lecture 5: antennas and wave propagation anders västberg [email protected] 08-790 44 55
TRANSCRIPT
Lecture 5: Antennas and Wave Propagation
Anders Västberg
08-790 44 55
Digital Communication System
Source of Information
SourceEncoder
Modulator RF-Stage
Channel
RF-StageInformation
SinkSource
DecoderDemodulator
ChannelEncoder
DigitalModulator
ChannelDecoder
DigitalDemodulator
[Slimane]
Maxwell's Equations
• Electrical field lines may either start and end on charges, or are continuous
• Magnetic field lines are continuous
• An electric field is produced by a time-varying magnetic field
• A magnetic field is produced by a time-varying electric field or by a current
Electromagnetic Fields
)cos(}{),( tetrE tj EE
(V/m),2
1ErmsE
HEP
H2
1rmsH
)(W/m,2
1
2
1 2HEP S
Poyntings Vector:
Power density:
Impedance of Free Space
• Both fields carry the same amount of energy
• Free space impedance is given by
• The power density can be expressed as
H/m104
F/m10854185.87
0
120
22
0
HE
3770
00
Z
20
0
2
rmsrms HZZ
ES
[Slimane]
Isotropic Antenna
• An isotropic radiator is an hypothetical antenna that generates a uniform field, i.e., energy flows with equal strength in all directions.
• Let Pt be the total power emitted by this antenna.
• This total power will be uniformly distributed over the surface of a sphere enclosing the antenna.
• The power density on a sphere of radius r is given by:
22
W/m,4 r
PS tr
[Slimane]
Effective Aperture of an Antenna
• Ae is defined as the area of a perfect lossless antenna
• The received power can be written as follows:
• Ae is dependent on the type of receiving antenna
24 r
APASP eterr
[Slimane]
Antenna Gain
2
2
2
44
c
AfAG ee
• The antenna gain is defined by its relative power density
),(max SG
24
),(),,(
r
PS
SSrS
tr
rr
Wave propagation
• The field at the receiver can be decomposed into three components– Direct wave, Line-of-Sight Path– Ground reflected wave– Ground Wave (less than 2 MHz, less than 10 MHz over water)
[Slimane]
Diffraction
• For radio wave propagation over rough terrain, the propagation is dependent on the size of the object encountered.
• Waves with wavelengths much shorter than the size of the object will be reflected
• Waves with wavelengths much larger than the size of the obstacle will pass virtually unaffected.
• Waves with intermediate wavelengths curve around the edges of the obstacles in their propagation (diffraction).
• Diffraction allows radio signals to propagate around the curved surface and propagate behind obstacles.
[Slimane]
Propagation in the Atmosphere
• The atmosphere around the earth contains a lot of gazes (1044 molecules)
• It is most dense at the earth surface (90% of molecules below a height of 20 km).
• It gets thinner as we reach higher and higher attitudes.
• The refractive index of the air in the atmosphere changes with the Height
• This affects the propagation of radio waves.• The straight line propagation assumption may
not be valid especially for long distances.
[Slimane]