Chapter4, Linear Wire Antennas

Example No. 4.2.1, page 4-17

In [3]:
from math import pi, acos, degrees, cos, sin, atan
import numpy as np
l=5 #cm(length of antenna)
f=100 #MHz(operating frequency)
Io=120 #mA(Terminal current)
t=1 #s(time)
theta=45 #degree(Angle)
r=3 #m(radius)
c=3*10**8 #m/s##Speed of light
omega=2*pi*f*10**6 #rad/sec(rotation)
k=omega/c #rad/m(Phase constant)
kr=2*pi*r/3 #degree(Phase constant)
Er=Io*10**-3*l*10**-2/(2*pi*r**2)*cos(theta*pi/180)*120*pi*(1+1/(1J*kr))*np.exp(-1J*kr+1J*omega*t) #V/m(Electric field)
Er=Er*1000 #mV/m(Electric field)
Er_mag=abs(Er) #mV/m(magnitude of Er)
Er_angle=degrees(atan(Er.imag/Er.real)) #degree(angle of Er)
print "Value of Er : magnitude = %0.2f mV/m & angle = %0.2f degree " %(Er_mag,Er_angle) 
Etheta=Io*10**-3*l*10**-2/(4*pi*r)*sin(theta*pi/180)*120*pi*1J*k*(1+1/(1J*kr)+1/(1J*kr)**2)*np.exp(-1J*kr+1J*omega*t) #V/m(Electric field)
Etheta_mag=abs(Etheta) #V/m(magnitude of Etheta)
Etheta_angle=degrees(atan(Etheta.imag/Etheta.real)) #degree(angle of Etheta)
print "Value of Etheta : magnitude = %0.2e V/m & angle = %0.2f degree " %(Etheta_mag,Etheta_angle) 
Hfi=Io*10**-3*l*10**-2/(4*pi*r)*sin(theta*pi/180)*1J*k*(1+1/(1J*kr))*np.exp(-1J*kr+1J*omega*t) #A/m(Magnetic field)
Hfi_mag=abs(Hfi) #A/m(magnitude of Hfi)
Hfi_angle=degrees(atan(Hfi.imag/Hfi.real)) #degree(angle of Hfi)
print "Value of HΦ : magnitude = %0.3e A/m & angle = %0.f degree " %(Hfi_mag,Hfi_angle) 
#Answer is not accurate in the book.

Value of Er : magnitude = 28.64 mV/m & angle = -9.04 degree 
Value of Etheta : magnitude = 8.78e-02 V/m & angle = 80.73 degree 
Value of HΦ : magnitude = 2.387e-04 A/m & angle = 81 degree

Example No. 4.5.1, page 4-35

In [4]:
from math import pi
f=500.0 #MHz(Operating Frequency)
Do=1.643 #for half wave dipole
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m(Wavelength)
Aem=lamda**2/(4*pi)*Do #m²(Effective area)
print "Effective area = %0.3f m² " %Aem 

Effective area = 0.047 m²

Example No. 4.6.1, page 4-37

In [5]:
from math import sqrt, pi
l=1 #m
Prad=4 #W
f=1.5 #MHz
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m
#here l/lamda<1/50 tells us it is a Hertzian monopole antenna
h=1 #m
Rr=40*pi**2*(h/lamda)**2 #mΩ
Io=sqrt(2*Prad/Rr) #A
print "Current required = %0.2f A " %Io 

Current required = 28.47 A

Example No. 4.9.1, page 4-51

In [8]:
from math import pi
le=100.0 #m
Irms=450.0 #A
f=40000.0 #Hz
c=3*10**8 #m/s##Speed of light
lamda=c/f #m
P=160*pi**2*(le/lamda)**2*Irms**2 #mW
Rr=160*pi**2*(le/lamda)**2 #Ω
print "Power radiated = %0.2f kW " %(P*10**-3) 
print "Radiation resistance = %0.3f Ω "%Rr
#Answer wrong for radiation resistance in the book.

Power radiated = 56.85 kW 
Radiation resistance = 0.281 Ω

Example No. 4.9.2, page 4-51

In [9]:
from math import pi

le=61.4 #m
Irms=50 #A
lamda=625 #m
P=160*pi**2*(le/lamda)**2*Irms**2 #kW
Rr=160*pi**2*(le/lamda)**2 #Ω
print "Power radiated = %0.2f kW " %(P*10**-3) 
print "Radiation resistance = %0.2f Ω "%Rr 

Power radiated = 38.10 kW 
Radiation resistance = 15.24 Ω

Example No. 4.9.3, page 4-51

In [11]:
from math import pi
le=10.0 #m(effective length)
Irms=450 #A(rms current)
Rl=1.5 #Ω(resistance)
f=50.0 #kHz(Operating frequency)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**3) #m(Wavelength)
P=160*pi**2*(le/lamda)**2*Irms**2 #kW(Power)
P=P*1000 #W(Power)
Rr=160*pi**2*(le/lamda)**2 #Ω(Radiation resistance)
Eta=Rr/(Rr+Rl)*100 #%(Efficiency)
print "Efficiency of antenna = %0.2f %% "%Eta 

Efficiency of antenna = 0.29 %

Example No. 4.9.4, page 4-52

In [14]:
from math import pi
#l=lamda/8
lBYlamda=1.0/8 #(length/Wavelength)
Rr=80*pi**2*(lBYlamda)**2 #Ω(Radiation resistance)
print "Radiation resistance = %0.4f Ω "%Rr 

Radiation resistance = 12.3370 Ω

Example No. 4.9.5, page 4-52

In [16]:
from __future__ import division
from math import pi
L=1 #m(Length of element)
f=10 #MHz(Operating frequency)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m(Wavelength)
Rr=80*pi**2*(L/lamda)**2 #Ω(Radiation resistance)
print "Radiation resistance = %0.3f Ω "%Rr 

Radiation resistance = 0.877 Ω