chapter 06 : Practical Antennas - II

Exa 6.1 : page 6.39

In [2]:
from math import sqrt
n=20 #no. of turns
#Clamda=lamda
#Slamda=lamda/4
#HPBW : 
# HPBW=52/(Clamda*sqrt(n*Slamda))
#Putting values below :
Clamda=1 #in Meter
Slamda=1.0/4 #in Meter
HPBW=52.0/(Clamda*sqrt(n*Slamda)) #in degree
print "HPBW = %0.2f degree " %HPBW 
#Axial Ratio
Aratio=(2*n+1)/2 #unitless
print "Axial Ratio = %0.2f "%Aratio 
#Gain
D=12*Clamda**2*n*Slamda #unitless
print "Gain = %0.2f "%D 

HPBW = 23.26 degree 
Axial Ratio = 20.00 
Gain = 60.00

Exa 6.2 : page 6.39

In [15]:
from math import pi
#Part (a): Given data :
n=20 #no. of turns
Slamda=0.472 #in meter
D=12*n*Slamda #in meter
from sympy import symbols, N, sqrt
lamda = symbols('lamda', real =True)
Ae=(lamda**2/(4*pi))*D
d=(sqrt(Ae))
print "Part (a) : d=",N(d,1)
print "Part (b) : With a space of 3*lamda the total effective area : " 
Ae=9.02*lamda**2*4
D=4*pi*Ae/lamda**2
print "\t   D = %0.2f" %D

Part (a) : d= 3.0*Abs(lamda)
Part (b) : With a space of 3*lamda the total effective area : 
	   D = 453.39

Exa 6.3 : page 6.40

In [16]:
from math import log10, ceil
#from 7dBi gain graph the data obtained is given below :
K=1.2 #Scale constant
alfa=1.5 #Apex angle in degree
Slamda=0.15 
print "K**n=F or n=logF/logK" 
F=4 
n=log10(F)/log10(K) 
n=ceil(n) 
nplus1=n+1 
print "Apex Angle = %0.2f degree " %alfa 
print "Sale constant = %0.2f" %K 
print "No. of elements = %d " %n 

K**n=F or n=logF/logK
Apex Angle = 1.50 degree 
Sale constant = 1.20
No. of elements = 8

Exa 6.4 : page 6.40

In [18]:
from math import log10
#Given data :
#d=10*lamda
print "d=10*lamda" 
print "Power Gain : G=6*(d/lamda)**2" 
print "Putting value of d, we get G=6*10**2"
G=6*10**2 #unitless
print "Power gain = %0.2f " %G 
G_dB=10*log10(G) #in dB
print "Power Gain = %0.1f dB  " %G_dB 

d=10*lamda
Power Gain : G=6*(d/lamda)**2
Putting value of d, we get G=6*10**2
Power gain = 600.00 
Power Gain = 27.8 dB

Exa 6.5 : page 6.40

In [19]:
from math import log10
#Given Data:
f=10.0 #in GHz
f=f*10**9 #in Hz
BWFN=10 #in degree
c=3*10**8 #Speed of light in m/s
lamda=c/f #in meter
#Part (a):
d=140*lamda/BWFN #in meter
print "Diameter of a parabolic Antenna = %0.2f m" %d
#Part (b):
HPBW=58.0*lamda/d #in degree
print "3-dB Beamwidth = %0.2f degree " %HPBW 
#Part (c):
Gp=6*(d/lamda)**2 #gain 
Gp_dB=10*log10(Gp) #in dB
print "Power Gain = %0.2f dB " %Gp_dB 

Diameter of a parabolic Antenna = 0.42 m
3-dB Beamwidth = 4.14 degree 
Power Gain = 30.70 dB

Exa 6.6 : page 6.41

In [22]:
from math import log10
#Given Data:
f=1430.0 #in MHz
f=f*10**6 #in Hz
d=64 #in meter
c=3*10**8 #Speed of light in m/s
lamda=c/f #in meter
#Part (a):
HPBW=70*lamda/d #in degree
print "HPBW = %0.2f degree " %HPBW 
#Part (b):
BWFN=140*lamda/d #in degree
print "BWFN = %0.2f degree " %BWFN 
#Part (c):
Gp=6*(d/lamda)**2 #gain 
Gp_dB=10*log10(Gp) #in dB
print "Power Gain = %0.f dB  " %Gp_dB 

HPBW = 0.23 degree 
BWFN = 0.46 degree 
Power Gain = 57 dB

Exa 6.7 : page 6.42

In [24]:
from math import sqrt
#Given Data:
f=15.0 #in GHz
f=f*10**9 #in Hz
Gp_dB=75.0 #in dB
c=3*10**8 #Speed of light in m/s
lamda=c/f #in meter
#Formula : Gp=9.87*(d/lamda)**2
#Formula : Gp_dB=10log10(Gp)
d=sqrt((10**(Gp_dB/10))*lamda**2/9.87) #in meter
print "Diameter of a parabolic reflector = %0.2f m" %d

Diameter of a parabolic reflector = 35.80 m

Exa 6.8 : page 6.42

In [27]:
#Given Data:
f=5000.0 #in MHz
f=f*10**6 #in Hz
d=10 #in feet
d=d*0.3048 #in meter
c=3*10**8 #Speed of light in m/s
lamda=c/f #in meter
r=2*d**2.0/lamda #in meter
print "Minimum distance between primary and secondary antenna = %0.f m" %r
# Ans wrong in the textbook

Minimum distance between primary and secondary antenna = 310 m

Exa 6.9 : page 6.42

In [29]:
#Given Data:
K=55.0 #Aperture Efficiency in %
K=K/100 #Aperture Efficiency
f=15.0 #in GHz
f=f*10**9 #in Hz
c=3*10**8 #Speed of light in m/s
lamda=c/f #in meter
G_dB=30 #in dB
G=10**(G_dB/10) #Gain unitless
#Formula : G=4*pi*K*A/lamda**2
A=(G*lamda**2)/(4*pi*K) #in m**2
print "Diameter of parabolic reflector = %0.3f m**2" %A 
#Part (b)
d=sqrt(4.0*A/pi) #in meter
HPBW=70*lamda/d #in degree
print "HPBW = %0.2f degree " %HPBW 
#Part (c)
BWFN=140*lamda/d #in Degree
print "BWFN = %0.2f degree " %BWFN 
#Note : Answer in the book is not accurate.

Diameter of parabolic reflector = 0.058 m**2
HPBW = 5.16 degree 
BWFN = 10.31 degree

Exa 6.10 : page 6.43

In [31]:
#Given Data:
Tau=0.7 #Design Factor
L1=0.3*2 #in meter
c=3*10**8 #speednof light in m/s
f1=(c/(2*L1))/10**6 #in MHz
#Design factor : L1/L2=L2/L3=L3/L4=.......=0.7
L2=0.7/L1 #in meter
f2=f1*0.7 #in MHz
f3=f2*0.7 #in MHz
f4=f3*0.7 #in MHz
f5=f4*0.7 #in MHz
f6=f5*0.7 #in MHz
f7=f6*0.7 #in MHz
f8=f7*0.7 #in MHz
f9=f8*0.7 #in MHz
f10=f9*0.7 #in MHz
print "Cutoff frequencies in MHz :"
print "f1 = %0.2f MHz " %f1 
print "f2 = %0.2f MHz " %f2
print "f3 = %0.2f MHz " %f3
print "f4 = %0.2f MHz " %f4
print "f5 = %0.2f MHz " %f5
print "f6 = %0.2f MHz " %f6
print "f7 = %0.2f MHz " %f7
print "f8 = %0.2f MHz " %f8
print "f9 = %0.2f MHz " %f9
print "f10 = %0.2f MHz " %f10
print "Passband = %0.2f"%(f1-f10 )

Cutoff frequencies in MHz :
f1 = 250.00 MHz 
f2 = 175.00 MHz 
f3 = 122.50 MHz 
f4 = 85.75 MHz 
f5 = 60.02 MHz 
f6 = 42.02 MHz 
f7 = 29.41 MHz 
f8 = 20.59 MHz 
f9 = 14.41 MHz 
f10 = 10.09 MHz 
Passband = 239.91

Exa 6.11 : page 6.44

In [30]:
from math import pi, tan, acos
#Given Data:
from sympy import symbols, simplify, atan, acos, N
lamda = symbols('lamda', real = True)
#Assuming typical values for f 
f1=0.2*lamda #in E-plane 
f2=0.375*lamda # in H-plane" 
b=10*lamda #  mouth height
delta=0.2*lamda
print "Length :"
L=pow(b,2)/(8*delta)
print (L)
print "Flare Angle (Theta):",
Theta=atan(b/(2*L))*180/pi
print round(Theta,1),'degree'
print "Flare Angle (fi):",
delta=0.375*lamda
fi=acos(L/(L+delta))*180/pi  # degree
print round(fi,1),'degree'
print "fi=",(acos((10**2/(8*0.2))/((10**2/(8*0.2))+0.375)))," radian" 
fi=(acos((10**2/(8*0.2))/((10**2/(8*0.2))+0.375))) #in Degree
print "Width :" 
a=2*L*tan(fi)
print N(a,3)

Length :
62.5*lamda
Flare Angle (Theta): 4.6 degree
Flare Angle (fi): 6.3 degree
fi= 0.109271705413178  radian
Width :
13.7*lamda