# Chapter 9:Radar Antennas¶

## Example 9.1,Page No:352¶

In :
import math

#variable declaration
Da    = 2.5;                #diameter of parabolic antenna in m
F     = 5*10**9;           #radar operating frequency in hz
Vo    = 3*10**8;            #velocity of EM wave in m/s

#Calculations
lamda = Vo/float(F);            #wavelength
NNBW  = 140*(lamda/float(Da));
HPBW  = 70*(lamda/float(Da));          #half power beamwidth in deg

#result

print'NNBW of parabolic reflector is %g'%(NNBW),' degrees';
print'HPBW of parabolic reflector is %g'%(HPBW),' degrees';

NNBW of parabolic reflector is 3.36  degrees
HPBW of parabolic reflector is 1.68  degrees


## Example 9.2,Page No:352¶

In :
import math

#variable declaration
Da    = 2.5;           #diameter of parabolic antenna in m
F     = 5*10**9;        #radar operating frequency in hz
Vo    = 3*10**8;        #velocity of EM wave in m/s

#Calculations
lamda = Vo/float(F);       #wavelength
Gp    = 6.4*(Da/float(lamda))**(2);     #gain of parabolic reflector
G     = 10*math.log10(Gp);           #gain in dB

#result

print'Gain of parabolic reflector is %3.2f'%G,' dB';

Gain of parabolic reflector is 40.46  dB


## Example 9.3,Page No:352¶

In :
import math

#variable declaration

Da    = 0.15;              #diameter of parabolic antenna in m
F     = 9*10**9;            #radar operating frequency in hz
Vo    = 3*10**8;            #velocity of EM wave in m/s

#Calculations

lamda   = Vo/float(F);                         #wavelength
Gp      = 6.4*(Da/float(lamda))**(2);          #gain of parabolic reflector
G       = 10*math.log10(Gp);                   #gain in dB
NNBW    = 140*(lamda/float(Da));
HPBW    = 70*(lamda/float(Da));                 #half power bandwidth in deg

#result
print'NNBW of parabolic reflector is %3.2f'%(NNBW),' degrees';
print'HPBW of parabolic reflector is %3.2f'%(HPBW),' degrees';
print'Gain of parabolic reflector is %3.2f'%G,;'dB';

NNBW of parabolic reflector is 31.11  degrees
HPBW of parabolic reflector is 15.56  degrees
Gain of parabolic reflector is 21.13


## Example 9.4,Page No:353¶

In :
import math

#variable declaration
Da    = 2;                       #diameter of parabolic antenna in m
F     = 2*10**9;                   #radar operating frequency in hz
Vo    = 3*10**8;                    #velocity of EM wave in m/s

#Calculations
lamda  = Vo/float(F);                  #wavelength
Gp     = 6.4*(Da/float(lamda))**(2);       #gain of parabolic reflector
G      = 10*math.log10(Gp);                   #gain in dB

#result
print'Gain of parabolic reflector is %3.2f'%G,' dB';

Gain of parabolic reflector is 30.56  dB


## Example 7.5,Page No:353¶

In :
import math

#variable declaration

F     = 6*10**9;                 #radar operating frequency in hz
Vo    = 3*10**8;                  #velocity of EM wave in m/s
NNBW  = 5;                        #Null to Null beamwidth

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

Da  = 140*(lamda/float(NNBW));
HPBW  = 70*(lamda/float(Da));              #half power beamwidth in deg
Gp    = 6.4*(Da/float(lamda))**2;           #gain of parabolic reflector
G     = 10*math.log10(Gp);                    #gain in dB

#result
print'Mouth Diameter of paraboloid is %g'%Da,' m';
print'HPBW of parabolic reflector is %g'%(HPBW),' degrees';

print'Gain of parabolic reflector is %g'%G,' dB';
print'Gain of parabolic reflector is %g'%Gp;

Mouth Diameter of paraboloid is 1.4  m
HPBW of parabolic reflector is 2.5  degrees
Gain of parabolic reflector is 37.005  dB
Gain of parabolic reflector is 5017.6


## Example 9.6,Page No:354¶

In :
import math

#variable declaration

F     = 9*10**9;            #radar operating frequency in hz
Vo    = 3*10**8;              #velocity of EM wave in m/s
NNBW  = 5;                    #Null to Null beamwidth
Da    = 5;                      #diameter of antenna in m

#Calculations

lamda = Vo/float(F);                    #wavelength
A     = (math.pi*Da*Da)/float(4);          #actural area of antenna
Ac    = 0.65*A;                         #Capture Area

D     = 6.4*(Da/float(lamda))**2;               #directivity of antenna
D1     = 10*math.log10(D);                      #gain in dB
HPBW  = 70*(lamda/float(Da));                    #half power beamwidth in deg
NNBW  = 2*HPBW;                                #null to null beamwidth

#result
print'HPBW of parabolic reflector is %2.2g'%(HPBW),' degrees';
print'NNBW of parabolic reflector is %2.2g'%(NNBW),' degrees';
print'Directivity is %g'%D1,' dB';
print'Capture area is %g'%Ac,' m^2';

HPBW of parabolic reflector is 0.47  degrees
NNBW of parabolic reflector is 0.93  degrees
Directivity is 51.5836  dB
Capture area is 12.7627  m^2


## Example 9.7,Page No:354¶

In :
import math

#variable declaration

Da    = 5;             #diameter of parabolic antenna in m
F     = 5*10**9;       #radar operating frequency in hz
Vo    = 3*10**8;       #velocity of EM wave in m/s

#Calculations

lamda = Vo/float(F);                 #wavelength
R     = (2*Da*Da)/float(lamda);       #min distance b/w antennas

#result
print'Minimum distance Required is %g'%R,' m';

Minimum distance Required is 833.333  m


## Example 9.8,Page No:354¶

In :
import math

#variable declaration

F     = 4*10**9;         #radar operating frequency in hz
Vo    = 3*10**8;         #velocity of EM wave in m/s
Gp    = 500;             #power gain of antenna

#Calculations

lamda = Vo/float(F);                       #wavelength
Da    = lamda*(Gp/float(6.4))**(0.5);      #diameter of parabolic antenna in m

NNBW  = 140*(lamda/float(Da));              #beamwidth b/w null to null
HPBW  = 70*(lamda/float(Da));                      #half power beamwidth in deg

#result
print'NNBW of parabolic reflector is %3.2f'%NNBW,' degrees';
print'HPBW of parabolic reflector is %3.2f'%HPBW,'degrees';
print'Mouth diameter of parabolic reflector is %3.2f '%Da,'m';

NNBW of parabolic reflector is 15.84  degrees
HPBW of parabolic reflector is 7.92 degrees
Mouth diameter of parabolic reflector is 0.66  m


## Example 9.9,Page No:355¶

In :
import math

#variable declaration

F     = 9*10**9;           #radar operating frequency in hz
Vo    = 3*10**8;           #velocity of EM wave in m/s
Gp    = 100;               #power gain of antenna in dB

#Calculations

lamda = Vo/float(F);          #wavelength
#antilog calculation
#100 = 10log10(Gp);
#10  = log(Gp)

G     = 10**10;                                  #gain of antenna
Da    = lamda*math.sqrt(G/float(6.4));           #diameter of parabolic antenna in m
A     = (math.pi*Da*Da)/float(4);               #Area of antenna
Ac    = 0.65*A;                                 #capture area
NNBW  = 140*(lamda/float(Da));                         #beamwidth b/w null to null
HPBW  = 70*(lamda/float(Da));                          #half power beamwidth in deg

#result
print'NNBW of parabolic reflector is %g'%NNBW,' degrees';
print'HPBW of parabolic reflector is %g'%HPBW,' degrees';

print'Mouth diameter of parabolic reflector is %3.3f'%Da,' m';
print'Capture area is %3.2f'%Ac,'m**2';

NNBW of parabolic reflector is 0.00354175  degrees
HPBW of parabolic reflector is 0.00177088  degrees
Mouth diameter of parabolic reflector is 1317.616  m
Capture area is 886300.01 m**2


## Example 9.10,Page No:356¶

In :
import math

#variable declaration

F     = 10*10**9;              #radar operating frequency in hz
Vo    = 3*10**8;                #velocity of EM wave in m/s
Da    = 5;                     #antenna diameter in m

#Calculations
lamda = Vo/float(F);                         #wavelength
Gp    = 6.4*(Da/float(lamda))**(2);          #gain of parabolic reflector
G     = 10*math.log10(Gp);                   #gain in dB

BWFN  = 140*(lamda/float(Da));             #beam width b/n nulls
HPBW  = 70*(lamda/float(Da));              #half power beamwidth in deg

#result
print'BWFN of parabolic reflector is %g'%BWFN,' degrees';
print'HPBW of parabolic reflector is %g'%HPBW,' degrees';

print'Gain of parabolic reflector is %g'%G,'dB';

BWFN of parabolic reflector is 0.84  degrees
HPBW of parabolic reflector is 0.42  degrees
Gain of parabolic reflector is 52.4988 dB


## Example 9.11,Page No:356¶

In :
import math

#variable declaration

F     = 10*10**9;               #radar operating frequency in hz
Vo    = 3*10**8;                #velocity of EM wave in m/s
IE    =0.6;                     #illumination efficiency
Da    =12;                      #diameter of antenna

#Calculations

lamda = Vo/float(F);                     #wavelength
Gp    = IE*(Da/float(lamda))**(2);       #gain of parabolic reflector
G     = 10*math.log10(Gp);              #gain in dB

#result
print' Gain of parabolic reflector is %3.2f'%G,'dB';

 Gain of parabolic reflector is 49.82 dB


## Example 9.12,Page No:357¶

In :
import math

#variable declaration

F     = 4*10**9;         #radar operating frequency in hz
Vo    = 3*10**8;          #velocity of EM wave in m/s
NNBW  = 8;                #Null to Null beamwidth in degrees

#Calculations

lamda = Vo/float(F);                      #wavelength
Da    = (140*lamda)/float(NNBW);
A     = (math.pi*Da*Da)/float(4);         #Area of antenna
Ac    = 0.65*A;                           #capture area

#result
print'Mouth diameter of parabolic reflector is %3.3f'%Da,' m';
print'Capture area is %3.2f'%Ac,' m**2';

Mouth diameter of parabolic reflector is 1.312  m
Capture area is 0.88  m**2


## Example 9.13,Page No:357¶

In :
import math

#variable declaration

F     = 4*10**9;              #radar operating frequency in hz
Vo    = 3*10**8;              #velocity of EM wave in m/s
NNBW  = 2;                     #Null to Null Beamwidth in degrees

#Calculations

lamda = Vo/float(F);                  #wavelength
Da    = (140*lamda)/float(2);         #diameter of antenna in m
Gp    = 6.4*(Da/float(lamda))**(2);   #gain of parabolic reflector
G     = 10*math.log10(Gp);                 #gain in dB

#result
print'Gain of parabolic reflector is %g'%G,'dB';
print'mouth diameter of the antenna is %g'%Da,'m';

Gain of parabolic reflector is 44.9638 dB
mouth diameter of the antenna is 5.25 m


## Example 9.14,Page No:358¶

In :
import math

#variable declaration

HPBW  = 6;                #Half power Beamwidth in degrees

#Calculations

NNBW  = 2*HPBW;           #Null to Null beamwidth in degrees

#HPBW = 70*(lamda/Da);
#(70/HPBW)= (Da/lamda);

Gp    = 6.4*(70/float(HPBW))**(2);            #gain of parabolic reflector
G     = 10*math.log10(Gp);                    #gain in dB

#result
print'Gain of parabolic reflector is %3.2f'%G,'dB';
print'NNBW of the antenna is %g'%NNBW,'degrees';

Gain of parabolic reflector is 29.40 dB
NNBW of the antenna is 12 degrees


## Example 9.15,Page No:358¶

In :
import math

#variable declaration

Gp    =6.4*(6)**2;
G     = 10*math.log10(Gp);           #gain in dB

#result

print'Gain of parabolic reflector is %3.2f'%G,'dB';

Gain of parabolic reflector is 23.62 dB


## Example 9.16,Page No:358¶

In :
import math

#variable declaration
HPBW   = 70/float(7);                #half power beamwidth
NNBW   = 2*HPBW;                     # null to null beamwidth
#Gp  = 6.4*(Da/float(lamda))**2;            #power gain

#Gp  = 6.4*((7*lamda)/lamda)^2 ;  power gain of parabolic reflector

Gp    =6.4*(7)**2;
G     = 10*math.log10(Gp);          #gain in dB

#reault
print'Gain of parabolic reflector is %3.1f'%Gp;
print'HPBW of Antenna is %3.1f'%HPBW,' degrees';
print'NNBW of Antenna is %3.1f'%NNBW,' degrees';

Gain of parabolic reflector is 313.6
HPBW of Antenna is 10.0  degrees
NNBW of Antenna is 20.0  degrees


## Example 9.17,Page No:359¶

In :
import math

#variable declaration

F     = 8*10**9;             #radar operating frequency in hz
Vo    = 3*10**10;            #velocity of EM wave in cm/s
D     = 9;                  #pyramida horn  diameter in cm
W     = 4;                  #pyramida horn  width in cm

#Calculations

lamda   = Vo/float(F);                       #wavelength in cm
HPBW_E  = 56*(lamda/float(D));               #halfpower beamwidth in E-plane;
HPBW_H  = 67*(lamda/float(W));               #halfpower beamwidth in H-plane;
Gp      = (4.5*W*D)/float((lamda*lamda));       #power gain
G       = 10*math.log10(Gp);                        #power gain in dB
Di      =(7.5*W*D)/float(lamda*lamda);              #directivity

#result
print'Halfpower beamwidth ib E-plane is %3.2f'%HPBW_E,' degrees';
print'Halfpower beamwidth iN H-plane is %3.2f'%HPBW_H,' de0grees';
print'Powergain is %3.2f'%G,' dB';
print'Directivity is %3.2f'%Di;

Halfpower beamwidth ib E-plane is 23.33  degrees
Halfpower beamwidth iN H-plane is 62.81  de0grees
Powergain is 10.61  dB
Directivity is 19.20


## Example 9.18,Page No:359¶

In :
import math

#variable declartaion
Gp   = (4.5*10*10);             #power gain of square horn antenna
G    = 10*math.log10(Gp);            #power gain in dB

#result
print'Power Gain of Square Horn Antenna is %3.2f'%G,'dB';

Power Gain of Square Horn Antenna is 26.53 dB


## Example 9.19,Page No:359¶

In :
import math

#variable declaration

F     = 8*10**9;          #radar operating frequency in hz
Vo    = 3*10**10;         #velocity of EM wave in cm/s
D     = 10;               #pyramida horn  diameter in cm
W     = 5;                 #pyramida horn  width in cm

#Calculations

lamda = Vo/float(F);                      #wavelength in cm
Gp     = (4.5*W*D)/float((lamda*lamda));      #power gain
G      = 10*math.log10(Gp);                   # power gain in dB
Di     =(7.5*W*D)/float((lamda*lamda));       #directivity
DI     =10*math.log10(Di);                         #Directivity in dB

#result
print'Powergain is %3.2f '%G,'dB';
print'Directivity is %3.2f'%DI,'dB';

Powergain is 12.04  dB
Directivity is 14.26 dB


## Example 9.20,Page No:359¶

In :
import math

#variable declaration
no    = 377;                   #Free space intrinsic impedance in ohms
Zd1   = complex(73,50);              #dipole impedance;
Zd2   = 70;                    #dipole impedance;
Zd3   = 800;                   #dipole impedance;
Zd4   = 400;                   #dipole impedance;
Zd5   = complex(50,10);              #dipole impedance;
Zd6   = complex(50,-30);              #dipole impedance;
Zd7   = 350;                   #dipole impedance;

#Calculations
K      = (no**2)/float(4);
#Zs   = (no*no)/(4*Zd); slot impedance
Zs1    = K/Zd1;           #slot impedance
Zs2    = K/(Zd2);           #slot impedance
Zs3    = K/(Zd3);           #slot impedance
Zs4    = K/(Zd4);           #slot impedance
Zs5    = K/(Zd5);           #slot impedance
Zs6    = K/(Zd6);           #slot impedance
Zs7    = K/(Zd7);           #slot impedance

#result

print'slot impedance if Zd = 73+i50 ohm is %3.3f'%(Zs1.real),'%3.3f i' %(Zs1.imag) ,'ohm';
print'slot impedance if Zd = 70 ohm is %3.3f'%(Zs2.real),'ohm';
print'slot impedance if Zd = 800 ohm is %3.3f'%(Zs3.real),'ohm';
print'slot impedance if Zd = 400 ohm is %3.3f'%(Zs4.real),'ohm';
print'slot impedance if Zd = 50+i10 ohm is %3.3f'%(Zs5.real),'%3.3f i' %(Zs5.imag) ,'ohm';
print'slot impedance if Zd = 50-i30 ohm is %3.3f'%(Zs6.real),'%3.3f i' %(Zs6.imag) ,'ohm';
print'slot impedance if Zd = 350 ohm is %3.3f'%(Zs7.real),'ohm';

slot impedance if Zd = 73+i50 ohm is 331.314 -226.927 i ohm
slot impedance if Zd = 70 ohm is 507.604 ohm
slot impedance if Zd = 800 ohm is 44.415 ohm
slot impedance if Zd = 400 ohm is 88.831 ohm
slot impedance if Zd = 50+i10 ohm is 683.312 -136.663 i ohm
slot impedance if Zd = 50-i30 ohm is 522.533 313.520 i ohm
slot impedance if Zd = 350 ohm is 101.521 ohm


## Example 9.21,Page No:360¶

In :
import math

#variable declaration
Rr1   =80*(math.pi*math.pi)*(1/float(20))**(2) ;
#Rr2 = 80*(pi*pi)*(dl2/lamda)^2 Radiation Resistance in ohms
#Rr2 = 80*(pi*pi)*((lamda/30)/lamda)^2 Radiation Resistance in ohms
Rr2   =80*(math.pi*math.pi)*(1/float(30))**2 ;
#Rr3 = 80*(pi*pi)*(dl3/lamda)^2 Radiation Resistance in ohms
#Rr3 = 80*(pi*pi)*((lamda/40)/lamda)^2 Radiation Resistance in ohms
Rr3   =80*(math.pi*math.pi)*(1/float(40))**(2 );

#result
print'If Hertzian dipole length is lamda/20 then Radiation Resistance = %3.3f' %Rr1,'ohm';
print'If Hertzian dipole length is lamda/30 then Radiation Resistance = %3.3f' %Rr2,' ohm';
print'If Hertzian dipole length is lamda/40 then Radiation Resistance = %3.3f' %Rr3,' ohm' ;

If Hertzian dipole length is lamda/20 then Radiation Resistance = 1.974 ohm
If Hertzian dipole length is lamda/30 then Radiation Resistance = 0.877  ohm
If Hertzian dipole length is lamda/40 then Radiation Resistance = 0.493  ohm


## Example 9.22,Page No:361¶

In :
import math

#variable declaration
print'For half wave dipole Emax  =  60*I/float(r)';
print'But Pr  = 73 I**2 Watts';
print'For Pr  = 1 W';
print'I = 1/sqrt(73)';
print'Emax = (60/r)*I';
print'Gdmax = (4*pi*phi)/Pr';
print'as Pr =1 and phi = ((r**(2))*(E**(2)))/no';
print'Gdmax = 4*pi*(r**2)*(E**2)/no';
print'      = (4*pi*(r**2)*60*60)/(no*r*r*73)' ;
print'      = (4*pi*60*60)/(120*math.pi*73)';
Gdmax       = float(120)/73;

print'Directivity of half wave dipole is %3.3g' %Gdmax ;

For half wave dipole Emax  =  60*I/float(r)
But Pr  = 73 I**2 Watts
For Pr  = 1 W
I = 1/sqrt(73)
Emax = (60/r)*I
Gdmax = (4*pi*phi)/Pr
as Pr =1 and phi = ((r**(2))*(E**(2)))/no
Gdmax = 4*pi*(r**2)*(E**2)/no
= (4*pi*(r**2)*60*60)/(no*r*r*73)
= (4*pi*60*60)/(120*math.pi*73)
Directivity of half wave dipole is 1.64


## Example 9.23,Page No:361¶

In :
import math

#variable declaration

F   = 12*10**9;           #operating frequency in Ghz
I   = 2;                  #current in amperes
Rr  = 300;                #  radiation resistance in ohms

#Calculations
Pr  = I*I*Rr;

#result
print'Radiated Power is %3.1f'%Pr,' Watts';

Radiated Power is 1200.0  Watts


## Example 9.24,Page No:362¶

In :
import math

#variable declaration

F     = 600*10**6;                #radar operating frequency in hz
Vo    = 3*10**8;                  #velocity of EM wave in m/s
D     = 1.644;                    #Directivity of the half wave dipole

#Calculations

lamda = Vo/float(F);                         #wavelength
Ae    = ((lamda**2)*D)/(float(4*math.pi));        #effective area of antenna

#result

print'Effective Area of the antenna is %3.4f'%Ae,' m^2';

Effective Area of the antenna is 0.0327  m^2


## Example 9.25,Page No:362¶

In :
import  math

#variable declaration

F     = 200*10**6;                #radar operating frequency in hz
Vo    = 3*10**8;                   #velocity of EM wave in m/s
D     = 1.5;                       #Directivity of the Hertzian dipole

#Calculations

lamda = Vo/float(F);                 #wavelength
Ae    = (lamda**2*D)/(4*math.pi);    #effective area of antenna

#result
print'Effective Area of the antenna is %3.4f'%Ae,'m^2';

Effective Area of the antenna is 0.2686 m^2

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