Antennas

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Antennas

• Theory, characteristics, and implementations

Chris Allen (callen_at_eecs.ku.edu) Course website
URL people.eecs.ku.edu/callen/823/EECS823.htm
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Topics

• Role of antennas
• Theory
• Antenna types
• Characteristics
• Radiation pattern beamwidth, pattern solid
  angle
• Directivity, gain, effective area
• Bandwidth
• Friis transmission formula
• Implementations
• Dipole, monopole, and ground planes
• Horn
• Parabolic reflector
• Arrays
• Terminology

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The role of antennas

• Antennas serve four primary functions
• Spatial filter
• directionally-dependent sensitivity
• Polarization filter
• polarization-dependent sensitivity
• Impedance transformer
• transition between free space and transmission
  line
• Propagation mode adapter
• from free-space fields to guided waves
• (e.g., transmission line, waveguide)

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Spatial filter

• Antennas have the property of being more
  sensitive in one direction than in another which
  provides the ability to spatially filter signals
  from its environment.

Radiation pattern of directive antenna.
Directive antenna.
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Polarization filter
Antennas have the property of being more
sensitive to one polarization than another which
provides the ability to filter signals based on
its polarization.
In this example, h is the antennas effective
height whose units are expressed in meters.
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Impedance transformer

• Intrinsic impedance of free-space, E/H
• Characteristic impedance of transmission line,
  V/I
• A typical value for Z0 is 50 ?.
• Clearly there is an impedance mismatch that must
  be addressed by the antenna.

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Propagation mode adapter

• In free space the waves spherically expand
  following Huygens principleeach point of an
  advancingwave front is in fact thecenter of a
  fresh disturbanceand the source of a new train
  of waves.
• Within the sensor, the waves are guided within a
  transmission line or waveguide that restricts
  propagation to one axis.

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Propagation mode adapter

• During both transmission and receive operations
  the antenna must provide the transition between
  these two propagation modes.

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Antenna types
Antennas come in a wide variety of sizes and
shapes
Horn antenna
Parabolic reflector antenna
Helical antenna
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Theory

• Antennas include wire and aperture types.
• Wire types include dipoles, monopoles, loops,
  rods, stubs, helicies, Yagi-Udas, spirals.
• Aperture types include horns, reflectors,
  parabolic, lenses.

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Theory

• In wire-type antennas the radiation
  characteristics are determined by the current
  distribution which produces the local magnetic
  field.

Yagi-Uda antenna
Helical antenna
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Theory wire antenna example
Some simplifying approximations can be made to
take advantage the far-field conditions.
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Theory wire antenna example
Once Eq and Ef are known, the radiation
characteristics can be determined. Defining the
directional function f (q, f) from
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Theory aperture antennas

• In aperture-type antennas the radiation
  characteristics are determined by the field
  distribution across the aperture.

Horn antenna
Parabolic reflector antenna
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Theory aperture antenna example
The far-field radiation pattern can be found from
the Fourier transform of the near-field pattern.
Where Sr is the radial component of the power
density, S0 is the maximum value of Sr, and Fn is
the normalized version of the radiation pattern
F(q, f)
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Theory

• Reciprocity
• If an emf is applied to the terminals of antenna
  A and the current measured at the terminals of
  another antenna B, then an equal current (both in
  amplitude and phase) will be obtained at the
  terminals of antenna A if the same emf is applied
  to the terminals of antenna B.
• emf electromotive force, i.e., voltage
• Result the radiation pattern of an antenna is
  the same regardless of whether it is used to
  transmit or receive a signal.

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Characteristics Radiation pattern
Radiation pattern variation of the field
intensity of an antenna as an angular function
with respect to the axis
Three-dimensional representation of the radiation
pattern of a dipole antenna
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Characteristics Radiation pattern
Spherical coordinate system
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Characteristics Radiation pattern
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Characteristics Radiation pattern
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Characteristics Radiation pattern
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Characteristics Radiation pattern
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Characteristics Radiation pattern
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Characteristics Beamwidth and beam solid angle
The beam or pattern solid angle, ?p steradians
or sr is defined as where d? is the elemental
solid angle given by
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Characteristics Directivity, gain, effective
area
Directivity the ratio of the radiation
intensity in a given direction from the antenna
to the radiation intensity averaged over all
directions.
unitless
Maximum directivity, Do, found in the direction
(?, ?) where Fn 1
and
or
Given Do, D can be found
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Characteristics Directivity, gain, effective
area
Gain ratio of the power at the input of a
loss-free isotropic antenna to the power supplied
to the input of the given antenna to produce, in
a given direction, the same field strength at the
same distance
Of the total power Pt supplied to the antenna, a
part Po is radiated out into space and the
remainder Pl is dissipated as heat in the antenna
structure. The radiation efficiency hl is
defined as the ratio of Po to Pt
Therefore gain, G, is related to directivity, D,
as
And maximum gain, Go, is related to maximum
directivity, Do, as
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Characteristics Directivity, gain, effective
area
Effective area the functional equivalent area
from which an antenna directed toward the source
of the received signal gathers or absorbs the
energy of an incident electromagnetic wave
It can be shown that the maximum directivity Do
of an antenna is related to an effective area (or
effective aperture) Aeff, by
where Ap is the physical aperture of the antenna
and ha Aeff / Ap is the aperture efficiency (0
ha 1) Consequently
m2
For a rectangular aperture with dimensions lx and
ly in the x- and y-axes, and an aperture
efficiency ha 1, we get
rad
rad
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Characteristics Directivity, gain, effective
area

• Therefore the maximum gain and the effective area
  can be used interchangeably by assuming a value
  for the radiation efficiency (e.g., ?l 1)

Example For a 30-cm x 10-cm aperture, f 10
GHz (? 3 cm)?xz ? 0.1 radian or 5.7, ?yz ?
0.3 radian or 17.2G0 ? 419 or 26 dBi (dBi
dB relative to an isotropic radiator)
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Characteristics Bandwidth

• The antennas bandwidth is the range of operating
  frequencies over which the antenna meets the
  operational requirements, including
• Spatial properties (radiation characteristics)
• Polarization properties
• Impedance properties
• Propagation mode properties
• Most antenna technologies can support operation
  over a frequency range that is 5 to 10 of the
  central frequency
• (e.g., 100 MHz bandwidth at 2 GHz)
• To achieve wideband operation requires
  specialized antenna technologies
• (e.g., Vivaldi, bowtie, spiral)

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Friis transmission formula

• At a fixed distance R from the transmitting
  antenna, the power intercepted by the receiving
  antenna with effective aperture Ar is
• where Sr is the received power density (W/m2),
  and Gt is the peak gain of the transmitting
  antenna.

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Friis transmission formula

• If the radiation efficiency of the receiving
  antenna is hr, then the power received at the
  receiving antennas output terminals is
• Therefore we can write
• which is known as Friis transmission formula

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Friis transmission formula

• as Friis transmission formula can be rewritten
  to explicitly represent the free-space
  transmission loss, LFS
• which represents the propagation loss experienced
  in transmission between two lossless isotropic
  antennas.With this definition, the Friis formula
  becomes

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Friis transmission formula

• Finally, a general form of the Friis
  transmission formula can be written that does not
  assume the antennas are oriented to achieve
  maximum power transfer
• where (?t, ?t) is the direction of the receiving
  antenna in the transmitting antenna coordinates,
  and vice versa for (?r, ?r).
• An additional term could be included to represent
  a polarization mismatch between the transmit and
  receive antennas.

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Implementation

• Dipole, monopole, and ground planes
• Horns
• Parabolic reflectors
• Arrays

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Implementation Dipole, monopole, and ground
plane

• For a center-fed, half-wave dipole oriented
  parallel to the z axis

(V/m)
(W/m2)
Tuned half-wave dipole antenna
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Dipole antennas
Versions of broadband dipole antennas
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Dipole antennas
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Monopole antenna
q
q
Ground plane
Radition pattern of vertical monopole above
ground of (A) perfect and (B) average
conductivity
Mirroring principle creates image of monopole,
transforming it into a dipole
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Ground plane

• A ground plane will produce an image of nearby
  currents. The image will have a phase shift of
  180 with respect to the original current.
  Therefore as the current element is placed close
  to the surface, the induced image current will
  effectively cancel the radiating fields from the
  current.
• The ground plane may be any conducting surface
  including a metal sheet, a water surface, or the
  ground (soil, pavement, rock).

Horizontal current element
Conducting surface(ground plane)
Current element image
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Implementation Horn antennas
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Implementation Horn antennas
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Implementation Parabolic reflector antennas

• Circular aperture with uniform illumination.
  Aperture radius a.
• Ap p a 2

where
where
J1( ) is the Bessel function of the first kind,
zero order
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Implementation Antenna arrays

• Antenna array composed of several similar
  radiating elements (e.g., dipoles or horns).
• Element spacing and the relative amplitudes and
  phases of the element excitation determine the
  arrays radiative properties.

Linear array examples
Two-dimensional array of microstrip patch antennas
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Implementation Antenna arrays

• The far-field radiation characteristics Sr(?, ?)
  of an N-element array composed of identical
  radiating elements can be expressed as a product
  of two functions
• Where Fa(?, ?) is the array factor, and Se(?, ?)
  is the power directional pattern of an individual
  element.
• This relationship is known as the pattern
  multiplication principle.
• The array factor, Fa(?, ?), is a range-dependent
  function and is therefore determined by the
  arrays geometry.
• The elemental pattern, Se(?, ?), depends on the
  range-independent far-field radiation pattern of
  the individual element. (Element-to-element
  coupling is ignored here.)

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Implementation Antenna arrays

• In the array factor, Ai is the feeding
  coefficient representing the complex excitation
  of each individual element in terms of the
  amplitude, ai, and the phase factor, ?i, as
• and ri is the range to the distant observation
  point.

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Implementation Antenna arrays

• For a linear array with equal spacing d between
  adjacent elements, which approximates to
• For this case, the array factor becomes
• Note that the e-jkR term which is common to all
  of the summation terms can be neglected as it
  evaluates to 1.

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Implementation Antenna arrays

• By adjusting the amplitude and phase of each
  elements excitation, the beam characteristics can
  be modified.

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Implementation Antenna arrays
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Implementation Antenna arrays
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Implementation Example 2-element
array Isotropic radiators
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Implementation Example 2-element
array Isotropic radiators
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Implementation Example 2-element
array Half-wave dipole radiators
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Implementation Example 2-element array
Half-wave dipole radiators
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Implementation Example 6-element array
Half-wave dipole radiators
grating lobes
d l produces two grating lobes
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Antenna arrays Beam steering effects

• Inter-element separation affects linear array
  gain and grating lobes
• The broadside array gain is approximatelywhere
  d is the inter-element spacing and N is the
  number of elements in the linear array
• To avoid grating lobes, the maximum inter-element
  spacing varies with beam steering angle or look
  angle, ?, as

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Antenna arrays Beamwidth and gain

• An 2-D planar array with uniform spacing, N x M
  elements in the two dimensions with inter-element
  spacing of ?/2 provides a broadside array gain of
  approximately
• The beamwidth of a steered beam from a uniform
  N-element array is approximately (for N gt
  5)where b is the window function broadening
  factor (b 1 for uniform window function) andd
  is the inter-element spacing

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Conclusions

• Antennas play an important role in microwave
  remote sensing systems.
• There are both art and science aspects to
  antennas.
• Antenna arrays enable the radiation
  characteristics to be changed electronically
  (i.e., very rapidly) unlike conventional
  mechanically-steered antennas.
• Digital beamforming (dedicated transmit or
  receive electronics for each element) enable
  simultaneous realization of multiple antenna
  beams and/or multiple independent signals.

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Terminology

• Antenna structure or device used to collect or
  radiate electromagnetic waves
• Array assembly of antenna elements with
  dimensions, spacing, and illumination sequency
  such that the fields of the individual elements
  combine to produce a maximum intensity in a
  particular direction and minimum intensities in
  other directions
• Beamwidth the angle between the half-power
  (3-dB) points of the main lobe, when referenced
  to the peak effective radiated power of the main
  lobe
• Directivity the ratio of the radiation
  intensity in a given direction from the antenna
  to the radiation intensity averaged over all
  directions
• Effective area the functional equivalent area
  from which an antenna directed toward the source
  of the received signal gathers or absorbs the
  energy of an incident electromagnetic wave
• Efficiency ratio of the total radiated power to
  the total input power
• Far field region where wavefront is considered
  planar
• Gain ratio of the power at the input of a
  loss-free isotropic antenna to the power supplied
  to the input of the given antenna to produce, in
  a given direction, the same field strength at the
  same distance
• Isotropic radiates equally in all directions
• Main lobe the lobe containing the maximum power
• Null a zone in which the effective radiated
  power is at a minimum relative to the maximum
  effective radiation power of the main lobe
• Radiation pattern variation of the field
  intensity of an antenna as an angular function
  with respect to the axis
• Radiation resistance resistance that, if
  inserted in place of the antenna, would consume
  that same amount of power that is radiated by the
  antenna
• Side lobe a lobe in any direction other than
  the main lobe