Basic Radar Concepts

Introduction

        Radio detection and ranging is basically a means of gathering information about distance objects or targets by sending electromagnetic EM waves to them and therefore analyzing the reflected wave or signal. If an EM wave encounters a sudden change in conductivity, permittivity or permeability in the medium, a part of the electromagnetic energy is absorbed by the second medium and is re-radiated normally called as ECHO. This sudden change in the electrical property of the medium constitutes the target.

       The re-radiated energy on being received back at the radar station gives the information about the location of the target. The location of the target includes range, angle and velocity parameters. The range is the distance of the target from the radar station the angle is the azimuth or elevation angle and velocity is the speed of the target.

Fig-I   :    The  radar echo and  measurable quantities (range, azimuth and elevation angles)

                Radar requires a more precise reference system. Radar surface angular measurements are normally made in a clockwise direction from TRUE NORTH, as shown in Fig-I, 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.

              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

          For satisfactory location of the target, the received power (echo power) must be appreciable. Accordingly, the amount of power required to be radiated by the radar transmitter must be tremendous, typically few KW to MW.

Block Diagram:

          The most common form of radar is shown in the Fig-II. The simple radar consists of transmitting antenna receiving antenna connected to the transmitted Tx and the receiver R_x. Such radars are called as bistatic radars. The T_x transmits the EM radiation. A portion of this transmitted signal is intercepted by the target and is re-radiated in all directions. The receiver antenna collects the returned echo signal and delivers it to the receiver where it is processed to detect the presence of the target and to extract the relative velocity of the target.

fig –II  mostaic and bi static radars

Improved radar uses a single for both transmission and reception. The duplexer will isolate the transmitter and the receiver during transmission and reception. It also protects the receiver from high power transmitter. A single antenna can be used for both transmission and reception.. The received echo signal after it is being processed by the receiver is displayed on the radar screen.

Classification:

   Radar systems are broadly classified into two basic categories..

          Continuous ware(CW)/Doppler radars

           Pulsed Radars

      A continuous radar transmits a continuous wave signal and is generally useful in Doppler radars which utilizes the Doppler effect

      Pulsed radar is more useful than CW radar. Here a pulse waveform generally a train of narrow rectangle shaped pulsed modulating a sine wave carried is transmitted. The range is measured by the measuring the time T taken by the pulse to travel to the target and return to the radar station.  Since EM waves travel with  velocity  of light c, the range of the stationary target is given by    2R =cT

                       R= cT/2

The general requirements of any radar system are summarized below.

1. The duplexer should be automatic in operation
2. The radar Tx should remain silent during the echo period
3. The transmission pulse should be quiet powerful to counter the attenuation during forward and return journeys
4. The received echo signal being weak, the receiver should be extremely sensitive and at the same time immune to noise (clutter) signal. It should have necessary amplification signal processing circuitry and capability to display the target information.
5. The radar antenna should be highly directive and have larger gain so that it can radiate can radiate a strong and receive a weak signal.
6. Pulse repetition frequency(prf) of the radar should be high compared to the target scanning period  where prf is given by relation prf = duty cycle /pulse width  ie  a small duty cycle provides the necessary time required for the pulse to go to the target , get reflected and provide echo pulse of the radar receiver. Normally pulse widths will be in the range of .1u to 10usec. The average power depends on the transmitted power Pt and the duty cycle

                           P_av = P_t * duty cycle = Pt * Pulse width *prf..         ———-(!)

Standard-radar frequency band designation:

Band Designation	Nominal Frequency range ( GHz)	Specific radar bands based on  ITU Assignment (GHz)
L S C X Ku K Ka	1.0   –  2.0 2.0  – 4.0 4.0   -8.0 8.0 – 12.5 12.5    – 18 18.0   – 26.5 26.5   –  40.0	1.215 – 1.400 2.300 –2.5 5.250 – 5.925 8.5 –  10.68 13.40 – 14.0 , 15.70 -17.70 24.05  – 24.25 33.40 – 36.00

Free space radar range equations:

The radar equations relates the range of the radar o the characteristics of the T_x , R_x , antenna and the target. Free space actually means the radar system and the target are isolated in an unbounded empty space. It basically indicates that there are no obstacles between the radar station and the target.

     If the power transmitted by the radar antenna is P_t and the antenna is isotropic, then the power density at a distance R from the radar is equal to the transmitted power divided by the surface area of the sphere of the radius R..

                        =     P_t/4 π R²      watts/m2             ——————–(2)

Radars usually employee directive antennas to direct the transmitted power P_t into some particular direction .The gain G of the antenna is a measure of the increased power radiated in the direction of the target as compare to the power that would have been radiated from an isotropic antenna. Power density at a distance R from the directive antenna of gain G is

                      ==     P_t G/4 π R²      watts/m2     ——————–(3)

The target intercepts a portion of the incident power and radiates it in the various directions. A measure of amount of incident power intercepted by the target and re-radiated back in the direction of the radar is denoted as radar cross- section of target. The total power intercepted by the target having an area of xx is

                          ==     P_t G σ  /(4 π R² )  watts     —————————-(4)

σ is characteristics of a particular target and is a measure of its size and shape. The power density of the echo signal at the radar station is

                          ==    P_t Gσ / (4 π R² )²     watts     —————————-(5)

The radar antenna captures a portion of the echo signal. If the effective area of the receiving antenna is denoted by A_e, the power received by the radar is given by

                      P_r   =  (P_t G σ A_e )/(4 π R² )²     watts.    ——————————(6)

Maximum radar range (R_max) is the distance beyond which the target cannot be detect. It occurs when the received echo signal power Pr just equals the minimum detectable signal (S_min)  i.e.  when P_r=S_min,   R=R_min and when substituted

               S_min    =  (P_t G σ A_e )/(4 π R² )²     i.e.

              R_max = [(P_t G σ A_e )/(4 π)² S_min    ] ^(1/4)..                       ———————–(7)

From antenna theory we know that gain G = 4 π A_e/λ² where λ is wavelength of the radiated energy, so R_max can now be as

                              R_max = [(P_t σ A_e²   )/(4 π λ² S_min  )      ] ^(1/4)     —————–(8)

                         Also     R_max = [(P_t G² σ λ²    )/((4 π)² S_min  )  ] ^(1/4)

Factors affecting the range of the radar:

AS seen from the relation of the R_max , Rmax depends on the Pt frequency of the transmitted signal, cross section area  of the target and the minimum receiver signal.

Transmitter power: In case the radar range is to be doubled the Pt should be increase by 16 times since Rmax & P_t^(1/4).

Frequency: Rmax α 1/√(λ) or √(freq), this implies that increase in the frequency will increase the range of the . However this requirement is in conflict with the dependence of the beam width of the antenna which is directly proportional to the wavelength.

Target cross sectional area:  is the area of the target seen by the radar. IT is a characteristic of a particular target and is a measure of its size, shape and composition. It can also be defined as the area of the perfectly conduction flat plane , facing the source that would reflect the same amount of power

Minimum received signal power

            The minimum detectable signal at the receiver sets a limit on the receiver sensitivity i.e., the noise figure of the radar receiver is a factor that is to be controlled for obtaining larger Rmax. If Si/Ni is the signal to noise ratio at the input of the radar receiver, S0/No is the receiver output and G is the overall gain of the receiver. Then noise figure is given by

            F=(S_i/N_i)/(S_o/N_o) = S_iN_o/N_iS_o      ————————-(9)

 As S_o=GS_i     N_o=GN_i+∆N     where ∆N is the equivalent noise generated in the receiver.   From mathematical modifications

     F=1/G *(G+(∆N/Ni)     or F= 1+ (∆N/GNi).    But NI =KT_oB   So     ——–(10)

   ∆N = (F-1)GkTB..   If this equivalent noise power  at the input of the  receiver is more that the minimum signal receiver Smin, then it is not possible to detect  the target in the receiver. For the detection to be possible the minimum signal power must at least be equal to  equivalent noise. This will now modify the radar detection range  Rmax as

                             R_max = [(P_t σ A_e²   )/(4 π λ²  (F-1) GkTB ] ^(1/4)             ————–(11)

Pulsed Radar System :

 The block diagram of a high power pulsed radar set is shown in the Fig-III.

Detector

Fig –III Pulse radar block Diagram

The trigger source provides pulses for the modulator. Pulse modulator provides rectangular voltage pulses which acts as  the supply voltage to the output tube, thus switching it on and off as required. The output tube is an higher power amplifier or Magnetron oscillator like Klystron. The pulse modulated sine wave carrier then travels via the duplexer to the antenna which is radiated into the space. A single antenna is generally used for both transmission and reception. Usually parabolic reflectors with center feed are made use of.

The receiver is usually super heterodyne receiver whose function is to det4ect desired echo signal I the presence of noise, interference and clutter. The receiver in the pulsed radar consists of the RF amplifier, mixer, local oscillator, IF amplifier, Detector, Video amplifier and the radar display.

Design Specification

               From  the  roof of engineering north building flight path of the Adelaide airport can be viewed.  The distance from the engineering north building to the Adelaide airport will be several kilometers. A radar is to be set up on the roof of the engineering north building.

Requirements  of the radar:

                     The radar is to be installed on the top of the roof of the engineering north building.  The radar should be capable of detecting aircraft using a single pulse . The equipment must be capable of   estimating the radial component of aircraft speed also.
As the specifications indicate it is a detection type of radar.  For this application The radar is placed fixed in the direction of the airport . Here the radar system is fixed. It need not move  to scan for the target. Here we also assume that there  are no obstacles from the line of sight(LOC) of the radar system and the aircraft.

                   The radar should operate in the upper UHF and microwave range. For this particular application we shall choose will choose to operate it at L-band. To comply with the ITU regulations  the operating frequency if fixed at 1.3GHz in the L-band. The bandwidth of operation is 10MHz.  The spectral characteristics are required to meet the ITU regulations.

                    Amongst the types of radar systems available, Pulsed radar system is used. The radar  transmits a pulse  modulated over the sine wave of frequency 1.3GHz. The transmitted pulse with power Pt will be intercepted by the target and is reflected back .The echo is received by the receiver   and the range can be determined.

                     Same antenna is used for both transiting and receiving the signal from the radar and the target. The antenna must be directive with high gain to detect the weak signal from the receiver. Proper selection of the antenna and its design is of much concern for estimating the target range and properties.

Antenna Design :

                 Transmitting and receiving antennas designed for use in  UHF (0.3 –  3GHz) and microwave (1-100GHz) regions tend to be directive. The dimensions of the antenna should be several wavelengths in order for it to have high gain.

                Parabolic antenna is fixed  on the top of the  engineering building. The  parts that are of concern for the  design of the parabolic antenna is  antenna feed and aperture area of the antenna. Consider a source of radiation is placed at the focal point. This is called feed. The feed is usually horn feed or center-fed paraboloid reflector with spherical shell. All waves coming from the feed are reflected by the parabola will  travel the same distance by the time they reach the directrix of the parabola ,i.e. all the waves are I phase. This makes the radiation very strong and concentrate along the axis, but cancellation will take place in any other direction. This lead to production of concentrated beam of radiation.

          For designing the  dimensions of the parabolic reflector the parameters we need to consider  are    (1) the gain that is required   (2) beamwidth between half power points.

The beamwidth (θ) of the parabolic antenna is given by

                                                        θ = 70(λ/D) ———————————-(12)

where D is mouth diameter and    λ is the wavelength.

The gain of the antenna A_p is given by

                                   A_p = 6.4(D/λ) ²   ————————————–(13)

For the above equation –(11) we have considered a parabola fed by half-wave dipole.

 The diameter of the parabola is decided by the beamwidth and the antenna gain.

 Transmitter power and range estimation:

         The range of the target is expected to be several kilometers. For an optimistic design let us consider the range to be around 100KM.  The minimum signal that is  received after being reflected by the target S_min  is to be known prior to finding the transmitted power.   This S_min is strongly dependent on the sensitivity of the receiver and noise figure of the receiver.  So calculating these values is of much importance before proceeding to the calculations of the transmitted power.

           The simple practical set up for the calculation of the noise figure is done by connecting the diode noise generation circuit at the input of the receiver. The noise generated by the input diode circuitry is measured by the noise meter Ni. Now as the noise is amplified by the gain of the receiver and it is measured the output of the receiver by using a power meter. From this the Noise Figure F is calculated.  As to make the design more optimistic the nominal case is taken and the noise figure F is calculated to be 9dB.

            This noise figure will put a limitation on the strength of the minimum receivable signal for successful operation. The S_min is calculated as..

          S_min = kT δf (F-1)     K= Boltzman constant, T = absolute temperature (300^oK)

                        δf  =bandwidth of the receiver(10MHz)    F= Noise figure(9dB)

             F = antilog (9/10) =7.943

              S_min  = 1.38*10^-23 *300 *10*10⁶ * [7.943 -1]

                        = 1.38 * 10^-23 * 3*10⁰⁹*[6.943]

                         = 28.98 * 10 ^-14 watts

Antenna Diameter and feed: 

         The  antenna that is selected is parabolic reflector with half wave dipole as the feed.

The beamwidth of the radiation is expected to be around 4 degrees.

                                                          θ = 70(λ/D) = 4

but the frequency of operation is 1.3GHz so values  λ

                                   λ=v/f = (3*10¹⁰)/(1.3*10⁹)

                                          = 30/1.3 = 23.07 cms

   The diameter of the parabolic antenna is now

                             D = (70 * 23.07 )/4

                                  = 403.8 cms

       The actual capture area of the antenna is  A₀

                                               A_{0   =}    πD²/4

But the actual capture area  also depends on the feed that is used    A = K A₀    where K is a constant that depends on both antenna and feed.

 As  the feed that is used is a half pole dipole   the K =0.65.

                                    A = K A₀    =0.65 * πD²/4

                                     = 0.65*(22*403²)/(4*7)

                                    = 83314.285 cms²       

if  K = 1 is chosen to be

                           A =  129175.38 cms²

The maximum range the radar should operate is approximated to be 100KM, or equivalently 10⁷   cms.  The power to be transmitter for this range  of operation is proportional to the  forth power of the range. This will lead to the power in the range of few kilo watts. After the modulation stage we need to have oscillators or amplifiers like magnetrons , klystrons , Gunn diodes to generate such high wattage of power.  Before going into the type of the amplifier for the transmitter we shall calculate the total power required to transmit.

                               R_max = [(P_t  σ A² )/(4 π S_min  λ² )   ] ^(1/4)

                                             R_max ⁴ = (P_t  σ A² )/(4 π λ² S_min )        The only unknown parameter here is σ which is called the cross section area of he target The most commonly used values for σ for different targets is presented in the table.

Targets	Radar crosssection(m2 )
Insect Bird Conventional missile Small fighter aircraft Large fighter aircraft Commercial aircraft Jumbo jet Pick up truck	0.0001 0.01 0.5 2.0 6.0 40 100 200

     The table presented here is purely practical result based .

As the design here need to monitor medium to heavier aircrafts the minimum crosssection is taken into account. For this  σ comes to be 4 m² 

With  this all the necessary parameters required to calculate  the total transmitter power P^t  are available. So

                                                   R_max ⁴ = (P_t  σ A² )/(4 π λ² S_min  ) 

         10²⁸ =  ( P_t *4 *10⁴ * 83314.285²  )/( 4 π²  * 23.02²  * 28.98 * 10 ^-14 )

                         P_t  =    69.5 K watts

The signal power that is transmitted in  dB is obtained to be 10log(69.5*1000).

The signal power that is received at the receiver is  given by

                                       S_received = ( P_t G_t G_r σ λ²  )/ ((4π)³ R_max⁴ )

 As the transmitting and receiving antenna is same and there by their gains A_p

                         S_received    = ( P_t  σ A² )/(4 π λ² R_max ⁴)  after substitute the gain   G_t G_r     by their aperture area A =  πD²/4 =

                       S_received  = (69.5 *1000 * 4*100 *100 *127491.2²  ) / (4 π  * 23.02²  * 10²⁸)

                                   =   6.72*10^-13

The noise power is calculated to be N = =  kT δf(F-1)

                                                                 = 10log(1.38*10^-23 *200 *10*10⁶ ) +9dB

                                                                = 18.9 * 10 ^-14 watts

The  S/N =  10 log(S/N) = 10 log( 6.72*10^-13/18.98 * 10 ^-14)

                                       = 10 log(2.3)  = 5.517

The signal to noise (S/N) ratio  at the input of the receiver is obtained  to be  5.517dB

As the range for which the radar is designed for 100KM, it’s a reasonably good SNR obtained . For the dectection to be more accurate a threshold must be set such that the level above is the threshold indicate a target. This threshold point setting need expertise. Receiver is maintained at 200K by using coolants.

Clutter:

   One of the important factor that effect the performance of the radar is Clutter. Clutter is defined as the unwanted radar echo. Ground targets returns will include ground clutter and airborne targets may include volume clutter. Area clutter is characterized by the average clutter cross-section per unit area ( σ_O). This is called backscatter coefficient. The amount of clutter received depends upon how much ground area is illuminated.   The width of the clutter patch depends on the antenna azimuth beam width and the range of the clutter patch. The length of the clutter patch depends on range gate size or the elevation beam width. The width of the clutter cell is

                                    W=Rθ_AZ        R= range to the center to clutter cell

                                                            θ_AZ    =Azimuth beam width

The length of the clutter is defined as..

                             L_bw = Rθ_EA    /sin ψ                ψ    = gazing angle  and

                                                                           Θ_EA = Elevation angle

                             L_rg   =   cPW/ 2cos ψ

Fig- V  The angles are of the clutter identification

                                         L_clutter  = min ( L_sw, L_rg)

The clutter cross section is given by Ac =  clutterwidth  * clutter length

                                                          Ac = = Rθ_AZ (cPW/2) sec ψ     for a pulse limited

The actual clutter cross section is Ac * ( σ_O).  .

 Now the clutter reflection power seen at the radar is

                      P_clutter   =  (P_t Ap² A_c )/((4 π) ³ R⁴  )

                     P_clutter   =  (P_t Ap² Rθ_AZ (cPW/2) sec ψ σ_O )/((4 π) ³ R⁴  )

                   P_clutter   =  (P_t Ap² θ_AZ (cPW/2) sec ψ σ_O )/((4 π) ³ R³  ) ————————(16)

     Thus as R increases, the clutter power drops by 1/ R³, where as the target power drops by 1/ R⁴. This is due to beam spreading distance increasing the amount of the clutter that is seen.

  The effect of clutter can be mitigated by using the following steps.

(1) Use of narrow antenna beams  (2) shorter pulses

From the equation –(16)  the clutter power for the design above is calculated as

                   P_clutter   =  (P_t Ap² θ_AZ (cPW/2) sec ψ σ_O )/((4 π) ³ R³  )

                              = (P_t  θ_AZ *(6(D/λ)²)² (cPW/2) sec ψ σ_O )/((4 π) ³ R³  )

θ_AZ    = 0.3 degrees                   PW = pulse width = 0.14 micro secs

ψ     = 5 degrees                     Pt = 69.5Kwatts    D = 403cm

σ_O    = 0.01                              R = 100KM

 With all the above known parameters the clutter power is

              P_{clutter  =}  16*10^-14 * sec 5

                P_{clutter  =}   16 *10^-14

Probability of detection and probability of false alarm:

The performance of the radar is given by each of the following four parameters..

1. target resent when it is present
2. target not present : when it is present
3. target not present when it is not present
4. target present when it is not present

The first is called probability of detection P_d and the third one is calle probability false alarm P_fa . Fot the  detection of targets from the noise it is necessary that a threshold must be set. The problem of target decision is to find the appropriate threshold so that  noise pulses are eliminated and signal pulses are shown up.

  The noise that pre dominantly effects the target detection is radar receiver therman noise. An exponential distribution for the noise well suited where square law detectors are used. The exponential distribution is given by

                     f(x) = ∫ (1/θ)(ei^-x/θ   ) dx    x > 0 and x is the peak noise power in the received sample and  θ is called the  rms noise power where μ = θ is the mean and σ² =  θ ² is the variance and σ = θ   is the standard deviation.. The probability with which the noise will exceed this threshold is called false alarm detection.

Choice of Thershold point:              

    The  probabiltity distribution of the signal is having a constant amplitude with spike as its distribution(let us take the spike point as S). This signal invariably has noise added to it and  distribution of the resulting quantity is convolution of the noise + signal  which is well approximated with Gaussian distribution with a mean at S, the rms signal power and S>N for the radar to operate effectively.

   If Pd is to be > 90% then for a single pulse , it would mean that the threshold would be set  at point > 1.38 times of standard deviation. For 99.99% of Pd standard deviation 3 is required.

 Although the threshold is set by Pd and Pfa the actual value is to be set by the SNR and mission it it meant for. Two pulse threshold technique is also used to determine whether target is present . This enhances the value of Pd. A threshold T1 is set and a pulse is sen to relatively lower SNR. The range and angle resolutions are  noted for the first pulse . Now  another pulse called verification pulse is sent . If T1 is crossed again in the same location the target is said detected. Due to sending of second pulse the signal power has doubled Pfa has reduced consistently(Pfa(2) = Pfa(1)².

Radar cross-section of the target:

            In the calculation of the power we used radar cross section of the target as  4m2. The analysis which obtained this value is dependent upon the radar beam width, Azimuth beam width, Elevation beam width  and gaze angle. If the target is large then whole of the  radar directed power will fall on the target, i.e. larger cross section area of the target is seen. The analysis for calculating the actual radar cross section can be done on the similar lines as it was calculated for the clutter area calculation..

The following are the design values that are obtained

Design Parameter	Value
Noise figure Transmitter power ( Pt ) Minimum received signal (Smin) Operating frequency (f) Bandwidth chosen Wavelength (λ) Detection Range Antenna chosen Antenna feed Antenna Diameter Antenna Beam width Clutter Power Azimuth angle Grazing angle Backscatter coefficient	9dB 69.5 Kwatts 28 1.3GHz 10MHz 23.07 cms 100KM Parabolic antenna Half wave dipole 403cms 4 degrees 16 *10-14 0.3 degrees 5 degrees 0.01

Transmitter and Receiver Design and analysis

 Transmitter:

     The block diagram of the pulse modulated radar is shown in Fig- III.. The main components of the transmitter section are the (1) triggering source    (2)pulse modulator (3) output tube or amplifier.  The trigger source  provides pulses for the modulator. The modulator provides rectangular output voltage pulses used as the supply voltage switching it on and off as required.

Pulse characteristics:

              The  trigger source and modulator are suitably designed to make flat topped and vertical sides pulses.  Flat top pulse is needed , otherwise its frequency will be altered and the efficiency of the output tube is reduced. Steep falling edge is required to see that the duplexer is immediately switched to receiver without any delay.

              The pulse characteristics is governed by two factors (1) maximum range required  (2) receiver bandwidth

               From equation –(1) we know the range of the pulsed radar is  2R = Tc where c is the velocity of EM wave equivalent to velocity of light.

             2*100KM = PRT  * 3*10⁵      PTR id pulse repetition time.

             PTR = 2*100/3*10⁵

                     PRF= 1500pps    is the pulse repetition frequency.

Minimum width of the pulse is governed by the minimum detectable range and the bandwidth of the receiver. If  shorter ranges are require then shorter pulses are to be transmitted.. But if shorter pulses are used then receiver bandwidth will increase and the radar detectable range will decrease.  As the receiver bandwidth is fixed to be 10MHz in calculating the power equation—(10, 11) the pulse width is obtained as

                      δf = nT    where n is a number whose value ranges from 1- 10. For the this design the most common value is 1.4.

           T= n/ δf

                                   T= 1.4/10MHz   =  0 .14µsecs

This pulse width (T)  puts a limit on the minimum range. As the receiver is off for this duration of time  no echo can be received if the target is as close as

                                   2R = c T

                                   R = 2.7m

  This implies that this pulse width cannot be problem for detecting the targets as close to 2.7m to a  distance of 100KM .

Output tube

               The output tube is usually a magnetron or Klystron. The selection of the output oscillator will depend upon the power and frequency.  The multicavity  Klystron is used as mediun , high and very high powers in UHF and microwave range. The Klystron amplifier  performance is sown in the table below.

Application and type of requirement	Freq. Range(GHz)	Needed power	Available power
UHF TV transmitter Long range radar (Pulsed) Linear particle accelerator Tranposcatter link Earth station transmitter	0.5 – 0.9 1 – 1.2 2.0 – 3.0 1.5 – 2 5.9 – 14	55KW 10MW 25MW 250KW 8KW	100KW 20MW 40MW 1000kW 25kW

The frequency range covered for the Klystron is from 250MHz to over 95GHz. The power available is also adequate. As our freq of operation is in  L-band (1.3Ghz)  and the power to be generated is around 65KW or more the  length of the Klystron will be above 2 meters and the weight will be above 250Kgs. It is possible to reduce the weight and length of the klystron if it uses a permanent- magnetic focusing.

 The output tube can be a magnetron also. This can be used fro about 100KW of power and for frequencies up to 3GHz.  From the advantages and the efficiency point magnetrons are mostly preferred for pulsed radars for around 100KW of power and  an efficiency of around 70 percent  is achieved..

Receiver:

         The block diagram in fig-(iii) shows the super heterodyne receiver. The components of the receiver are (1) Local oscillator (2) IF amplifier (3) Low noise RF Amplifier (4) detector. The receiver bandwidth is 10MHz as per the specifications so as the IF amplifier bandwidth.

 Low noise RF amplifier:

        The receiver is designed to have good sensitivity and selectivity. Sensitivity is defined as the ability to amplify weak signal and is expressed in volts. As the received input signal is weak in the order of 28.83* 10-23 watts, we need to have a low noise RF amplifier to convert this signal to a equally high voltage levels of micro volts.  The noise figure of this amplifier is calculated to be 9dB. The RF amplifier is usually implemented to suppress the unwanted noise by using standard ICs.

Local Oscillator:

    As the intermediate frequency that is chosen is 60MHz, the local oscillator is suitably selected at 1.36MHz. It may take two or more down conversions to reach IF from the microwave RF to have adequate image frequency. As operation is at microwave frequencies ,  the frequency of the local oscillator may 40Mhz higher or lower than the RF microwave , but is usually at higher value that that of the input RF wave.   This is because the  ratio tunable ranges of highest frequency of operation to the lowest frequency of operation must be kept close to each other.

Mixer and  IF amplifier:

       The frequency from the local oscillator is now mixed with the received RF signal in the mixer. The mixer is mostly a diode mixer in the first stage. The IF stage  must be designed such that the over all noise figure is not deteriorated.

   The choice of intermediate frequency must be adequate.

If the IF is too high, poor selectivity and poor adjacent channel rejection is caused unless sharp cutoff filters are used.  A high value of IF will cause tracking problems. As IF is lowered image frequency frequency rejections becomes lower. For low intermediate frequency the local oscillator frequency must be very stable, because any drift is now a larger proportion of the low IF than of high IF. IF should not fall with in the tuning range of the receiver, else instability will occur and heterodyne whistles are heard.

Radial Velocity of the Target:

                  The artifact from the Adelaide airport are detected on their flight. It is also necessary to calculate the radial velocity of the aircraft. As the radar station is fixed and the target is moving, we can easily calculate the velocity of the aircraft  by using Doppler effect.

       The apparent frequency of the electromagnetic or sound waves depends on the relative radial motion of the source or the observer. If the source and the observer are moving away from each other then the apparent frequency will decrease and vice versa.

In our design the Radar is fixed and the and the target is moving.

          Let the relative velocity be V_r and frequency of the transmitted wave is ft. The aircraft is moving towards the fixed radar. So the number of crests recovered by the radar will be more now by fd.

                            f_t + f_d  = ft (1+ V_r/V_c)        consequently,

                             f_d = ft (V_r/V_c)

f_t + f_d  =new observed frequency  and      f_d = Doppler frequency difference

V_r = velocity of the target             V_c =velocity of the EM wave

  The effective Doppler frequency of  the radar due to two way travel of the signal will be

                                 f_deffe = 2 f_t (V_r/V_c)

 The above conclusion holds only for the targets moving with velocities with in less than about 10 percent of the velocity of light (EM wave). The velocity of light is 300 KMPS and 10% of this velocity is 30KMPS. The usually speediest aircraft will have speeds less that this value. So all the above discussion will hold good  for our design.. This analysis can only estimate the radial velocity, not the tangential velocity

Limiters to protect various elements of the receiver and the digital RF board.

           The receiver must be protected from various  ditortiona and noise elements for properly detecting the target.

Pulse Compressor:   

                  Pulsee compressions are used to increase the transmitted   average   power   while   retaining   the  range  resolution of a narrow pulse width. .Pulse compression  radar  has  additional  advantages  over  normal pulse   radar—it   has   better   discrimination   of   target echoes  in  clutter  and  is  less  susceptible  to  jamming. Two   basic   types   of   pulse   compression   are

  (1)   linear FM   and (2)   phase   coding.   Both   encode   the   transmitted pulse   with   information   that   is   compressed   (decoded) in the receiver of the radar.  Radars  that  use  pulse  compression  can  compress  pulses  with  durations  of  many microseconds  down  to  a  tenth  of  a  microsecond. The ratio of transmitted pulse width to compressed pulse width  is  called  the   pulse-compression    ratio. Ratios of  up  to  160:1  are  currently  in  use.

 FFT Processor:

             The FFT processor is the commonly used signal processing function that extracts the frequency and phase information from the sensor signal. Here used to recover signal frequency from the pulse compressor. It analysis the target tracking , localization and  radar by comparing the phase difference between multiple sensors.

Parameter	Value
Pulse repetition freq Pulse width IF bandwidth Minimum range that is detected Intermediate frequency Local oscillator frequency Noise Figure Output tube Output tube  dimensions(klystron) Mixer	1500pps 0.14 micro secs 10MHz 2.7 mts 60MHz 1.36GHz 9dB Magnetron(efficiency 70) 2mts and 250kgs Balanced Mixture

Performance validation and testing

                             The effectiveness of radar system depends largely upon the care and attention given to it . An improperly adjusted transmitter, can reduce the accuracy of a perfectly aligned receiver; the entire system then becomes essentially useless. Maintenance, therefore, must encompass the entire system for best operation.

Component testing: 

                           Before  the equipment is installed in the work place each component need  to be checked individually. This will effectively improve the performance of the system . The reinstalling losses can be reduced if any component is found malfunctioning. Checking individual blocks can also help in reducing the damages caused at the total system level.

 Complete Tx test :

                  The transmitter should operate in a band of frequencies designed for. If there is any deviation in the frequencies of interests then this will produce false results at the receiver there by affecting the performance of both the transmitter and receiver. This can be avoided by making constant checks of the frequency that is transmitted by the spectrum analyzer. Wave meter, Electronic frequency counter, Echo box are used to measure the carrier frequency. It also need to be checked whether the transmitted power is for the fullest range. This can be done by sampling a part of the transmitted power. Pick up horns are used to sample a part of the transmitter power by placing it in front of the antenna and the total power can analyzed. .

Complete Receiver test:

                   Usually the signal that is received by the receiver is very week. So the receiver sensitivity must be very high so as to detect even a weak signal.   As this minimum signal depends on the noise level in the circuit either can measured to determine the sensitivity of the receiver.  The  IF anmplier Local oscillator and RF amplifier must operate with  the specified. Their frequency response can be analysed by the spectrum analyzer.

  Complete Transmitter and receiver test:

               The complete radar system must be checked before the installation . This can avoid re installing  if any problem is encounter after installation. This can be done by using echo box  which will pick up some energy   generated by the radar transmitter by means of the directional coupler.

Fig-V   rader test setup with optical fiber repeters

This picked up energy will cause oscillations in the  after the end of the pulse. These oscillations are as echo’s . These oscillations are fed back to the receiver after some time by using directional couplers. Now the receiver can process this oscillations received from the echo box and process it.

One of the  techniques that are used to test the radar is by using optical fiber link. These optical fiber links or repeaters can effectively meet the stringent requirements of the  S/N phase linearity and stability requirements of pulse Doppler radars that uses pulse compressions techniques  to obtain long range operations with high resolution. These repeaters test the targets located several miles from the radar to achieve sufficient delay for the radar to receiver the transmitted pulse. The fiber optics repeater provides the long delays required  equivalent to original target.

Cooling systems:

           Radar require cooling systems in particular the transmitter as it generates high power in the range og kilo to mega watts , so a lot of power is dissipated which results in heating of the equipments. So cooling is o be provide for the radar equipment, by air borne cooling or liquid cooling for better performance.
Antenna tests : 

               Testing of the antenna in its performance is also important in the performance of the radar. The antenna parameter metrics  that are needed to be tested are directivity, polarization, gain , radiation efficiency, radiation pattern. Antenna test ranges are dependent on many factors such as directivity of antenna , frequency range. Often physical parameters also play a key role in the testing process. The commonly used test ranges are rectangular anechoic chamber, near field testing, far field testing, ground reflected range

Sources:

 1.http://dbr.library.ncnu.edu.tw/itu-r/
2.http://www.tenix.com/PDFLibrary/213.pdf
3.http://www.entegra.co.uk/data_acquisition_adc_dac_cf.htm
4.http://www.tekmicro.com/PDFs/Neptune2_datasheet.pdf
5.http://www.acqiris.com/products/digitizers/
6.http://www.tpub.com/content/neets/14190/index.htm

7.Kennedy and Davis , “Electronic communication systems “ , Tata McGraw Hill edition.

8.I L Newberg, et.al, “Long microwave delay fiber optic link for rada test”, IEEE transactions or microwave theory and techniques, vol.38 , no.5 may 1990.

9.http://www.lehman-inc/pdf/mag.pdf

10.Jim D Echard, “ Estimation Radar detection and false alarm probabilities” IEEE transactions on Aerospace and Electronics systems, Vol.27 no 2 march 1991