Lecture 2: Introduction to case studies: Radiolink

Anders Västberg

vastberg@kth.se

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

25