An Antenna Array Approach for Propagation of Electromagnetic Waves - - PowerPoint PPT Presentation

An Antenna Array Approach for Propagation of Electromagnetic Waves

Author:António E. M. S. Casimiro Email:acasimi@ualg.pt Affiliation: Science and Technology Faculty-CEFAT, University of Algarve, Mailing address: Campus de Gambelas, 8000-117 Faro, Portugal

Effort made in the framework of COST 296, sponsored by the Air Force Office of Scientific Research, USAF, and presented at the 2nd COST IC0603 Workshop as a COST cooperation activity.

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus

The Huygens principle

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus

The “array approach”

• (d)=

2 d sin 2 2 medium 1 medium 2

2

• d

1

• f

v

1 2

• f

v

2

"virtual antenna"

2

• d=

Phase shift with sinusoidal waves

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus

The shift in the Fourier Transform

A() A(d)

<-------->

F

A( ) A(d)e

d

<-------->

F

2

2

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus

The Fourier Relation

F F

A

• d

d A A

• = 2 sin 2

2 ejd

• A

2

• 2
• (the particular case of transversal

and endfire arrays)

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus

The shift in the “antenna” pattern

• A

2

• 1

2

• 2
• 2

2 2

• =

2 1

medium 1 medium 2 2 1 > >

2 1

• 2

1

1= 1

sin 1 = 2 sin 2 = sin 1 sin 2 = 1 2

1

n n2 = v2 v

1

2

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus

The Snell’s law

medium 1 medium 2

2

• 1
• 1

n n2 sin 1 sin 2 =

1

n n2 = v2 v

1

The Snell’s law does not take in hand the reflected ray

COST IC0603 Workshop, 9-11 April 2008 Limassol, Cyprus