# Chapter 6 : HF,VHF and UHF Antennas¶

## EXAMPLE 6.1,PAGE NUMBER 278¶

In :
from math import pi,sin

# Variable Declaration

f = 30        # frequency in MHz
f = 30*10**6  # frequency in Hz
c = 3*10**8   # speed of light in m/s
lamda = c/f   # wavelength in meter
Delta = 30    # angle of elevation in Degrees

#calculation

H = lamda/(4 * sin(Delta*pi/180))     # Rhombic height in m
l = lamda/(2 * sin(Delta*pi/180) **2) # wire length in m
phi = 90-Delta # tilt angle in Degrees

#Results

print "Rhombic height is:",round(H,2),"meter"
print "Tilt angle is:",round(phi,2),"degrees"
print "length of wire is:",round(l,2),"meter"

Rhombic height is: 5.0 meter
Tilt angle is: 60.0 degrees
length of wire is: 20.0 meter


## EXAMPLE 6.2,PAGE NUMBER 278¶

In :
from math import pi,sin

# Variable Declaration

f = 20        # frequency in MHz
f = 20*10**6  # frequency in Hz
c = 3*10**8   # speed of light in m/s
lamda = c/f   # wavelength in meter

#calculation

Delta = 10    # angle of elevation in Degrees
H = lamda/(4 * sin(Delta*pi/180))     # Rhombic height in m
l = lamda/(2 * sin(Delta*pi/180) **2) # wire length in m
phi = 90-Delta # tilt angle in Degrees

#Results

print "Rhombic height is:",round(H,3),"meter"
print "Tilt angle is:",round(phi,2),"degrees"
print "length of wire is:",round(l,3),"meter"

Rhombic height is: 21.595 meter
Tilt angle is: 80.0 degrees
length of wire is: 248.726 meter


## EXAMPLE 6.3,PAGE NUMBER 279-281¶

In :
from math import pi,sin,cos

# Variable Declaration

f = 30        # frequency in MHz
f = 30*10**6  # frequency in Hz
c = 3*10**8   # speed of light in m/s
lamda = c/f   # wavelength in meter

#calculation and results:

print "for Delta = 10 degrees"

Delta1 = 10    # angle of elevation in Degrees
H1 = lamda/(4 * sin(Delta1*pi/180))     # Rhombic height in m
l1 = lamda/(2 * sin(Delta1*pi/180) **2) # wire length in m
phi1 = 90-Delta1 # tilt angle in Degrees
print "Rhombic height is:",round(H1,3),"meter"
print "Tilt angle is:",round(phi1,2),"degrees"
print "length of wire is:",round(l1,2),"meter"

print "for Delta = 15 degrees"

Delta2 = 15    # angle of elevation in Degrees
H2 = lamda/(4 * sin(Delta2*pi/180))     # Rhombic height in m
l2 = lamda/(2 * sin(Delta2*pi/180) **2) # wire length in m
phi2 = 90-Delta2 # tilt angle in Degrees
print "Rhombic height is:",round(H2,3),"meter"
print "Tilt angle is:",round(phi2,2),"degrees"
print "length of wire is:",round(l2,2),"meter"

print "for Delta = 20 degrees"

Delta3 = 20    # angle of elevation in Degrees
H3 = lamda/(4 * sin(Delta3*pi/180))     # Rhombic height in m
l3 = lamda/(2 * sin(Delta3*pi/180) **2) # wire length in m
phi3 = 90-Delta3 # tilt angle in Degrees
print "Rhombic height is:",round(H3,3),"meter"
print "Tilt angle is:",round(phi3,2),"degrees"
print "length of wire is:",round(l3,2),"meter"

print "for Delta = 25 degrees"

Delta4 = 25    # angle of elevation in Degrees
H4 = lamda/(4 * sin(Delta4*pi/180))     # Rhombic height in m
l4 = lamda/(2 * sin(Delta4*pi/180) **2) # wire length in m
phi4 = 90-Delta4 # tilt angle in Degrees
print "Rhombic height is:",round(H4,3),"meter"
print "Tilt angle is:",round(phi4,2),"degrees"
print "length of wire is:",round(l4,2),"meter"

print "for Delta = 30 degrees"

Delta5 = 30    # angle of elevation in Degrees
H5 = lamda/(4 * sin(Delta5*pi/180))     # Rhombic height in m
l5 = lamda/(2 * sin(Delta5*pi/180) **2) # wire length in m
phi5 = 90-Delta5 # tilt angle in Degrees
print "Rhombic height is:",round(H5,3),"meter"
print "Tilt angle is:",round(phi5,2),"degrees"
print "length of wire is:",round(l5,2),"meter"

print "for Delta = 35 degrees"

Delta6 = 35    # angle of elevation in Degrees
H6 = lamda/(4 * sin(Delta6*pi/180))     # Rhombic height in m
l6 = lamda/(2 * sin(Delta6*pi/180) **2) # wire length in m
phi6 = 90-Delta6 # tilt angle in Degrees
print "Rhombic height is:",round(H6,3),"meter"
print "Tilt angle is:",round(phi6,2),"degrees"
print "length of wire is:",round(l6,2),"meter"

print "for Delta = 40 degrees"

Delta7 = 40    # angle of elevation in Degrees
H7 = lamda/(4 * sin(Delta7*pi/180))     # Rhombic height in m
l7 = lamda/(2 * sin(Delta7*pi/180) **2) # wire length in m
phi7 = 90-Delta7 # tilt angle in Degrees
print "Rhombic height is:",round(H7,3),"meter"
print "Tilt angle is:",round(phi7,2),"degrees"
print "length of wire is:",round(l7,2),"meter"

for Delta = 10 degrees
Rhombic height is: 14.397 meter
Tilt angle is: 80.0 degrees
length of wire is: 165.82 meter
for Delta = 15 degrees
Rhombic height is: 9.659 meter
Tilt angle is: 75.0 degrees
length of wire is: 74.64 meter
for Delta = 20 degrees
Rhombic height is: 7.31 meter
Tilt angle is: 70.0 degrees
length of wire is: 42.74 meter
for Delta = 25 degrees
Rhombic height is: 5.916 meter
Tilt angle is: 65.0 degrees
length of wire is: 27.99 meter
for Delta = 30 degrees
Rhombic height is: 5.0 meter
Tilt angle is: 60.0 degrees
length of wire is: 20.0 meter
for Delta = 35 degrees
Rhombic height is: 4.359 meter
Tilt angle is: 55.0 degrees
length of wire is: 15.2 meter
for Delta = 40 degrees
Rhombic height is: 3.889 meter
Tilt angle is: 50.0 degrees
length of wire is: 12.1 meter


## EXAMPLE 6.4,PAGE NUMBER 281¶

In :
from math import pi,sin,cos

# Variable Declaration

f = 30        # frequency in MHz
f = 30*10**6  # frequency in Hz
c = 3*10**8   # speed of light in m/s
lamda = c/f   # wavelength in meter
Delta = 30    # angle of elevation in Degrees

#calculation

k = 0.74      # constant
H = lamda/(4 * sin(Delta*pi/180))     # Rhombic height in m
l = lamda/(2 * sin(Delta*pi/180) **2)*k # wire length in m
phi = 90-Delta # tilt angle in Degrees

#Results

print "Rhombic height is:",round(H,2),"meter"
print "Tilt angle is:",round(phi,2),"degrees"
print "length of wire is:",round(l,2),"meter"

Rhombic height is: 5.0 meter
Tilt angle is: 60.0 degrees
length of wire is: 14.8 meter


## EXAMPLE 6.5,PAGE NUMBER 282¶

In :
from math import pi,sin

# Variable Declaration

f = 20        # frequency in MHz
f = 20*10**6  # frequency in Hz
c = 3*10**8   # speed of light in m/s
lamda = c/f   # wavelength in meter
Delta = 20    # angle of elevation in Degrees
k = 0.74      # constant

#calculation

H = lamda/(4 * sin(Delta*pi/180))     # Rhombic height in m
l = lamda/(2 * sin(Delta*pi/180) **2)*k # wire length in m
phi = 90-Delta # tilt angle in Degrees

#Results

print "Rhombic height is:",round(H,2),"meter"
print "Tilt angle is:",round(phi,2),"degrees"
print "length of wire is:",round(l,2),"meter"

Rhombic height is: 10.96 meter
Tilt angle is: 70.0 degrees
length of wire is: 47.44 meter


## EXAMPLE 6.6,PAGE NUMBER 282¶

In :
from __future__ import division

# Variable Declaration

f_MHz = 172        # frequency in MHz
c = 3*10**8        # speed of light in m/s

#calculation

lamda = c/f_MHz    # wavelength in m
La = 478/f_MHz     # length of driven element in feet
Lr = 492/f_MHz     # length of reflector in feet
Ld = 461.5/f_MHz   # length of director in feet
S = 142/f_MHz      # element spacing in feet

#Results

print "length of driven element is:", round(La,2),"feet"
print "length of reflector is:", round(Lr,2),"feet"
print "length of director is:", round(Ld,3),"feet"
print "element spacing is:",round(S,3),"feet"

length of driven element is: 2.78 feet
length of reflector is: 2.86 feet
length of director is: 2.683 feet
element spacing is: 0.826 feet


## EXAMPLE 6.7,PAGE NUMBER 283¶

In :
from __future__ import division

# Variable Declaration

G = 12        # required gain in dB
f = 200       # frequency in MHz
f = 200*10**6  # frequency in Hz
c = 3*10**8    # speed of light in m/s

#calculations

lamda = c/f   # wavelength in m
La = 0.46*lamda   # length of driven element in m    (note: in book La is given 0.416*lamda misprint)
Lr = 0.475*lamda  # length of reflector in m
Ld1 = 0.44*lamda  # length of director1 in m
Ld2 = 0.44*lamda  # length of director2 in m
Ld3 = 0.43*lamda  # length of director3 in m
Ld4 = 0.40*lamda  # length of director4 in m
SL = 0.25*lamda   # spacing between reflector and driver in m
Sd = 0.31*lamda   # spacing director and driving element in m
d = 0.01*lamda    # diameter of elements in m
l = 1.5*lamda     # length of array in m

#Results

print "length of driven element is:" ,round(La,2),"m"
print "length of reflector is:",round(Lr,4),"m"
print "length of director1 is:",round(Ld1,2),"m"
print "length of director2 is:",round(Ld2,2),"m"
print "length of director3 is:",round(Ld3,3),"m"
print "length of director4 is:",round(Ld4,2),"m"
print "spacing between reflector and driver is:",round(SL,3),"m"
print "spacing director and driving element is:",round(Sd,3),"m"
print "diameter of elements is:",round(d,3),"m"
print "length of array is:",round(l,2),"m"

length of driven element is: 0.69 m
length of reflector is: 0.7125 m
length of director1 is: 0.66 m
length of director2 is: 0.66 m
length of director3 is: 0.645 m
length of director4 is: 0.6 m
spacing between reflector and driver is: 0.375 m
spacing director and driving element is: 0.465 m
diameter of elements is: 0.015 m
length of array is: 2.25 m


## EXAMPLE 6.8,PAGE NUMBER 283¶

In :
from __future__ import division
from math import atan

# Variable Declaration

G = 9             # required gain in dB
f_l = 125         # lowest frequency in MHz
f_l = 125*10**6   # lowest frequency in Hz
f_h = 500         # highest frequency in MHz
f_h = 500*10**6   # lowest frequency in Hz
c = 3*10**8       # speed of light in m/s
tau = 0.861       # scaling factor
sigma = 0.162     # spacing factor

#calculation

lamda_l = c/f_l  # longest wavelength in m
lamda_s = c/f_h  # shortest wavelength in m
alpha = 2*atan((1-tau)/(4*sigma))  # wedge angle in Degrees
L1 =  lamda_l/2  # in m
L2 = tau*L1  # in m
L3 = tau*L2  # in m
L4 = tau*L3  # in m
L5 = tau*L4  # in m
L6 = tau*L5  # in m
L7 = tau*L6  # in m
L8 = tau*L7  # in m
L9 = tau*L8  # in m
L10 = tau*L9  # in m
L11 = tau*L10  # in m

# element spacing relation
#formula : sn = 2*sigma*Ln

S1 = 2*sigma*L1  # in m
S2 = 2*sigma*L2  # in m
S3 = 2*sigma*L3  # in m
S4 = 2*sigma*L4  # in m
S5 = 2*sigma*L5  # in m
S6 = 2*sigma*L6  # in m
S7 = 2*sigma*L7  # in m
S8 = 2*sigma*L8  # in m
S9 = 2*sigma*L9  # in m
S10 = 2*sigma*L10  # in m
S11 = 2*sigma*L11  # in m

#results

print("designing of log-periodic antenna:")

print "L1 is:",round(L1,4),"m"
print "L2 is:",round(L2,4),"m"
print "L3 is:",round(L3,4),"m"
print "L4 is:",round(L4,4),"m"
print "L5 is:",round(L5,4),"m"
print "L6 is:",round(L6,4),"m"
print "L7 is:",round(L7,4),"m"
print "L8 is:",round(L8,4),"m"
print "L9 is:",round(L9,4),"m"
print "L10 is:",round(L10,4),"m"
print "L11 is:",round(L11,4),"m"

print "elements spacing relation:"

print "S1 is:",round(S1,4),"m"
print "S2 is:",round(S2,4),"m"
print "S3 is:",round(S3,4),"m"
print "S4 is:",round(S4,4),"m"
print "S5 is:",round(S5,4),"m"
print "S6 is:",round(S6,4),"m"
print "S7 is:",round(S7,4),"m"
print "S8 is:",round(S8,4),"m"
print "S9 is:",round(S9,4),"m"
print "S10 is:",round(S10,4),"m"
print "S11 is:",round(S11,4),"m"

designing of log-periodic antenna:
L1 is: 1.2 m
L2 is: 1.0332 m
L3 is: 0.8896 m
L4 is: 0.7659 m
L5 is: 0.6595 m
L6 is: 0.5678 m
L7 is: 0.4889 m
L8 is: 0.4209 m
L9 is: 0.3624 m
L10 is: 0.312 m
L11 is: 0.2687 m
elements spacing relation:
S1 is: 0.3888 m
S2 is: 0.3348 m
S3 is: 0.2882 m
S4 is: 0.2482 m
S5 is: 0.2137 m
S6 is: 0.184 m
S7 is: 0.1584 m
S8 is: 0.1364 m
S9 is: 0.1174 m
S10 is: 0.1011 m
S11 is: 0.087 m


## EXAMPLE 6.9,PAGE NUMBER 285¶

In :
from math import pi,cos,sqrt

# Variable Declaration

E_rms = 10  # electric field in mV/m
E_rms = 10*10 **-3  # electric field in V/m
f = 2  # frequency in MHz
f = 2*10 **6  # frequency in Hz
N = 10  # number of turns
phi = 0  # angle between the plane of loop and direction of incident wave in Degrees
S = 1.4  # area of loop antenna in m **2
c = 3*10 **8  # speed of light in m/s

#calculation

lamda = c/f  # wavelength in m
E_max = sqrt(2)*E_rms  # electric field in V/m
V_rms = (2*pi*E_max*S*N/lamda)*cos(phi)  # induced voltage

#Result

print "induced voltage is:",round(V_rms*1000,2),"mV"

induced voltage is: 8.29 mV


## EXAMPLE 6.10,PAGE NUMBER 285¶

In :
# Variable Declaration

D = 0.5  # diameter of loop antenna in m
a = D/2  # radius of loop antenna in m
f = 1  # frequency in MHz
f = 1*10**6  # frequency in Hz
c = 3*10**8  # speed of light in m/s

#calculation

lamda = c/f  # wavelength in m
Rr = 3720*(a/lamda)  # radiation resistance of loop antenna in ohm

#Results

print "radiation resistance of loop antenna is:",Rr,"ohm"

radiation resistance of loop antenna is: 3.1 ohm


## EXAMPLE 6.11,PAGE NUMBER 285-286¶

In :
from __future__ import division
from math import pi

# Variable Declaration

a = 0.5  # radius of loop antenna in m
f = 0.9  # frequency in MHz
f = 0.9*10**6  # frequency in Hz
c = 3*10**8  # speed of light in m/s

#calculation

lamda = c/f  # wavelength in m
k = (2*pi*a)/lamda  # constant

#Results

print "the value of k is:",round(k,2)
print "since,k<1/3"
print "So Directivity of loop antenna is D = 1.5"

the value of k is: 0.01
since,k<1/3
So Directivity of loop antenna is D = 1.5


## EXAMPLE 6.13,PAGE NUMBER 286¶

In :
from sympy import Symbol

#variable declaration and calculation

Lm = Symbol('Lm')  # defining Lm as lambda
d = 1.5*Lm  # diameter of antenna in m
a = d/2  # radius of antenna in m
Rr = 3720*(a/Lm)  # radiation resistance of loop antenna in ohm
D = 4.25*(a/Lm) # Directivity of the loop antenna

#results

print "radiation resistance of the loop antenna is:",round(Rr,0),"ohm"
print "Directivity of the loop antenna is:",round(D,4)

radiation resistance of the loop antenna is: 2790.0 ohm
Directivity of the loop antenna is: 3.1875


## EXAMPLE 6.14,PAGE NUMBER 287¶

In :
from math import sqrt,pi
from sympy import Symbol

#Variable declaration

Gp = 28  # power gain

#calculations

Lm = Symbol('Lm')  # defining Lm as lamda
d = Lm/2           # length of dipole

#formula : Gp = 4*(L/lamda)

L = Gp*Lm/4  # array length
N = 7*2      # Number of elements in the array when spaced at lamda/2

# formula : B.W = 2*sqrt((2*/N)*(lamda/d))

BW = 2*sqrt(2*Lm/(N*d))  # null-to-null beam width in radians
BW_d = BW*180/pi         # null-to-null beam width in degrees

#Results

print "Number of elements in the array when spaced at lamda/2 are:",N
print "array length(where Lm is wavelength in m) is:",L,"m"
print "null-to-null beam width is:",round(BW_d,1),"degrees"

Number of elements in the array when spaced at lamda/2 are: 14
array length(where Lm is wavelength in m) is: 7*Lm m
null-to-null beam width is: 61.3 degrees


## EXAMPLE 6.15,PAGE NUMBER 287¶

In :
from __future__ import division
from math import pi,sqrt

# Variable Declaration

S = 0.05        # spacing in m
Dh = 0.1        # diameter of helical antenna in m
N = 20          # number of turns
f = 1000        # frequency in MHz
f = 1000*10**6  # frequency in MHz
c = 3*10**8     # speed of light in m/s

#calculation

lamda = c/f     # wavelength in m
C = pi*Dh       # circumfrence of helix in m
La = N*S        # axial legth in m
phi_not = (115*(lamda**(3/2))/(C*sqrt(La)))   # B.W.F.N., null-to-null beamwidth of main beam in Degreess
phi = (52*lamda**(3/2)/(C*sqrt(La)))          # H.P.B.W, half power beamwidth in Degreess
D = (15*N*C**2*S/(lamda)**3)                  # Directivity

#Results

print "B.W.F.N., null-to-null beamwidth of main beam is:",round(phi_not,1),"degrees"
print "H.P.B.W, half power beamwidth is:",round(phi,1),"degrees"
print "Directivity is:",round(D,2)

B.W.F.N., null-to-null beamwidth of main beam is: 60.1 degrees
H.P.B.W, half power beamwidth is: 27.2 degrees
Directivity is: 54.83