Radar uses electromagnetic pulses and antennas to detect objects at a distance. It works by transmitting pulses that reflect off objects and return to the radar receiver. This allows radar to determine characteristics of detected objects like range, velocity, and bearing. The key components of a radar system are the transmitter, receiver, power supply, synchronizer, duplexer, antenna, and display. The radar equation relates system parameters like transmitted power, antenna gain, target radar cross section, and wavelength to the maximum detectable range. Common pulse parameters include pulse width, repetition time and frequency, and duty cycle. Bearing is the angular position of a target measured in the horizontal or vertical plane.

1. Radar Fundamentals
Bewnet Getachew
Radar System Engineering
Chapter -1

2. 1.1 Introduction
1.2 Radar Block Diagram
1.3 Determination of co-ordinates in Radar
1.4 Parameters of Radar pulse.
1.5 Applications of Radar
1.6 Radar Frequencies
1.7 Different types of Radar
1.8 Basic Pulse Radar system
1.9 Radar range equation

3. 1.1 Introduction
The word radar is an abbreviation for Radio Detection And
Ranging. In general, radar systems use modulated
waveforms and directive antennas to transmit
electromagnetic energy into a specific volume in space to
search for targets. Objects (targets) within a search volume
will reflect portions of this energy (radar returns or echoes)
back to the radar. These echoes are then processed by the
radar receiver to extract target information such as range,
velocity, angular position, and other target identifying
characteristics.
Radar has ability to measure distance with high accuracy in
all weather conditions.
Radar uses EM energy
Pulses in the same way,
Shown in Fig 1.1
Fig 1.1 Radar principles

4. 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.
Radar set use the echo to determine the direction and distance

5. Transmitter Receiver
Modulator
Master
clock
Signal
processor
(computer)
Duplexer
Waveguide
Target
Antenna
Simplified Radar Block Diagram

6. Pulse Radar
Components
Synchronizer Transmitter
Display Unit Receiver
Power
Supply
ANT.
Duplexer
Antenna Control

7. A practical Radar system requires seven basic components.
1. Transmitter
The transmitter creates the radio waves to be sent and
modulates it to form the pulse train. The transmitter must also
amplify the signal to a high power level to provide adequate
range.
The source of the carrier wave could be:
--Klystron
--Travelling wave Tube (TWT)
--Magnetron
2. Receiver
The receiver is sensitive to the range of frequencies being
transmitted and provides amplification of the returned signal.
In order to provide the greatest range, the receiver must be
very sensitive without introducing excessive noise. The ability
to discern a received signal from background noise depends
on the signal-to-noise ratio (S/N).

8. 3. Power Supply
The power supply provides the electrical power for all the
components. The largest consumer of power is the
transmitter, which may require several KW of average power.
4. Synchronizer
The synchronizer coordinates the timing for range
determination. It regulates the rate at which pulses are sent
(i.e sets PRF) and resets the timing clock for range
determination for each pulse. Signals from the synchronizer
are sent simultaneously to the transmitter, which sends a new
pulse, and to the display, which resets the return sweep.
5. Duplexer
This is a switch that alternately connects the transmitter or
receiver to the antenna. Its purpose is to protect the receiver
from high power output of the transmitter. During the
transmission of an outgoing pulse, the duplexer will be
aligned to the transmitter for the duration of the pulse, PW.

9. 6. Antenna
The antenna takes the radar pulse from the transmitter and
puts it into the air. Furthermore, the antenna must focus the
energy into a well-defined beam, which increases the power
and permits a determination of the direction of the target.
Tracking antenna
1. synchro-transmitter (physically moved)
2. Phased array antenna (electronically steered)
7. Display
The display unit may take a variety of forms but in general is
designed to present the received information to an operator.
Radar display
1. A-scan (amplitude Vs Time delay)
--Provides no information about the direction of the
target.
2. Plan Position Indicator (PPI)
-- Provides information about both the direction and

11. Fig 1.2 Radar reference coordinates
1.3 Determination of co-ordinates in Radar
Radar requires a more precise reference system.

13. Radar surface angular measurements are normally made in
clockwise direction from TRUE NORTH.
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.
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.

14. 1.3.1 RANGE
The detection and ranging part of the radar is accomplished by timing the
delay between transmission of a pulse of radio energy and its subsequent
return.
If the time delay is ∆t, then the range may be determined by simple formula:
R=c x ( )
Where c=3x108 m/s, the speed of light at which all EM waves propagate.
The factor of two in the formula comes from the observation that the radar
pulse must travel to the target and back before detection, or twice the
range.
A radar pulse train is a type of amplitude modulation of the radar frequency
carrier wave. The common radar carrier modulation, known as the pulse
train is shown below. PRT
Time
Amplitud
e
R
PW

15. 1.8 The Radar Equation
The Radar equation is an important tool for following aspects:
1. Assessing the performance of radar.
2. Designing of new radar systems.
3. Assessing the technical requirement for new radar
procurement.
power density at range R from an isotropic antenna
Pt = power of radar Tx
R = Distance from radar
power density at range R from directive antenna of power gain “G”
The target intercepts a portion of the incident energy and re
radiates it in various directions. It is only the power density re
radiates in the direction of radar that is of interest. The radar cross
section of the target determines the power density returned to the
radar.
Reradiated power density back at the radar

17. The Radar antenna received a portion of the echo power. If the
effective area of receiving antenna is denoted Ae , the power
received by the radar is
The maximum range of radar Rmax is the distance beyond
which the target can not detected. It occurs when the received
signal power Pr just equals the minimum detectable signal
(Smin).
Substituting Smin = Pr
Where Pt=transmitter power
G= maximum gain of antenna
Ae= Effective area of receiving antenna
s = target cross section
Smin = minimum detectable signal

18. Example
Calculate the maximum range (Rmax) for radar system shown below.
Pt = 150Kw
G = 40dB
σ = 6 m2
S
min = 2.5x10-9 mw

19. Common parameters of Radar Pulse
Pulse Width (PW)
PW has units of time and commonly expressed in ms. PW is
the duration of the pulse.
Rest Time (RT)
RT is the interval between pulses. This is the period when Tx
is silence (not firing) and Rx is ready to receive the reflected
signal from the target. It is measured in ms.
Pulse Repetition Time (PRT)
PRT has units of time and is commonly expressed in ms. PRT
is the interval between the start of one pulse and the start of
another. PRT is equal to the sum of pulse width and rest time.
PRT=PW+RT
Pulse Repetition Frequency (PRF)
PRF has units of time-1 and is commonly expressed in Hz
(1Hz=1/s) or as pulse per second (pps). PRF is the number of
pulses transmitted per second and is equal to the inverse of
PRT.

20. Radio Frequency (RF)
RF has units of time-1 or Hz and is commonly expressed in
GHz or MHz. RF is the frequency of the carrier wave which is
being modulated to form the pulse train.
Peak power (Pt)
The power Pt in the radar equation is called by the radar
engineer, the peak power. The Peak power as used in the
radar equation is not the instantaneous peak power of the sine
wave. It is defined as the power averaged over that carrier
frequency cycle which occurs at the maximum of the pulse
power. Peak power is usually equal to one-half of the
maximum instantaneous power.
Average Power (Pav)
The Average Power (Pav) is defined as the average
transmitted power over the pulse repetition time or period. If
the transmitted waveform is a train of rectangular pulses of
width and pulse repetition period or time
PRT=

21. Average Power = Peak Power x Pulse width/PRT
= Peak power x Pulse width x PRF
Duty Cycle
The ratio of average power to the peak power or pulse width to the PRT or
pulse width multiplied by PRF is called Duty Cycle of the radar.
Duty Cycle = Pav/Pt
= PW/PRT
= PW x PRF
Example 1
The pulse width of a radar is 1μs and PRF of 1000 Hz. If the radar peak
power is 500 KW, calculate the Duty cycle and average power of the radar.
Example 2
Calculate the range of a target if the time taken by the radar signal to travel
to the target and back is 100μs.
Example 3
If the transmitted peak power of a radar is 100KW, pulse repetition
frequency is 1000 pps and pulse width is 1 μs then calculate the average
power in dbs.

22. Example 4
A typical pulse waveform of a radar is shown below. In which
some parameters of radar is shown. Calculate the (a) Average
power, (b) Duty Cycle
c) Maximum range of radar
power
1Mw
Time
1 μs
1ms
1.3.2 BEARING
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.

23. Fig 1.3 True
and Relative
Bearing
Fig 1.4 Determination of Bearing
Antenna in position A
Antenna in position B

24. 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 Fig
1.4, the shape of the beam is such that the echo signal
strength varies in amplitude as the antenna beam moves
across the target.
At antenna position A, the echo is minimal; at position B,
where the beam axis is pointing directly at the target, the echo
strength is maximum.
1.3.3 Altitude
Many radar systems are designed to determine only the range
and bearing of an object. Such radar systems are called
TWO-DIMENTIONAL (2D) radars. In most cases these
systems are further described as SEARCH RADAR
SYSTEMS and function as early-warning devices that search
a fixed volume of space. The range and bearing coordinates
provide enough information to place the target in a general

25. However, when action must be taken against an airborne
target, altitude must be known as well. An altitude is height of
the target from the ground plane. A search radar system that
detects altitude as well as range and bearing is called a
THREE-DIMENSIONAL (3D) radar. The display system use
for indicating the height of the target is known as Height
Measuring Indicator (HMI).
1.4 Target Resolution
The Target Resolution of a radar is its ability to distinguish
between targets that are very close together in either range or
bearing.
Resolution is usually divided into two categories:
1. Range Resolution
2. Bearing Resolution
1.4.1 Range Resolution
Range Resolution is the ability of a radar system to distinguish
between two or more targets on the same bearing but different

26. The degree of range resolution depends on
 width of transmitted pulse
 types and sizes of targets
 the efficiency of the receiver and indicator.
A well designed radar system should be able to distinguish
targets separated by one-half the pulse width time.
RRES = c x PW/2
The above formula is often written as:
RRES = c/2β (PW = 1/ β)
Where β is the bandwidth of transmitted pulse.
Example
If a radar system has a pulse width of 5 microseconds,
calculate the range resolution.
RRES = c x PW/2
RRES = 3 x 108 x 5 x 10-6 /2
= 3 x 5 x 102 /2 = 7.5 x 100
= 750 m

28. 1.4.2 Bearing Resolution
Bearing, or azimuth resolution is the ability of a radar system
to separate objects at the same range but at different bearings.
The degree of bearing resolution depends on
1. radar beam width
2. range of the targets.
Fig 1.5 Beam
half power
points
Only the targets
within the half
power points reflect
a useful echo.
Two targets at the
same range must
be separated by at
least one beam
width to be

29. Example 1
Determine the maximum unambiguous range and range
resolution of a pulse radar having pulse width of 5μs at a rate
of 1000Hz.
Example 2
A radar is to have a maximum range of 250 Km. Determine the
maximum allowable PRF for unambiguous reception.

30. 1.5 Radar Classifications
Radars can be classified as
 ground based,
 airborne,
 spaceborne, or
 ship based radar systems.
Another classification is concerned with the mission and/or the
functionality of the radar. This includes:
 weather,
 acquisition and search,
 tracking,
 track-while-scan,
 fire control,
 early warning,
 Over the horizon,
 terrain following, and
 terrain avoidance radars.

31. Fig 1.6 Radar Classifications

32. Primary Radar
A Primary radar transmits high-frequency signals which are
reflected at targets. The echoes are received and evaluated.
This means, unlike secondary radar units a primary radar unit
receives its own emitted signals as echo again.
Secondary Radar
At these radar units the airplane must have a transponder
(transmitting responder) on board and receives an encoded
signal of the secondary radar unit. An active also encoded
response signal, which is returned to the radar unit then is
generated in the transponder. In this response can be obtained
much more information, as a primary radar unit is able to
acquire (Eg. An altitude, an identification code or also any
technical problems on board such as a radio contact lose…).
Example of secondary radar is IFF (Identification of Friend and
Foe).

33. Radars are most often classified by the types of waveforms
they use, or by their operating frequency. Considering the
waveforms first, radars can be
 Continuous Wave (CW) or
 Pulsed Radars (PR).

34. CW radars
 are those that continuously emit electromagnetic energy,
and
use separate transmit and receive antennas.
Unmodulated CW radars can accurately measure target
radial velocity (Doppler shift) and angular position.
Target range information cannot be extracted without
utilizing some form of modulation.
The primary use of Unmodulated CW radars is in target
velocity search and track, and in missile guidance.

35. Pulsed radars
use a train of pulsed waveforms (mainly with modulation).
In this category, radar systems can be classified on the basis
of the Pulse Repetition Frequency (PRF), as
 low PRF, medium PRF, and
 high PRF radars.
Low PRF radars are primarily used for ranging where target
velocity (Doppler shift) is not of interest. High PRF radars are
mainly used to measure target velocity. Continuous wave as
well as pulsed radars can measure both target range and
radial velocity by utilizing different modulation schemes.

36. 1.7 Radar Frequencies

37. Radar Frequency Band
Band Designation Frequency Range Typical Usage
VHF 50-330 MHz Very long-range
surveillance
UHF 300-1,000 MHz Very long-range
surveillance
L 1-2 GHz. Long-range surveillance,
enroot traffic control
S 2-4 GHz. Moderate-range
surveillance, terminal
traffic control, long-range
weather
C 4-8 GHz. Long-range tracking,
airborne weather
X 8-12 GHz. Short-range tracking,
missile guidance,
mapping, marine radar,
airborne intercept
K u 12-18 GHz. High resolution mapping,
satellite altimetry

38. 1. HF (3 to 30MHz)
 Detect targets at long ranges (>2000Km)
 The targets for such HF Radar might be aircraft, ships, and
ballistic missile.
 Application example: weather radar (detects the echo from
sea surface which provides information about the direction
and speed of the wind)
2. VHF (30 to 300MHz)
 At the beginning of radar development in the 1930s, radars
were in this frequency band.
 It is good frequency for long range air surveillance or
detection of ballistic missiles.
 Very large reflection coefficient from earth surface and
water.
 Rarely used because this band is crowded with FM and TV
transmissions and interference.
 Application example: widely used in Russia as air
surveillance radar because it is less expensive.

39. 3. UHF (300 to 3000MHz)
 Good frequency for Airborne Moving Target Indicator
(AMTI) Radar.
 Long range radars for the detection and tracking of
satellites and ballistic missiles.
 Long range shipboard air surveillance radars.
 Wind profilers (radar used to measure speed and direction
of wind).
 Ground Penetrating Radar (GPR)
4. L-band (1.0 to 2.0 GHz)
 Air Route Surveillance Radar (ARSR).
 The effect of rain is significant.
5. S-band (2.0 to 4.0 GHz)
 The Aircraft Surveillance Radar (ASR) that monitors air
traffic within the region of an airport is at S- band.
 3D radars operates at S-band.
6. C-band (4.0 to 8.0 GHz)
 has properties of S-band and X-band.

40. 7. X-band (8.0 to 12GHz)
 Popular radar band for military applications. (Interceptor
and fighter)
 Imaging radars, civil marine radar, airborne weather
avoidance radar, airborne Doppler navigation radar, and
Police speed meter radar.
 High resolution applications.
8. Ku, K, and Ka Bands (12.0 to 40 GHz)
 The Airport Surface Detection Equipment (ASDE)
generally found on top of the control tower at major
airports has been at Ku band, primarily because of better
resolution than X-band.

41. Example 1
The following table lists the characteristics of the ground pulse
echo type search radar. Complete the table.
frequency 5600MHz
wavelength
Pulse width, PW 1.3μ sec
Pulse repetition frequency, PRF
Pulse repetition Time, PRT
Peak power
Average power
Duty cycle 0.00083
Effective area, Ae 0.9 m2
Power gain, G 3940
Receiver sensitivity, Smin -5.012x10-12
Maximum anambiguous range
Maximum range, Rmax 50Km
Minimum range, Rmin
Range resolution, Rres
Radar cross section, s 5 m2