Module 18 − Radar Principles
Index−1 to 3
Learning objectives are stated at the beginning of each chapter. These learning objectives serve as a preview
of the information you are expected to learn in the chapter. The comprehensive check questions are based on the
objectives. By successfully completing the OCC/ECC, you indicate that you have met the objectives and have learned
the information. The learning objectives are listed below.
1. Define range, bearing, and altitude as they
relate to a radar system.
2. Discuss how pulse width, peak power, and beam width affect radar performance.
3. Describe the factors that contribute to or detract from radar accuracy.
4. Using a block diagram,
describe the basic function, principles of operation, and interrelationships of the basic units of a radar system.
5. Explain the various ways in which radar systems are classified, including the standard
6. Explain the basic operation of cw, pulse, and Doppler radar systems.
Introduction to RADAR FUNDAMENTALS
The term RADAR is common in today's everyday language. You probably use it yourself when referring to a method
of recording the speed of a moving object. The term Radar is an acronym made up of the words radio detection and
ranging. The term is used to refer to electronic equipment that detect the presence, direction, height, and
distance of objects by using reflected electromagnetic energy. Electromagnetic energy of the frequency used for
radar is unaffected by darkness and also penetrates weather to some degree, depending on frequency. It permits
radar systems to determine the positions of ships, planes, and land masses that are invisible to the naked eye
because of distance, darkness, or weather.
The develoPMent of radar into the highly complex systems in use
today represents the accumulated develoPMents of many people and nations. The general principles of radar have
been known for a long time, but many electronics discoveries were necessary before a useful radar system could be
developed. World War II provided a strong incentive to develop practical radar, and early versions were in use
soon after the war began. Radar technology has improved in the years since the war. We now have radar systems that
are smaller, more efficient, and better than those early versions.
Modern radar systems are used for early
detection of surface or air objects and provide extremely accurate information on distance, direction, height, and
speed of the objects. Radar is also used to guide missiles to targets and direct the firing of gun systems. Other
types of radar provide long-distance surveillance and navigation information.
Basic RADAR CONCEPTS
The electronics 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 a return echo 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 figure 1-1. The radio-frequency (RF) energy is transmitted to and reflects from the reflecting object. a small
portion of the energy is reflected and 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
Figure 1-1. - Radar echo.
Note: The terms TARGET, RETurn, ECHO, CONTACT, OBJECT, and REFLECTING OBJECT are used
interchangeably throughout this module to indicate a surface or airborne object that has been detected by a radar
Radar systems also have some characteristics in common with telescopes. Both provide only a limited field of view
and require reference coordinate systems to define the positions of detected objects. If you describe the location
of an object as you see it through a telescope, you will most likely refer to prominent features of the landscape.
Radar requires a more precise reference system. Radar surface angular measurements are normally made in a
clockwise direction from TRUE NORTH, as shown in figure 1-2, or from the heading line of a ship or aircraft. The
surface of the earth is represented by an imaginary flat plane, tangent (or parallel) to the earth's surface at
that location. This plane is referred to as the HORIZONTAL Plane. All angles in the up direction are measured in a
second imaginary plane that is perpendicular to the horizontal plane.
Figure 1-2. - Radar reference coordinates.
This second plane is called the VERTICAL Plane. The radar location is the center of this coordinate system.
The line from the radar set directly to the object is referred to as the LINE of SIGHT (los). The length of this
line is called RANGE. The angle between the horizontal plane and the los is the ELEVATION ANGLE. The angle
measured clockwise from true north in the horizontal plane is called the TRUE BEARING or AZIMUTH angle. These
three coordinates of range, bearing, and elevation describe the location of an object with respect to the antenna.
Q1. Radar surface-angular measurements are referenced to true north and measured in what plane?
distance from a radar set to a target measured along the line of sight is identified by what
Radar measurement of range, or distance, is made possible because of the properties of radiated
electromagnetic energy. This energy normally travels through space in a straight line, at a constant speed, and
will vary only slightly because of atmospheric and weather conditions. The effects atmosphere and weather have on
this energy will be discussed later in this chapter; however, for this discussion on determining range, these
effects will be temporarily ignored.
Electromagnetic energy travels through air at approximately the speed
of light, which is 186,000
STATUTE MILES per second. The Navy uses NAUTICAL MILES to calculate distances;
186,000 statute miles is approximately 162,000 nautical miles. While the distance of the statute mile is
approximately 5,280 feet, the distance for a nautical mile is approximately 6,080 feet.
Radar timing is
usually expressed in microseconds. To relate radar timing to distances traveled by radar energy, you should know
that radiated energy from a radar set travels at approximately 984 feet per microsecond. With the knowledge that a
nautical mile is approximately 6,080 feet, we can figure the approximate time required for radar energy to travel
one nautical mile using the following calculation:
The same answer can be obtained using yards instead of feet. In the following calculation, the 6,080 foot
approximation of a nautical mile is converted to 2,027 yards and energy speed is changed from 984 feet to 328
yards per microsecond:
A pulse-type radar set transmits a short burst of electromagnetic energy. Target range is determined by
measuring elapsed time while the pulse travels to and returns from the target. Because two-way travel
involved, a total time of 12.36 (6.18 x 2) microseconds per nautical mile will elapse between the start of the
pulse from the antenna and its return to the antenna from a target. This 12.36 microsecond time
sometimes referred to as a RADAR MILE, RADAR NAUTICAL MILE, or NAUTICAL RADAR MILE. The range in nautical miles to
an object can be found by measuring the elapsed time during a round trip of a radar pulse and dividing this
quantity by 12.36. In equation form, this is:
For example, if the elapsed time for an echo is 62 microseconds, then the distance is 5 miles, as shown in
the following calculation:
Note: Unless otherwise stated all distances will be expressed as nautical miles throughout this module.
Recall from NEETS, Module 11, Microwave Principles, that 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. As you probably already realize, timing of this switching action is
critical to the operation of the radar system. What you may not realize is that the minimum range ability of the
radar system is also affected by this timing. The two most important times in this action are PULSE WIDTH and
This timing action must be such that during the transmitted pulse (pulse width), only the transmitter
can be connected to the antenna. Immediately after the pulse is transmitted, the antenna must be reconnected to
The leading edge of the transmitted pulse causes the duplexer to align the antenna to the
transmitter. This action is essentially instantaneous. At the end of the transmitted pulse, the trailing edge of
the pulse causes the duplexer to line up the antenna with the receiver; however, this action is not instantaneous.
a small amount of time elapses at this point that is referred to as recovery time. Therefore, the total time in
which the receiver is unable to receive the reflected pulse is equal to the pulse width plus the recovery time.
Note that any reflected pulses from close targets returning before the receiver is connected to the antenna will
be undetected. The minimum range, in yards, at which a target can be detected is determined using the following
formula (pulse width and recovery time are expressed in microseconds or fractions of microseconds):
For example, minimum range for a radar system with a pulse width of 25 microseconds and a recovery time of
0.1 microseconds is figured as follows:
Most modern radar systems are designed with such small recovery times that this figure can often be ignored
when figuring minimum range.
The maximum range of a pulse
radar system depends upon CARRIER Frequency, PEAK Power of the transmitted pulse, PULSE-REPETITION Frequency (prf)
or PULSE REPETITION RATE (prr), and RECEIVER SENSITIVITY with PRF as the primary limiting factor. The peak power
of the pulse determines what maximum range the pulse can travel to a target and still return a usable echo. a
usable echo is the smallest signal detectable by a receiver system that can be processed and presented on an
The frequency of the RF energy in the pulse radiated by a radar is referred to as the CARRIER
Frequency of the radar system. The carrier frequency is often a limiting factor in the maximum range capability of
a radar system because radio frequency energy above 3,000 megahertz is rapidly attenuated by the atmosphere. This
decreases the usable range of radio-frequency energy. Therefore, as the carrier frequency is increased, the
transmitted power must also be increased to cover the same range. Long-range coverage is more easily achieved at
lower frequencies because atmospheric conditions have less effect on low-frequency energy.
radiate each pulse at the carrier frequency during transmit time, wait for returning echoes during listening or
rest time, and then radiate a second pulse, as shown in figure 1-3. The number of pulses radiated in one second is
called the pulse-repetition frequency (prf), or the pulse-repetition rate (prr). The time between the beginning of
one pulse and the start of the next pulse is called PULSE- REPETITION TIME (prt) and is equal to the reciprocal of
PRF as follows:
Figure 1-3. - Radar pulse relationships.
AMBIGUOUS RETurns. - The radar timing system must be reset to zero each time a pulse
is radiated. This is to ensure that the range detected is measured from time zero each time. The prt of the radar
becomes important in maximum range determination because target return times that exceed the prt of the radar
system appear at incorrect locations (ranges) on the radar screen. Returns that appear at these incorrect ranges
are referred to as AMBIGUOUS RETurns or SECOND-SWEEP ECHOES.
Figure 1-4 illustrates a radar system with a
1 millisecond prt. The pulses are shown at the top, and examples of two transmitted pulses hitting targets and
returning are shown at the bottom. In the case of target A, the pulse travels round trip in 0.5 millisecond, which
equates to a target range of 82,000 yards. Since 0.5 millisecond is less than 1 millisecond, displaying a correct
range is no problem. However, target B is 196,800 yards distant from the radar system. In this case, total pulse
travel time is 1.2 milliseconds and exceeds the prt limitation of 1 millisecond for this radar. While the first
transmitted pulse is traveling to and returning from target B, a second pulse is transmitted and the radar system
is reset to 0 again. The first pulse from target B continues its journey back to the radar system, but arrives
during the timing period for the second pulse. This results in an inaccurate reading. In this case, the first
return pulse from target B arrives 0.2 millisecond into the second timing period. This results in a range of
32,800 yards instead of the actual 196,800 yards. You should see from this example that pulse returns in excess of
the prt of the radar system result in ambiguous ranges while pulse returns within the prt limits result in
normal (unambiguous) ranges. The maximum unambiguous range for a given radar system can be
determined by the following formula:
Figure 1-4. - Maximum unambiguous range.
Q3. What is the speed of electromagnetic energy traveling through air?
Q4. How much time is
required for electromagnetic energy to travel 1 nautical mile and return to the source?
Q5. In addition
to recovery time, what determines the minimum range of a radar set?
Frequency and Power CALCULATIONS. - The energy content of a continuous-wave radar transmission may be
easily figured because the transmitter operates continuously. However, pulsed radar transmitters are switched on
and off to provide range timing information with each pulse. The resulting waveform for a transmitter was shown in
figure 1-3. The amount of energy in this waveform is important because maximum range is directly related to
transmitter output power. The more energy the radar system transmits, the greater the target detection range will
be. The energy content of the pulse is equal to the PEAK (maximum) Power LEVEL of the pulse multiplied by the
pulse width. However, meters used to measure power in a radar system do so over a period of time that is longer
than the pulse width. For this reason, pulse-repetition time is included in the power calculations for
transmitters. Power measured over such a period of time is referred to as AVERAGE Power. Figure 1-5 illustrates
the way this average power would be shown as the total energy content of the pulse. The shaded area represents the
total energy content of the pulse; the crosshatched area represents average power and is equal to peak power
spread out over the prt. (Keep in mind, as you look at figure 1-5, that no energy is actually present between
pulses in a pulsed radar
system. The figure is drawn just to show you how average power is calculated.) Pulse-repetition time
is used to help figure average power because it defines the total time from the beginning of one pulse to the
beginning of the next pulse. Average power is figured as follows:
Figure 1-5. - Pulse energy content.
Because 1/prt is equal to prf, the formula may be written as follows:
The product of pulse width (pw) and pulse-repetition frequency (prf) in the above formula is called the DUTY
Cycle of a radar system. The duty cycle is a ratio of the time on to the time off of the transmitter, as shown in
figure 1-6. The duty cycle is used to calculate both the peak power and average power of a radar system. The
formula for duty cycle is shown below:
Note: Pulse repetition frequency (prf) and pulse repetition rate (prr) are interchangeable
Figure 1-6. - Duty cycle.
Since the duty cycle of a radar is usually known, the most common formula for average power is
Transposing the above formula gives us a common formula for peak power:
Peak power must be calculated more often than average power. This is because, as previously mentioned, most
measurement instruments measure average power directly. An example is shown below:
Before figuring Pp, you must figure duty cycle as follows:
Now that you have duty cycle, Pp may be calculated as follows:
Antenna HEIGHT and SPEED. - Another factor affecting radar range is antenna height. The
high-frequency energy transmitted by a radar system travels in a straight line and does not normally bend to
conform to the curvature of the earth. Because of this, the height of both the antenna and the target are factors
in detection range. The distance to the horizon (in nautical miles) for a radar system varies with the height of
the antenna according to the following formula:
For example, assume antenna height to be 64 feet in the following calculations:
A target at a range greater than the radar horizon will not be detected unless it is high enough to be above
the horizon. An example of the antenna- and target-height relationship is shown in figure 1-7.
Figure 1-7. - Radar horizon.
The antenna-rotation rate also affects maximum detection range. The slower an antenna rotates, the greater
the detection range of a radar system. When the antenna is rotated at 10 revolutions per minute (rPM), the beam of
energy strikes each target for just one-half the time it would if the rotation were 5 rPM.
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