Radar System Engineering
Chapter -1
Radar Fundamentals
   Bewnet Getachew
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
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, as
                                            Shown in Fig 1.1
                            Fig 1.1 Radar principles
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 of the
reflecting object.
   Simplified Radar Block Diagram
                     Antenna
                                                       Target
              Waveguide
Transmitter                                 Receiver
                     Duplexer
                                  Signal
                   Master       processor
Modulator          clock       (computer)
     Pulse Radar Components
Synchronizer                     Transmitter
                                                 RF
                                                    Ou
                                                      t
               Power
                                      Duplexer              ANT.
               Supply
                                                     o In
                                                 Ec h
Display Unit                      Receiver
               Antenna Control
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).
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. After the pulse has been sent, the
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 range
            of the target.
1.3 Determination of co-ordinates in Radar
Radar requires a more precise reference system.
     Fig 1.2 Radar reference coordinates
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.
These three coordinates of range, bearing and elevation describes the
location of an object with respect to the antenna.
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
   Amplitud
                                                                 Time
   e
                   PW          R
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
  where σ = target cross section
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
Example
Calculate the maximum range (Rmax) for radar system shown below.
Pt = 150Kw
G = 40dB
σ = 6 m2
  min = 2.5x10 mw
S             -9
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.
                PRF=1/PRT
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=
      Pav(Average Power)=Pt x
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.
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
   Maximum range of radar1ms
c) power
               1Mw
                 1 μs             Time
 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.
                                                Fig 1.3 True
                                                and Relative
                                                Bearing
Antenna in position A
                               Antenna in position B
                Fig 1.4 Determination of 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 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 area with respect to the radar site and to
determine distance, direction of travel, and relative speed.
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
ranges.
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
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
                                               Onlypoints
                                                        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
                                                distinguished as two
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.
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.
Fig 1.6 Radar Classifications
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).
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).
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.
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.
1.7 Radar Frequencies
              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
       K              18-27 GHz.      Little used (H20 absorption)
       K a            27-40 GHz.     Very high resolution mapping,
                                          airport surveillance
      mm             40-100+ GHz.            Experimental
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.
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.
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.
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