency
Since the propagation speed of electromagnetic radiation in free space
is 300,000,000 meters per second, then for electromagnetic radiation this
is:
wavelength = 300,000,000 / frequency
If frequency is given in megahertz, this simplifies to:
wavelength = 300 / frequency
For example:
1 kHz = 300 kilometers
3 kHz = 100 kilometers
10 kHz = 30 kilometers
30 kHz = 10 kilometers
100 kHz = 3 kilometers
300 kHz = 1 kilometer
1 MHz = 300 meters
3 MHz = 100 meters
10 MHz = 30 meters
30 MHz = 10 meters
100 MHz = 3 meters
300 MHz = 1 meter
1 GHz = 30 centimeters
3 GHz = 10 centimeters
10 GHz = 3 centimeters
30 GHz = 1 centimeter
100 GHz = 3 millimeters
300 GHz = 1 millimeter
Various frequency / wavelength ranges, or "bands", have been
defined for radars, with general classes of equipment usually operating
in one or a few bands. The band names, with the frequency / wavelength
corresponding to the low end of each band, are as follows:
ELF (Extremely Low Frequency) 30 Hz 10,000 kilometers
VF (Voice Frequency) 300 Hz 1,000 kilometers
VLF (Very Low Frequency) 3 kHz 100 kilometers
LF (Low Frequency) 30 kHz 10 kilometers
MF (Medium Frequency) 300 kHz 1 kilometer
HF (High Frequency) 3 MHz 100 meters
VHF (Very High Frequency) 30 MHz 10 meters
UHF (Ultra High Frequency) 300 MHz 1 meter
L 1 GHz 30 centimeters
S 2 GHz 15 centimeters
C 4 GHz 7.5 centimeters
X 8 GHz 3.75 centimeters
Ku 12 GHz 2.5 centimeters
K 18 GHz 1.67 centimeters
Ka 27 GHz 1.1 centimeters
V 40 GHz 7.5 millimeters
W 75 GHz 4 millimeters
mm 110 GHz 2.73 millimeters
The VLF through UHF band definitions were inherited from radio engineering.
The bands above UHF don't follow a clear order, which apparently was partly
by intent, as a security measure. The K band originally included the Ku
and Ka bands, but it turned out that the center portion of the K-band
was useless for most military purposes as water vapor in the atmosphere
soaked up radio waves in that range. The portion of the K-band "above"
the absorption range became the "Ka-band", while the portion
"under" the absorption range became the "Ku-band".
Just to make things more confusing, different band definitions are used
in other electronic fields. Radio engineers retain the ELF through UHF
definitions, but take the UHF band up to 3 GHz, and then cover the higher
frequencies with the "Super High Frequency (SHF)" band from
3 to 30 GHz, covering the centimetric / microwave region, and then the
"Extremely High Frequency (EHF)" band from 30 to 300 GHz, covering
the millimeter wave region.
Electronic countermeasures systems are defined by a band scheme entirely different from the radar and radio scheme, with the bands much more conveniently arranged from "A" to "M" in order of increasing frequency. Oddly, there isn't a one-to-one correspondence between the countermeasures bands and the radar bands, and though there was some interest at one time at applying the more rational countermeasures scheme to radar, it wasn't practical.
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[1.2] RADIO WAVE POLARIZATION, PHASE, INTERFERENCE, & PROPAGATION
* As electromagnetic radiation is a wave phenomenon, it has certain characteristics
associated with waves, such as "polarization", "phase",
and "wave interference".
The oscillations of an electromagnetic wave occur back and forth across the direction of the wave's propagation. This means that the wave has a certain "polarity". If the wave's oscillations are up and down, the wave is said to be "vertically polarized"; if they are back and forth, the wave is said to be "horizontally polarized". Of course, the wave could also be polarized at any angle between those two extremes.
The concepts of "phase" and "wave interference" are a bit trickier to explain. Suppose you have a tank of water, and are using some sort of vibrating element to generate waves. If you stick another vibrating element in the water operating at the same vibration rate and same intensity, it will generate waves of the same frequency and height (or "amplitude"), but the peaks and valleys of the waves generated by the second vibrating element will not necessarily coincide with those of the first. In other words, they won't have the same "phase".
The phase of the two sets of waves could be matched up, with the peaks and valleys of both coinciding; or they could be completely out of phase, with the peaks of one coinciding with the valleys of the other and the reverse, a condition known as "antiphase"; or they could have a phase difference anywhere between those two extremes.
The really interesting thing is that the two sets of waves add to each other. If the two sets of waves are exactly in phase, they add up into a single set of waves of twice the amplitude of one of the sets of waves. If they are exactly antiphase, they cancel out, and the water in the tank is smooth. If they are between those two extremes, the additive effect is intermediate. This phenomenon is known as "interference".
Radio waves also have phase and can interfere. A single transmission may go from point A to point B by various paths. For example, one path may be a straight line, while another may be a long path due to a reflection or "bounce" off a mountain. Such "multipath effects" cause the "ghosting" sometimes seen on TV transmissions, with a faint image slightly offset from the main image. They can also cause "phase delays" that seem to alter the direction of the beam by interference. Controlled interference effects can be used to deliberately shift the direction of a radio beam, a scheme known as "electronic steering" and discussed later.
* One final comment before moving on to radio and radar technology: radio waves generally propagate over a line-of-sight, weakening with distance, as anybody who's driven from town to town in a car with a radio realizes, with the music fading out as one town is left behind, and becoming stronger as another town is approached.
The radio waves can propagate through the sky or over the ground, and as noted can often propagate by multiple paths. At night, radio waves can bounce off the ionospheric layer in the upper atmosphere, allowing them to propagate over the horizon, if in a somewhat unpredictable fashion. Such "ionospheric bounce" tends to work better at lower frequencies. Anybody's who's ever played around with a broadcast radio receiver late at night knows remote stations can be picked up, sometimes over great distances.
Other atmospheric effects can interfere with radio signals. Higher frequencies can be blocked by heavy rainstorms or snowstorms, and lightning can thrown "noise" into radio transmissions. Particle flows from eruptions on the Sun can cause massive disruptions of radio communications. There is also a variable background of radio noise from human sources that can cause unwanted interference.
Radio waves vary in their interactions with solid matter. Radio waves, like light, can be absorbed or reflected by matter. Metals and water, for example, tend to reflect radio waves, while soils tend to absorb them. Also as with light, radio reflections can be "specular", as if bounced off a mirror, or "diffuse", as if bounced off a rough and uneven surface.
If radio waves can penetrate a material, the penetration is greater at longer wavelengths. Radio wave can penetrate buildings well enough, and very long wavelength can even penetrate a good depth through the sea or into the ground. Very short wavelengths are strongly attenuated and have limited range.
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[1.3] RADIO SYSTEM BASICS
* A radar system is basically an evolution of a radio system, and it is
useful to define the basic elements of a radio system first.
A radio system consists of a "transmitter" that produces radio waves and one or more "receivers" that pick them up, with both transmitter and receiver(s) fitted with antennas. The very earliest "wireless telegraphy" radio systems used a transmitter that simply generated a burst of radio energy by opening an electric circuit with a telegraph key and causing a spark. The radio waves propagated through space and set up an electric current in a receiving antenna, which in turn closed a relay switch, possibly using an "amplifier" circuit to boost the electrical signal. Messages were sent using Morse code.
The problem with this simple scheme is that the spark generated waves over a wide and indiscriminate range of frequencies, with a single receiver picking up and mixing up transmissions from every transmitter in the line of sight.
The way to get around this problem is to fit each transmitter with a "variable oscillator", an electronic circuit that generates electrical signals at different frequencies, as set by a knob turned by the transmitter operator. Receivers are then fitted with a "variable filter", another electronic circuit that can be set by a knob turned by the receiver operator to block out all frequencies except one.
This scheme allows multiple transmitters to operate in a given area without interference. The transmitter operator sets the transmitter oscillator to a given frequency; the receiver operator sets the receiver filter to the same frequency; and the transmitter operator uses a telegraph key to turn the output of an oscillator on and off, with the receiver operator picking up the output over the airwaves. The receiver will usually be fitted with a "detector" circuit to convert high-frequency signals into a direct-current signal to activate the relay switch.
This is obviously the same concept that is used in tuning a voice radio to different channels, though a voice radio works somewhat differently from a radio telegraph. A voice radio also uses a variable oscillator. The voice of a user is converted into an electrical waveform which is "mixed" with the output of the oscillator, shifting the voice signal up in frequency to that of the oscillator, and transmitted. The oscillator frequency is known as the "carrier" frequency, since it "carries" the voice signal.
The receiver has its own variable oscillator, tuned to the same carrier frequency, which is mixed with the received signal, a process that somewhat magically obtains the original voice waveform. The voice waveform is converted back into sound through a loudspeaker.
The process of converting a voice (or music or whatever) into an electrical signal is known as "modulation". There are two classic forms of modulation: "amplitude modulation (AM)", in which the electrical signal varies in amplitude along with variations in amplitude of the voice input; and "frequency modulation (FM)", in which the electrical signal varies in frequency along with variations in the amplitude of the voice input. The process of mixing and unmixing frequencies is known as "heterodyning".
In many cases, heterodyning is used to translate a voice or other signal up to an "intermediate frequency", which is then heterodyned again to produce an output signal of even higher frequency. This is done because it gets more difficult to handle signals at higher frequencies, and this scheme, known as "superheterodyning", allows most of the handling to be performed at the intermediate frequency.
A traditional analog television signal is conceptually much the same as a voice radio. The TV sound track is transmitted with FM, while the basic visual signal, which is black and white, is transmitted by AM. There are various schemes used in different nations for overlaying color signals, but they are devious and irrelevant to this discussion.
Incidentally, transmitter output power is measured in watts, or (as far as radar is concerned) more usually kilowatts (kW, thousands of watts) and megawatts (MW, millions of watts). Receiver "sensititivity", or the ability of the receiver to amplify received signals, is determined in terms of "decibels", defined as:
decibels = 10 * LOG10( output_power / input_power )
The amplification factor is commonly referred to as "gain".
Incidentally, a radio doesn't transmit or receive on a single frequency
but on a range or band of frequencies. Although the details are beyond
the scope of this simple document, the "bandwidth" is roughly
proportional to the amount of information carried by the signal. A TV
channel needs more bandwidth than a hi-fidelity radio channel, for example,
just as a hi-fidelity radio channel needs more bandwidth than a low-fidelity
radio channel.
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[1.4] ANTENNA BASICS
* A transmitter needs an antenna to send its radio signal, and a receiver
needs an antenna to pick up that radio signal. The design of these antennas
is not trivial.
The simplest form of antenna is the "dipole". Suppose the electrical output of an oscillator is directed down two conductors, not connected at the ends. This will produce radiate electromagnetic energy from the open-circuit ends. It radiates energy much more effectively if the conductors are bent at the ends to form a right angle, with each bend being a quarter-wavelength long relative to the oscillator frequency.
This is a "half-wave" dipole. It is not only effective in generating radio waves at a particular frequency, it is also effective in picking them up. This is true in general of all antennas: they are "reciprocal", working much the same in transmission or reception, just in different directions.
By itself, a dipole "broadcasts" in all radial directions evenly, but a directed focus can be obtained, through interference effects, by building an antenna with multiple dipoles, spaced at carefully designed intervals. Such "dipole arrays" were common with early longwave radars, and in a modified form persist today.
Another way to create a "directional" antenna with a dipole is to mount it within a row of parallel conductive rods, with the rods of decreasing length to the "front" of the dipole (relative to the direction of focus) and of increasing length to the "back" of the dipole. This type of antenna is known as a "Yagi-Uda" or just "Yagi" antenna. It is recognizable as the modern broadcast TV antenna.
A conceptually simpler directional antenna is the parabolic dish. This is configuration familiar with a modern satellite-TV receiver. It's really very much the same as using a parabolic mirror to focus light, only the wavelength of electromagnetic radiation is longer. While parabolic dishes are usually circular, elliptical or cylindrical dishes with parabolic curvature can also be used if the radio beam needs to be focused along one axis but not along the other. An elliptical dish with the long axis vertical is used to create a narrow horizontal beam, useful for height-finding, while one with the long axis horizontal gives a narrow vertical beam, useful for surface targeting.
* Incidentally, directional antennas don't always generate all their radio output in a nice neat directional beam. They may generate "sidelobes" that cause unwanted transmissions to the sides of the beam, or a "backlobe" in the reverse direction. The sidelobes and backlobe not only produce signals in undesired directions, they also rob the main lobe of energy.
In addition, as a general rule, the larger the receiver dish, the greater the receiver sensitivity, since it creates a bigger "bucket" or "eye" to collect radio waves. However, the longer the wavelength, the bigger the dish has to be to focus the radio waves. Another little related fact is that the dish doesn't have to be solid. It can be a mesh, just as long as the mesh grid spacing is less than that of the radar operating wavelengths. This makes for a lighter antenna, and also one not so easily disturbed by the wind.
BACK_TO_TOP
[1.5] A SIMPLE PULSE RADAR SYSTEM
* A discussion of voice radio is useful for background in discussing simple
radar systems, but is also somewhat incidental, since a simple radar works
more like a wireless telegraphy set.
The best way to explain radar is to imagine that you are standing on one side of a canyon, and shout in the direction of the distant wall of the canyon. After a few moments, you will hear an echo. The length of time it takes an echo to come back is directly related to how far away the distant canyon wall is. Double the distance, and the length of time doubles as well.
If you know that the speed of sound is about 1,200 KPH (745 MPH) at sea level, then if you have a stopwatch you can actually figure out how far away the distant canyon wall is. If it takes four seconds for the echo to come back, then since sound travels about 330 meters (1,080 feet) in a second, the distance is about 660 meters (2,160 feet).
Radar uses exactly the same principle, but it times echoes of radio or microwave pulses and not sound. Like a wireless telegraphy set, a simple radar has a transmitter and a receiver that can usually be tuned to a range of frequencies, with the transmitter sending out pulses, short bursts, of electromagnetic radiation and the receiver picking them up.
In the case of the radar, the receiver is picking up echoes from a distant target, which are then timed to determine the distance to the target. Early radars simply used an oscilloscope to perform the timing. An oscilloscope measures an electrical signal on a beam that moves or "sweeps" from one side of a display to the other at a certain rate. The rate is determined by a "timebase" circuit in the oscilloscope.
For example, the sweep rate might push the sweep from one side of the display to the other in 100 microseconds (millionths of a second). If the display were marked into ten intervals, that would mean the sweep would pass through each interval in ten microseconds. While 100 microseconds would be shorter than the human eye could follow, the sweep is normally generated repeatedly, allowing the eye to see it.
Since electromagnetic radiation propagates at 300,000,000 meters per second, or 300 meters per microsecond, then each 10 microsecond interval would correspond to 3,000 meters, or 3 kilometers. If the sweep on the scope is "triggered" to start when the radar transmitter sends out the radio pulse, and the sweep displays an echo on the eighth interval on the display, then the pulse has traveled a total of 8 kilometers. Since this is the two-way distance, that means that the target is 4 kilometers away.
* The display scheme described here is known as an "A scope", and allows the user to determine the range to a target. It would also be nice to know what the direction to the target is, in terms of its "altitude (vertical direction)" and "range (left to right direction".
This is a bit trickier to describe, but no more complicated in the end. Some early radars, like the famous British "Chain Home" sets that helped win the Battle of Britain, simply transmitted radio waves out in a flood over their field of view, and used a directional receiver antenna to determine the direction of the echo. Chain Home actually used a scheme where the power of the echo was compared at separated receiver antennas to give the direction, which astoundingly actually worked reasonably well. Other such "floodlight" radars used directional receiver antennas that could be steered to identify the direction of the echo.
Floodlight radars were quickly abandoned. They spread their radio energy over a wide area, meaning that any echo was faint and so range was limited. The next step was to make a radar with steerable antennas. For example, two directional antennas, one for the transmitter and the other for the receiver, could be placed on a steerable mount and pointed like a searchlight.
The transmitter antenna generated a narrow beam that could be steered like a searchlight, and if the beam hit a target, an echo would be picked up by the receiving antenna on the same mount. The direction of the antennas naturally gave the direction to the target, at least to an accuracy limited by the width in degrees of the beam, while the distance to the target was given by the trace on the A-scope.
Of course, it would be more economical and easier to use one antenna for both transmit and receive instead of separate antennas, and it was possible because a radar transmits a pulse and then waits for an echo, meaning it doesn't transmit and receive at the same time. The problem is that the receiver is designed to listen for a faint echo, while the transmitter is designed to send out a powerful pulse. If the receiver were directly linked to the transmitter when a pulse is sent out, the receiver would be fried.
The solution to this problem was the "duplexer", a circuit element that protects the receiver, effectively becoming an open connection while the transmit pulse was being sent, and then closing again immediately afterward so that the receiver could pick up the echo. The receiver is also generally fitted with a "limiter" circuit that blocked out any signals above a certain power level. This prevents, say, transmissions from another nearby radar from destroying the receiver.
* After this evolution of steps, we have a simple, workable radar. It has a single, steerable antenna that can be pointed like a searchlight. The antenna repeatedly sends out a radio pulse and picks up any echoes reflected from a target. An A-scope display gives the interval from the time the pulse is sent out and the time the echo is received, allowing the operator to determine the distance to the target.
The transmitter emits pulses on a regular interval, typically a few dozen or a few hundred times a second, with the A scope trace triggered each time the transmitter sends out a pulse. The number of pulses sent out each second is known as the "pulse repetition rate" or more generally as the "pulse repetition frequency (PRF)", measured in hertz.
The width of a pulse is an important but tricky consideration. The longer the pulse, the more energy sent out, improving sensitivity and range. Unfortunately, the longer the pulse, the harder it is to precisely estimate range. For example, a pulse that last 2 microseconds is 600 meters long, and in that case there is no real way to determine the range to an accuracy of better than 600 meters, and there is also no way to track a target that is closer than 600 meters. In addition, a long pulse makes it hard to pick out two targets that are close together, since they show up as a single echo.
PRF is another tricky consideration. The higher the PRF, the more energy is pumped out, again improving sensitivity and range. The problem is that it makes no sense to send out pulses at a rate faster than echoes come back, since if the radar sends a pulse and then gets back an echo from an earlier pulse, the operator is likely to be confused by the "ghost echo". This is actually not too much of a problem, since a little quick calculation shows that even a PRF of 1,000 gives enough time to get an echo back from 150 kilometers (185 miles) away before the next pulse goes out.
However, propagation of radar waves can be freakishly affected by atmospheric conditions, and sometimes radars can get back echoes from well beyond their design range. This is why radars were developed that could be switched between two different PRFs. Switching from one PRF to another would not affect an echo from the current pulse, since the timing would remain the same, but such a switching would cause a ghost return from a current pulse to jump on the display.
* Incidentally, the power of the pulse is given as "peak power", usually in kilowatts or megawatts. This may be an impressive value, but it's only the power that goes into the pulse itself. Suppose we have a pulse width of 2 microseconds with a peak power of 150 kilowatts. If we have a PRF of 500, then the time from pulse to pulse, or "pulse period", is 1/500 = 2 milliseconds, or two thousandths of a second.
This means that the average power transmitted by our radar is only:
150 kW * ( 2 microseconds / 2 milliseconds) = 0.15 kW = 150 watts
-- which is about as much as the power draw of a bright household light bulb.
