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EELE 5333
Antenna & Radio
Propagation
Part I:
Antenna Basics
Winter 2020
Re-Prepared by
Dr. Mohammed Taha El Astal
Chapter 2:
Fundamental Parameters of Antennas
Session 3
Chapter 2 - Antenna Parameters
Antenna Parameters
Radiation Pattern
Radiation Intensity
Field Regions
Directivity
Antenna Efficiency
2
Chapter 2 - Antenna Parameters
Antenna Parameters (2)
Antenna Gain
Beamwidths and Sidelobes
Impedance
Polarization
3
4
Field Regions of Pattern
5
The fields surrounding an antenna
are divided into 3 regions:
• Reactive Near Field
• Radiating Near Field (Fresnel
Region)
• Far Field (Fraunhofer Region)
The far field region is the most
important, as this determines the
antenna's radiation pattern.
Also, antennas are used to
communicate wirelessly from long
distances, so this is the region of
operation for most antennas.
Field Regions
is defined as “that portion of the near-field region immediately
surrounding the antenna (immediate vicinity of the antenna)
wherein the reactive field predominates.”
• For most antennas, the outer boundary of this region is commonly
taken to exist at a distance:
from the antenna surface, where λ is the wavelength and D is the
largest dimension of the antenna.
3
0 62D
R .
Reactive Near-Field Region
• Region of the field of an antenna between the reactive near-field
region and the far-field region.
• the reactive fields are not dominate; the radiating fields begin to
emerge.
• However, unlike the Far Field region, here the shape of the
radiation pattern may vary appreciably with distance.
• The region is commonly given by:
3 220 62
D D. R
Radiating Near-Field (Fresnel) Region
• In this region, the radiation pattern does not change shape with
distance (although the fields still die off as 1/R, the power
density dies off as 1/R2).
• This region is dominated by radiated fields, with the E- and H-
fields orthogonal to each other and the direction of propagation
as with plane waves.
• condition must be satisfied to be in the far field region:
22DR
Far-field (Fraunhofer) Region
Field Regions
10
Field Regions
Continue with Antenna parameters: Solid Angle & SteradianRadiation power density
Radiation intensity
12
Solid Angle Concept
https://www.youtube.com/watch?v=V1bOThT1GKI
13
Radian• The measure of a plane angle is a
radian.
• One radian is defined as the plane angle
with its vertex at the center of a circle
of radius r that is subtended by an arc
whose length is r.
• How many rad in a circle of radius r?
1 Rad
Solid Angle - Radian and Steradian
Since the circumference of a circle of radius r is C = 2πr, there
are 2π rad (2πr/r) in a full circle.
d𝜃 =𝑑ℓ
𝑟
(unitless)
Solid Angle - Radian and Steradian
• Since the area of a sphere of radius r is A = 4πr2, there are 4π
sr (4πr2/r2) in a closed sphere.
• Steradian
• The measure of a solid angle is a
steradian.
• One steradian is defined as the solid angle
with its vertex at the center of a sphere of
radius r that is subtended by a spherical
surface area equal to that of a square with
each side of length r.
• How many sr in sphere of radius r?
dΩ =𝑑𝐴
𝑟2
(uniitless)
r
r
2
2
2 2
solid angle = Area r
dAdifferential solid angle d
r
where dA is differential area , dA r sin d d (m )
d sin d d (sr)
Solid Angle - Radian and Steradian
𝑟
𝑟𝑑𝜃
Plan where ∅ is constant
Plan where ∅ is constant
𝑟𝑠𝑖𝑛𝜃
𝑟𝑠𝑖𝑛𝜃𝑑∅
16
For a sphere of radius r, find the solid angle ΩA (in square radians or
steradians) of a spherical cap on the surface of the sphere over the
north-pole region defined by spherical angles of :
0 ≤ θ ≤ 30◦, 0 ≤ φ ≤ 360◦.
Solid Angle - Radian and Steradian
The quantity used to describe the power associated with an electromagnetic wave is the instantaneous Poynting vector, which is defined :
The total power crossing a closed surface can be obtained by
integrating the Poynting vector ( since it is a power density)
over the entire surface:
17
Dipole radiation of a dipole
vertically in the page
showing electric field
strength (colour) and
Poynting vector (arrows) in
the plane of the page.
Radiation Power Density
It is often more desirable to find the average power density which is
obtained by integrating the instantaneous Poynting vector over one
period and dividing by the period.
The 1/2 factor appears in the equation because the E and H fields
represent peak values, and it should be omitted for RMS values.
E and H are in phasor forms
Radiation Power Density
19
The average power radiated by an antenna (radiated power) is:
For a closed surface, a sphere of radius r is chosen and dS is taken as:
r2 sinθ dθ dφ ˆar
Radiation Power Density
20
Example
21
Isotropic radiator case
Because of its symmetric radiation, its Poynting vector will not be a function of the spherical coordinateangles 𝜃 and 𝜙. In addition, it will have only a radial component. Thus the total power radiated by it isgiven by
EELE 5333
Antenna & Radio
Propagation
Part I:
Antenna Basics
Winter 2020
Re-Prepared by
Dr. Mohammed Taha El Astal
Chapter 2:
Fundamental Parameters of Antennas
Session 4
Radiation Intensity
Radiation Intensity: in a given direction is defined as “the power radiated
from an antenna per unit solid angle.”
It can be obtained by simply multiplying the radiation density by the square of
the distance. In mathematical form:
U = radiation intensity (W/unit solid angle)Wrad = radiation density (W/m2)
Whereas the Poynting vector depends on the distance from the antenna (varyinginversely as the square of the distance), the radiation intensity U is independent of thedistance, assuming in both cases that we are in the far field of the antenna
Radiation Intensity
The total power is obtained by integrating the radiation intensity,
as given over the entire solid angle of 4π. Thus
where dΩ = element of solid angle = sinθ dθ dφ.
Radiation Intensity
The radiated power density of an antenna is given by (continuing of previous example)
where A0 is the peak value of the power density, θ is the usual spherical coordinate, and
ˆar is the radial unit vector.
(a) Determine the total radiated power.
(b) Find the radiation Intensity (U)
(c) Find the radiated power using part (b).
(a)
Example
(b)
(c)
Example
Directivity of an antenna is “the ratio of the radiation intensity
in a given direction from the antenna to its average value over a
sphere (to radiation intensity of isotropic source)”.
The average radiation intensity (same meaning of radiation intensity
of isotropic source) is equal to the total power radiated by the antenna
divided by 4π.
If the direction is not specified, it implies the direction of maximum
radiation intensity (maximum directivity) expressed as
Directivity
Radiation Intensity
(U): The power
radiated from an
antenna per unit
solid angle (watts
per steradian).
in a given direction
D = directivity (dimensionless).D0 = maximum directivity (dimensionless).U = radiation intensity (W/unit solid angle).Umax = maximum radiation intensity (W/unit solid angle).U0 = radiation intensity of isotropic source (W/unit solid angle).Prad = total radiated power (W).
For an isotropic source, it is very obvious that the directivity is
unity since U, Umax, and U0 are all equal to each other.
Directivity
The radiated power density of an antenna is given by
(a) Find the maximum directivity of the antenna and write an expression
for the directivity as a function of θ and φ.
(b) Repeat (a) for radiated power density of:
Example
(a)
Example
(b)
Example
Example’s discussion
At this time it will be proper to comment on the results of Examples 2.5 and 2.6. To better understand the discussion, we have plotted in Figure 2.12 the relative radiation intensities of Example 2.5 (U = A0 sin 𝜃) and Example 2.6 (U = A0 sin2 𝜃) where A0 was set equal to unity. We see that both patterns are omnidirectional but that of Example 2.6 has more directional characteristics (is narrower) in the elevation plane. Since the directivity is a “figure of merit” describing how well the radiator directs energy in a certain direction, it should be convincing from Figure 2.12 that the directivity of Example 2.6 should be higher than that of Example 2.5.
Directivity of a half-wavelength dipole (l = λ/2), can be approximated by (will be derived
later/skipped ): 𝐷 = 𝐷0 sin3𝜃 = 1.67 sin3𝜃, where θ is measured from the axis along
the length of the dipole.
Example
• For 57.44◦< θ < 122.56◦, the dipole radiator has greater
directivity (greater intensity concentration) in those
directions than that of an isotropic source. Outside this
range of angles, the isotropic radiator has higher
directivity (more intense radiation).
• The maximum directivity of the dipole (relative to the
isotropic radiator) occurs when θ = π/2, and it is 1.67 (or
2.23 dB) more intense than that of the isotropic radiator
(with the same radiated power).
Example
Example
The maximum Directivity can be found by:
Example
Exact expression
Dr. Talal Skaik 2016 IUG
Approximate Directivity – Directional Patterns
40
The maximum Directivity D0 can be approximated for pattern that has
only one major lobe and any minor lobes with very low intensity:
Approximate Directivity – Directional Patterns
41
The radiation intensity of the major lobe of many antennas can be adequately represented by:
U = B0 cos θ
where B0 is the maximum radiation intensity. The radiation intensity exists only in the upper
hemisphere (0 ≤ θ ≤ π/2, 0 ≤ φ ≤ 2π), and it is shown next slide. Find the:
(a) beam solid angle; exact and approximate.
(b) maximum directivity; exact and approximate.
The half-power point of the pattern occurs at θ = 60◦. Thus the
beamwidth in the θ direction is 120◦ or:
Since the pattern is independent of the φ coordinate, the
beamwidth in the other plane is also equal to:
Example
Example
Example
Many times it is desirable to express the directivity in decibels
(dB) instead of dimensionless quantities. The expressions for
converting the dimensionless quantities of directivity and
maximum directivity to decibels (dB) are:
D(dB) = 10 log10[D (dimensionless)]
D0(dB) = 10 log10[D0 (dimensionless)]
Example
Single lobe directional patterns can be approximated by:
U=B0 cosn(θ) 0 ≤ θ ≤ π/2, 0 ≤ φ ≤ 2π.
Some antennas (such as dipoles, loops, broadside arrays) exhibit
omnidirectional patterns, as illustrated by the three-dimensional
patterns in next slide.
Omni-directional patterns can often be approximated by:
U = |sinn(θ)| 0 ≤ θ ≤ π, 0 ≤ φ ≤ 2π
where n represents both integer and noninteger values.
Approximate Directivity – Omnidirectional Patterns
Dr. Talal Skaik 2016 IUG 46
• The approximate directivity formula for an omnidirectional pattern whose
main lobe is approximated by the previous equation is given by (McDonald):
• Another approximation is given by (Pozar) as:
• Note: The first equation by McDonald is more accurate for omnidirectional
patterns with minor lobes, as shown in Figure (a) next slide, while second
equation by Pozar should be more accurate for omnidirectional patterns with
minor lobes of very low intensity (ideally no minor lobes), as shown in Figure
(b).
Approximate Directivity – Omnidirectional Patterns
Approximate Directivity – Omnidirectional Patterns
The normalized radiation intensity of an antenna is represented by:
Find the: a. half-power beamwidth HPBW (in radians and degrees)b. first-null beamwidth FNBW (in radians and degrees)
Example
(a)
Example
(b)
Example
