Chapter 11:SOLVED EXAMPLES¶

Example 1, Page No:404¶

In :
import math

# variable declaration
F          = 10*10**9;      # radar operating frequency in Hz
Vo         = 3*10**8;       # vel in m/s
G          = 20;            # antenna gain in dBi
R          = 20*10**3;      # distance of radar reflected signal from target
Pt         = 10*10**3       # Tx power in watts
CS         = 10;            # cross sectional area in m^2

# Calculations

Gain      = 10**(G/10)      # G = 10log(Gain) ==>gain - antilog(20/10)
Gr        = Gain;           # gain of tx antenna and Rx antenna
Gt        = Gain;
lamda     = float(Vo)/F;
Pr        = (lamda*lamda*Pt*Gt*Gr*CS)/((4*4*4*math.pi*math.pi*math.pi)*(R**4));   #received power in watts

# result

print'Received signal Power is %3.5g' %Pr;
print'Note : Calculation error in Textbook';
Note : Calculation error in Textbook

Example 2, Page No:405¶

In :
import math

#variable declaration
Vo       = 3*10**8;      #velocity of EM wave in m/s
t        = 20*10**-6;    #echo time in sec

# calculations

R = (Vo*t)/2;            #distance b/n target and Radar in m

# Output
print'Distance of Target from the Radar is ', R/1000,'km' ;
Distance of Target from the Radar is  3.0 km

Example 3,Page No:405¶

In :
import math

# variable declaration

Vo       = 3*10**8;         #velocity of EM wave in m/s
F        = 0.8*10**3;       #pulse repetitive frequency
Tp       = 1.2*10**-6;      #pulse width in sec

# calculations
Rmax = Vo/(2*F);             # maximum Range of Radar in m
Rmin = (Vo*Tp)/2;            # minimum Range of radar in m

# Output

print'Maximum Range of Radar is ',Rmax/1000,'Km';
print'Minimum Range of the Radar is',Rmin,'m';
Maximum Range of Radar is  187.5 Km
Minimum Range of the Radar is 180.0 m

Example 4,Page No:405¶

In :
import math

# variable declaration

PW     = 1.5*10**-6;      #pulse width in sec
PRF    = 2000;           #per second

# calculations
Dc = PW*PRF;             #duty cycle

# Output
print'Duty Cycle is  %3.4e' %Dc;
Duty Cycle is  3.0000e-03

Example 5,Page No:406¶

In :
import math

# variable declaration

PW  =  2*10**-6;        #pulse width in sec
PRF =  1000;           #pulse repetitive frequency
Pp  = 1*10**6;          #peak power in watts

# Calculations
Dc        =  PW*PRF;        # duty cycle
AvgTp     = Pp*Dc;          # average transmitted power in watts

# Output
print'Average Transmitted power is ',AvgTp/1000,'KW';
Average Transmitted power is  2.0 KW

Example 6,Page No:406¶

In :
import math

#variable declaration

PW  = 2*10**-6;      #pulse width in sec
Vo  = 3*10**8;       #velocity of EM wave in m/s

#Calculations

RR  = (Vo*PW)/2;    #Range Resolution in m

# result
print'Range Resolution is ',RR,'m';
Range Resolution is  300.0 m

Example 7,Page No:406¶

In :
import math

# variable declaration

t   = 50*10**-6;    #echo time in sec
Vo  = 3*10**8;      #velocity of EM wave in m/s

# Calculations

R  = (Vo*t)/2;      #Range in m

# result

print'Target Range is ',R/1000,'Kms';
Target Range is  7.5 Kms

Example 8,Page No:406¶

In :
import math

# variable declaration

Tvel  = 1000;        #target speed in kmph
F     = float(10*10**9);     #radar operating frequency in hz
Vo    = 3*10**8;      #velocity of EM wave in m/s

#Calculations

Vr    = 1000*(5/float(18));      #target speed in m/s
Fd    = float(2*Vr*F)/float(Vo);      #Doppler Frequency shift in Hz

#result
print'Doppler Frequency shift Caused by aircraft is %g' %(Fd/1000),'KHz';
Doppler Frequency shift Caused by aircraft is 18.5185 KHz

Example 9,Page No:407¶

In :
import math

# variable declaration

F  = 6*10**9;       # Transmitting Frequency of Radar
Vr = 250;          # velocity of automobile in Kmph
Vo    = 3*10**8;    #velocity of EM wave in m/s

#Calculations

Va    = Vr*(5/float(18));      #velocity of automobile in m/s
Fd    = (2*Va*F)/float(Vo);    #Doppler Frequency shift in Hz

#result
print'Doppler Frequency shift is %3.3f ' %(Fd/10**3),'KHz';
Doppler Frequency shift is 2.778  KHz

Example 10,Page No:407¶

In :
import math

# variable declaration

F  = 9*10**9;        #Transmitting Frequency of Radar
Vr = 800;            #velocity of aircraft in Kmph
Vo = 3*10**8;       #velocity of EM wave in m/s

#Calculations

Va    = Vr*(5/float(18));     #velocity of aircraft in m/s
Fd    = (2*Va*F)/float(Vo);   #Doppler Frequency shift in Hz
Fr    = F+Fd;         #frequency of reflected echo in Hz

#result
print'Doppler Frequency shift is %3.2e'%Fd,'Hz';
print'frequency of reflectedecho is %4e'%(Fr/1000),'Khz';
print'Note: doppler frequency shift wrongly printed in Text Book as 1333.3 Hz';
Doppler Frequency shift is 1.33e+04 Hz
frequency of reflectedecho is 9.000013e+06 Khz
Note: doppler frequency shift wrongly printed in Text Book as 1333.3 Hz

Example 11,Page No:407¶

In :
import math

#variable declaration

F  = 2*10**9;        #Transmitting Frequency of Radar
Vr = 350;            #velocity of sports Car in Kmph
Vo = 3*10**8;         #velocity of EM wave in m/s

#Calculations

Va    = Vr*(5/float(18));    #velocity of aircraft in m/s
Fd    = (2*Va*F)/float(Vo);  #Doppler Frequency shift in Hz

Fr    = F-Fd;       #frequency of reflected signal in Hz

#result

print'Doppler Frequency shift is %g'%Fd,'Hz';
print'frequency of reflected echo is %3.3g'%(Fr/10**9),'GHz','-',Fd,'Hz';
print'Note: doppler frequency shift wrongly printed in Text Book as 129.6 Hz\nVr is printed as 9.72 m/s instead of 97.2 m/s';
Doppler Frequency shift is 1296.3 Hz
frequency of reflected echo is   2 GHz - 1296.2962963 Hz
Note: doppler frequency shift wrongly printed in Text Book as 129.6 Hz
Vr is printed as 9.72 m/s instead of 97.2 m/s

Example 12,Page No:408¶

In :
import math

#variable declaration
PRF   =  2000;      #pulse repetition frequency per second
PW    =  1*10**-6;  #pulse width in sec
Pp    =  500*10**3;  #Peak power in watts

#Calculations

Dc    =  PW*PRF;      #Duty Cycle
Pav   =  Pp*Dc;       #average power in watts
pavdB = 10*math.log10(Pav);

#result

print'Average power is ',Pav/1000,'KW';
print'Average Power is ',pavdB,'dB';
Average power is  1.0 KW
Average Power is  30.0 dB

Example 13,Page No:408¶

In :
import math

#variable declaration

PRF   =  1000;      #pulse repetition frequency per second
PW    =  0.8*10**-6;    #pulse width in sec
Pp    =  10*10**6;  #Peak power in watts
Vo    =  3*10**8;    #velocity of EM wave in m/s;

#Calculations

Dc    =  PW*PRF;     #Duty Cycle
Pav   =  Pp*Dc;  #average power in watts
Rmax  =  Vo/(2*PRF);

#result
print'Average power is ',Pav/1000,' KW';
Average power is  8.0  KW
Maximum Radar Range is  150 Km

Example 14,Page No:409¶

In :
import math

# variable declaration

Rmax  =  500*10**3; #maximum Range of Radar in ms
Vo    =  3*10**8;     #Velocity of EM wave in m/s

#Calculations

PRF   = Vo/(2*Rmax);     #pulse repetitive frequency in Hz

#result

print'Pulse repetive frequency required for the range of 500km is ',PRF,'Hz';
Pulse repetive frequency required for the range of 500km is  300 Hz

Example 15,Page No:409¶

In :
import math

#variable declaration

Te    =  0.2*10**-3;    #echo time in sec
PRF   =  1000;         #pulse repetitive Frequency in Hz
Vo    =  3*10**8;      #Velocity of EM wave in m/s

#Calculations

R     =  (Vo*Te)/2;       #Range of the target in m
Runamb  =  (Vo/(2*PRF));  #Maximum unambiguous Range in m

#result

print'Target range is ',R/1000,' Km';
print'Maximum Unambiguous Range is  ',Runamb/1000,'Km';
Target range is  30.0  Km
Maximum Unambiguous Range is   150 Km

Example 16,Page No:409¶

In :
import math

#variable declaration

F     = 10*10**9;      #operating frequency of radar in Hz
Vo    =  3*10**8;       #Velocity of EM wave in m/s
Vr    =  100;           #velocity of car in kmph

#Calculations

lamda = Vo/float(F);         #wavelength in m
Vc    = Vr*(5/float(18));    #velocity of car in m/s
Fd    = (2*Vc)/float(lamda);  #doppler shift in Hz

#result

print'Doppler Shift is %3.2f '%(Fd/1000),' KHz';
print'Frequency of the Received echo when car is approaching radar is %g'%(F/10^9),'Ghz','+',Fd/1000,' Khz';
print'Frequency of the Received echo when car is moving away from radar is %g '%(F/10^9),'Ghz','-',Fd/1000,'Khz';
Doppler Shift is 1.85   KHz
Frequency of the Received echo when car is approaching radar is 1e+09 Ghz + 1.85185185185  Khz
Frequency of the Received echo when car is moving away from radar is 1e+09  Ghz - 1.85185185185 Khz

Example 17,Page No:410¶

In :
import math

#variable declaration

D   =  200;   #azimuth distance between two radars
R   =  10*10**3;    #Range of radar

#Calculations
BWdB = (float(D)/R)*(180/math.pi);   #3dB beam width in degrees

#result
print'Maximum 3db beamwidth of radar resolving the target is %3.3f'%BWdB, 'degrees';
Maximum 3db beamwidth of radar resolving the target is 1.146 degrees

Example 18,Page No:410¶

In :
import math

#variable declaration

F     = 10*10**9;    #operating frequency of radar in Hz
Vo    =  3*10**8;    #Velocity of EM wave in m/s
Vr1    =  100;       #velocity of one aircraft in m/s
theta  = 45;         #angle b/n velocity vector and radar axis for second aircraft
Vr     = 200;        #vel in m/s

#Calculations

lamda = Vo/float(F);                #wavelength in m
Fd1   = (2*Vr1)/float(lamda);       #doppler shift due to 1st aircraft
Vr2   = Vr*math.cos(45*math.pi/180);  #radial velocity of the second aircraft
Fd2   = (2*Vr2)/float(lamda);       #doppler shift due to 2nd aircraft
Fd    = Fd2-Fd1;             #difference in doppler shift in Hz
T     = 1/float(Fd);                #time required to resolve the aircraft in sec

#result
print'Minimum time required to resolve the aircrafts is %g'%(T*10**6),'usec';
print'Note: in textbook there is a mistake in the calculation of doppler shift Fd1';
Minimum time required to resolve the aircrafts is 362.132 usec
Note: in textbook there is a mistake in the calculation of doppler shift Fd1

Example 19,Page No:410¶

In :
import math

#variable declareation

Pp  = 100*10**3;  #peak power in watts
Pav = 100;        #average power in watts

#Calculations

PdB = 10*math.log10(Pp);      #peak power in dB
PavdB = 10*math.log10(Pav);    #average power in dB;
DCC  = PdB-PavdB;        #Duty Cycle Correction factor

#result
print'Duty Cycle Correction Factor is ',DCC, 'dB';
print'Note: In question given peak power  is 100KW but while solving 1KW is taken instead of 100KW';
Duty Cycle Correction Factor is  30.0 dB
Note: In question given peak power  is 100KW but while solving 1KW is taken instead of 100KW

Example 20,Page No:411¶

In :
import math

#variable declaration
Pp   = 1*10**6;   #peak power in watts
PW   = 1*10**-6;   #pulse width in sec
NPd   = 20;      #pulses in one dwell period
PRF  = 1000;      #pulse repetitive frequency

#calculations
PE   = Pp*PW;     #pulse energy in joule
PED  = NPd*PE;      #pulse energy in one dwell period
D    = PW*PRF;     #Duty cycle
Pav  = Pp*D;      #average power in watts

#output
print'Average Power is ',Pav,'watts';
print'Duty Cycle is %2.2e'%D;
print'Pulse Energy is ',PE,' Joules';
print'Pulse Energy in one Dwell Period is  ',PED,'Joules';
print'Note: In textbook Values of PRF and pulses in one dwell period are varied from given values in question while solving ' ;
Average Power is  1000.0 watts
Duty Cycle is 1.00e-03
Pulse Energy is  1.0  Joules
Pulse Energy in one Dwell Period is   20.0 Joules
Note: In textbook Values of PRF and pulses in one dwell period are varied from given values in question while solving

Example 21,Page No:411¶

In :
import math

#variable declaration
Noise_power = -50;      #noise power in dBm
Fl = 1*10**6;#lower cutoff frequency in Hz
Fh = 21*10**6;#upper cutoff frequency in Hz

#calculation
BW = Fh-Fl;#bandwidth
NP =10**-8;#noise power in watts; -50dBm = 10log10(NP) =>10^-5 mwatts
NPSD = NP/BW;#noise power spectral density in W/Hz

#result
print'Noise Power Spectral Density is %3.0e'%NPSD,' W/Hz';
Noise Power Spectral Density is 5e-16  W/Hz

Example 22,Page No: 411¶

In :
import math

#variable declaration

Ra = 1000;    #Range of target A in Kms

#Calculations
Rb =Ra*math.cos(45*math.pi/180);      #range of target B in kms

#result
print'Range of target B is %g '%Rb,'Kms';
print'Note:value of cos(45) is incorrectly taken as 1/2 in textbook';
Range of target B is 707.107  Kms
Note:value of cos(45) is incorrectly taken as 1/2 in textbook

Example 23,Page No:412¶

In :
import math

#variable declaration

Az      = 60;   #azimuth angle of the target in degrees
Height  = 10;#height of target in kms

#Calculations
R      = 10/math.sin(Az*math.pi/180);

#result

print'Range of the Target is %g '%R,'Kms';
Range of the Target is 11.547  Kms

Example 24,Page No:412¶

In :
import math

#variable declaration
F = 10*10**9;     #MTI radar operating Frequency
Vo = 3*10**8;      #velocity of EM wave in m/s;
PRF = 2*10**3;     #pulse repetitive frequency in hz
n=1;               #for lowest blind speed

#Calculations

lamda = Vo/float(F);                #wavelength in m
BS   =((n*lamda)/float(2))*PRF;     #blind speed

#result
print'Lowest Blind Speed is ',BS,'m/s';
Lowest Blind Speed is  30.0 m/s

Example 25,Page No:412¶

In :
import math

# variable declaration

PRF = 2*10**3; # pulse repetitive frequency in Hz
Vo  = 3*10**8;   #velocity of EM wave in m/s
print'f1 = first operating frequency of MTI Radar\n';
print' f2 = second operating frequency of MTI Radar\n';
print' 2nd blind speed of 1st radar = (2Vo/2f1)*PRF\n 5th blind speed of 2nd radar = (5Vo/2f2)*PRF\n';
print' PRF(V0/f1) = (5/2)*(Vo/f2)*PRF\n';
print' (f2/f1) = 5/2\n';
f1 = first operating frequency of MTI Radar

f2 = second operating frequency of MTI Radar

2nd blind speed of 1st radar = (2Vo/2f1)*PRF
5th blind speed of 2nd radar = (5Vo/2f2)*PRF

PRF(V0/f1) = (5/2)*(Vo/f2)*PRF

(f2/f1) = 5/2

Example 26,Page No:413¶

In :
import math

print'(PRF1)  =  2(PRF2)\n';
print' Vb3 = 4Vb5\n';
print' (3Vo/2F1)(PRF1)) = 4(5Vo/2F2)(2PRF2)\n';
print' 3/2F1  =  20/F2\n';
print' Ratio of operating frequencies is F2/F1  =  40/3\n';
(PRF1)  =  2(PRF2)

Vb3 = 4Vb5

(3Vo/2F1)(PRF1)) = 4(5Vo/2F2)(2PRF2)

3/2F1  =  20/F2

Ratio of operating frequencies is F2/F1  =  40/3

Example 27,Page No:413¶

In :
import math

#variable declaration
PW  = 5;    #FM pulse width before compression in us
Fl  = 40;    #lower cut off Frequency in Mhz
Fh  = 60;    #upper cut off Frequency in Mhz

#Calculations
BW   = Fh-Fl;       #bandwidth of signal in Mhz
CPW  = 1/float(BW);        #Compression pulse width in us
CR   = PW/float(CPW);     #compression ratio

#result
print'Compression ratio is %g'%CR;
print'Compression Pulse Width is %g'%CPW,'us';
Compression ratio is 100
Compression Pulse Width is 0.05 us

Example 28,Page No:413¶

In :
import math

#variable declaration
BW = 100;   #band width in Mhz
PW = 4;     #pulse width in us

#Calculations

CPW  = 1/float(BW);      #compressed pulse width in us
CR   = PW/float(CPW);    #compression ratio

#result
print'compressed pulse width is %g'%CPW,' us';
print'compression ratio is %g'%CR;
print'Note: In textbook compression ratio is wrongly printed as 40';
compressed pulse width is 0.01  us
compression ratio is 400
Note: In textbook compression ratio is wrongly printed as 40

Example 29,Page No:414¶

In :
import math

#variable declaration

CR = 50;      #compression ratio
PW = 2;       #pulse width in us

#Calculations

CPW = PW/float(CR);    #compression pulse width in us
BW  = 1/float(CPW);     # compression band width in Mhz

#result
print'compressed pulse width is %g'%CPW,'us';
print'compression Bandwidth is %g'%BW,'MHz'
compressed pulse width is 0.04 us
compression Bandwidth is 25 MHz

Example 30,Page No:414¶

In :
import math

#variable declaration
PW  = 1*10**-6;    #transmitted pulse width in sec
Vo  = 3*10**8;     #velocity of EM wave in m/s

#Calculations
RR  = (Vo*PW)/2;
#result
print'Range Resolution is ',RR,' m';
print'As the targets are separated by 100m it is possible to resolve';
Range Resolution is  150.0  m
As the targets are separated by 100m it is possible to resolve

Example 31,Page No:414¶

In :
import math

# variable declaration
F = 10*10**9;    #operating frequency in Hz
PRF = 1000;   #pulse repetitive frequency in Hz
Fm  = PRF;    #modulating frequency
#Calculations
Fc1  = float(F+Fm);    #closest frequency in Hz
Fc2  = float(F-Fm); #closest frequency in Hz
#result
print'Closest Frequencies are %3.3f'%(Fc1/10**6),' Mhz';
print'Closest Frequencies are %3.3f'%(Fc2/10**6),' Mhz';
Closest Frequencies are 10000.001  Mhz
Closest Frequencies are 9999.999  Mhz

Example 32,Page No:414¶

In :
import math

#variable declaration
F1  = 490;   #freq shift lower limit in Mhz
F2  = 510;   #freq shift upper limit in Mhz

#calculations

SC = (F1+F2)/2;    #Spectrum Centre in Mhz
BW = F2-F1;   #bandwidth in Mhz
CPW = float(1)/BW;   #compressed bandwidth in us

#result
print'Spectrum centre is %g'%SC,' MHz';
print'BandWidth is %g'%BW,' MHz';
print'Compressed pulse Width is %3.2f'%CPW,'us';
Spectrum centre is 500  MHz
BandWidth is 20  MHz
Compressed pulse Width is 0.05 us

Example 33,Page No:415¶

In :
import math

#variable declaration
F          = 9;                #Noise figure in dB
BW         = 2*10**6;          # Bandwidth
To         = 300;              # Temperature in kelvin
K          = 1.38*10**-23;     # Boltzman constant

#Calculations

F1         = 10**(F/float(10));         #antilog calculation
Pmin       = (K*To*BW)*(F1-1);   #minimum receivable power

#result
print'Minimum receivable power Pmin  %3.3e'%Pmin,' W';
Minimum receivable power Pmin  5.749e-14  W

Example 34,Page No:415¶

In :
import math

#variable declaration
Pt = 500*10**3;    #peal pulse power in watts
Pmin = 1*10**-12;   #minimum receivable power
Ac   = 5;           #area of capture in m^s
RCS  = 16;         #radar cross sectional area in m^2
F    = 10*10**9;    #radar operating frequency
Vo   = 3*10**8;   #vel of Em wave in m/s;

#calculations
lamda = Vo/float(F);    #wavelength

Rmax = ((Pt*Ac*Ac*RCS)/float((4*math.pi*lamda*lamda*Pmin)))**0.25;

#result
print'Note:Calculation mistake in textbook instead of RCS,RCS^2 is calculated';
Note:Calculation mistake in textbook instead of RCS,RCS^2 is calculated

Example 35,Page No:415¶

In :
import math

#variable declaration

lamda         = 0.03;           #wavelength in m
RCS           = 5;              # Radar cross section in m^2
D             = 1;              #  antenna diameter in m
F             = 5;              # noise figure in dB
Rmax          = 10*10**3         # Radar range
BW            = 500*10**3;      # bandwidth

#Calculation
F1            = 10**(F/float(10));       # antilog calculation

#Rmax        = 48*((Pt*D**(4*RCS))/float((BW*lamda*lamda(F-1))))**(0.25);

Pt            = ((Rmax/float(48))**(4))*((BW*lamda*lamda*(F1-1))/float(((D**4)*RCS)));

#result
print'Peak Transmitted Power is %e' %Pt;
print'Note: Antilog Calculation error in textbook at F'
Peak Transmitted Power is 3.665971e+11
Note: Antilog Calculation error in textbook at F

Example 36,Page No:416¶

In :
import math;

# variable Declaration
Pt = float(20*10**6);     #peak pulse power in watts
RCS  = 1;           # radar cross sectional area in m^2
f   = 3*(10**9);    #radar operating frequency
Vo   = 3*(10**8);   #vel of Em wave in m/s;
D    = 50;          #diameter of antenna in m
F    = 2;           #receiver noise figure

# calculations

lamda = float(Vo)/float(f)        # wavelength in m
Rmax = 48*((Pt*(D**4)*RCS)/(BW*lamda*lamda*(F-1)))**0.25;

# output
print 'Maximum Radar range of the Radar system is %f kms' %(Rmax/1000);
print 'Note:In textbook All values are correctly substituted in calculating Rmax but incorrect final answer is printed in the book'
Note:In textbook All values are correctly substituted in calculating Rmax but incorrect final answer is printed in the book

Example 37,Page No:417¶

In :
import math

#variable declaration
lamda     = 6*10**-2;    #Wavelength in m
PRF       = 800;        #Pulse Repetitive frequency in Hz
n1        = 1 ;         #n value for first blind speed
n2        = 2 ;         #n value for first blind speed
n3        = 3 ;         #n value for first blind speed

#Calculations

#Vb      = (n*lamda/2)*PRF;  Blind speed of the Radar

#For n = 1

Vb1       = ((n1*lamda)/float(2))*PRF;   #Blind speed of the Radar in m/s
Vb2       = ((n2*lamda)/float(2))*PRF;   #Blind speed of the Radar in m/s
Vb3       = ((n3*lamda)/float(2))*PRF;   #Blind speed of the Radar in m/s

#multiply by 18/5 to convert from m/s to kmph

#result
print'The lowest Blind speeds are %3.1f' %(Vb1*(18/float(5))),'Km/hr';
print'The lowest Blind speeds are %3.2f' %(Vb2*(18/float(5))),'Km/hr';
print'The lowest Blind speeds are %3.2f' %(Vb3*(18/float(5))),'Km/hr';
The lowest Blind speeds are 86.4 Km/hr
The lowest Blind speeds are 172.80 Km/hr
The lowest Blind speeds are 259.20 Km/hr

Example 38,Page No:417¶

In :
import math

# variable declaration

Pt        = 500*10**3;   # Peak pulse power in Watts
pt        = 50;         # peak power transmitted by beacon in watts
f         = 2500*10**6;  # Radar Operating frequency in Hz
lamda     = 0.12;       # wavelength in m
D         = 64;         # antenna diameter in m
BW        = 5000;       # Radar Bandwidth
Ab        = 0.51;
k         =  1.38*10**-23;  # Boltzmann constant
F         = 20             # Noise figure
Fb        = 1.1            # Noise figure of beacon
To        = 290;           # Temperature in kelvin

#Calculations

Ar        = (0.65*math.pi*D*D)/float(4);
Rmax      = math.sqrt((Ar*Pt*Ab)/float((lamda*lamda*k*To*BW*(F-1))));  # Max tracking range of radar

Rmax1      = math.sqrt((Ar*pt*Ab)/float((lamda*lamda*k*To*BW*(Fb-1)))); # Max tracking range of radar if Fb = 1.1

#result
print'Maximum Tracking Range of Radar is %3.3e'%(Rmax/1000),' Km';
print'Range of beacon if noise figure is 1.1  %3.3e'%(Rmax1/1000),'Km';
print'Note: Calculation mistake in textbook in calculating Range of beacon instead of 1.36*10^9 km range is wrongly printed as 136*10^6 km';
Maximum Tracking Range of Radar is 9.869e+09  Km
Range of beacon if noise figure is 1.1  1.360e+09 Km
Note: Calculation mistake in textbook in calculating Range of beacon instead of 1.36*10^9 km range is wrongly printed as 136*10^6 km

Example 39,Page No:417¶

In :
import math;

# Variable Declaration
lamda     = 0.06;       # wavelength in m
Vr        = 100 ;       # Radial velocity of target in kmph

#Calculations
Vr1       = Vr*(float(5)/18);  #Radial vel. in m/s
fd        = (2*Vr1)/lamda; #doppler shift

#Output

print 'Doppler Shift is %3.3f Khz' %(fd/1000);
Doppler Shift is 0.926 Khz

Example 40,Page No:418¶

In :
import math

#variable declaration
F  = 9.5*10**9;      #radar operating frequency in Hz
Vo = 3*10**8;        #vel in m/s;
G  = 20;            #antenna gain in dBi;
R  = 50*10**3;       #distance of radar reflected signal from target
Pt = 10*10**3        #Tx power in watts
CS = 10;            #cross sectional area in m^2

#Calculations
Gain  = 10**(G/float(10));  #G = 10log(Gain) ==>gain - antilog(20/10);
Gr    = Gain;       #gain of tx antenna and Rx antenna
Gt    = Gain
lamda = float(Vo)/F
Pr= (lamda*lamda*Pt*Gt*Gr*CS)/((4*4*4*math.pi*math.pi*math.pi)*(R**4))
#result
print'Received signal Power is %g'%Pr,' Watts';
Received signal Power is 8.04055e-17  Watts

Example 41,Page No:418¶

In :
import math

#variable declaration

Vo    = 3*10**8;        #vel of EM wave m/s;
t     = 10*10**-6;      # time taken to rx echo

#Calculations

R     = (Vo*t)/2;      #Distance of the Target

#result

print'Distance of the target is ',R/1000,' Km';
Distance of the target is  1.5  Km

Example 42,Page No:419¶

In :
import math

# variable declaration
PW    = 10**-6;        # Pulse Width in sec
PRF   = 1000;          #Pulse Repetitive Freq in Hz
Vo    = 3*10**8;      # vel of EM wave m/s;

#Calculations

Rmax  = Vo/(2*PRF);    #max range of radar
Rmin  = (Vo*PW)/2 ;    # min range of radar

#result
print'Maximum Range of radar is %e'%Rmax,' m';
print'Minimum Range of radar is ',Rmin,'m';
Maximum Range of radar is 1.500000e+05  m
Minimum Range of radar is  150.0 m

Example 43,Page No:419¶

In :
import math

#variable declaration
Vr         = 100;      # speed of car in kmph
f          = 10*10**9;  # Radar operating frequency
Vo         = 3*10**8;  # vel. of EM wave

#Calculations

Vr1        = Vr*(5/float(18));      # kmph to m/s conversion
fd         = (2*Vr1*f)/float(Vo);   # Doppler shift in Hz

#result
print'Doppler shift %3.3g'%(fd/1000),'Khz';
Doppler shift 1.85 Khz

Example 44,Page No:420¶

In :
import math

#variable declaration
Vo    = 3*10**8;        # vel of EM wave m/s;
t     = 200*10**-6;    # time taken to rx echo

#Calculations

R     = (Vo*t)/2;      # Distance of the Target

#result
print'Distance of the target is ',R/1000,'Km';
Distance of the target is  30.0  Km

Example 45,Page No:420¶

In :
import math

#variable declaration
Pt      = 100*10**3;         # Peak tx. power
PRF     = 1000;             # pulse repetitive freq. in Hz
PW      = 1.2*10**-6;        # Pulse Width in sec

#Calculations
DC      = PRF*PW            # Duty cycle
Pav     = Pt*DC             # Avg. power

#Output
print'Duty cycle is ',DC;
print'Average power is ',Pav,' Watts';
Duty cycle is  0.0012
Average power is  120.0  Watts

Example 46,Page No:420¶

In :
import math

#variable declaration
Runamb      = 300*10**3;     # unambiguous range in m
Vo          = 3*10**8;       # Vel. of EM wave in m/s

#Calculations

PRF         = Vo/(2*(Runamb)); # Pulse repetitive freq.

#result

print'Pulse repetitive frequency ',PRF,'Hz';
Pulse repetitive frequency  500 Hz

Example 47,Page No:420¶

In :
import math

#variable declartation
Vo    = 3*10**8;         #vel of EM wave m/s;
PRF   = 1000;          # pulse repetitive freq. in Hz
PW    = 10**-6;         # Pulse width in sec

#Calculations

DC      = PRF*PW;         # Duty cycle

Runamb  = Vo/(2*PRF);      # Distance of the Target

#result

print'Duty cycle  ',DC;
print'Maximum unambiguous range', Runamb/1000,'Km' ;
Duty cycle   0.001
Maximum unambiguous range 150 Km

Example 48,Page No:421¶

In :
import math

#variable declaration
Vo    = 3*10**8;        # vel of EM wave m/s;
PRF   = 1000;          # pulse repetitive freq. in Hz
PW    = 4*10**-6;       # Pulse width in sec

#Calculations

Runamb  = Vo/(2*PRF);      # Distance of the Target
RR      = (Vo*PW)/2;       # Range Resolution

#result

print'Maximum unambiguous range ',Runamb/1000,' Km';
print'Range Resolution ',RR,'m';
Maximum unambiguous range  150  Km
Range Resolution  600.0 m

Example 49,Page No:421¶

In :
import math

# variable declaration
f     = 6*10**9;        # Radar operating freq. in Hz
Vo    = 3*10**8;        # vel of EM wave m/s;
PRF   = 1000;          # pulse repetitive freq. in Hz
PW    = 1.2*10**-6;     # Pulse width in sec
DC    = 10**-3;         # Duty Cycle
Smin  = 5*10**-12;      # min. detectable signal
R     = 60*10**3;       # Max. Range in m
G     = 4000;          #power gain of antenna
Ae    = 1              #  effective area in m*2
RCS   = 2              # Radar cross sec. in m*2

#Calculations

lamda   = Vo/float(f);            # Wavelength in m
PRT     = PW/float(DC);           # pulse repetitive time
PRF     = 1/float(PRT);           # Pulse repetitive freq.
Pt      = ((Smin*(4*math.pi*R*R)**2))/(float((Ae*G*RCS)));  #Peak power
Pav     = Pt*DC;           # average power

Runamb  = Vo/float((2*PRF));      # Distance of the Target
RR      = (Vo*PW)/float(2);       # Range Resolution

#result

print' Operating Wavelength = %g'%lamda,' m';
print'\n PRT  %3.2f'%(PRT*1000),' ms';
print'\n PRF  %3.1f'%PRF,'Hz';
print'\n Peak power  %3.3f'%(Pt/1000),' KW';
print'\n Average power  %3.3f'%Pav,' Watts';
print'\n unambiguous range %g'%(Runamb/1000),' Km';
print'\n Range Resolution %g'%RR ,'m';
print '\n Note: Calculation error in textbook for Pt and Pav';
Operating Wavelength = 0.05  m

PRT  1.20  ms

PRF  833.3 Hz

Peak power  1279.101  KW

Average power  1279.101  Watts

unambiguous range 180  Km

Range Resolution 180 m

Note: Calculation error in textbook for Pt and Pav

Example 50,Page No:423¶

In :
import math

#variable declaration
Vo    = 3*10**8;          # vel of EM wave m/s;
PRT   = 1.4*10**-3;       # pulse repetitive time. in sec
PW    = 5 *10**-6;        # Pulse width in sec
Pt    = 1000*10**3;       #Peak power in watts

#Calculations

DC      = PW/float(PRT);           # Duty cycle
Pav     = Pt*DC            # avg. power in W

#result

print'Duty cycle  %3.3e'%DC;
print'Average power %g '%Pav,'W' ;
Duty cycle  3.571e-03
Average power 3571.43  W

Example 51,Page No:423¶

In :
import math

#variable declaration
F       = 5;            # Noise Figure in dB
BW      = 1.2*10**6;     # Bandwidth in Hz
T       = 290;          # Ambient temp in kelvin
K       = 1.38*10**-23;  # boltzmann constant

#Calculations
F1      = 10**(5/float(10)) ;    # antilog calc of noise figure
Prmin   = K*(F1-1)*T*BW;  # min. rx. signal

#result
print'Minimum Receivable signal  %3.4e'%Prmin,' W\n ';
print'Note:In textbook All values are correctly substituted in calculating Prmin.\nbut incorrect final answer is printed in the book';
Minimum Receivable signal  1.0384e-14  W

Note:In textbook All values are correctly substituted in calculating Prmin.
but incorrect final answer is printed in the book

Example 52,Page No:423¶

In :
import math

#variable declaration
Pt   = 1*10**6;         #peak pulse power in watts
Pmin = 1*10**-12;       #minimum receivable power
Ae   = 16;             #effective area in m^s
RCS  = 4;              #radar cross sectional area in m^2
F    = 9*10**9;         #radar operating frequency
Vo   = 3*10**8;         #vel of Em wave in m/s;
G    = 5000;           #Power gain of antenna

#calculations

Rmax = ((Pt*G*Ae*RCS)/(16*math.pi*math.pi*Pmin))**(0.25);

#result

Example 53,Page No:424¶

In :
import math

#variable declaration
Pt   = 500*10**3;     #peal pulse power in watts
Pmin = 1*10**-12;     #minimum receivable power
Ac   = 5;             #area of capture in m^s
RCS  = 20;            #radar cross sectional area in m^2
F    = 10*10**9;      #radar operating frequency
Vo   = 3*10**8;       #vel of Em wave in m/s;
lamda = 3*10**-2;     # wavelength in cms

#calculations

Rmax = ((Pt*Ac*Ac*RCS)/(4*math.pi*lamda*lamda*Pmin))**(0.25);

#result

Example 54,Page no:425¶

In :
import math

#variable declaration
f       = 10*10**9;      # operating freq. of radar in Hz
Vo      = 3*10**8;       #vel of Em wave in m/s;
D       = 5;            #Diameter of antenna in m

#calculations
lamda   = Vo/float(f);         # wavelength in m
BW      = 70*(lamda/float(D));  # BeamWidth in degrees

#result
print'Beamwidth  = %3.3g'%BW,' degrees';
Beamwidth  = 0.42  degrees

Example 55,Page No:425¶

In :
import math

#variable declaration
Pav  = 200;     #average power in watts
PRF  = 1000;    #pulse repetitive frequency in Hz
PW   = 1*10**-6;  #pulse width in sec
Pmin = 1*10**-12;   #minimum receivable power
Ac   = 10;          #area of capture in m^s
RCS  = 2;           #radar cross sectional area in m^2
Vo   = 3*10**8;      #vel of Em wave in m/s;
lamda = 0.1;         #wavelength in cms

#calculations
F    = Vo/float(lamda);    #operating frequency in hz
Pt   = Pav/float(PRF*PW);

Rmax = ((Pt*Ac*Ac*RCS)/float((4*math.pi*lamda*lamda*Pmin)))**(0.25);

#result
print'Operating frequency is %g'%(F/10**9),'Ghz';
Operating frequency is 3 Ghz
Radar peak power is 200 KW

Example 56,Page No:426¶

In :
import math

#variable declaration
f       = 9*10**9;       # operating freq. of radar in Hz
Vo      = 3*10**8;       # vel of Em wave in m/s;
fd      = 1000;         #doppler shift freq. in Hz

#Calculations
lamda   = Vo/float(f);        # Wavelength in m
Vr      = lamda*fd/float(2);  # radial velocity of target

#result
print'Radial velocity of target Vr %g'%Vr,' m/s';
Radial velocity of target Vr 16.6667  m/s

Example 57,Page No:426¶

In :
import math

#variable declaration
f       = 10*10**9;       # operating freq. of radar in Hz
Vr      = 800;            # radial ve. of of aircraft in kmph
Vo      = 3*10**8;         #vel of Em wave in m/s;

#calculations

lamda   = Vo/float(f);        # Wavelength in m
Vr1     = Vr*5/float(18);      # kmph to m/s conversion
fd      = 2*Vr1/float(lamda);  # Doppler shift freq, in Hz

#result
print'Doppler shift frequency fd = %3.2e'%fd,' Hz';
Doppler shift frequency fd = 1.48e+04  Hz

Example 58,Page No:426¶

In :
import math

#variable declaration
f       = 6*10**9;       # operating freq. of radar in Hz
Vr      = 600;           # radial ve. of of aircraft in kmph
Vo      = 3*10**8;       #vel of Em wave in m/s;

#calculations

lamda   = Vo/float(f);        # Wavelength in m
Vr1     = Vr*5/float(18);      # kmph to m/s conversion
fd      = 2*Vr1/float(lamda);  # Doppler shift freq, in Hz

V       = Vr1*math.cos((45*math.pi/float(180))); # vel in direction of radar if  target direction changes by 45 deg
fd1     = 2*V/float(lamda);   #doppler shift freq. in Hz

#result
print'Doppler shift frequency fd = %3.3g'%(fd/1000),'KHz';
print'Doppler shift frequency if the target changes its direction by 45deg %3.2f'%(fd1/1000),'KHz';
Doppler shift frequency fd = 6.67 KHz
Doppler shift frequency if the target changes its direction by 45deg 4.71 KHz

Example 59,Page No:427¶

In :
import math

#variable declaration
lamda     = 3*10**-2;    #Wavelength in m
PRF       = 1000;       # Pulse Repetitive frequency in Hz
n         = 1;          # n value for lowest blind speed

#Calculations
Vb        = (n*lamda/float(2))*PRF;   #Blind speed of the Radar in m/s

#result
print'Lowet blind speed  %g'%Vb,'m/s';
Lowet blind speed  15 m/s

Example 60,Page No:427¶

In :
import math

#variable declaration
PRF         = 1000;                  # pulse repetitive frequency
print'V1b1  = (1* λ1*PRF1)/2';
print'V1b1  = (Vo*PRF1)/(2*f1)';
print'V2b3  = (3* λ1*PRF2)/2';
print'V2b3  = (3*Vo*PRF2)/(2*f2)';
print'But PRF1 = PRF2 and V1b1 = V2b3';
print'(Vo*PRF)/(2*f1) = (3*Vo*PRF)/(2*f2)' ;
print'f1/f2 = 1/3';
V1b1  = (1* λ1*PRF1)/2
V1b1  = (Vo*PRF1)/(2*f1)
V2b3  = (3* λ1*PRF2)/2
V2b3  = (3*Vo*PRF2)/(2*f2)
But PRF1 = PRF2 and V1b1 = V2b3
(Vo*PRF)/(2*f1) = (3*Vo*PRF)/(2*f2)
f1/f2 = 1/3

Example 61,Page No:428¶

In :
import math

#variable declaration
PRF1        = 10*10**3;         #pulse repetitive freq.1
PRF2        = 20*10**3;          #pulse repetitive freq.2
Pav         = 1000;             # average tx. power
Pt          = 10*10**3;          # peak power

#Calculations
PRT1        = 1/float(PRF1);           # pulse repetitive interval in sec
PRT2        = 1/float(PRF2);           # pulse repetitive interval in sec
DC          = Pav/float(Pt);           # duty cycle
PW1         = DC*PRT1           # pulse width for freq1
PW2         = DC*PRT2           # pulse width for freq2
E1          = Pt*PW1;           # energy of first pulse
E2          = Pt*PW2;           # energy of second pulse

#result
print'PW1 = ',PW1*1000,' ms';
print'PW2 =',PW2*1000,' ms';
print'Pulse Energy for PRF 10KHz is ',E1,' Joules';
print'Pulse Energy for PRF  20KHz is ',E2 ,' Joules';
PW1 =  0.01  ms
PW2 = 0.005  ms
Pulse Energy for PRF 10KHz is  0.1  Joules
Pulse Energy for PRF  20KHz is  0.05  Joules

Example 62,Page No:428¶

In :
import math

#variable declaration
Runamb     = 150*10**3;      # unambigiuous range in m
BW         = 10**6;          # bandwidth in Hz
Vo         = 3*10**8;        #vel of Em wave in m/s;

#Calculations
PRF         = Vo/float((2*Runamb)) ;   #pulse repetitive freq. in Hz
PRT         = 1/float(PRF);            # pulse repetition interval
RR          = Vo/float((2*BW));        # Range Resolution
PW          = (2*RR)/float(Vo);        #Pulse width in sec

#result
print'PRF = %3.2f' %PRF,'Hz';
print'pulse repetition interval %3.3g'%(PRT*1000),' ms';
print'Range Resolution = %d' %RR,'m';
print'PulseWidth = %3.2f' %(PW*10**6),'us';
PRF = 1000.00 Hz
pulse repetition interval   1  ms
Range Resolution = 150 m
PulseWidth = 1.00 us

Example 63,Page No:429¶

In :
import math

#variable declaration
Vr      = 300;           # Velocity of radar in m/s
Vair    = 200;           # velocty of aircraft in m/s
f       = 10*10**9;      # Radar operating frequency
Vo      = 3*10**8;       # vel of Em wave in m/s;

#Calculations

lamda   = Vo/float(f);            # wavelength in m
Vrel    = Vr+Vair;         #relative radial vel. b/w radar and aircraft when approaching each other
fd      = (2*Vrel)/float(lamda);  #Doppler frequency

#result
print'Doppler frequency = %3.2f'%(fd/1000),'KHz';
Doppler frequency = 33.33 KHz

Example 64,Page No:429¶

In :
import math

#variable declaration
Pt      = 2*10**6;      # Peak power in Watts
G       = 45;          # antenna gain in dB
f       = 6*10**9;      # operating frequency
Te      = 290;          # effective temp in kelvin
SNRmin  = 20;           # min SNR in dB
PW      = 0.2*10**-3     # pulse width in sec
F       = 3;            # Noise Figure
B       = 10*10**3;      # bandwidth in KHz
RCS     = 0.1;          # Radar cross section in m^2
K       = 1.38*10**-23;  # boltzman constant
Vo      = 3*10**8;       #vel of Em wave in m/s;

#antilog acalculations
G1     = 10**(45/float(10));    # antilog conversion of gain
SNR    = 10**(20/float(10));    # antilog conversion of SNRmin
F1     = 10**(3/float(10));     # antilog conversion of Noise Figure

lamda  = Vo/float(f);          #wavelength in m
Rmax   = ((Pt*G1*G1*lamda*lamda*RCS)/float(((64*math.pi*math.pi*math.pi)*(K*Te*B*F1*SNR))))**(0.25);
#pt1    = 10*log10(Pt)
#lamda1 = 10*log10(lamda^2)
#G2     = 2*G
#KTB    = 10*log10(K*Te*B)
#RCS1   = 10*log10(RCS)
#p      = 10*log10((4*%pi)^3)
#R4max  = [pt1+G1+lamda1+RCS1-p-KTB-F-SNRmin];

#result
print'Maximum Range of the Radar is %3.2f'%(Rmax/100),'Km';
print'\n Note: Calculation error is Textbook in multiplying K*Te*B';
Maximum Range of the Radar is 4214.69 Km

Note: Calculation error is Textbook in multiplying K*Te*B

Example 65,Page No:430¶

In :
import math

#variable declaration
G       = 50;           # antenna gain in dB
f       = 6*10**9;       # operating frequency
Te      = 1000;         # Noise temp in kelvin
SNR     = 20;           # min SNR in dB
L       = 10;           # Losses in dB
F       = 3;            # Noise Figure in dB
RCS     = -10;          # Radar cross section in dB
K       = 1.38*10**-23;  # boltzman constant
Vo      = 3*10**8;       # vel of Em wave in m/s;
DC      = 0.3;          # Duty cycle
R       = 300*10**3;     # Range in kms
Pav     = 1000;         # Average power in watts
SV      = 20;           # search volume
Ts      = 3;            # Scan time

#calculations

Pav1    = 10*math.log10(Pav)             #conversion to dB
KT       = 10*math.log10(Te*K)             #conversion to dB
R4      = 10*math.log10(R**4)             #conversion to dB
Ts1     = 10*math.log10(Ts)               #conversion to dB
#SNR   = (Pav*A*RCS*Ts)/(16*R**(4)*KT*L*F*SV));
A       = (SNR-Pav1-Ts-RCS+16+R4+KT+L+F+SV); #aperture
Pt      = Pav/DC;                   #peak ower in watts
#A1      =10^(A/10);                 # antilog calculation

#result
print'A = %3.4g' %A,'dB';
print'Peak power Pt = %3.2f'%(Pt/1000),'KW';
print'Note: calculation error in textbook at KT';
A = 66.48 dB
Peak power Pt = 3.33 KW
Note: calculation error in textbook at KT
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