Lecture 2: Introduction to case

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16 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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Lecture

2:
Introduction

to

case

studies:
Radiolink

Anders Västberg

vastberg@kth.se

08
-
790 44 55

Digital Communication
System

Source of

Information

Source

Encoder

Modulator

RF
-
Stage

Channel

RF
-
Stage

Information

Sink

Source

Decoder

Demodulator

Channel

Encoder

Digital

Modulator

Channel

Decoder

Digital

Demodulator

[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 MHz

No Ionospheric Wave for Frequencies > ~30 Mhz

Direct Wave
Ground Reflected
Wave
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

P
t
r
A
e
2
2
4
4
r
A
P
A
S
P
r
P
S
e
t
e
r
r
t
r





Radiation Patterns

𝑆
𝑑

,
𝜙
=
1
.
64
cos

(
𝜋
/
2


cos



)

sin
2



Beam width


Front
-
back ratio


Side lobe level

Antenna Gain

(maximum gain or directivity)

2
2
2
4
4
c
A
f
A
G
e
e






The antenna gain is defined by its relative power
density

)
,
(
max


S
G

2
4
)
,
(
)
,
,
(
r
P
S
S
S
r
S
t
r
r
r








Real antennas


Directivity,
D
, is equal to the maximum
gain


The actual power gain of the antenna is

𝐺
=
𝐷


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(
}
{
)
,
(







t
e
t
r
E
t
j
E
E
(V/m)
,
2
1
E

rms
E
H
E
P


H
2
1

rms
H
)
(W/m
,
2
1
2
1
2
H
E
P


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/m
10
4
F/m
10
854185
.
8
7
0
12
0
2
2
0












H
E



377
0
0
0


Z
2
0
0
2
rms
rms
H
Z
Z
E
S


[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,
P
ref
.











ref
bel
P
P
P
10
]
[
log









ref
dB
P
P
P
10
]
[
log
10

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):











ref
dB
V
V
V
10
]
[
log
20
[Saunders, 1999]

decibels

Unit

Reference Power

Application

dBW

1 W

Absolute power

dBm

1 mW

Absolute power

P
[dbW] =
P
[dBm]
-

30

dB

V

1

V

Absolute voltage, typically at the input
terminals of a receiver

dB

any

Gain or loss of a network

dB

V/m

1

V/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 antenna

0 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.

23

Uppgifter

inför

F2


Bestäm

frekvens
,
vinkelfrekvens
,
periodtid

och

amplitud

för

följande

sinuskurva

24

0.5
0.5
1.0
t
1.5
1.0
0.5
0.5
1.0
1.5
s
t
Uppgifter

inför

F2


Plotta
följande

Fourierserie

och

bestäm

typ

av

periodisk

funktion
.

𝑓
𝑥
=
1
2
+
4
𝜋
2

1
2𝑛

1
2
cos
[
2𝑛

1
𝜋𝑥
]

𝑛
=
1


Plotta

också

amplitudspektrum

25