Antennas: from Theory to Practice 3. Field Concepts and Radio Waves

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Antennas from Theory to Practice3. Field
Concepts and Radio Waves

• Yi HUANG
• Department of Electrical Engineering
  Electronics
• The University of Liverpool
• Liverpool L69 3GJ
• Email Yi.Huang_at_liv.ac.uk

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Objectives of This Chapter

• Use Maxwells equations to obtain wave solutions.
  
• Introduce the concepts of the plane wave,
  intrinsic impedance, and polarisation
• Discuss radio propagation mechanisms and
  propagation characteristics in various media
• Review basic radio propagation models
• Compare the circuit concepts and field concepts
• Examine the concept of skin depth from both the
  field and circuit points of views.

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3.1 Wave Equation and Solutions
For a time harmonic case the time factor is
Maxwells equations
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In source free region, we obtain the wave equation
A solution is
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For the loss-free case,
the velocity of an electromagnetic wave
(including light) in free space is about
30,000,000 m/s
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3.2 Plane Wave, Intrinsic Impedance and
Polarisation
Plane wave
H ? E? z
The power density
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Polarisation is described by the locus of the
tip of the E vector as time progresses. For a
wave propagating towards z-direction
y
y
E
E
E
x
x
Circular a b
Linear a or b 0
Elliptical Axial ratio a/b
Note there are RCP and LCP
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Intrinsic impedance of the material is defined as
the ratio of the electric and magnetic fields. In
a loss-free medium
In free space
Generally speaking
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3.3 Radiowave Propagation Mechanisms

• Reflection and transmission

Snells law
Reflection and transmission coefficients
How to obtain them?
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Two principal polarisations
To obtain the reflection and transmission
coefficients, we introduce equivalent
transmission line model
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The characteristic Impedances are
Thus
From the power point of view
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Example 3.1

• Perfect conductor obtain the reflection and
  transmission coefficients between air and a
  perfect conductor.

The conductivity of a perfect conductor is
infinite the characteristic impedance of its
equivalent transmission line is zero for any
polarisation and incident angle, i.e. Z2 0,
thus
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Example 3.2

• Ground if the relative permittivity of a ground
  is 9 and the conductivity is very small and
  negligible, plot the reflection coefficient as a
  function of the incident angle for both parallel
  and perpendicular polarisations.

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Brewsters angle

• For parallel polarisation, the reflection
  coefficient vanishes ( 0) at a particular
  incident angle, this angle is called Brewsters
  angle
• When the incident angle is greater than the
  Brewsters angle for parallel polarisation,

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• The critical angle is the incident angle that
  gives a transmitted angle of 90 degrees when the
  wave is from a dense medium to a less dense
  medium, such as from water into air. From Snells
  law, we obtain this special angle
• For non-normal incidence, the reflection
  coefficients are different for the two principle
  polarisations. As a result, if an incident wave
  is a combination of these two orthogonal waves,
  the combined signal after the reflection will be
  changed. e.g., for a conductor RCP wave becomes
  a LCP wave!

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Radio propagation through a wall
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Example 3.3

• A brick wall has a relative permittivity of 4 and
  a thickness of 20 cm, the loss is negligible.
• a). If the operational frequency is 2.45 GHz for
  wireless applications (such as bluetooth), plot
  the reflection coefficient as a function of the
  incident angle for both parallel and
  perpendicular polarisations.
• b). If the incident angle is 45 degrees, plot the
  reflection coefficient as a function of the
  frequency for both parallel and perpendicular
  polarisations.

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The reflection is minimised when the thickness of
the wall is an integer of half of the effective
wavelength.
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Diffraction and Huygenss Principle
Huygens Principle states that each point on a
primary wave front can be considered as a new
source of a secondary spherical wave. The
relative (to the direct ray) power density
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Scattering

• Unlike the other propagation mechanisms where the
  size of the medium or the obstacle is much larger
  than the wavelength, scattering occurs when the
  obstacle is comparable or even small than the
  wavelength.
• In scattering, there are no energy transformation
  results, only a change in the spatial
  distribution of the radiation.

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3.4 Radio Wave Propagation Characteristics in
Media

• Media classification

This classification is useful for evaluating the
EM properties in terms of the loss tangent but is
not accurate for classifying whether a medium is
lossy or not!
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A more accurate consideration should take the
complex permittivity spectrum into account
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Propagation Through the Ionosphere

• The ionosphere is the region above the
  troposphere (where the air is), from about 80 to
  400 km above the earth. It is a collection of
  ions, which are atoms that have some of their
  electrons stripped off leaving two or more
  electrically charged objects. The sun's rays
  cause the ions to form which slowly recombine. 
• Reflection at low frequencies (up to about 30
  MHz).
• Scattering, refraction and absorption when high
  frequency waves (above 100 MHz) pass through it.
• Faraday rotation the wave polarisation
  plane/line is rotated through the ionosphere .

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Propagation in Rain

• The major effect of rain on radiowaves is
  attenuation due to absorption and scattering over
  a wide range of the spectrum

where R is the rain rate in mm/h, and a and b are
constants that depend on frequency and
temperature of the rain.
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3.5 Radio Wave Propagation Models

• Free space model

Received power
Path loss
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Two-ray Model/Plane Earth Model
The 1st Fresnel zone Path-loss (not a
function of freq) 20 dB/dec, d lt Df
Received power
40 dB/dec, d gt Df
Path-loss
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Multipath Models

• No analytical equations to give an accurate
  prediction of the radio propagation pathloss.
• Empirical and statistical representations are
  available for various scenarios.
• Most of the popular outdoor pathloss prediction
  tools are based on Okumura and Hatas formulation
• based on measured data for 100 MHz and 3 GHz
• General form for pathloss

1.5 lt n lt 4 0 lt X lt 20
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• Multipath fast fading the received signal
  changes significantly (gt 30 dB) over a very short
  distance (few wavelengths), resulted from the
  complex and vector summation of signals.
• Delay spread multi-copies of the original signal
  arrive at the destination at different time
  through different paths, which may cause
  dispersion and inter-symbol interference
• The delay spread is often employed to define the
  channels coherence bandwidth BC (similar to a
  filters bandwidth in certain sense).
• Doppler frequency shift is employed to define the
  channels coherence time Tc

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Fading channels
Freq selective
Signal BW
Freq selective
Slow fading
Fast fading
Bc
Flat
Flat
Slow fading
Fast fading
Tc
Pulse duration

• Typical values of RMS delay spread is,
• 2 ms for outdoor urban cellular (Bc 100kHz)
• 100 ns for indoor environment (Bc 2MHz)

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• Statistically, the power density function (PDF)
  of the received (short-term) signal envelope
  follows certain distribution
• When there is a line-of-sight ray, it follows the
  Gaussian distribution and this channel is
  therefore called the Gaussian channel
• When there is a partial line-of-sight ray (the
  path is partially blocked by obstacles such as
  trees), it follows the Rician distribution and
  this channel is therefore called the Rician
  channel
• When there is no line-of-sight ray, it follows
  the Rayleigh distribution and this channel is
  therefore called the Rayleigh channel.

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3.6 Comparison of Circuit Concepts and Field
Concepts
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Correspondence of the Circuit Concepts and the
Field Concepts
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Skin Depth d

• Field concept skin depth is defined as the
  distance d through which the amplitude of a
  traveling plane wave decreases by factor 1/e, or
  37, or 8.686 dB over one skin depth
• Circuit concept skin depth is defined as the
  depth below the surface of the conductor at which
  the current density decays to 1/e (about 37) of
  the current density at the surface. The per unit
  resistance of a wire

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• Mathematically

Skin depth and resistance of a gold track of
dimensions 7mm x 16mm x 30000mm