chapter 03 : Antenna Terminology

Exa 3.1 : page 3.42

In [2]:
from math import pi
#given data :
E=10.0 #in V/m
ETA_o=120.0*pi #Constant
H=E/ETA_o #in A/m
print "The Magnetic Field Strength = %0.4f A/m  " %H 

The Magnetic Field Strength = 0.0265 A/m

Exa 3.2 : page 3.42

In [3]:
from math import sqrt
#given data :
W=25.0 #in KW
W=W*10**3 #in W
r=3 #in Km
r=r*10**3 #in m
Erms=sqrt(90*W)/r #in V/m
print "Field strength at receiver = %0.2f V/m " %Erms 

Field strength at receiver = 0.50 V/m

Exa 3.3 : page 3.42

In [4]:
from math import pi
#given data :
le=125 #in m
Irms=5 #in A
lamda=1.25 #in Km
lamda=lamda*10**3 #in m
Rl=10 #in Ohm
#radiation Resistance
Rr=(80*pi**2)*(le/lamda)**2 #in Ohm
Rr=round(Rr) #in Ohm : approx
print "Radiation resistance = %0.2f Ohm " %Rr 
#Power radiated
W=(Irms**2)*Rr #in 
print "Power radiated = %0.2f W " %W
#Antenna efficiency 
ETA=Rr/(Rr+Rl)
print "Antenna efficiency = %0.2f %% " %(ETA*100) 

Radiation resistance = 8.00 Ohm 
Power radiated = 200.00 W 
Antenna efficiency = 44.44 %

Exa 3.4 : page 3.43

In [8]:
from math import cos, pi, sin
#given data :
r=1 #in Km
r=r*10**3 #in m
I=0.5 #in A
#For theta = 45 degree
theta=45  #in degree
E=(60*I/r)*((cos(pi*cos(theta*pi/180)/2))/sin(theta*pi/180)) 
print "E-Field for 45 degree angle = %0.2f mV/m " %(E*10**3) 
ETA_o=120*pi #constant
H=E/ETA_o #in A/m
print "H-Field for 45 degree angle = %0.5f mV/m " %(H*10**3) 

#For theta = 90 degree
theta=90  #in degree
E=(60*I/r)*((cos(pi*cos(theta*pi/180)/2))/sin(theta*pi/180)) 
print "E-Field for 90 degree angle = %0.2f mV/m " %(E*10**3) 
ETA_o=120*pi #constant
H=E/ETA_o #in A/m
print "H-Field for 90 degree angle = %0.4f mV/m " %(H*10**3) 

E-Field for 45 degree angle = 18.84 mV/m 
H-Field for 45 degree angle = 0.04997 mV/m 
E-Field for 90 degree angle = 30.00 mV/m 
H-Field for 90 degree angle = 0.0796 mV/m

Exa 3.5 : page 3.44

In [11]:
from math import pi
#given data :
#l=lambda/10 meter
#Assume pi**2 = 10
Rl=2.0 #in Ohm
#Rr=80*pi**2*(dl/lambda)**2
Rr=80*10*(1.0/10)**2 #in Ohm
print "Radiation Resistance = %0.2f Ohm" %(Rr)
ETA=Rr/(Rr+Rl) #in Ohm
print "Efficiency = %0.2f %%" %(ETA*100)

Radiation Resistance = 8.00 Ohm
Efficiency = 80.00 %

Exa 3.6 : page 3.44

In [22]:
#given data :
#l=lambda/15 meter
#Assume pi**2 = 10
Rl=2.0 #in Ohm
#Gain : 
Gain=5.33/4 #Unitless
#Directivity
Rr=80*10*(1.0/15)**2 #in Ohm
ETA=Rr/(Rr+Rl) #Unitless
Directivity=Gain/ETA #unitless
#Beam solid angle 
BSA=4.0*pi/Directivity #in steradian
print "Directivity = %0.4f " %Directivity 
print "Gain = %0.2f "%Gain 
#Effective aperture
print "Effective aperture = " ,
print round((Gain/(4*pi)),3),"lambda**2" 
print "Beam Solid Angle = %0.2f steradian  "%BSA 
Rr=80*10*(1.0/15)**2 #in Ohm
print "Radiation Resistance = %0.2f Ohm " %Rr 
print "Pt =",120*10/225,"I**2" 
print "Pr = 4*I**2" 

Directivity = 2.0820 
Gain = 1.33 
Effective aperture =  0.106 lambda**2
Beam Solid Angle = 6.04 steradian  
Radiation Resistance = 3.56 Ohm 
Pt = 5 I**2
Pr = 4*I**2

Exa 3.7 : page 3.45

In [25]:
from math import pi
#given data :
D=30.0 #in m
k=0.55 #illumination efficiency
f=4.0 #in GHz
f=f*10**9 #in Hz
c=3*10**8 #speed of light in m/s
lamda=c/f #in Meter
r=D/2 #in m
A=pi*(r**2) #in m**2
G=(4*pi/lamda**2)*k*A #Unitless
print "Gain = %0.5e"%G
HPBW=70*lamda/D #in Degree
print "HPBW = %0.3f Degree " % HPBW
BWFN=2*70*lamda/D #in Degree
print "BWFN = %0.2f Degree " %BWFN 

Gain = 8.68525e+05
HPBW = 0.175 Degree 
BWFN = 0.35 Degree

Exa 3.8 : page 3.46

In [30]:
#given data :
Rl=20.0 #in Ohm
Rr=100.0 #in Ohm
Gp=25.0 #power gain 
ETA=Rr/(Rr+Rl) #Unitless
D=Gp/ETA #unitless
print "Directivity = %0.2f" %D

Directivity = 30.00

Exa 3.9 : page 3.46

In [31]:
#given data :
lamda=10 #in m
D=80 #unitless
Aem=D*lamda**2/(4*pi) #in m**2
print "Maximum effective aperture = %0.2f m^2" %Aem

Maximum effective aperture = 636.62 m^2

Exa 3.10 : page 3.47

In [34]:
from math import log10
#given data :
P1=30 #in KW
P1=P1*1000 #in W
P2=5000 #in W
Gdb=10*log10(P1/P2) #unitless
print "Front to back ratio, Gdb =",round(Gdb ,3)

Front to back ratio, Gdb = 7.782

Exa 3.11 : page 3.47

In [36]:
#given data :
f=10 #in GHz
f=f*10**9 #in Hz
Gt=40 #in dB
Gr=40 #in dB
print "Gain = Gt = Gr =",Gt ,"dB"

Gain = Gt = Gr = 40 dB

Exa 3.12 : page 3.47

In [38]:
from math import pi
#given data :
L=10 #in m
f=1.5 #in MHz
f=f*10**6 #in Hz
X=350 #in Ohm
Q=100 #Coil parameter
c=3*10**8 #speed of light in m/s
lamda=c/f #in Meter
l_eff=2*L/2 #in m
Re=2*X/Q #in Ohm
Rr=40*pi**2*(l_eff/lamda)**2 #in hm
Gd=(3/2)*(lamda**2/(4*pi)) #unitless
ETA=Rr/(Rr+Re) #Efficiency unitless
Gp=Gd*ETA ##unitless
print "Antenna Efficiency = %0.1f %%" %(ETA*100)
print "Power gain = %0.2f " %(Gp)
#Note : Answer of Gp is wrong in the book.

Antenna Efficiency = 12.4 %
Power gain = 393.34

Exa 3.13 : page 3.48

In [41]:
#given data :
delf=600.0 #in KHz
fr=50 #in MHz
Q=(fr*10**6)/(delf*10**3) #unitless
print "Quality Factor = %0.2f " %(Q) 

Quality Factor = 83.33

Exa 3.14 : page 3.48

In [42]:
from math import pi
#given data :
OmegaA=4.0*pi #For isotropic Antenna
D=4.0*pi/OmegaA #Directivity : Unitless
print "Directivity of Isotropic Antenna = %0.2f" %D 

Directivity of Isotropic Antenna = 1.00

Exa 3.15 : page 3.48

In [50]:
from sympy import symbols, N
lamda = symbols('lamda')
#given data :
D=500.0 #Directivity : Unitless
Aem = D*lamda**2/(4*pi)
print "Aem =",N(Aem,4)

Aem = 39.79*lamda**2

Exa 3.16 : page 3.48

In [52]:
#given data
Fn_dB=1.1 #in dB
Fn=10**(Fn_dB/10) #unitless
To=290 #in Kelvin
Te=To*(Fn-1) #in Kelvin
print "Effective Noise Temperature = %0.2f degree Kelvin " %Te 

Effective Noise Temperature = 83.59 degree Kelvin

Exa 3.19 : page 3.50

In [54]:
from math import pi, log10
#given data
D=6.0 #in meter
f=10.0 #in GHz
f=f*10**9 #in Hz
Aactual=pi*D**2/4 #in m**2
Ae=0.6*Aactual #in m**2
c=3*10**8 #speed of light in m/s
lamda=c/f #in Meter
G=4*pi*Ae/lamda**2 #Unitless
Gdb=10*log10(G) #gain in dB
BWFN=140*lamda/D #in degree
print "Gain = %0.1f " %G 
print "Gain = %0.2f dB  " %Gdb 
print "Beamwidth = %0.2f degree " %BWFN 
print "Capture Area = %0.2f m**2  " %Ae 
#Note : Answer in the book is not accurate.

Gain = 236870.5 
Gain = 53.75 dB  
Beamwidth = 0.70 degree 
Capture Area = 16.96 m**2

Exa 3.20 : page 3.50

In [56]:
from math import pi
#given data
Gdb=44 #gain in dB
G=10**(Gdb/10) #gain unitless
OmegaB=4*pi/G #n steradian
THETA3db=sqrt(4*OmegaB/pi) #in Radian
print "Beamwidth THETA3db = %0.4f degree " %THETA3db 
#Note : Answer in the book is not accurate.

Beamwidth THETA3db = 0.0400 degree