EC2353-Antenna and Wave Propagation

EC1352 – Antenna Wave Propagation /J. Alexander/ AP/ECE / AAMEC

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Antenna

An antenna may be defined as a conductor or group of conductors used either for

radiating electromagnetic energy into space or for collecting it from space.

Electrical energy from the transmitter is converted into electromagnetic energy by the

antenna and radiated into space.

On the receiving end, electromagnetic energy is converted into electrical energy by the

antenna and fed into the receiver.

The electromagnetic radiation from an antenna is made up of two components, the E field

and the H field. The total energy in the radiated wave remains constant in space except

for some absorption of energy by the earth.

However, as the wave advances, the energy spreads out over a greater area. This causes

the amount of energy in a given area to decrease as distance from the source increases.

In other words the antenna is the transitional structure between free-space and a guiding

device.

The guiding device or transmission line may take the form of a coaxial line or a hollow

pipe (waveguide), and it is used to transport electromagnetic energy from the transmitting

source to the antenna, or from the antenna to the receiver.

The IEEE Standard Definitions of Terms for Antennas (IEEE Std 145–1983) defines the

antenna or aerial as “a usually metallic device (as a rod or wire) means for radiating or

receiving radio waves.”


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Radiation intensity

Radiation intensity is defined as “the power radiated from an antenna per unit solid

angle.”

The radiation intensity is a far-field parameter.

It can be obtained by simply multiplying the radiation density by the square of the

distance.

In mathematical form it is expressed as U = r2. Wrad

o Where

U = radiation intensity (W/unit solid angle)

Wrad = radiation density (W/m2)

Directivity

The directivity of an antenna defined as “the ratio of the radiation intensity in a given

direction from the antenna to the radiation intensity averaged over all directions”.

The average radiation intensity is equal to the total power radiated by the antenna divided

by 4π.

If the direction is not specified, the direction of maximum radiation intensity is implied.”

The directivity of a nonisotropic source is equal to the ratio of its radiation intensity in a

given direction over that of an isotropic source.

In mathematical form,

Directive Gain:

Directive Gain Gd = =

Power Gain or Gain = =

Total Input Power ( = Radiated Power + Power loss in ohmic resistance

Directivity Vs Gain.

If an antenna has no ohmic loss or dielectric mismatch loss, i.e., 100% efficient, then directivity and Gain

are the same.


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G = k .D

K= Efficiency factor =1 for 100% efficiency

< 1 if losses are present.

D = Directivity

G = Gain

Antenna Efficiency:

Antenna Efficiency (η) =

=

If the current flowing in the antenna is „I‟ , then

η =

η % = 100

Beam width

The beamwidth of a pattern is defined as the angular separation between two identical

points on the opposite side of the pattern maximum.

In an antenna pattern, there are a number of beamwidths.

One of the most widely used beamwidths is the Half-PowerBeamwidth (HPBW ).

HPBW is defined as:

“In a plane containing the direction of the maximum of a beam,

the angle between the two directions in which the radiation

intensity is one-half value of the beam.”


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Another important beamwidth is the angular separation between the first nulls of the

pattern, and it is referred to as the First-Null Beamwidth (FNBW ).

Bandwidth

The bandwidth of an antenna is defined as

o “The range of frequencies within which the performance of the antenna, with

respect to some characteristic, conforms to a specified standard.”

The bandwidth can be considered to be the range of frequencies, on either side of a center

frequency (usually the resonance frequency for a dipole), where the antenna

characteristics (such as input impedance, pattern, beamwidth, polarization, side lobe

level, gain, beam direction, radiation efficiency) are within an acceptable value of those

at the center frequency.

Reciprocity principle

In any network composed of linear, bilateral, lumped elements, if one places a constant

current (voltage) source between two nodes (in any branch) and places a voltage

(current) meter between any other two nodes (in any other branch), makes observation of

the meter reading, then interchanges the locations of the source and the meter, the meter

reading will be unchanged”

RECIPROCITY is the ability to use the same antenna for both transmitting and receiving.

The electrical characteristics of an antenna apply equally, regardless of whether it has

been used for transmitting or receiving.

The more efficient an antenna is for transmitting a certain frequency, the more efficient it

will be as a receiving antenna for the same frequency.

Reciprocity for antenna patterns is generally provided the materials used for the antennas

and feeds, and the media of wave propagation are linear. Nonlinear devices, such as

diodes, can make the antenna system nonreciprocal. Radian and Steradian

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. A graphical illustration is shown in Figure (a).

Since the circumference of a circle of radius r is C = 2πr,

There is 2π rad (2πr/r) in a full circle.

Steradian

The measure of a solid angle is a steradian.


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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.

A graphical illustration is shown in Figure (b).

Since the area of a sphere of radius r is A = 4πr2,

There is 4π Sr (4πr2/r

2) in a closed sphere.

Solid Angle Of A Sphere (dΩ)

Cartesian (x,y,z) Cylindrical (r, φ , z) Spherical (r, ϴ, φ)

Differential length dx , dy , dz dr, r.dφ , dz dr, r.dϴ, r sinϴ dφ

Differential Area dx.dy = dy.dz = dz.dx

r. dr.dφ

r.dφ.dz

dr dz

r.dr.dϴ

r sinϴ dφ dr

r2 sinϴ dϴ dφ


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The infinitesimal area dA on the surface of a sphere of radius r, shown in Figure 2.1, is given by

dA = r2 sinϴ dϴ dφ

Therefore, the element of solid angle dΩ of a sphere can be written as

dΩ = dA/ r2 = sinθ dθ dφ (sr)

Effective Area (or) Effective Aperture (or) Capture Area

Effective Area = =

Consider a receiving antenna situated in the field of a passing electromagnetic wave.

The antenna collects power from the wave and deliver it to the terminating or Load impedance „ZT‟

connected in series.

The antenna may be replaced by a thevenin‟s equivalent Circuit ( series combination of V and RA)

The voltage V is induced by the passing wave and produces a current I through the terminating

impedance ZT.

………………………(1)

Terminating and antenna impedances are complex.

Thus, ZT = RT +j XT ; ZA = RA +j XA ………………………….(2)

Antenna Resistance may be divided into two parts (i) Radiation Resistance (ii) Loss Resistance

RA = Rrad + Rloss

From (1) & (2)

Since, Power (W) = I2RT ;


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Power = Power density x Area ; W = S . A

Let us consider now the situation where the terminating impedance is the complex conjugate of the

antenna impedance, so that maximum power is transferred.

XT = – XA ; RT = Rrad + Rloss

The above said condition yields the effective aperture (Aeff) of the Antenna.

Thus, Aeff = =

Effective Length (Effective Height)

Effective length is defined as “the ratio of the magnitude of the open-circuit voltage developed at the terminals of

the antenna to the magnitude of the electric-field strength in the direction of the antenna polarization.

The effective length represents the antenna in its transmitting and receiving modes, and it is particularly useful in

relating the open-circuit voltage Voc of receiving antennas.

This relation can be expressed as

Voc = Ei . le where

Voc = open-circuit voltage at antenna terminals (volts)

Ei = incident electric field (Volts / meter)

le = vector effective length (meter)

le =

Where,

le = Effective Length (metre)

lp = Physical length (metre)

Iav = Average Current (Ampere)

Io = Instantaneous Current (Ampere)

Relation between Effective length and effective area

For an antenna of radiation resistance Rrad matched to its load, the power delivered to the load is

equal to

= …………….. (1)


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Power (W) = Poynting vector x Effective Aperture

= S x Aeff

= ……………(2)

Where, Z0 = intrinsic impedance of space (= 377 Ω)

Equate (1) and (2)

&

Thus, effective length and effective aperture are related via radiation resistance and the intrinsic

impedance of space.

Radiation Resistance:

The antenna is a radiating device, in which the power (i.e., energy per unit time) is radiated into

space in the form of electromagnetic waves.

Hence there must be power dissipation which may be expressed in the usual manner as, W = I2R

If it is assumed that all this power appears as electromagnetic waves, then the power can be

divided by the square of the current. I.e., at the point where it is fed to the antenna and obtain a

fictitious resistance called as radiation resistance.

The radiation resistance (Rrad) is thus defined as that fictitious resistance which, when substituted

in series with the antenna, will consume the same power as it actually radiated.

Relation between gain, effective length and radiation resistance.

Documents

EC2353-Antenna and Wave Propagation