Lecture 2: Introduction to case studies: Radiolink
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]
The Radio Link
• Design considerations– The distance over which the system meets
the performance objectives– The capacity of the link.
• Performance determined by– Frequency– Transmitted Power– Antennas– Technology used
[Black et. al]
Propagation between two antennas (not to scale)
No Ground Wave for Frequencies > ~2 MHzNo Ionospheric Wave for Frequencies > ~30 Mhz
Direct Wave
Ground ReflectedWave
Ground Wave
Sky Wave
Radiation
Only accelerating charges produce radiation
[Saunders, 1999]
Antennas
• The antenna converts a radio frequency signal to an electromagnetic wave
• An isotropic antenna radiates power in all directions equally – an ideal antenna
• Real antennas does not perform equally well in all directions
Free Space Propagation
Ptr
Ae
2
2
4
4
r
APASP
r
PS
eterr
tr
Radiation Patterns
𝑆𝑑 (𝜃 ,𝜙 )=1.64cos (𝜋 /2cos 𝜃)
sin2𝜃
• Beam width• Front-back ratio• Side lobe level
Antenna Gain(maximum gain or directivity)
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
Real antennas
• Directivity, D, is equal to the maximum gain
• The actual power gain of the antenna is
where is the efficiency of the antenna (<1).
Antennas
• Isotropic antenna• Omnidirectional• Directional antenna
[Stallings, 2005]
Transmission media
• Microwaves 1 GHz-100 GHz• Broadcast Radio 30 MHz-1 GHz• HF 3-30 MHz• Infrared
Wave Propagation
• Reflection – Results in multipath propagation
• Diffraction – Radio waves propagates behind obstacles
• Scattering – Rough surfaces scatter radio wave in a
multitude directions
Reflection (R), Diffraction (D) and Scattering (S)
[Stallings, 2005]
Multipath propagation
[Saunders, 1999]
Diffraction
[Saunders, 1999]
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]
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]
decibels• The bel is a logarithmic unit of power ratios. One bel corresponds to an
increase of power by a factor of 10 relative to some reference power, Pref.
refbel P
PP 10][ log
refdB P
PP 10][ log10
• The bel is a large unit, so that decibel (dB) is almost always used:
• The above equation may also be used to express a ratio of voltages (or field strengths) provided that they appear across the same impedance (or in a medium with the same wave impedance):
refdB V
VV 10][ log20
[Saunders, 1999]
decibelsUnit Reference Power Application
dBW 1 W Absolute power
dBm 1 mW Absolute powerP [dbW] = P [dBm] - 30
dBmV 1 mV Absolute voltage, typically at the input terminals of a receiver
dB any Gain or loss of a network
dBmV/m 1 mV/m Electric field strength
dBi Power radiated by and isotropic reference antenna
Gain of an antenna
dBd Power radiated by a half-wave dipole
Gain of an antenna0 dBd = 2.15 dBi
[Saunders, 1999]
dB Problems
• Convert the following to linear scale:3 dB, -6 dB, 10 dB, 20 dB, 23 dB, -30 dB
• Convert the following to dBm and mW:-3 dBW, 0 dBW, 20 dBW, -10 dBW.
• Convert 22 mW to dBW and 63 to dB.• Convert 15 dB to linear scale.
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Uppgifter inför F2
• Bestäm frekvens, vinkelfrekvens, periodtid och amplitud för följande sinuskurva
24
0 .5 0 .5 1 .0t
1 .5
1 .0
0 .5
0 .5
1 .0
1 .5
st
Uppgifter inför F2
• Plotta följande Fourierserie och bestäm typ av periodisk funktion.
• Plotta också amplitudspektrum
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