Chapter 7 : Microwave Antennas¶

Example 7.1,Page Number 337¶

In :
from __future__ import division

#variable declaration
D = 2 # Diameter of paraboloid reflector in m
c = 3*10**8 # speed of light in m/s
f = 5 # frequency in GHz
f = 5*10**9 # frequency in Hz

#calculations
lamda = c/f # wavelength in m
BWFN = 140*(lamda/D) # null-to-null beamwidth in degrees
HPBW = 70*(lamda/D)  # half power beamwidth in degrees

#result
print "null-to-null beamwidth in degrees:",round(BWFN,3)
print "half power beamwidth in degrees:",round(HPBW,3)
null-to-null beamwidth in degrees: 4.2
half power beamwidth in degrees: 2.1

Example 7.2,Page Number 337¶

In :
from __future__ import division
from math import log10

#variable declaration
D  = 2      # mouth diameter of paraboloid reflector in m
c  = 3*10**8 # speed of light in m/s
f  = 5      # frequency in GHz
f  = 5*10**9 # frequency in Hz

#calculations
lamda  = c/f # wavelength in m
G  = 6.4*(D/lamda)**2 # power gain of paraboloid
G_p  = 10*log10(G) #power gain in dB

#result
print "power gain in dB:",round(G_p,3)
power gain in dB: 38.519

Example 7.3,Page Number 337¶

In :
from __future__ import division
from math import log10

#variable declaration

D_a = 0.15   # mouth Diameter of paraboloid in m
c = 3*10**8  # speed of light in m/s
f = 10       # frequency in GHz
f = 10*10**9 # frequency in Hz

#calculations
lamda = c/f  # wavelength in m
BWFN = 140*(lamda/D_a)   # null-to-null beamwidth in degrees
HPBW = 70*(lamda/D_a)    # half power beamwidth in degrees
G_p = 6.4*(D_a/lamda)**2 # power gain of paraboloid
G_p = 10*log10(G_p)      # power gain in dB

#result
print "null-to-null beamwidth in degrees:",round(BWFN,3)
print "half power beamwidth in degrees:",round(HPBW,3)
print "power gain in dB:",round(G_p,3)
null-to-null beamwidth in degrees: 28.0
half power beamwidth in degrees: 14.0
power gain in dB: 22.041

Example 7.4,Page Number 338¶

In :
from __future__ import division
from math import log10

#variable declaration
D_a = 1.8 #mouth diameter of paraboloid reflector in m
c = 3*10**8 # speed of light in m/s
f = 2       # frequency in GHz
f = 2*10**9 # frequency in Hz

#calculations
lamda = c/f              # wavelength in m
G_p = 6.4*(D_a/lamda)**2 # power gain of paraboloid
G_p = 10*log10(G_p)      # power gain in dB

#result
print "power gain in dB:",round(G_p,3)
power gain in dB: 29.645

Example 7.5,Page Number 338¶

In :
from __future__ import division
from math import log10

#variable declaration
c = 3*10**8 # speed of light in m/s
f = 5 # frequency in GHz
f = 5*10**9 # frequency in Hz
lamda = c/f # wavelength in m
BWFN = 10 # null-to-null beamwidth in degrees

#calculations
# formula: BWFN = 140*(lamda/D_a)
D_a = 140*lamda/BWFN # mouth Diameter of paraboloid reflector in m
HPBW = 70*(lamda/D_a) # half power beamwidth in degrees
G_p = 6.4*(D_a/lamda)**2 # power gain of paraboloid

#result
print "half power beamwidth in degrees:",round(HPBW,3)
print "mouth Diameter of paraboloid reflector in m:",round(D_a,3)
print "power gain of paraboloid:",round(G_p,3)
half power beamwidth in degrees: 5.0
mouth Diameter of paraboloid reflector in m: 0.84
power gain of paraboloid: 1254.4

Example 7.6,Page Number 339¶

In :
from __future__ import division
from math import log10,pi

#variable declaration
b = 0.65 # illumination efficiency
D_a = 6 # mouth diameter of paraboloid reflector in m
c = 3*10**8 # speed of light in m/s
f = 10 # frequency in GHz
f = 10*10**9 # frequency in Hz

#calculations
lamda = c/f # wavelength in m
A = pi*(D_a)**2/4 # Actual area in m**2
A_c = 0.65*A # capture area in m**2
D = 6.4*(D_a/lamda)**2 # directivity
D = 10*log10(D) # directivity in dB
phi = 70*(lamda/D_a) # half power beam width in degrees
phi_not = 2*phi # null-to-null main beam width in degrees

#result
print "directivity in dB:",round(D,3)
print "half power beam width in degrees:",round(phi,3)
print "null-to-null main beam width in degrees:",round(phi_not,3)
print "capture area in m**2:",round(A_c,3)
directivity in dB: 54.082
half power beam width in degrees: 0.35
null-to-null main beam width in degrees: 0.7
capture area in m**2: 18.378

Example 7.7,Page Number 339¶

In :
from __future__ import division

#variable declaration
D_a = 6     # Diameter of paraboloid reflector in m
c = 3*10**8 # speed of light in m/s
f = 4       # frequency in GHz
f = 4*10**9 # frequency in Hz

#calculations
lamda = c/f # wavelength in m
r = (2*D_a**2)/lamda # required minimum distance between two antennae in m

#result
print "required minimum distance between two antennae in m:",round(r,3)
required minimum distance between two antennae in m: 960.0

Example 7.8,Page Number 340¶

In :
from __future__ import division
from math import sqrt

#variable declaration
G_p = 1000 # gain
c = 3*10**8 # speed of light in m/s
f = 3 # frequency in GHz
f = 3*10**9 # frequency in Hz
lamda = c/f # wavelength in m

#calculations
# formula : G_p = 6.4*(D_a/lambda)**2 # power gain
D_a = lamda*(sqrt(G_p/6.4)) # mouth Diameter of paraboloid in m
BWFN = 140*(lamda/D_a) # null-to-null beamwidth in degrees
HPBW = 70*(lamda/D_a) # half power beamwidth in degrees

#result
print "mouth Diameter of paraboloid in m",round(D_a,3)
print "null-to-null beamwidth in degrees:",round(BWFN,3)
print "half power beamwidth in degrees:",round(HPBW,3)
mouth Diameter of paraboloid in m 1.25
null-to-null beamwidth in degrees: 11.2
half power beamwidth in degrees: 5.6

Example 7.9,Page Number 340¶

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

#variable declaration
c = 3*10**8 # speed of light in m/s
f = 10 # frequency in GHz
f = 10*10**9 # frequency in Hz
lamda = c/f # wavelength in m
G_p = 75 # power gain in dB

#calculations

# formula : G_p = 10*log10(G_p) # power gain in dB
G = 10**(G_p/10) # simple power gain
# formula : G = 6.4*(D_a/lamda)**2 # power gain
D_a = lamda*(sqrt(G/6.4)) # mouth Diameter of paraboloid in m
A = pi*(D_a)**2/4 # Actual area in m**2
A_c = 0.65*A # capture area in m**2
BWFN = 140*(lamda/D_a) # null-to-null beamwidth in degrees
HPBW = 70*(lamda/D_a) # half power beamwidth in degrees

#result
print "null-to-null beamwidth in degrees:",round(BWFN,3)
print "half power beamwidth in degrees:",round(HPBW,3)
print "capture area in m**2:",round(A_c,3)

#answer of capture area is slightly more as compare to the book
null-to-null beamwidth in degrees: 0.063
half power beamwidth in degrees: 0.031
capture area in m**2: 2270.209

Example 7.10,Page Number 341¶

In :
from __future__ import division
from math import log10,pi

#variable declaration
D_a = 60 # mouth diameter of paraboloid reflector in m
c = 3*10**8 # speed of light in m/s
f = 2 # frequency in GHz
f = 2*10**9 # frequency in Hz

#calculations
lamda = c/f # wavelength in m
phi = 70*(lamda/D_a) # half power beam width in degrees
phi_not = 140*(lamda/D_a) # null-to-null main beam width in degrees
G_p = 6.4*(D_a/lamda)**2 # power gain of paraboloid
G_p = 10*log10(G_p) #power gain in dB

#result
print "half power beam width in degrees:",round(phi,3)
print "null-to-null main beam width in degrees:",round(phi_not,3)
print "power gain in dB:",round(G_p,3)
half power beam width in degrees: 0.175
null-to-null main beam width in degrees: 0.35
power gain in dB: 60.103

Example 7.11,Page Number 342¶

In :
from __future__ import division
from math import log10

#variable declaration
D = 22 # mouth diameter of paraboloid reflector in m
c = 3*10**8 # speed of light in m/s
f = 5 # frequency in GHz
f = 5*10**9 # frequency in Hz
lamda = c/f # wavelength in m
b = 0.6 # illumination efficiency

#calculations
G_p = b*(D/lamda)**2 # power gain of paraboloid
G_p = 10*log10(G_p) #power gain in dB

#result
print "power gain in dB:",round(G_p,3)
power gain in dB: 49.067

Example 7.12,Page Number 342¶

In :
from __future__ import division
from math import pi

#variable declaration
c = 3*10**8 # speed of light in m/s
f = 2 # frequency in GHz
f = 2*10**9 # frequency in Hz
lamda = c/f # wavelength in m
BWFN = 12 # null-to-null main beam width in degrees

#calculalations
# formula : BWFN = 140*(lamda/D_a)
D_a = 140*lamda/BWFN # mouth diameter of paraboloid reflector in m
A = pi*(D_a)**2/4 # Actual area in m**2
A_c = 0.65*A # capture area in m**2

#result
print "mouth diameter of paraboloid reflector in m:",round(D_a,3)
print "capture area in m**2:",round(A_c,4)
mouth diameter of paraboloid reflector in m: 1.75
capture area in m**2: 1.5634

Example 7.13,Page Number 343¶

In :
from __future__ import division
from math import log10

#variable declaration
c=3*10**8   # speed of light in m/s
f=2.5       # frequency in GHz
f=2.5*10**9 # frequency in Hz
lamda=c/f   # wavelength in m
BWFN=3 # null-to-null main beam width in degrees

#calculations
# formula : BWFN=140*(lamda/D_a)
D_a=140*lamda/BWFN # mouth diameter of paraboloid reflector in m
G=6.4*(D_a/lamda)**2 # power gain of paraboloid
G_p=10*log10(G) #power gain in dB

#calculations
print "power gain in dB:",round(G_p,3)
print "mouth diameter of paraboloid reflector in m:",round(D_a,3)
power gain in dB: 41.442
mouth diameter of paraboloid reflector in m: 5.6

Example 7.14,Page Number 343¶

In :
from __future__ import division
from math import log10
from sympy import Symbol

#variable declaration
phi = 5 # HPBW,half power beam width in Degrees
phi_not = 2*phi # BWFN, null-to-null beam width in degrees
Lm = Symbol('Lm') # defining Lm as lambda

#calculations
# formula : phi = 70*(Lm/D_a) # where Lm is wavelength in m and D_a is mouth diameter in m
D_a = (70*Lm)/phi
G_p = 6.4*(D_a/Lm)**2
G_p = 10*log10(G_p) # power gain in dB

#result
print "BWFN, null-to-null beam width in degrees:",round(phi_not,3)
print "power gain in dB:",round(G_p,3)
BWFN, null-to-null beam width in degrees: 10.0
power gain in dB: 30.984

Example 7.15,Page Number 344¶

In :
from __future__ import division
from math import log10
from sympy import Symbol

#variable declaration
Lm = Symbol('Lm')# defining Lm as lambda
D_a = 8*Lm # where D_a is mouth diameter in m and Lm is wavelength in m

#calculations
# formula : G_p = 6.4*(D/lambda)**2
G_p = 6.4*(D_a/Lm)**2 #power gain
G_p = 10*log10(G_p) # power gain in dB

#result
print "power gain in dB:",round(G_p,3)
power gain in dB: 26.124

Example 7.16,Page Number 344¶

In :
from __future__ import division
from sympy import Symbol

#variable declaration
Lm = Symbol('Lm') # defining Lm as lamda
D_a = 6*Lm        # where D_a is mouth diameter in m and Lm is wavelength

#calculations
# formula : HPBW = phi = 70*(lamda/D_a)
phi = 70*(Lm/D_a) # half power beam width in degrees
phi_not = 2*phi   # null-to-null beam width in degrees
# formula : D = 6.4*(D_a/lambda)**2
D = 6.4*(D_a/Lm)**2

#result
print "Directivity:",round(D,3)
print "half power beam width in degrees:",round(phi,3)
print "null-to-null beam width in degrees:",round(phi_not,3)
Directivity: 230.4
half power beam width in degrees: 11.667
null-to-null beam width in degrees: 23.333

Example 7.17,Page Number 344¶

In :
from __future__ import division
from math import log10

#variable declaration
f = 6 # frequency in GHz
f = 6*10**9 # frequency in Hz
c = 3*10**8 # speed of light in m/s
lamda = c/f # wavelength in m
d = 12 # aperture length in cm
d = 12*10**-2 # aperture length in m
w = 6 # aperture width in cm
w = 6*10**-2 # aperture width in m

#calculations
phi_E = 56*(lamda/d) # half power beam width for aperture length d in Degrees
phi_H = 67*(lamda/w) # half power beam width for aperture width w in Degrees
G_p = (4.5*w*d)/(lamda)**2 # power gain
G_p = 10*log10(G_p) # power gain in dB
D =(7.5*w*d)/(lamda)**2 # Directivity

#result
print "half power beam width for aperture length d in Degrees:",round(phi_E,3)
print "half power beam width for aperture width w in Degrees:",round(phi_H,3)
print "power gain in dB:",round(G_p,2)
print "Directivity:",round(D,3)
half power beam width for aperture length d in Degrees: 23.333
half power beam width for aperture width w in Degrees: 55.833
power gain in dB: 11.13
Directivity: 21.6

Example 7.18,Page Number 345¶

In :
from __future__ import division
from math import log10
from sympy import Symbol

#variable declaration
Lm = Symbol('Lm') # defining Lm as lambda
d = 8*Lm # where d is aperture length and Lm is wavelength
w = 8*Lm # where w is aperture width

#calculations
#formula : G_p = (4.5*w*d)/lambda**2
G_p = (4.5*w*d)/Lm**2 # power gain
G_p = 10*log10(G_p)   # power gain in dB

#result
print "power gain in dB:",round(G_p,3)
power gain in dB: 24.594

Example 7.19,Page Number 345¶

In :
from __future__ import division
from math import log10

#variable declaration
f = 6 # frequency in GHz
f = 6*10**9 # frequency in Hz
c = 3*10**8 # speed of light in m/s
lamda = c/f # wavelength in m
d = 10      # aperture length in cm
d = 10*10**-2 # aperture length in m
w = 5        # aperture width in cm
w = 5*10**-2 # aperture width in m

#calculations
G_p = (4.5*w*d)/(lamda)**2 # power gain
G_p = 10*log10(G_p)        # power gain in dB
D = (7.5*w*d)/(lamda)**2   # Directivity
D = 10*log10(D) # directivity in dB

#result
print "power gain in dB:",round(G_p,3)
print "Directivity in dB:",round(D,3)
power gain in dB: 9.542
Directivity in dB: 11.761

Example 7.20,Page Number 345¶

In :
from __future__ import division
import numpy as np

eta_0 = 377 #intrinsic impedance in ohm
print "when Zd = 73+42.5j"
Zd = 73+42.5j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)

print "when Zd = 67+0j"
Zd = 67+0j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)

print "when Zd = 710+0j"
Zd = 710+0j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)

print "when Zd = 500+0j"
Zd = 500+0j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)

print "when Zd = 50+20j"
Zd = 50+20j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)

print "when Zd = 50-25j"
Zd = 50-25j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)

print "when Zd = 300+0j"
Zd = 300+0j # dipole impedance
# formula : zs*zd = (eta_0)**2/4
Zs = eta_0**2/(4*Zd) # slot impedance in ohm
print "complementary slot impedance in ohm:",np.around(Zs,2)
when Zd = 73+42.5j
complementary slot impedance in ohm: (363.53-211.64j)
when Zd = 67+0j
complementary slot impedance in ohm: (530.33+0j)
when Zd = 710+0j
complementary slot impedance in ohm: (50.05+0j)
when Zd = 500+0j
complementary slot impedance in ohm: (71.06+0j)
when Zd = 50+20j
complementary slot impedance in ohm: (612.62-245.05j)
when Zd = 50-25j
complementary slot impedance in ohm: (568.52+284.26j)
when Zd = 300+0j
complementary slot impedance in ohm: (118.44+0j)