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Propagation in wireless media Fundamentals
D. Vanhoenacker-Janvier, Microwave Laboratory
UCL, Louvain-la-Neuve, Belgium
AT1-Propagation in wired, wireless and optical
communications
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Content of the presentation

• Propagation in free space
• TEM plane wave in a lossless medium
• TEM plane wave in a lossy medium
• Polarisation
• Propagation mechanisms in wireless media
• Tropospheric effects
• Gases
• Rain and clouds
• Effects of the environment
• Reflection
• Scattering
• Diffraction
• Refraction

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Propagation of radiowaves in free space
In the absence of charges and currents, the
electric and magnetic fields are solutions of the
Helmholtz equation with k2 w2
em Solutions uniform plane waves spherical
waves cylindrical waves
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TEM Plane wave
TEM Plane wave
with
In a lossless medium
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TEM Plane wave
Surfaces with a constant phase are planes
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TEM Plane wave
Wave impedance
In free space
Phase velocity
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TEM Plane wave
Lossy media
a is the attenuation constant m-1 k is the
propagation constant m-1 g ajk
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TEM Plane wave
Propagation in a lossy medium (conductor or lossy
dielectric)
The second equation becomes
and can be written
with
Two particular cases
good dielectric
good conductor
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TEM Plane wave
Attenuation constant
Simplified expression for
A good dielectric
A good conductor
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Plane wave
Wavenumber
Simplified expression for
A good dielectric
A good conductor
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Plane wave
Wave impedance
Simplified expression for
A good dielectric
A good conductor
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Plane wave
Phase velocity
Simplified expression for
A good dielectric
A good conductor
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Polarisation
The alignment of the electric field vector of a
plane wave relative to the direction of
propagation defines the polarisation of the wave.
Vertically polarised
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Polarisation
vertically
horizontally
Axial ratio
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Polarisation
Mathematical representation of the polarisation
(phasors)
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Propagation mechanisms
? Tropospheric effects gases rain and
clouds ? Effects of the environment buildings v
egetation
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Propagation in the troposphere
How to model the troposphere? The constituents
are gases (water vapour, oxygen,
nitrogen,) uniform dielectric
medium hydrometeors clouds rain snow hail
, uniform dielectric medium (dltltl) ???? or dis
tribution of scatterers (dgtgtl) d is the
characteristic dimension of the scatterers
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Propagation in gases
Uniform dielectric medium
Dipolar polarisation
O2-
H
H
Tendency to align with the electric field
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Propagation in gases
Uniform dielectric medium
Ionic and electronic polarisation
Resonant effect
Ions or electrons
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Propagation in gases
Losses are due to the presence of an imaginary
part in the dielectric permittivity (even in the
absence of conductivity)
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Propagation in gases
Absorption by tropospheric gases
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Propagation in rain and clouds
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Propagation in rain and clouds
Scattering by a raindrop
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Propagation in rain and clouds
Specific attenuation in dB/km, for various rain
rates (mm/h)
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Propagation in rain and clouds
Scattering pattern of a rains drop using Mie
Theory
Ex
10 GHz
5 GHz
20 GHz
15 GHz
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Propagation in rain and clouds
140 GHz
150 GHz
130 GHz
160 GHz
180 GHz
170 GHz
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Propagation in rain and clouds
400 GHz
500 GHz
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Effects of the environment
Impact of the environment on the propagation of
radiowaves ?? reflection, refraction ??
scattering ?? diffraction Geometrical theory of
diffraction (GTD) Uniform theory of diffraction
(UTD)
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Reflection, refraction
Reflection of plane wave onto a plane boundary
Lossless media
The scattering plane contains k, the rays and the
surface normal
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Reflection, refraction
Solving Maxwells equations gives 2 waves - the
reflected wave - the transmitted wave both at the
same frequency as the incident wave both having
their Poynting vectors in the incident plane. It
is usual to work with rays, perpendicular to
the wavefronts ?ray tracing method.
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Reflection, refraction
The angle of the reflected wave is related to the
angle of incidence
Snell law of reflection
This law is also a consequence of the Fermat
principle every path represents an extremum
(usually a minimum) of the total electrical
length of the ray.
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Reflection, refraction
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Reflection, refraction
The angle of the refracted wave is related to the
angle of incidence
Snell law of refraction
The phase velocity of the wave in the medium
with higher permittivity and permeability is
reduced, causing the transmitted wave to bend
toward the surface normal. The Fermat principle
is also applicable the quantity to be minimised
is
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Reflection, refraction
The refractive index is defined as the ratio of
the free space velocity to the phase velocity in
the medium
The Snells law becomes
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Reflection, refraction
Refraction by layers of different refractive
index. The refractive index depends on the
pressure and the temperature of the gases.
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Reflection, refraction
Fresnel reflection and transmission
coefficients the energy of the wave is split
into reflected and refracted wave
Z1 and Z2 are the wave impedances
// means // to the scattering plane ? means ? to
the scattering plane
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Reflection, refraction
The total reflected field is is given by
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Reflection, refraction
Matrix representation (easier to take
polarisation into account)
In case of anisotropic media, the non-diagonal
terms of the matrix are non-zero.
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Reflection, refraction
Lossy media
Fresnel refraction law does not hold for lossy
media Fresnel reflection law is still valid with
the correct value of the wave impedance in the
lossy medium
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Reflection, refraction
Typical lossy media parameters
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Reflection, refraction
// represents vertical polarisation ? represents
horizontal polarisation above the ground
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Reflection, refraction
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Reflection, refraction
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Reflection, refraction
Reflected polarisation
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Reflection by rough surfaces
Effect of the roughness of the reflecting surface
Smooth the waves reflected are only slightly
shifted with respect to each other Rough the
waves are scattered by the surface. The degree
of scattering depends on the angle of incidence
and the roughness of the surface.
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Reflection by rough surfaces
q
Dh
Phase shift less than p/2 (Rayleigh criterion),
but usually, the surfaces are considered smooth
if the phase shift is less than p/8
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Reflection by rough surfaces
When the surface is rough, the amplitude of the
specular component is reduced by a factor f
dependent on the standard deviation of the
surface height Beckman
and
P. Beckman, A. Spizzichino, The scattering of
electromagnetic waves from rough surfaces,
Macmillan, New York, 1963.
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Reflection by rough surfaces
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Diffraction
Diffraction of light by a strip (sharp edges)
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Diffraction
Diffraction of light by an ellipsoidal cylinder
(rounded shape)
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Diffraction
Evaluation of the field in the shadow region
behind the obstacle by using the Huyghens
principle.
Incident plane wave
Shadow region
Absorbing obstacle
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Diffraction
Knife-edge diffraction parameters
Diffraction parameter
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Diffraction
In most of the cases d1,d2 gtgth and the
diffraction parameter can be approximated by
values measured on the ground
The propagation loss is defined as
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Diffraction
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Diffraction
Definition of the Fresnel zones the nth Fresnel
zone is defined as the region inside an ellipsoid
defined by the locus of points where the distance
between the emitter and the receiver (ab) is
larger than the direct path (d1d2) by nl/2
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Diffraction
Radius of the nth Fresnel zone
Fresnel clearance zone (zero dB obstruction
losses)
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Diffraction
Geometrical theory of diffraction - accounts for
obstacles that cannot be considered as absorbing
knife-edges - introduced by Keller1 but - only
valid if the dimensions of the obstacle are large
vs wavelength - does not predict accurately the
field variations close to the obstacle ? UTD2
1 J. B. Keller, Geometrical theory of
diffraction, Jl. Optical Soc. Am., vol. 52, pp.
116-130, 1962. 2 R. G. Kouyoumijan, P. Pathak, A
uniform geometrical theory of adiffraction for an
edge in a perfectly conducting surface
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Diffraction
Generation of edge-diffracted rays from a wedge,
according to GTD
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Diffraction
Geometry for wedge diffraction
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Diffraction
Evaluation of the electric field around a
conducting half-plane for // polarisation, with
UTD