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Radiation Pattern Definitions

Normalized field pattern:

Power pattern: In dB scale

ExamplesIdeal dipole:

Line current:

Main lobe (major lobe, main beam)Side lobe (minor lobe)

Maximum side lobe level:

Half-power beamwidth: Pattern types: Broadside, Intermediate, Endfire.

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Directivity

Solid angle:

Radiation intensity:

where

Directivity:

Beam solid angle:

Power Gain (Gain)

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or

Radiation efficiency:

Referenced Gain:

dBi: referenced to isotropic antenna.dBd: referenced to dipole antenna.

The origin of radiation – short dipoles.

Phasor retarded potential

and

,

Consider an infinite small short dipole pointing in z direction andlocated at origin, where is a line current, and is the length, i.e.,

or at , since .

then,

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In spherical coordinate

and

that is

Near Field:

The same as the static magnetic field calculated by Biot-Savart’s law

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since .

The same as the static electric field generated by dipole moment .

Far field:

Spherical TEM wave

,

Propagating in ,

In general,

Summary:

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1. All radiation of finite current distribution is spherical TEM waveat far field.

2. Both and varies as at far field.

Half-wave dipole

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Poynting vector:

Power radiated:

Radiation resistance:

Importance of half-wave dipole:1. consider the dipole as an open transmission line, then

. At , ,..., . Which means zero

reactance. In reality, the length is a little be shorter. Since a goodtransmission’s intrinsic impedance is near pure real, this allowsmatching to transmission lines.

2. The efficiency is the best at .

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Antenna Arrays

Suppose there are N identical antennas each located at location, then

where Thus,

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where is called array factor, is the vector potential of singleelement located at origin.

General Uniform Linear Arrays

Let , and then the normalized array factor,

where ,then

1. Main-beam direction. Maximum occurs when , i.e.,

a. Broadside array,

b. Endfire array,

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2. Null locations:

3. Side lobe locations:

Pattern Multiplication

Example: Two-Collinear, Half-Wavelength Spaced Short Dipoles

Parameters:

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Example: Two Parallel, Half-Wavelength Spaced Short Dipoles

Since

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Antenna in Communication Systems

Open circuit voltage: for ideal dipole receiving antenna andpolarization match.

When

Maximum power transfer:

Power density:

Maximum effective aperture

For a dipole

In general, or

Effective aperture: Available power:

In general,

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Aperture efficiency: , where is the physical aperture size.

Communication Links

Power delivered to the load : polarization mismatch factor, : impedance mismatch factor,

In dB form or

where dBm is power in decibels above a milliwatt.

EIRP: effective (equivalent) isotropically radiated powerERP: effective radiated power by a half-dipole

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Other Antenna Types

1. Traveling wave antennas

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2. Helix

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3. Yagi-Uda

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4. Broadband antennasa. Spiralb. log-periodic

5. Aperture

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6. Patch