Chapter 2: Antenna & Fundamental Parameters of Radio...

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

Dr. Mohammed Taha El Astalmtastal@iugaza.edu.psDr.mastal@gmail.com

10/2020

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

Dr. Mohammed Taha El Astalmtastal@iugaza.edu.psDr.mastal@gmail.com

10/2020