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I:\cgu\Antenna\antenna.wpd! Textbook: Warren L. Stutzman and Gary
A.

Thiele, “Antenna Theory and Design, 2nd Ed.”

! Matlab programming may be needed.

! Contents

radiation power or field strength around the

antenna, including: directive, single or

multiple narrow beams, omnidirectional,

from the antenna.

the antenna.

- Linear

- Circular

- Elliptical

" Impedance

" Bandwidth

wavelength.

- Properties

as a single of selectd narrow frequency bands.

- Properties

(opening) through which waves flow.

- Properties

Antennas 8

: electric flux density : electric current density : magnetic flux density : electric charge density : magnetic charge density

: permittivity : permeability

! Constituent Relationship

! Continuity Equations

! Boundary Conditions

Antennas 9

! Time-Harmonic Fields

Time-harmonic:

: a real function in both space and time. : a real function in space.

: a complex function in space. A phaser.

Thus, all derivative of time becomes .

For a partial deferential equation, all derivative of time can be replace with , and all time dependence of can be removed and becomes a partial deferential equation of space only.

Representing all field quantities as

, then the original Maxwell’s equation becomes

Antennas 10

! Power Relationship

! Poynting vector:

,

where is called the wave number. The above equations are called nonhomogeneous Helmholtz’s equations. The Lorentz condition becomes

Also

Antennas 11

The wave functions for electric and magnetic fields in source free region becomes

Antennas 12

Short Dipole:

E-plane pattern: plane containing E-fields. H-plane pattern: plane containing H-fields. Radiated power,

.

.

Antennas 15

Similarly,

and

Antennas 16

3. At various frequency and antenna size scaled,

Example 1-1

Antennas 17

Line current:

Main lobe (major lobe, main beam) Side lobe (minor lobe) Maximum side lobe level:

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

Antennas 18

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

Antenna Impedance

Ideal dipole:

where

Antennas 20

Considering the effect of continuity at the end of the dipole, use triangular current distribution

Example 1-4

Antennas 24

Maximum power transfer:

aperture size.

Communication Links

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

In dB form or

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

Example 2-3

Antennas 27

Arrays

Phased array: electronic scan. Radars, smart antennas. Active array: each antenna element is powered individually. Passive array: all antenna elements are powered by one source.

Array type by positioning: 1. Linear arrays, 2. Planar arrays, 3. Conformal arrays.

Array Factor

Antennas 28

In general the radiation pattern is

where is the excitation current of n-th antenna, the location vector, and the field pattern. If all antenna elements are the same

AF is called array factor. It is determine only by two parameters: the excitations and the locations of the antennas.

Equal Space Linear Array

Then

where .

Antennas 29

If the amplitude of the excitation is the same, that is ,

then

Broadside: Endfire:

Antennas 30

Antennas 31

Then, for long array

broadside.

Similarly, half power beamwidth

Main beam

Antennas 33

Single Mainbeam Oridinary Endfire Array Oridinary Endfire: main beam at exactly or . Range of :

Half-width of a grating lobe:

Choose to eliminate most of the grating

lobe, or

Antennas 34

Hansen-Woodyard Endfire Array

Purpose: increase directivity by increasing to reduce the visible region of the main beam. Formula:

Example 3-7 Five-Element Hansen-Woodyard Endfire Linear Array Parameters:

Antennas 35

Antennas 36

Pattern Multiplication

Parameters:

Since

For and ,

Antennas 39

Combining element pattern:

Let , then the array factor

is a polynomial of 1. Binomial distribution:

Properties: no sidelobe, broader beam width, lower directivity. 2. Dolph-Chebyshev distribution:

Properties: equal sidelobe levels, narrower beam width, higher directivity. Sidelobe level can be specified.

Antennas 41

Antennas 42

General expression of directivity of non-equal spaced and non-uniform excitation:

where is the current amplitude of k-th element, the position, and . For equal space, broadside array, , , we have

Furthermore, if , we have

Issue of Array

1. Mutual Coupling a. Effect impedances b. Effect radiation patterns c. Scan Blindness

2. Feed network a. Increase loss b. Effect bandwidth c. Increase space

Feed Network

Antennas 44

Antennas 45

From the general equation,

Thiele, “Antenna Theory and Design, 2nd Ed.”

! Matlab programming may be needed.

! Contents

radiation power or field strength around the

antenna, including: directive, single or

multiple narrow beams, omnidirectional,

from the antenna.

the antenna.

- Linear

- Circular

- Elliptical

" Impedance

" Bandwidth

wavelength.

- Properties

as a single of selectd narrow frequency bands.

- Properties

(opening) through which waves flow.

- Properties

Antennas 8

: electric flux density : electric current density : magnetic flux density : electric charge density : magnetic charge density

: permittivity : permeability

! Constituent Relationship

! Continuity Equations

! Boundary Conditions

Antennas 9

! Time-Harmonic Fields

Time-harmonic:

: a real function in both space and time. : a real function in space.

: a complex function in space. A phaser.

Thus, all derivative of time becomes .

For a partial deferential equation, all derivative of time can be replace with , and all time dependence of can be removed and becomes a partial deferential equation of space only.

Representing all field quantities as

, then the original Maxwell’s equation becomes

Antennas 10

! Power Relationship

! Poynting vector:

,

where is called the wave number. The above equations are called nonhomogeneous Helmholtz’s equations. The Lorentz condition becomes

Also

Antennas 11

The wave functions for electric and magnetic fields in source free region becomes

Antennas 12

Short Dipole:

E-plane pattern: plane containing E-fields. H-plane pattern: plane containing H-fields. Radiated power,

.

.

Antennas 15

Similarly,

and

Antennas 16

3. At various frequency and antenna size scaled,

Example 1-1

Antennas 17

Line current:

Main lobe (major lobe, main beam) Side lobe (minor lobe) Maximum side lobe level:

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

Antennas 18

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

Antenna Impedance

Ideal dipole:

where

Antennas 20

Considering the effect of continuity at the end of the dipole, use triangular current distribution

Example 1-4

Antennas 24

Maximum power transfer:

aperture size.

Communication Links

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

In dB form or

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

Example 2-3

Antennas 27

Arrays

Phased array: electronic scan. Radars, smart antennas. Active array: each antenna element is powered individually. Passive array: all antenna elements are powered by one source.

Array type by positioning: 1. Linear arrays, 2. Planar arrays, 3. Conformal arrays.

Array Factor

Antennas 28

In general the radiation pattern is

where is the excitation current of n-th antenna, the location vector, and the field pattern. If all antenna elements are the same

AF is called array factor. It is determine only by two parameters: the excitations and the locations of the antennas.

Equal Space Linear Array

Then

where .

Antennas 29

If the amplitude of the excitation is the same, that is ,

then

Broadside: Endfire:

Antennas 30

Antennas 31

Then, for long array

broadside.

Similarly, half power beamwidth

Main beam

Antennas 33

Single Mainbeam Oridinary Endfire Array Oridinary Endfire: main beam at exactly or . Range of :

Half-width of a grating lobe:

Choose to eliminate most of the grating

lobe, or

Antennas 34

Hansen-Woodyard Endfire Array

Purpose: increase directivity by increasing to reduce the visible region of the main beam. Formula:

Example 3-7 Five-Element Hansen-Woodyard Endfire Linear Array Parameters:

Antennas 35

Antennas 36

Pattern Multiplication

Parameters:

Since

For and ,

Antennas 39

Combining element pattern:

Let , then the array factor

is a polynomial of 1. Binomial distribution:

Properties: no sidelobe, broader beam width, lower directivity. 2. Dolph-Chebyshev distribution:

Properties: equal sidelobe levels, narrower beam width, higher directivity. Sidelobe level can be specified.

Antennas 41

Antennas 42

General expression of directivity of non-equal spaced and non-uniform excitation:

where is the current amplitude of k-th element, the position, and . For equal space, broadside array, , , we have

Furthermore, if , we have

Issue of Array

1. Mutual Coupling a. Effect impedances b. Effect radiation patterns c. Scan Blindness

2. Feed network a. Increase loss b. Effect bandwidth c. Increase space

Feed Network

Antennas 44

Antennas 45

From the general equation,