# Antennas and Propagation

```Antennas and Propagation
(William Stallings, “Wireless Communications and Networks” 2nd Ed, PrenticeHall, 2005, Chapter 5)
by Ya Bao
http://eent3.sbu.ac.uk/staff/baoy
b/acs
1
Introduction

An antenna is an electrical conductor or
system of conductors



into space
Reception - collects electromagnetic energy
from space
In two-way communication, the same
antenna can be used for transmission and
reception
2
Types of Antennas

Isotropic antenna (idealized)


Dipole antennas



Radiates power equally in all directions
Half-wave dipole antenna (or Hertz
antenna)
Quarter-wave vertical antenna (or Marconi
antenna)
Parabolic Reflective Antenna
3




Graphical representation of
Depicted as two-dimensional
cross section
Beam width (or half-power
beam width)

Measure of directivity of antenna
4
Pdirectional
G
Pisotropic
5
Three-dimensional
patterns. The top shows
the directive pattern of a
horn antenna, the bottom
shows the omnidirectional
pattern of a dipole
antenna.
6
or as separate graphs in the vertical plane (E or V plane) and
horizontal plane (H plane). This is often known as a polar
diagram
7
8
9
outdoor enclosure featuring a wide band
2.5GHz panel antenna
Gain (max)
Frequency
3 dB beamwidth
16 dBi (+-0.5 dB)
2300 - 2700 MHz
30° (± 5°)
Front to back (F/B ratio)
20 dB (± 3 dB)
10
Other antennas
Helical Antenna
Patch (microstrip) antenna
Multiband antenna: for GSM 900+GSM
1800+GSM 1900+Bluetooth; or GSM and 3G
11
Antenna Gain

Antenna gain


Power output, in a particular direction,
compared to that produced in any direction by a
perfect omnidirectional antenna (isotropic
antenna)
Effective area

Related to physical size and shape of antenna
12
Antenna Gain

Relationship between antenna gain and effective
area
G





4Ae
2
4f Ae

c2
2
G = antenna gain
Ae = effective area
f = carrier frequency
c = speed of light ( 3  108 m/s)
 = carrier wavelength
13
14
Propagation Models



Ground Wave (GW) Propagation: < 3MHz
Sky Wave (SW) Propagation: 3MHz to 30MHz
Effective Line-of-Sight (LOS) Propagation: >
30MHz
15
Ground Wave Propagation
–
–
–
–
Follows contour of the earth.
Can propagate considerable distances.
Frequency bands: ELF, VF, VLF, LF, MF.
Spectrum range: 30Hz ~ 3MHz, e.g. AM radio.
16
Sky Wave Propagation
–
–
–
Signal reflected from ionized layer of upper atmosphere back down to earth, wh
can travel a number of hops, back and forth between ionosphere and earth’s
surface.
HF band with intermediate frequency range: 3MHz ~ 30MHz.
17
Line-of-Sight Propagation
Tx. and Rx. antennas are in the effective ‘line of sight’ range.
Includes both LOS and non-LOS (NLOS) case
For satellite communication, signal above 30 MHz not reflected by
ionosphere.
For ground communication, antennas within effective LOS due to
refraction.
Frequency bands: VHF, UHF, SHF, EHF, Infrared, optical light
Spectrum range : 30MHz ~ 900THz.
18
LOS calculations
dr
do
earth

optical horizon
What is the relationship between h and d ?
– For optical LOS:
where
do  3.57 h
– For effective or radio LOS:
dr  3.57 Kh
h = antenna height (m)
d = distance between
antenna and horizon (km)
refraction, K = 4/3
Line-of-Sight Equations
Effective, or radio, line of sight
d  3.57 h



d = distance between antenna and horizon (km)
h = antenna height (m)
K = adjustment factor to account for refraction, rule of
thumb K = 4/3
Maximum distance between two antennas for LOS
propagation:


d  3.57 h1  h2

20
LOS Wireless Transmission Impairments







Attenuation and attenuation distortion
Free space loss
Noise
Atmospheric absorption
Multipath
Refraction
Thermal noise
21
Attenuation


Strength of signal falls off with distance over
transmission medium
Attenuation factors for unguided media:



Received signal must have sufficient strength so that
circuitry in the receiver can interpret the signal
Signal must maintain a level sufficiently higher than
noise to be received without error
Attenuation is greater at higher frequencies, causing
distortion
22
Free Space Loss

Free space loss, ideal isotropic antenna
Pt 4d  4fd 


2
2
Pr

c
2
2
Pt = signal power at transmitting antenna
 Pr = signal power at receiving antenna
  = carrier wavelength
 d = propagation distance between antennas
8
 c = speed of light ( 3  10 m/s)
where d and  are in the same units (e.g., meters)

23
Free Space Loss

Free space loss equation can be recast:
Pt
 4d 
LdB  10 log  20 log

Pr
  
 20log   20logd   21.98 dB
 4fd 
 20log
  20log f   20logd   147.56 dB
 c 
24
Pt



4fd 
4fd 
4d 
 20 log
 10 log
 10 log

2
2
c
c

Pr
2
LdB
2
 20 log( f )  20 log(d )  20 log 4  20 log  20 log c
 20 log( f )  20 log(d )  12.04  9.94  20 log(3  108 )
 20 log( f )  20 log(d )  12.04  9.94  9.54  20  8
 20 log( f )  20 log(d )  147.56dB
25
Free Space Loss

Free space loss accounting for gain of other
antennas can be recast as
LdB  20log   20logd  10log At Ar 
 20log f   20logd  10log At Ar   169.54dB
26
Categories of Noise




Thermal Noise
Intermodulation noise
Crosstalk
Impulse Noise
27
Noise (1)






Thermal noise due to thermal agitation of electrons.
Present in all electronic devices and transmission media.
As a function of temperature.
Uniformly distributed across the frequency spectrum,
hence often referred as white noise.
Cannot be eliminated – places an upper bound on the
communication system performance.
Can cause erroneous to the transmitted digital data bits.
28
Noise (2): Noise on digital data
Error in bits
29
Thermal Noise

The noise power density (amount of thermal
noise to be found in a bandwidth of 1Hz in
any device or conductor) is:
N0  kT W/Hz
N0 = noise power density in watts per 1 Hz of
bandwidth
k = Boltzmann's constant = 1.3803  10-23 J/K
T = temperature, in kelvins (absolute
temperature)
0oC = 273 Kelvin
30
Thermal Noise


Noise is assumed to be independent of frequency
Thermal noise present in a bandwidth of B Hertz
(in watts):
N  kTB
or, in decibel-watts (dBW),
N  10log k  10 log T  10log B
 228.6 dBW  10 log T  10log B
31
Noise Terminology

Intermodulation noise – occurs if signals with
different frequencies share the same medium



Interference caused by a signal produced at a frequency
that is the sum or difference of original frequencies
Crosstalk – unwanted coupling between signal
paths
Impulse noise – irregular pulses or noise spikes


Short duration and of relatively high amplitude
Caused by external electromagnetic disturbances, or
faults and flaws in the communications system
32
Signal to Noise Ratio – SNR (1)



Ratio of the power in a signal to the power contained in
the noise present at a particular point in the transmission.
Normally measured at the receiver with the attempt to
eliminate/suppressed the unwanted noise.
In decibel unit,
 PS 
SNR dB  10log10  
 PN 
where PS = Signal Power, PN = Noise Power

Higher SNR means better quality of signal.
33
Signal to Noise Ratio – SNR (2)


SNR is vital in digital transmission because it can be
used to sets the upper bound on the achievable data rate.
Shannon’s formula states the maximum channel capacity
(error-free capacity) as:
C  B log2 1  SNR 



Given the knowledge of the receiver’s SNR and the signal
bandwidth, B. C is expressed in bits/sec.
In practice, however, lower data rate are achieved.
For a fixed level of noise, data rate can be increased by
34
increasing the signal strength or bandwidth.
Expression of Eb/N0 (1)

Another parameter that related to SNR for determine data rates
and error rates is the ratio of signal energy per bit, Eb to noise
power density per Hertz, N0; → Eb/N0.

The energy per bit in a signal is given by:



Eb  PS  Tb
PS = signal power & Tb = time required to send one bit which can be
related to the transmission bit rate, R, as Tb = 1/ R.
Thus,
Eb PS / R
PS


N0
N0
kTR
– 228.6 dBW
In decibels:
 Eb   P
S ( dB )  10log10 R  10log10 k  10log10T


 N 0  dB
35
Expression of Eb/N0 (2)

As the bit rate R increases, the
signal power PS relative to the
noise must also be increased to
maintain the required Eb/N0.

The bit error rate (BER) for the
data sent is a function of Eb/N0
(see the BER versus Eb/N0 plot).

Eb/N0 is related to SNR as:
 PS  B
Eb
B
     SNR 
N0
R
 PN  R
where B = Bandwidth, R = Bit rate
BER versus Eb/N0 plot
Higher Eb/N0,
lower BER
36
Wireless Propagation Mechanisms

Basic types of propagation mechanisms




Free space propagation
 LOS wave travels large
distance with obstacle-free
reflection
Reflection
 Wave impinges on an object
which is large compared to
the wave-length 
diffraction
Diffraction
 Occurs when wave hits the sharp edge of the
obstacles and bent around to propagate further
in the ‘shadowed’ regions – Fresnel zones.
Scattering
 Wave hits the objects smaller than  itself. e.g.
street signs and lamp posts.
Lamp
post
scattering
37
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