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Antennas

- Radiated Power
- Radiation Pattern
- Beamwidth
- Pattern Solid Angle
- Directivity
- Efficiency
- Gain

Antennas

Transmitting Antenna Any structure designed to

efficiently radiate electromagnetic radiation in

a preferred direction is called a transmitting

antenna.

Wires passing an alternating current emit, or

radiate, electromagnetic energy. The shape and

size of the current carrying structure determines

how much energy is radiated as well as the

direction of radiation.

Receiving Antenna Any structure designed to

efficiently receive electromagnetic radiation is

called a transmitting antenna

We also know that an electromagnetic field will

induce current in a wire. The shape and size of

the structure determines how efficiently the

field is converted into current, or put another

way, determines how well the radiation is

captured. The shape and size also determines

from which direction the radiation is

preferentially captured.

Antennas Radiation Power

Let us consider a transmitting antenna

(transmitter) is located at the origin of a

spherical coordinate system. In the far-field,

the radiated waves resemble plane waves

propagating in the radiation direction and

time-harmonic fields can be related by the

chapter 5 equations.

Electric and Magnetic Fields

The time-averaged power density vector of the

wave is found by the Poynting Theorem

Power Density

The total power radiated by the antenna is found

by integrating over a closed spherical surface,

Radiated Power

Antennas Radiation Patterns

Radiation patterns usually indicate either

electric field intensity or power intensity.

Magnetic field intensity has the same radiation

pattern as the electric field intensity, related

by ?o

It is customary to divide the field or power

component by its maximum value and to plot a

normalized function

Normalized radiation intensity

Isotropic antenna The antenna radiates

electromagnetic waves equally in all directions.

Antennas Radiation Patterns

Radiation Pattern

A polar plot

A directional antenna radiates and receives

preferentially in some direction.

It is customary, then, to take slices of the

pattern and generate two-dimensional plots.

The polar plot can also be in terms of decibels.

A rectangular plot

It is interesting to note that a normalized

electric field pattern in dB will be identical to

the power pattern in dB.

Antennas Radiation Patterns

A polar plot

Radiation Pattern

It is clear in Figure that in some very specific

directions there are zeros, or nulls, in the

pattern indicating no radiation. The

protuberances between the nulls are referred to

as lobes, and the main, or major, lobe is in the

direction of maximum radiation. There are also

side lobes and back lobes. These other lobes

divert power away from the main beam and are

desired as small as possible.

A rectangular plot

Beam Width

One measure of a beams directional nature is the

beamwidth, also called the half-power beamwidth

or 3-dB beamwidth.

Antennas S

Antenna Pattern Solid Angle

A differential solid angle, d?, in sr, is defined

as

For a sphere, the solid angle is found by

integrating

A radian is defined with the aid of Figure a).

It is the angle subtended by an arc along the

perimeter of the circle with length equal to the

radius. A steradian may be defined using Figure

(b). Here, one steradian (sr) is subtended by an

area r2 at the surface of a sphere of radius r.

An antennas pattern solid angle,

All of the radiation emitted by the antenna is

concentrated in a cone of solid angle ?p over

which the radiation is constant and equal to the

antennas maximum radiation value.

Antennas Directivity

Directivity

The directive gain,, of an antenna is the ratio

of the normalized power in a particular direction

to the average normalized power, or

Where the normalized powers average value taken

over the entire spherical solid angle is

The directivity, Dmax, is the maximum directive

gain,

Using

Example

8.1 In free space, suppose a wave propagating

radially away from an antenna at the origin has

where the driving current phasor

Find (1) Es

Find (2) P(r,?,?)

Magnitude

Find (3) Prad

We make use of the formula

Find (4) Pn(r,?,?) Normalized Power Pattern

Find (5) Beam Width

and

(6) Pattern Solid Angle ?p (Integrate over the

entire sphere!)

(7) directivity Dmax

(8) Half-power Pattern Solid Angle ?p,HP

(Integrate over the beamwidth!)

Power radiated through the beam width

Antennas Efficiency

Efficiency

Power is fed to an antenna through a T-Line and

the antenna appears as a complex impedance

where the antenna resistance consists of

radiation resistance and and a dissipative

resistance.

For the antenna is driven by phasor current

The power dissipated by ohmic losses is

The power radiated by the antenna is

An antenna efficiency e can be defined as the

ratio of the radiated power to the total power

fed to the antenna.

Antennas Gain

Gain

The power gain, G, of an antenna is very much

like its directive gain, but also takes into

account efficiency

The maximum power gain

The maximum power gain is often expressed in dB.

Example

D8.3 Suppose an antenna has D 4, Rrad 40 ?

and Rdiss 10 ?. Find antenna efficiency and

maximum power gain. (Ans e 0.80, Gmax 3.2).

Antenna efficiency

Maximum power gain

Maximum power gain in dB

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