Chapter 7:Antennas

Example 1,Page No:332

In [1]:
import math

# Variable Declaration
Ldipole    = 50;         # Length of dipole in cm
c          = 3*10**10;   # velocity of EM wave in cm/s
BW         = 10*10**6;   # bandwidth in Hz

# Calculations
lamda      = 2*Ldipole;     # wavelength in cm
fo         = c/lamda;       # operating frequency in Hz
Q          = fo/BW;          # quality factor

# Result
print'Q = %d'%Q;
Q = 30

Example 2,Page No:332

In [3]:
import math

# Variable Declaration
Rr      = 72;       # Radiation resistance in ohms
Rl      = 8;        # Loss resistance in ohms
Ap      = 27;       # power gain 

# Calculations
n       = Rr/float((Rr + Rl));     # radiation efficiency
D       = Ap/float(n);             # Directivity
D_dB    = 10*math.log10(D);      # directivity in dB

# Result
print'Directivity = %3.2f dB'%D_dB;
Directivity = 14.77 dB

Example 3,Page No:333

In [1]:
import math

# Variable Declaration
AZ_BW      = 0.5;      # beamwidth in degrees
E_BW       = 0.5;      # beamwidth in degrees
lamda      = 3*10**-2; # radar emission wavelength

# Calculations

AZ_BW_r    = AZ_BW*math.pi/float(180);     # azimuth beamwidth in radians
E_BW_r     = E_BW*math.pi/float(180);      # elevation beamwidth in radians
G          = (4*math.pi)/float((AZ_BW_r *E_BW_r ))     # antenna gain
G_db       = 10*math.log10(G);        # gain in dB
A          = (G*lamda*lamda)/float((4*math.pi));   # antenna aperture

# Output
print'Gain of Antenna = %3.2f dB\n'%G_db,'Antenna Aperture = %3.3f m'%A;
Gain of Antenna = 52.18 dB
Antenna Aperture = 11.818 m

Example 4,Page No:333

In [8]:
import math

# Variable Declaration
n_az      = 0.5;        #length efficiency in azimuth direction
n_el      = 0.7;        #length efficiency in elevation direction
A         = 10;         # area in square mts

# Calculations
n         = n_az * n_el;    # aperture efficiency
Ae        = n*A;            # Effective aperture

# Output
print'Effective aperture of the antenna = %3.1f sq.m'%Ae;
Effective aperture of the antenna = 3.5 sq.m

Example 5,Page No:333

In [9]:
import math

# Variable Declaration
Ptot        = 100;      # certain antenna radiating power
Ptot_iso    = 10*10**3;  # isotropic antenna radiating power

# Calculations
D           = 10*math.log10(Ptot_iso/Ptot);  # Directivity of antenna

# Output
print'Directivity of antenna = %d dB'%D;
Directivity of antenna = 20 dB

Example 6,Page No:334

In [4]:
import math

# Variable Declaration
D       = 3;        # diameter of the antenna in m
nl      = 0.7;      # length efficiency
nr      = 0.9;      # radiation efficiency
f       = 10*10**9;  # antenna operating freq.
c       = 3*10**8;   # vel of EM waves in m/s

# calculations
de     = D*(nl)  # Effective diameter
lamda   = c/float(f);      # wavelength in m
Beam_w  = lamda/de # beamwidth in radian
Beam_w_d= Beam_w*180/math.pi;       # beam width in degree;
n_a     = nl * nl;    # Aperture efficiency
AA      = (math.pi*D*D)/4;  # actual area in sq m
Ae      = AA*n_a;       # Effective aperture
G       = (4*math.pi*Ae)/float((lamda**2)); # Gain
G_db    = 10*math.log10(G);

# Output
print'Beam Width = %3.2f degrees\n '%Beam_w_d;
print'Effective Aperture = %3.2fsq m\n'%Ae;
print'Gain = %3.1f dB'%G_db;
Beam Width = 0.82 degrees
 
Effective Aperture = 3.46sq m

Gain = 46.8 dB

Example 7,Page No:334

In [12]:
import math
# given data
# given (lamda/10) wire dipole
# Radiation resistance of short dipoles is Rr  = 790*(1/lamda)**2;
# Rr   = 790*(lamda/(10*lamda))**2;
# Rr   = 7.9;
print'Radiation resistance = 7.9 ohms';
Radiation resistance = 7.9 ohms

Example 8,Page No:334

In [9]:
import math

# Variable Declaration
a_l     = 6;        # Azimuth length in m
n_a     = 0.7;      # Azimuth length efficiency
n_e     = 0.5;      # elevation length efficiency
e_l     = 4;        # elevation length in m
w       = 6;        # width of antenna
h       = 4;        # height of antenna 
lamda   = 3*10**-2;  # wavelength

# Calculations
Eff_A_l = a_l*n_a;  # effective azimuth length
Eff_E_l = e_l*n_e;  # effective elevation length
A       = w*h       # actual area
n       = n_a*n_e;  # aperture efficiency
Ae      = A*n;      # effective aperture
Az_BW   = lamda/float(Eff_A_l) # Azimuth beam width
E_BW    = lamda/float(Eff_E_l)  # elevation beam width
Az_BW_d = Az_BW*180/float(math.pi)  # rad to deg conv
E_BW_d  = E_BW*180/float(math.pi);  # rad to deg conv
G       = (4*math.pi*Ae)/float((lamda**2)); #Gain
G_dB    = 10*math.log10(G);  # gain in dB

# Result
print'Azimuth Beamwidth = %3.2f degrees'%Az_BW_d; 
print'Elevation Beamwidth = %3.2f degrees'%E_BW_d; 
print'Gain = %3.1f dB'%G_dB;
Azimuth Beamwidth = 0.41 degrees
Elevation Beamwidth = 0.86 degrees
Gain = 50.7 dB

Example 9,Page No:335

In [39]:
import math
# given data
Beam_w_3db  = 0.4;

# Calculations
N2N_Beam_w  = 2*Beam_w_3db; # Null to Null beamwidth

# output
print'Null to Null Beam width = degrees',N2N_Beam_w;
Null to Null Beam width = degrees 0.8

Example 10,Page No:335

In [11]:
import math

# given data
RSSR        = 20;   # Rx signal strength in horizontal polarised antenna when rx RHCP

# Calculations
# When incident polarisation is circularly polarised and the antenna is linearly polarised,there is a ploarisation loss of 3dB
ISS         = RSSR + 3;     
# a
# when the Rx polarisation is same as the antenna polarisation , the polarisation loss is zero
RSS_HP      = ISS;      # rx signal strength for incident wave horizontally polarised
# b
# when the incident wave is vertically polarised ,the angle between the incident polarisation and the antenna polarisation is 90
# polarisation loss = 20log(1/cos( φ))
#                   = 20log(1/cos90) = ∞
RSS_VP      = 0;        # rx signal strength for incident wave vertically polarised
# c
# When the incident wave is LHCP and the antenna polarisation is linear ,there will be a 3dB polarisation loss and the 
# Rx signal strength therefore will be 20 dB only
RSS_LHCP    = RSSR;      # rx signal strength for incident wave Left hand circularly polarised
# d
# The angle between the incident wave polarisation and the antenna polarisation is 60 degrees
phi         = 60;                               # rx wave polarisation angle with horizontal
PL          = 20*math.log10(1/float(math.cos(60*math.pi/float(180))));      # polarisation loss in dB
RSS_Pangle  = ISS - PL;
# Result
print'Received signal strength if incident wave horizontally polarised = %d dB'%RSS_HP;
print'Received signal strength if incident wave vertically polarised = %d dB'%RSS_VP;
print'Received signal strength if incident wave Left hand circularly polarised is %d dB'%RSS_LHCP;
print'Received signal strength if Received wave polarisation making 60deg angle with horizontal is %3.0f dB'%RSS_Pangle;
Received signal strength if incident wave horizontally polarised = 23 dB
Received signal strength if incident wave vertically polarised = 0 dB
Received signal strength if incident wave Left hand circularly polarised is 20 dB
Received signal strength if Received wave polarisation making 60deg angle with horizontal is  17 dB

Example 11,Page No:337

In [12]:
import math

# Variable Declaration
f       = 300*10**6;     # operating frequency in Hz
c       = 3*10**10;      # velocity of EM wave in cm/s

# Calculations
lamda   = c/float(f);          # wavelength in cm
# Physical length of antenna is made 5% shorter than desired length as per rule of thumb
l       = lamda/float(2);      # length of halfwave dipole
lphy    = l-(5/float(100))*l;  # as per rule of thumb

# Output
print'Length of a half wave dipole to be cut = %3.1f cm'%lphy;
Length of a half wave dipole to be cut = 47.5 cm

Example 12,Page No:342

In [25]:
import math

# Variable Declaration
Zi      = 72;       # input impedance in ohms
# A    = 1.5a      # area of cross section in sq.cm
# Zif  = Zi*[(sum of areas of cross section of various components)/(Area of cross section of the driven element )]**2;
# Zif  = 72*((a + 1.5a)/a)**2;
# Zif  = 72*(2.5*a/a)**2;
Zif     = 72*(2.5)**2;

print'Input impedance for a folded dipole = %d Ω'%Zif;
Input impedance for a folded dipole = 450 Ω

Example 13,Page No:342

In [14]:
import math
# given data
f       = 60*10**6;      # frequency in Hz
c       = 3*10**8;      # velocity of EM wave in m/s

# Calculations
lamda   = c/float(f);          # wavelength in m
l_dipole= lamda/float(2);      # length of diplole
# Physical length of antenna is made 5% shorter than desired length as per rule of thumb
L       = l_dipole - (5/float(100))*l_dipole;  # actual physical length
L_D     = L - (4/float(100))*L;                # length of director
L_R     = L + (4/float(100))*L;                # length of reflector
DDS     = 0.12*lamda;                   # director dipole spacing
RDS     = 0.2*lamda;                    # Reflector dipole spacing

# Output
print'Length of dipole = %3.3f m'%L;
print'length of Director = %3.2f m'%L_D;
print'length of Reflector = %3.2f m'%L_R;
print'director dipole spacing = %3.1f m'%DDS;
print'Reflector dipole spacing = %3.1f m'%RDS;
Length of dipole = 2.375 m
length of Director = 2.28 m
length of Reflector = 2.47 m
director dipole spacing = 0.6 m
Reflector dipole spacing = 1.0 m

Example 14,Page No:352

In [17]:
import math
# given data
D       = 2;        # Mouth diameter in m
f       = 2;        # focal length in m
bw3db   = 90/float(100);   # beamwidth of antenna chosen to be 90% of angle subtended by feed

# Calculations
theta   = 4*math.atan(1/float((4*f/float(D))));    # angle subtended by the focal point feed at edges of reflector
theta_d = theta*180/float(math.pi);
Beam_w_3dB = bw3db*theta_d;       # 3 dB beam width
NNBW    = 2*(Beam_w_3dB );

# Output
print '3 dB Beamwidth = %3.1f°'%Beam_w_3dB,' Null-to-Null beam width = %3.2f°'%(NNBW);
3 dB Beamwidth = 50.5°  Null-to-Null beam width = 101.06°

Example 15,Page No:352

In [21]:
import math

# Variable DECLARATION
f       = 3;        # focal length in m
fpos    = 1.5;      # feed is placed 1.5m from pt of intersection os sec.reflector and antenna axis

# Calculation
f_hyp   = f-fpos;   # focal length of hyperboloid from figure;

# Result
print'focal length of hyperboloid = %3.1f m'%f_hyp;
focal length of hyperboloid = 1.5 m

Example 16,Page No:353

In [42]:
import math

# Variable Declaration
D       = 3;        # Mouth diameter in m
#f       = 2;      # focal length in m
bw3db   = 63;       # 3dB beam width
k       = 0.9;      # beam width is k times subtended angle

# Calculations
theta   = bw3db/k;  # subtended angle
theta_r = theta
#theta   = 4*atan(1/(4*f/D));
f       = D/(4*math.tan((theta_r/4)*(math.pi/180)));

# Result
print'Distance of feed from the point of intersection of antenna axis and the reflector surface = %3.2f m'%f;
Distance of feed from the point of intersection of antenna axis and the reflector surface = 2.38 m

Example 17,Page No:365

In [36]:
import math

# Variable Declaration
c       = 3*10**8;       # velocity of EM waves in m/s
f       = 2.5*10**9;     # operating frequency in Ghz
S       = 10*10**-2;     # inter element spacing
theta   = 10;            # steering angle 

# Calculations
lamda   = c/f          # Wavelength in m
phi     = (360*(S/lamda))*math.sin(theta*(math.pi/180))
phi1    = 0*phi        # phase angle for element 1
phi2    = 1*phi        # phase angle for element 2
phi3    = 2*phi        # phase angle for element 3
phi4    = 3*phi        # phase angle for element 4
phi5    = 4*phi        # phase angle for element 5

# Result
print'Phase angles for elements 1,2,3,4,5 are %d°'%phi1, '%d°'%phi2,'%d°' %phi3,'%d°' %phi4,'%d°' %phi5
Phase angles for elements 1,2,3,4,5 are 0° 52° 104° 156° 208°

Example 18,Page No:365

In [35]:
import math
# Data is taken from Example 17. The beam steers towards left of the axis with all parameters remaining in Ex 17 are same
c       = 3*10**8;       # velocity of EM waves in m/s
f       = 2.5*10**9;     # operating frequency in Ghz
S       = 10*10**-2;     # inter element spacing
theta   = -10;          # steering angle 

# Calculations
lamda   = c/f          # Wavelength in m
phi     = (360*S/lamda)*math.sin(theta*math.pi/180)
phi1    = 0*phi        # phase angle for element 1
phi2    = 1*phi        # phase angle for element 2
phi3    = 2*phi        # phase angle for element 3
phi4    = 3*phi        # phase angle for element 4
phi5    = 4*phi        # phase angle for element 5

# Output
print'Phase angles for elements 1,2,3,4,5 are %d°'%phi1, '%d°'%phi2,'%d°' %phi3,'%d°' %phi4,'%d°' %phi5
Phase angles for elements 1,2,3,4,5 are 0° -52° -104° -156° -208°

Example 19,Page No:365

In [39]:
import math
# given data
S       = 5*10**-2;      # inter spacing distance
lamda   = 6*10**-2;      # operating wavelength in cms
phi_Az   = 25            # angle in azimuth direction
phi_E    = 35            # angle in Elevation direction

# Calculations
theta_Az  = math.asin((lamda*phi_Az)/(360*S))
theta_E   = math.asin((lamda*phi_E)/(360*S))
Theta_Az  = theta_Az*(180/math.pi)
Theta_E   = theta_E*(180/math.pi)

# Output
print'Steering angle in Azimuth = %3.1f°'%Theta_Az
print 'Steering angle in Elevation = %3.1f°'%Theta_E;
Steering angle in Azimuth = 4.8°
Steering angle in Elevation = 6.7°