EE 543 Theory and Principles of Remote Sensing

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EE 543Theory and Principles of Remote Sensing

• Antenna Systems

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Outline

• Introduction
• Overview of antenna terminology and antenna
  parameters
• Radiation Pattern
• Isotropic, omni-directional, directional
• Principal planes
• HPBW
• Sidelobes
• Power Density
• Radiation Intensity
• Directivity
• Beam Solid Angle
• Gain and Efficiency
• Polarization and Polarization Loss Factor (PLF)
• Bandwidth
• Antennas as Receivers
• Circuit representation of an antenna
• Reciprocity
• Friis transmission equation

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Outline

• Radiation from currents and apertures
• Sources of radiation
• Current (wire) antennas
• Vector and scalar potentail
• Short (Hertzian) dipole
• Linear antennas
• Aperture fields (e.g. horn antennas)
• Kirchoffs scalar diffraction theory
• Vector diffraction theory
• Array Antennas
• Array Factor
• Main beam scanning
• Endfire antennas
• Pattern Multiplication
• Directivity calculations

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Summary

• So far we have discussed how waves interact with
  their surrounding in various ways
• Wave equation
• Lossy medium
• Plane waves, propagation
• Reflection and transmission
• In this topic we discuss how waves are generated
  and received by antennas.

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What is an antenna?
Antenna is a device capable of transmitting power
in free space along a desired direction and vice
versa.
An antenna acts like a transducer between a
guided em wave and a free space wave.
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What is an antenna

• Any conductor or dielectric could serve this
  function but an antenna is designed to radiate
  (or receive) em energy with directional and
  polarization properties suitable for the intended
  application.
• An antenna designer is concerned with making this
  transition as efficient as possible, ensuring as
  much power as possible is radiated in the desired
  direction.

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Transmission Mode
Horn antenna
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Reception Mode
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Antenna Types

• Antennas come in various shapes and sizes.
• Key parameters of an antenna are its size, shape
  and the material it is made of.
• The dimensions of an antenna is typically in
  wavelength, l, of the wave it launches.

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Some examples
loop
Biconal dipole
Thin dipole
microstrip
Parabolic reflector
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Examples Wire Antennas
Wire antennas are used as extensions of ordinary
circuits are most often found in Lower
frequency applications. They can operate with
two terminals in a Balanced configuration like
the dipole or with an Unbalanced configuration
using a Ground Plane for the other half of the
structure.
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Examples Aperture Antennas
Aperture antennas radiate from an opening or from
a surface rather than a line and are found at
Higher frequencies where wavelengths are Shorter.
Aperture antennas often have handfuls of sq.
wavelengths of area are very seldom fractions
of a wavelength.
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Examples Reflector Antennas
Reflector antennas collect or transmit (focus)
energy by using a large (many wavelength) dish
(or parabolic mirror). These are very high gain
(directional) antennas used to communicate with
or detect objects in space.
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How do these structures launch em energy?

• EM energy can be radiated by two types of
  sources
• Currents (e.g. dipole, loop antennas. Time
  varying currents flowing in the conducting wires
  radiate em energy.)
• Aperture fields (e.g. horn antenna. E and H
  fields across the aperture serve as the source of
  the radiated fields.)
• Ultimately ALL radiation is due to time varying
  currents. (E and H fields across the horn
  aperture is created by the time varying currents
  on the walls of the horn.)

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Fundamental Concept of Maxwells Equations

• A current at a point in space induces potential,
  hence currents at another point far away.

V(R)
R
Ri
R
(0,0,0)
rv
Charge distribution
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Overview of Antenna Parameters

• Radiation Pattern
• Radiation Power Density
• Radiation Intensity
• Directivity
• Gain and Efficiency
• HPBW
• Polarization and Polarization Loss Factor (PLF)
• Bandwidth
• Beam Solid Angle

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Radiation Pattern (Antenna Pattern)

• An antenna pattern describes the directional
  properties of an antenna at a far away distance
  from it.
• In general the antenna pattern is a plot that
  displays the strength of the radiated field or
  power density as a function of direction i.e. q,
  j angles.

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Coordinate System
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Solid Angle
Solid angle defines a subtended area over a
spherical surface divided by R2. Units
Steradians (Sr)
For unit solid angle
For unit angle
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Solid Angle
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Types of Radiation Patterns
Idealized Point Radiator
Vertical Dipole
Radar Dish
Omni-directional
Directional
Isotropic
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Isotropic Antenna
Polar plot

• Isotropic radiator is a hypothetical lossless
  antenna with equal radiation in ALL directions.
• Although it is not realizable, it is used to
  define other antenna parameters, such as
  directivity.
• It is represented by a sphere whose center
  coincides with the location of the isotropic
  radiator.

Isotropic pattern
Rectangular plot
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Directional Antenna

• Directional antennas radiate (or receive) em
  waves more efficiently in some directions than
  others.
• Usually, this term is applied to antennas whose
  directivity is much higher than that of a
  half-wavelength dipole.

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Omni-directional Antenna

• Omni-directional antennas are special kind of
  directional antennas having non-directional
  properties in one plane (e.g. single wire
  antennas).

q
p
-p
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Principal Planes

• E and H planes
• Antenna performance is often described in terms
  of its principal E and H plane patterns.
• E-plane the plane containing the electric field
  vector and the direction of maximum radiation.
• H-plane the plane containing the magnetic field
  vector and the direction of maximum radiation.

Note that it is usual practice to orient most
antennas so that at least one of the principal
plane patterns coincide with one of the
geometrical planes
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Principal Planes
Another definition for principal planes is
elevation (q) and azimuth (j) plane.
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Antenna Pattern Lobes
A pattern lobe is a portion of the radiation
pattern bounded by regions of relatively weak
radiation intensity.
0dB
Half power beamwidth
-3dB
Main lobe
nulls
Full Null Beamwidth
Between
1st NULLS
Side lobes
q
p
-p
Back lobes
PEAK
SIDE LOBE LEVEL
( SLL )
-20dB
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HPBW, FNBW
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Field Regions

• Close to the antenna, the field patterns change
  rapidly with distance, and include both radiating
  energy and reactive energy ? energy oscillates
  toward and away from the antenna.
• In the near field region non-radiating energy
  dominates.
• Further away, the reactive fields are negligible
  and only the radiating energy is present.
• Sufficiently far away i.e. far field
  (Fraunhofer) region field components are
  orthogonal. The angular distribution of fields
  and power density are independent of distance.
  Equipartition between electric and magnetic
  stored energy.
• In between is the transitional, radiating near
  field region also known as Fresnel region. The
  angular field distribution is dependent on the
  distance.
• Note that there is no abrupt change in the fields
  as the boundary between these regions is crossed.

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Field Regions
These regions can be categorized as a function of
distance R from the antenna.
R lt
R lt R1 lt
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Radiation Power Density

• The time average Poynting vector of the radiated
  wave is known as the power density of the antenna.

Function of q and j.
Function of 1/r in the far field
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Example on Power Density (1)

• Calculate the total radiated power from an
  isotropic source.

An isotropic source radiates equal power in all
directions
The radiated power is the sum of the power
density in all directions
So
Increasing power with distance???
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Reiterate isotropic source

• An isotropic source radiates equal power in all
  directions at a given distance form the source.
• The distance is in the far field, and the power
  density is a function of 1/r2
• The power density of an isotropic source is

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Example on Power Density (2)
The radiated power density of an antenna is given
by
Calculate the total radiated power.
Solution
1/2
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Radiation Intensity

• Power radiated from an antenna per solid angle is
  defined as radiation intensity.
• It is a function of q, j only.

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Power Pattern Radiation Intensity
Decays as 1/r2)
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Example on Radiation Intensity (1)
Show that the radiation intensity is constant for
an isotropic source.
Proof
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Example on Radiation Intensity (2)
For an antenna with average power density given
by calculate the power density of an equivalent
isotropic radiator, which radiates the same
amount of power.
Solution
From previous example, the total radiated power
for this antenna is given as
For an isotropic source to radiate the same power
as this antenna
So
p
-p
Sav
-p
p
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Example on Radiation Intensity (3)
Calculate the radiation intensity for a Hertzian
dipole.
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Beam Solid Angle

• The solid angle, WA, required to radiate all the
  power of the antenna if the radiation intensity U
  were uniform and equal to its maximum value
  within the beam and zero elsewhere.

WA
WA
Umax. WA Ptot
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Beam Solid Angle

• Thus the total radiated power is given by Prad
  Umax WA

Normalized radiation intensity
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Directivity

• Directivity is the ratio of the radiation
  intensity of an antenna in a given direction to
  the radiation intensity of an equivalent
  isotropic antenna.

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Directivity

• Directivity is a measure of how well antennas
  direct (focus) energy in one direction.
• For an isotropic source, the directivity is 1
  i.e. exhibits no preference for a particular
  direction.
• Directivity is typically expressed in dB.
• If a direction is not specified, typically the
  maximum value is implied.

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Directivity Example (1)
Show that the directivity of an isotropic source
is 1.
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Directivity Example (2)
The power density of an antenna is given by
Calculate its directivity.
Solution
Note that we have solved for the equivalent
isotropic source in Example (2) for radiation
intensity.
Therefore
From the previous solution
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Directivity Example (3)
Calculate the directivity of a Hertzian dipole.
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Antenna Gain

• Gain is the ratio of the radiation intensity in a
  given direction to the radiation intensity that
  would be obtained if the power accepted by the
  antenna were radiated isotropically.

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Gain

• Gain is closely related to the directivity.
• It accounts for the antenna efficiency as well as
  the directional capabilities, whereas directivity
  is only controlled by the antenna pattern.

Antenna efficiency
Does not involve the input power to the antenna
? If the antenna has ohmic losses Gain lt
Directivity.
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Efficiency
Accounts for losses associated with the antenna

• Sources of Antenna System Loss
• losses due to impedance mismatches (reflection)
• losses due to the transmission line
• conductive and dielectric losses in the antenna
• losses due to polarization mismatches

reflection
dielectric
conduction
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Overall Antenna Efficiency
The overall antenna efficiency is a coefficient
that accounts for all the different losses
present in an antenna system.
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Antenna Circuit Model

• The Tx antenna is a region of transition from a
  guided wave on a transmission line to a free
  space wave.
• The Rx antenna is a region of transition from a
  space wave to a guided wave on a transmission
  line.
• Thus, the antenna is a transitional circuit which
  interfaces a circuit and space.

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Antenna as a Circuit

• The input impedance of an antenna is the
  impedance presented by the antenna at its
  terminals.
• The input impedance will be affected by other
  antennas or objects that are nearby.

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Antenna and How It Responds to the Environment
Rr
TX or RX Antenna
Rr
Virtual transmission line linking the antenna
with space
Region of space within the antenna response
pattern
The radiation resistance can be thought of as a
virtual resistance that couples the
transmission line terminals to distant regions of
space via a virtual transmission line.
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Antenna Impedance

• For the discussions that follow, we will assume
  that the antenna is in an isolated environment.
• The input impedance of the antenna is composed of
  real and imaginary parts
• Zin Rin jXin
• The input resistance, Rin represents dissipation
  in the form of heating losses (Ohmic losses) or
  radiation.
• The input reactance, Xin represents power stored
  in the near field of the antenna.

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Antenna Input Impedance
An antennas input impedance describes the
terminal behavior of the antenna as seen from the
source (transmit mode) or receiving amplifier
(receive mode).

Antenna
-
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Reflection Efficiency
The reflection efficiency through a reflection
coefficient (G) at the input (or feed) to the
antenna.
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Transmitting Antenna Circuit Model
Vggenerator voltage (peak) Rggenerator output
resistance Xggenerator output reactance Rgantenn
a conductor loss resistance Rrantenna radiation
loss resistance XAantenna input reactance
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Transmitting Antenna Circuit Model
Maximum power transfer to antenna when
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Receiving Antenna Circuit Model
VAantenna voltage (peak) RLreceiver load
resistance XLreceiver load reactance Rgantenna
conductor loss resistance Rrantenna radiation
loss resistance XAantenna input reactance
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Radiation Resistance
The radiation resistance is relatively straight
forward to calculate.
Example Hertzian Dipole
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Radiation Resistance
Example Hertzian Dipole (continued)
Very low. It can be increased by increasing the
antenna length.
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Antenna Conduction and Dielectric Efficiency
Conduction and dielectric losses of an antenna
are very difficult to separate and are usually
lumped together to form the hcd efficiency. Let
Rcd represent the actual losses due to conduction
and dielectric heating. Then the efficiency is
given as
For wire antennas (without insulation) there is
no dielectric losses only conductor losses from
the metal antenna. For those cases we can
approximate Rcd by
where b is the radius of the wire, w is the
angular frequency, s is the conductivity of the
metal and l is the antenna length
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Polarization Loss Factor
In general, the polarization of the receiving
antenna will not be the same as the polarization
of the incident wave ? Polarization mismatch
Thus the power extracted by the antenna from the
incident wave will not be maximum. ?
Polarization loss factor
Incoming wave
Receiving antenna polarization
The polarization loss factor
The amount of incident power lost by mismatches
in polarization between the incident field and
the antenna.
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Effective Aperture
How much power can we pick up with a receive
antenna???
plane wave incident
Aphysical
Pload
Question
Answer Usually NOT
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Effective Aperture
Measure of how effectively the antenna converts
incident power density into received power.
under matched conditions
maximum effective aperture
Note that typically Sinc is assumed uniform over
the effective area.
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Directivity and Maximum Effective Aperture
The transmitted power density supplied by Antenna
1 at a distance R if Antenna 1 were isotropic
would be
Since actual antennas are not isotropic the
actual power density would be multiplied by the
directivity in that direction
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Directivity and Maximum Effective Aperture
The power collected (received) by Antenna 2 is
given by
If Antenna 2 is now the transmitter and Antenna
1 the receiver
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Directivity and Maximum Effective Aperture (no
losses)
Equating
and
gives
Assume one of the antennas (say Antenna 1) is
isotropic
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Maximum Directivity, Effective Aperture and Beam
Solid Angle
Also
For a fixed wavelength Aem and WA are inversely
proportional.
Therefore
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Effective Aperture (as a function of direction)
Can be used for received power when the direction
of incident radiation is arbitrary, not
necessarily along maximum directivity. Useful
when dealing with incoherent radiation form
extended sources such as sky or terrain.
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Directivity and Maximum Effective Aperture
(include losses)
conductor and dielectric losses
reflection losses (impedance mismatch)
polarization mismatch
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Friis Transmission Equation (no loss)
Antenna 1
Antenna 2
(qr,fr)
Atm, Dt
(qt,ft)
The transmitted power density supplied by Antenna
1 at a distance R and direction (qr,fr) is given
by
The power collected (received) by Antenna 2 is
given by
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Friis Transmission Equation (no loss)
Antenna 1
Antenna 2
(qr,fr)
Atm, Dt
(qt,ft)
If both antennas are pointing in the direction of
their maximum radiation pattern
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Friis Transmission Equation ( loss)
Antenna 1
Antenna 2
(qr,fr)
Atm, Dt
(qt,ft)
conductor and dielectric losses receiving antenna
reflection losses in receiving (impedance
mismatch)
free space loss factor
conductor and dielectric losses transmitting
antenna
reflection losses in transmitter (impedance
mismatch)
polarization mismatch
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Friis Transmission Equation Example
Two losses X-band (10.0 GHz) horns are separated
by distance of 100l. The reflection coefficients
measured at the terminals of the transmitting and
receiving antennas are 0.1 and 0.2 respectively.
The directivities of the transmitting and
receiving antennas are 16 dB and 20 dB
respectively. Assuming that the power at the
input terminals of the transmitting antenna is
3.0 W, and the antennas are aligned for maximum
radiation between them and the polarizations are
matched, find the power delivered to the receiver.
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References

• Stutzman Antenna Theory and Design
• Microwave Remote Sensing, F. T. Ulaby, et.al.
  Addison-Wesley
• Kraus
• Balanis, Antenna Theory.
• EE 540 lectures, Prof. Mirotznik