Chapter 13: Antennas

Example 13.1, Page number: 601

In [2]:
 
import scipy

#Variable Declaration

H=5*10**-6              #magnetic field strentgh in A/m
theta=scipy.pi/2        
r=2*10**3               #distance in m
Bdl=2*scipy.pi/25
N=10                    #number of turns

#Calculations

Ia=4*scipy.pi*r*H/(Bdl*scipy.sin(theta))        #current for part (a) in A
Pa=40*scipy.pi**2*(1/25.0)**2*Ia**2             #power for part (a) in W
def pow(Io,Rrad):
    P=0.5*Io**2*Rrad
    print round(P*10**3,0),'mW'

denom=scipy.cos(scipy.pi*scipy.cos(theta)/2)    
Ib=H*2*scipy.pi*r*scipy.sin(theta)/denom        #current for part (b) in A
Rradb=73                                        #wave impedance in ohms for (b)
Ic=Ib                                           #current for part (c) in A
Rradc=36.56                                     #wave impedance in ohms for (c)
Id=H*r*400/(10*scipy.pi**2)                     #current for part (d) in A
Rradd=320*scipy.pi**6*N**2/20**4                #wave impedance in ohms for (d)

#Results

print 'The power transmitted in mW if antenna is ;'
print '(a) A Hertzian dipole of length lambda/25 =','\n',round(Pa*10**3,0),'mW'
print '(b) A half-wave dipole ='
pow(Ib,Rradb)
print '(c) A quarter-wave monopole ='
pow(Ic,Rradc)
print '(d) A 10-turn loop antenna of radius Po = lambda/20 ='
pow(Id,Rradd)

The power transmitted in mW if antenna is ;
(a) A Hertzian dipole of length lambda/25 = 
158.0 mW
(b) A half-wave dipole =
144.0 mW
(c) A quarter-wave monopole =
72.0 mW
(d) A 10-turn loop antenna of radius Po = lambda/20 =
158.0 mW

Example 13.2, Page number: 603

In [3]:
import scipy
import cmath
from numpy import *

#Variable Declaration

c=3*10**8               #speed of wave in m/s
f=50*10**6              #frequency in Hz
E=10*10**-6             #field strength in V/m
theta=scipy.pi/2
r=500*10**3             #distance in m
eta=120*scipy.pi        #wave impedance in ohms
Rrad=73                 #in ohms
Zo=75                   #in ohms
Zl=73+42.5j

#Calculations

l=c/(2*f)
I=E*2*r*scipy.pi*sin(theta)/(eta*(cos((scipy.pi/2)*cos(theta))))
P=0.5*I**2*Rrad
T=(Zl-Zo)/(Zl+Zo)
s=(1+abs(T))/(1-abs(T))

#Results

print 'The length of the dipole =',l,'m'
print 'The current that must be fed to the antenna =',round(I*10**3,2),'mA'
print 'The average power radiated by the antenna =',round(P*10**3,1),'mW'
print 'The standing wave ratio =',round(s,4)

The length of the dipole = 3 m
The current that must be fed to the antenna = 83.33 mA
The average power radiated by the antenna = 253.5 mW
The standing wave ratio = 1.7636

Example 13.4, Page number: 610

In [4]:
 
import scipy

#Variable Declaration

G=5
r=10*10**3      #in m
P=20*10**3      #power in W
n=120*scipy.pi  #wave impedance in ohms

#Calculations

Gd=10**(G/10.0)
E=scipy.sqrt(n*Gd*P/(2*scipy.pi*r*r))    #field intensity in V/m

#Result

print 'electric field intensity =',round(E,4),'V/m'

electric field intensity = 0.1948 V/m

Example 13.5, Page number: 611

In [5]:
 
import scipy
import scipy.integrate

#Variable Declaration

Umax=2.0

def U(phi,theta):
    s=2*scipy.sin(theta)*(scipy.sin(phi))**3/(4.0*scipy.pi)
    return s
    
#Calculations

if __name__ == '__main__':
        
 Uav,er=scipy.integrate.dblquad(lambda theta,phi:U(phi,theta)*scipy.sin(theta),    
             0, scipy.pi, lambda theta: 0, lambda theta: scipy.pi)

D=Umax/Uav   #Directivity

#Result

print 'directivity of the antenna =',D

directivity of the antenna = 6.0

Example 13.8, Page number: 624

In [6]:
 
import scipy

#Variable Declaration

c=3*10**8           #speed of wave in m/s
f=30*10**6          #frequency in Hz
E=2*10**-3          #field strength in V/m
n=120*scipy.pi
R=73 

#Calculations

l=c/f                             #wavelength in m
Gdmax=round(n/(scipy.pi*R),2)  
Amax=(l**2/(4*scipy.pi))*Gdmax    #maximum effective area in m^2
Pr=(E*E*Amax)/(2*n)               #power received in W

#Results

print 'maximum effective area =',round(Amax,2),'m^2'
print 'power received =',round(Pr*10**9,2),'nW'

maximum effective area = 13.05 m^2
power received = 69.24 nW

Example 13.9, Page number: 624

In [7]:
 
import scipy

#Variable Declaration

Gt=25           #in dB
Gr=18           #in dB
r=200           #in units of lambda
Pr=5*10**-3     #power received in W

#Calculations

Gdt=10**(Gt/10.0) 
Gdr=10**(Gr/10.0)
Pt=Pr*(4*scipy.pi*r)**2/(Gdr*Gdt)

#Result

print 'minimum transmitted power =',round(Pt,3),'W'

minimum transmitted power = 1.583 W

Example 13.10, Page number: 627

In [8]:
 
import scipy

#Variable Declaration

c=3*(10)**8                 #speed of wave in m/s
f=3.0*(10)**9               #frequency in Hz
Aet=9                       #effective area in m^2
r1=1.852*(10)**5            #distance in m
r2=4*r1                     #distance in m
r3=5.556*10**5              #distance in m
Pr=200*(10)**3              #in W
a=20                        #target area in m^2

#Calculations

l=c/f                                       #wavelength in m
Gdt=4*scipy.pi*Aet/(l*l)
P1=Gdt*Pr/(4*scipy.pi*r1*r1)                #power at 100 nmiles in W/m^2
P2=Gdt*Pr/(4*scipy.pi*r2*r2)                #power at 400 nmiles in W/m^2
Pr=Aet*a*Gdt*Pr/(4*scipy.pi*r3*r3)**2       #power of reflected signal in W

#Results

print 'Signal power density at 100 nautical miles =',round(P1*1000,3),'mW/m^2'
print 'Signal power density at 400 nautical miles =',round(P2*1000,3),'mW/m^2'
print 'Power of reflected signal =',round(Pr*10**12,5),'pico W'

Signal power density at 100 nautical miles = 5.248 mW/m^2
Signal power density at 400 nautical miles = 0.328 mW/m^2
Power of reflected signal = 0.02706 pico W