Electromagnetic Waves

Transcription

2. Radio related fundamentals
2.1 Electromagnetic waves
Version
0.1
2.1.1
Mobile Communication Technologies @ BFH MAT 2012
0.
Preamble
1.
Surrounding fields
2.
Radio related fundamentals

2.0
Overview & summaries

2.1
Electromagnetic waves

2.2
Antennas

2.3
Propagation aspects

2.4
Radio coverage
3.
Communication related fundamentals
4.
Long range cellular systems
5.
Short range systems
6.
Satellite communications & broadcasting
7.
Use case: Evaluation of alternative technologies
for the Broadband Universal Service Obligation
cell wave

mobile communications
 2.1.0 Summary & major references
 2.1.1 History, electric & magnetic field fundamentals
 2.1.2 Maxwell equations & electromagnetic waves

innovative consulting
0
2.1.2
1
2
Summary & Major References
 Summary

History:

3

Electric field:

4


6
B-field in Tesla [T] produced by bar magnet or electric current.
Maxwell equations:

5
E-field lines in Volt per Meter [V/m] are perpendicular on conducting surfaces
Magnetic field:


Ampère (1775 – 1836)  Coulomb (1736 – 1806)  Faraday (1791 – 1867)  Gauss (1777 – 1855)  Maxwell (1831 – 1879).
4 basic equations based on Coulomb, Gauss, Ampère & Faraday laws allow Maxwell to predict electromagnetic waves.
Electromagnetic waves:

E-field & B-field are perpendicular to each other

Poynting vector
S
1
0
E  B points into the direction of the propagation of the wave.
7
S
8

Electromagnetic spectrum:

9
Long waves, radio waves, infrared, visible spectrum, ultraviolet, x-rays, gamma rays.
cell wave


0
2.1.3
1
2
Summary & Major References
 Major References
3
4
5
6
7
8
9
Jochen Schiller, "Mobile Communications",
Addison-Wesley, Second Edition, 2003,
ISBN 978-0-321-12381-7,
Section 2.1 "Frequencies for radio transmission",
pages 25-30.
cell wave


0
2.1.4
1
2
3
4
History, Electric & Magnetic Field Fundamentals
 History

1775 – 1836:
André Ampère  changing electrical current into magnetic field

1736 – 1806:
Charles Augustin Coulomb  electrostatic forces

1791 – 1867:
Michael Faraday  changing magnetic flux into electrical current

1777 – 1855:
Carl Friedrich Gauss  general relation of field and charge

1831 – 1879:
James Clerk Maxwell  electromagnetic theory
5
6
7
8
9
André Ampère
Charles A. Coulomb
cell wave

Michel Faraday

Carl Friedrich Gauss James Clark Maxwell
0
2.1.5
1
2
 Electric Field Fundamentals

3
4
5
6

Concept:

A field is a condition of space around a charge

Force is equal to charge times E-field (F = q E)

Test charge (+) will move in the direction of the E-field

Properties of fields are described by field lines – the charge trajectory
Properties of E-fields:

E-field lines start at + charge end at – charge

E-field lines are perpendicular on conducting surfaces

Two or more E-field lines cannot cross

Density of field lines is proportional to the magnitude of the field.

Field propagates with the speed of light.

Unit: Volt per Meter [V/m]
7
8
9
cell wave


0
2.1.6
1
2
 Magnetic Field Fundamentals

Field of a bar magnet:

Electric current produces magnetism:

Unit: Tesla [T]

3
Aurora Borealis – Charged particles
in solar wind interacting with Earth's
magnetic field:
4
5
6
7
8
9
cell wave


0
2.1.7
1
2
Maxwell Equations & Electromagnetic Waves
 Maxwell's Equations

Maxwell's equations – mathematically:
3
1.
2.
4
3.
4.
5

6
Maxwell's equations – in words:
1.
Charges produce electric field: Coulomb's law, more general form is Gauss' law.
2.
Magnets produce magnetic fields but no magnetic monopoles: Gauss' law for magnetism.
3.
Electric currents or time varying electric fields produce magnetic fields: Ampere's law.
4.
Changing magnetic field across a wire loop or moving a wire loop in a magnetic field induces a
voltage in the wire: Faraday's law
7

8
9
Maxwell's interpretations:

In 1865, Maxwell combined these with a modification to Ampere's law (#3).

Solution to the 4 equations in vacuum predicted oscillating electric and magnetic fields
perpendicular to each other  electromagnetic field.

Maxwell predicted the wave velocity that agreed with measurements of the speed of light.
cell wave


0
2.1.8
1
2
3
4
 Electromagnetic Waves

E-field and B-field are perpendicular to each other.

Electromagnetic waves propagate at the speed of light.

The Poynting vector S = 1/0(E x B) points into the
propagation direction (0 = magnetic permeability).
5
6
7
S
8
9
cell wave


0
2.1.9
1
2
 Important Relations & Parameters
 Time and location dependence of fields:
3
4
5


Electric field:
E(t) = Em sin (kx – t)

Magnetic field:
B(t) = Bm sin (kx – t)
with

Wavelength:
 = 2/ k

Frequency:
f =  / 2

Speed of light:
c = Em / Bm =  /k = (0 0)–1/2 = 299792458.0 m/s (exactly)
 3  108 m/s

Permittivity constant:
0 = 8.85  10-12 F/m

Permeability constant:
0 = 4  10-7 Tm/A = 1.26  10-6 Tm/A
6
7
 Poynting vector and intensity:
8
9

Poynting vector:
S = 1/0 E x B

Intensity:
I = Average (S)
cell wave


0
2.1.10
1
2
 Electromagnetic Spectrum
3
4
5
6
7
8
9
cell wave



Electromagnetic Waves

Transcription

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