Ch7_Wave Propagation (2).pptx FOR FDFKASDFASFSADFASDFA
1. 1
Wave Propagation
Waves transmitted from an antenna can reach the receiving
antenna through different ways. They may encounter different
effects including reflection, refraction, diffraction, attenuation
scattering and depolarization and travel through different
regions like earth surface, troposphere, ionosphere and outer
space.
3. 3
Modes of Propagation
• There are may propagation mechanisms by which signals can
travel between the transmitter and receiver.
• Except for line-of-sight path, the mechanism’s effectiveness is
generally a strong function of the frequency and transmitter-
receiver geometry.
• Direct Path or “Line of Sight”: SHF links from ground to
satellites
• Direct plus Reflections or “Multipath”: UHF broadcast, air-to-
air and ground-to-air communications
4. 4
Modes of Propagation
• Ground Wave: AM Broadcasts
• Ionospheric Hop: MF and HF broadcast and communications
• Wave guide modes or “ionospheric Ducting”: VLF and LF
Communications
7. 7
Ground waves and Sky waves
• The most important modes based on which a reliable wireless
terrestrial communication link can be designed are:
• Ground Waves: This includes waves propagating in lower
atmosphere (near to ground). Primarily space waves and
surface waves are considered as ground waves.
• Space Waves: Waves propagating in lower atmosphere near
earth: Direct waves and Earth reflected waves.
• Surface waves: Waves that creep and travel along to the
earth surface and follow the earth curvature.
• Sky waves: This includes waves propagating (or reflected)
from the outer atmosphere. Primarily ionospheric
propagation are included as sky waves.
8. 8
Ground Wave
• Sommerfield was first to introduce of ground reflected wave in
1909.
• He proposed that the ground wave field strength could be
divided into two parts: surface wave and space wave.
• Norton simplified the mathematical solution.
• Norton computed the field due to a vertical dipole antenna
above the surface of the finitely conducting plane earth.
• It clearly shows the components of the far fields.
9. 9
Ground Wave
• The first two terms are due to direct and ground reflected
waves while the third is due to the surface wave.
• Rv is the reflection factor and F is the attenuation factor
depending on earth’s constants and distance.
10. 10
Surface Wave
• When the dipole is at the earth surface,
• where,
• Thus F introduces an attenuation depending upon, distance,
frequency and constants of the earth.
11. 11
Surface Wave
• For distances within few wavelengths, the factor is nearly
equal to unity. So, the field is unattenuated.
• For low frequencies and good conductivity of the ground, the
field is very small except at angles near grazing.
• For higher frequencies and poorer conductivities, fields have
value even at other angles of incidence.
• However it attenuates fast with distance due to factor F.
• The absolute value of F for =0 is called ground wave
attenuation factor.
15. 15
Reflection Coefficient for Earth Reflection
• By the principle of conservation of energy,
2
2
2
1
2
1
1
2
1
cos
1
cos
1
cos
1
t
r
i E
E
E
1
2
1
2
2
2
1
2
2
2
2
1
2
2
cos
cos
1
cos
cos
1
i
t
i
t
i
r
E
E
E
E
E
E
16. 16
Reflection Coefficient for Earth Reflection
• Now for horizontally polarized wave, tangential component of
E is continuous:
• So,
Or
Or,
By Snell’s law:
t
r
i E
E
E
1
2
2
1
2
2
2
cos
cos
1
1
i
r
i
r
E
E
E
E
i
r
i
t
E
E
E
E
1
1
2
1
2
cos
cos
1
1
i
r
i
r
E
E
E
E
2
2
1
1
2
2
1
1
cos
cos
cos
cos
i
r
E
E
1
2
2
1
sin
sin
17. 17
Reflection Coefficient for Earth Reflection
• which yields,
• So,
For vertical polarization,
1
2
1
2
1
1
1
2
1
2
1
1
sin
cos
sin
cos
i
r
E
E
1
2
1
2
2
2
2
2
2 sin
sin
1
cos
2
1 cos
cos
t
r
i E
E
E
2
1
cos
cos
1
i
r
i
t
E
E
E
E
1
2
1
1
2
1
sin
cos
sin
cos
1
2
1
2
1
2
1
2
i
r
E
E
1
2
1
1
2
1
sin
cos
sin
cos
1
2
1
2
i
r
E
E
18. Reflection Coefficient for Earth Reflection
• the above expressions are for perfect dielectrics. The earth
however is neither a conductor nor a perfect dielectric. It can
be considered as a partially conducting dielectric with complex
dielectric constant,
• So, considering first medium as air and second as earth the
reflection factors can then be obtained as:
• If the incident angle is measured from the earth surface,
2
2
sin
cos
sin
cos
0
0
j
j
i
r
h
E
E
R
90
2
2
cos
sin
cos
sin
0
0
0
0
j
j
Rh
j
1
19. Reflection Coefficient for Earth Reflection
Where,
• Similarly for vertical polarization,
2
2
cos
sin
cos
sin
jx
jx
R
r
r
h
MHz
f
x
3
0
10
18
2
2
cos
sin
cos
sin
jx
jx
jx
jx
R
r
r
r
r
v
24. 24
Ionosphere
• Region of earth’s atmosphere in which the constituent gases
are ionized by radiations from outer space.
• Extends from about 50 km above the earth to several
thousand kilometers.
• Maximum ionization density occurs approximately at about
300 km.
• State of ionosphere varies from hour to hour, day to day, and
season to season.
• The major variation is between night and day.
25. 25
Layers of Ionosphere
• Based on the ionization density, different layers exists.
• Designated as C, D, E and F.
• The F layer splits in F1 and F2 during day.
• At great heights, the ionization
radiation is intense but only few
molecules present to be ionized
resulting low ionization density.
• As height decreases ionization
density increases till reaches
maximum.
• The ionization density again
decreases due to weak ionization
radiation present.
27. 27
Refractive Index of Ionospheric Layers
• Consider a uniform plane wave with sinusoidal variations
travelling through a region with free electrons with electron
density N.
Such that where
• Electrons in a electric field experience a force given by,
The force causes electron to accelerate.
So,
y
y
x
x a
H
H
and
a
E
E ˆ
ˆ
t
E
Ex
sin
0
x
x E
e
F
c
e 19
10
59
.
1
t
E
e
E
e
dt
x
d
m x
sin
0
2
2
m
t
E
e
dt
x
d cos
0
28. Refractive Index of Ionospheric Layers
• The current density thus created is:
• The Maxwell’s equation for field in region with free charges
and
Since, the fields have only x and y components respectively,
So,
m
t
E
e
N
dt
x
d
e
N
J
cos
0
2
t
E
J
t
D
J
H
0
t
H
t
B
E
0
t
E
J
z
H x
y
0
t
H
z
E y
x
0
t
t
E
m
t
E
e
N
z
Hy
sin
cos 0
0
0
2
t
E
m
e
N
z
Hy
cos
0
2
2
0
29. Refractive Index of Ionospheric Layers
• Comparing with
We get,
The refractive index of any medium is given by:
For a lossless medium,
z
H
t
E
m
e
N y
cos
1 0
0
2
2
0
z
H
t
E y
x
0
2
2
0
1
m
e
N
r
)
(
)
(
p
v
medium
in
velocity
phase
c
vacuum
in
light
of
velocity
n
r
p
c
v
ty
permittivi
relative
r
30. 30
Refractive Index of Ionospheric Layers
So,
For ionized gas, the relative permittivity is given as
Using known values,
Thus,
Thus the refractive index of a particular ionospheric layer
depends on the electron density and also the frequency.
r
n
2
0
2
1
m
Ne
r
Hertz
in
frequency
f
frequency
radian
mass
electron
m
electron
an
of
charge
e
vacuum
of
ty
permittivi
density
electron
N
31
19
12
0
10
9
10
59
.
1
10
85
.
8
2
81
1
f
N
r
2
81
1
f
N
n
31. 31
Wave Propagation in Ionosphere
• Radio waves travelling in ionosphere suffer refraction as well
as reflection.
• For low frequencies, the change in ion density within a
wavelength is large and the layer will present an abrupt
discontinuity. The waves will be reflected back with some
reflection coefficient which is function of frequency.
• For sufficiently large frequencies, the change in ion density
within a wavelength is small and the layer acts as an dielectric
with continuously varying refractive index.
• As the wave travels from lower ion density to the higher one,
it is curved away.
• As the wave travels further up, the ion density increases and
the refractive index decreases.
32. 32
Reflection from Ionosphere
• The bending of the wave follows Snell’s Law of refraction.
• If we consider ionosphere to have many tiny layers we can
write
•On successive refraction, the angle of refraction increases and
at some point becomes equal to 90°.
• After that the waves will be reflected
back. This occurs when,
Or,
Thus the waves will be reflected when it
reaches a layer with electron density
2
2
1
1
Sin
n
Sin
n
k
i n
sin
i
Sin
f
N
2
81
1
81
2
2
' i
Cos
f
N
.....
sin
sin
sin
sin 3
3
2
2
1
1
0
n
n
n
n i
34. 34
Critical Frequency and MUF
• For a particular layer, if Nmax is the highest possible electron
density, the highest frequency that will be reflected from that
layer is,
• The highest frequency that will be reflected back from a
particular layer is for vertical incidence is called critical
frequency of that layer.
• This highest frequency that can be reflected back from a
particular layer is called maximum usable frequency (MUF).
• MUF typically for a n ionosphere is less than 40 MHz (even up
to 25-30 MHz)
i
i Cos
N
Cos
N
f
max
2
max
max
81
81
max
81 N
fcr
i
cr Sec
f
MUF
35. 35
Maximum Usable Frequency and Distance
• For a particular layer, there is a limit of maximum incidence
angle possible (eg, for F layer, It is 74°).
•
•The MUF for a particular distance is seen in example below
• Owing to the variation of the ionosphere, the optimum
frequency used for communication between any two points is
selected to be lower than the MUF for that distance and is
usually about 50 to 85 percent of the MUF.
36. 36
Virtual Height
• It is that height from which a wave sent up at an angle
appears to be reflected.
• The time delay for the actual curved path is approximately
same if the wave have been reflected from the virtual height
following the straight paths.
• The path lengths are however not equal.
37. 37
Virtual Height
• From the geometry,
• The maximum skip distance is achieved by aiming the antenna
beam leaving the antenna parallel to the earth’s surface.
• where, K Re is the effective earth radius=8497 km
38. 38
Skip Distance
• The distance within which a signal of the given frequency fails
to be reflected back is called the Skip distance for that
frequency.
•
