main cv report
-
Upload
avinash00000 -
Category
Documents
-
view
62 -
download
3
Transcript of main cv report
CONTENTS
I CELLULAR MOBILE COMMUNICATION
1. MOBILE SYSTEMS 8
1.1 The concept 9
1.2 Cell Signal Encoding 9
1.3 Frequency Reuse 10
2 FEATURS OF A CELLULAR NETWORK 13
2.1 Directional Antennas 13
2.2 Sectorization 14
2.3 Broadcast messages and paging 14
2.4 Movement from cell to cell and handover/handoff 15
3 MOBILE NETWORK : A CELLULAR NETWORK 16
3.1 Example of a cellular network: the mobile phone network 16
3.2 GSM 17
3.3 Handoff in mobile networks 18
4 GSM Frequency Bands 19
4.1 Coverage Comparison of different frequencies 19
5 Cellular Traffic 21
5.1 Quality of Service targets 21
5.2 Traffic Load and Cell size 22
5.3 Traffic capacity vs Coverage 23
5.4 Channel Holding time 24
6 GSM Architecture 26
6.1 Base Station Subsystem 26
6.2 Network Station Subsystem 28
7 Channel Reuse and Signal Strength 31
7.1 Channel Reuse 31
7.2 Cell Phone tower power Emission 32
7.3 Signal Strength 32
8 Reasons for weak signals 34
8.1 Rural Areas 34
8.2 Building Construction Material 34
8.3 Building Size 35
8.4 Multipath Interference 35
8.5 Diffraction and general attenuation 35
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 2
8.6 Different operating frequencies 36
9 Code Division Multiple Access 37
9.1 CDMA basics 37
9.2 Steps in CDMA Modulation 38
9.3 Code Division Multiplexing(Synchronous CDMA) 38
10 The Future of Mobile Networking 41
10.1 Future Evolution: (Broadband )4G 41
10.2 Comparison to Similar Systems 41
II MICROWAVE ENGINEERING
1 Introduction 45
1.1 Microwave Frequencies 45
1.2 Microwave History Of Device 47
1.3 Microwave Applications 48
2 Waveguide -1 50
2.1 Modes of Operation 50
2.2 Rectangular Vs Circular Waveguides 50
2.3 Rectangular Waveguide 51
3 Waveguide Components -1 53
3.1 Attenuators 53
3.2 Electronically Controlled Attenuators 53
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 3
3.3 Phase Shifters 54
3.4 Directional Couplers 55
4 Waveguide Components-2 57
4.1 Hybride Junctions 57
4.2 Hybride Ring or Rat Race 58
5 Microwave Propagation In Ferrites 59
5.1 Microwave Devices Employing Faraday rotation 59
5.2 Gyrator 59
5.3 Isolator 60
5.4 Other Ferrite Devices 61
6 Microwave Tubes 62
6.1 Klystron Amplifier 62
6.2 Two Cavity Klystron 63
6.3 Reflex Klystron 64
6.4 Cavity Magnetron 65
6.5 Other Types Of Microwave Tubes 66
7 Gunn Effect And Its Applications 68
7.1 The Gunn Effect 68
7.2 Gunn Diode 68
7.3 Gunn Diode Theory 68
7.4 Appications 70
8 Transmission Lines And Characteristic Impedance 72
8.1 Impedance Matching 73
8.2 Dielectric Constant And Effective Dielectric Constant 73
8.3 Lumped Elements Vs Distributed Elements 75
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 4
8.4 VSWR And Return Loss 76
9 Microwave Measurements 78
9.1 Band Widths 78
9.2 Frequency Conventions 79
9.3 Harmonic Frequencies 79
9.4 Decibels 79
III DIGITAL COMMUNICATION
1 Basics of Digital communication 82
1.1 Introduction 82
2 Pulse code modulation 85
2.1 Modulation 85
2.2 Limitations 88
3 Digital modulation techquie-I 91
3.1 Amplitude shift keying 92
3.2 Phase shift keying 92
3.3 Differential phase shift keying 93
3.4 Binary phase shift keying 94
3.5 Quaternary phase shift keying 94
3.6 Frequency shift keying 97
4 Delta modulation 98
4.1 Principles 99
4.2 Adaptive delta modulation 99
5 Information theory101
5.1 Source theory 102
5.2 Information rate 102
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 5
5.3 Channel capacity 102
6 Shannon Hartley theorem 104
6.1 Statement of theorem 104
6.2 Nyquist rate 105
6.3 Noisy channel coding theorem 105
6.4 Shannon Hartley theorem 106
7 Linear block codes 108
7.1 Formal definations 108
7.2 Hamming codes 109
7.3 Hadamard codes 110
IMAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 6
CELLULAR
MOBILE
COMMUNICATION
Chapter 1
Mobile Systems
Limitations of conventional mobile telephone systems:
One of the many reasons for developing a cellular mobile telephone systems and deploying it
in many cities is the operational limitations of conventional mobile telephone system
1. Service capability
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 7
2. Poor service performance
3. Frequency utilization.
A mobile network is a radio network distributed over land areas called cells, each
served by at least one fixed-location transceiver known as a cell site or base station. When
joined together these cells provide radio coverage over a wide geographic area. This enables
a large number of portable transceivers (mobile phones, pagers, etc) to communicate with
each other and with fixed transceivers and telephones anywhere in the network, via base
stations, even if some of the transceivers are moving through more than one cell during
transmission.
Mobile networks offer a number of advantages over alternative solutions:
increased capacity
reduced power usage
larger coverage area
reduced interference from other signals
An example of a simple non-telephone Mobile system is an old taxi driver's radio system
where the taxi company has several transmitters based around a city that can communicate
directly with each taxi.
1.1 The concept
In a Mobile radio system, a land area to be supplied with radio service is divided into
regular shaped cells, which can be hexagonal, square, circular or some other irregular shapes,
although hexagonal cells are conventional. Each of these cells is assigned multiple
frequencies (f1 - f6) which have corresponding radio base stations. The group of frequencies
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 8
can be reused in other cells, provided that the same frequencies are not reused in adjacent
neighboring cells as that would cause co-channel interference.
The increased capacity in a cellular network, compared with a network with a single
transmitter, comes from the fact that the same radio frequency can be reused in a different
area for a completely different transmission. If there is a single plain transmitter, only one
transmission can be used on any given frequency. Unfortunately, there is inevitably some
level of interference from the signal from the other cells which use the same frequency. This
means that, in a standard FDMA system, there must be at least a one cell gap between cells
which reuse the same frequency.
In the simple case of the taxi company, each radio had a manually operated channel
selector knob to tune to different frequencies. As the drivers moved around, they would
change from channel to channel. The drivers know which frequency covers approximately
what area. When they do not receive a signal from the transmitter, they will try other
channels until they find one that works. The taxi drivers only speak one at a time, when
invited by the base station operator (in a sense TDMA).
1.2 Cell signal encoding
To distinguish signals from several different transmitters, frequency division multiple
access (FDMA) and code division multiple access (CDMA) were developed.
With FDMA, the transmitting and receiving frequencies used in each cell are different from
the frequencies used in each neighbouring cell. In a simple taxi system, the taxi driver
manually tuned to a frequency of a chosen cell to obtain a strong signal and to avoid
interference from signals from other cells.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 9
The principle of CDMA is more complex, but achieves the same result; the distributed
transceivers can select one cell and listen to it. Other available methods of multiplexing such
as polarization division multiple access (PDMA) and time division multiple access (TDMA)
cannot be used to separate signals from one cell to the next since the effects of both vary with
position and this would make signal separation practically impossible. Time division multiple
access, however, is used in combination with either FDMA or CDMA in a number of systems
to give multiple channels within the coverage area of a single cell.
1.3 Frequency reuse
The key characteristic of a cellular network is the ability to re-use frequencies to increase
both coverage and capacity. As described above, adjacent cells must utilise different
frequencies, however there is no problem with two cells sufficiently far apart operating on the
same frequency. The elements that determine frequency reuse are the reuse distance and the
reuse factor.
The reuse distance, D is calculated as
D=(√K)R
where R is the cell radius and N is the number of cells per cluster. Cells may vary in radius in
the ranges (1 km to 30 km). The boundaries of the cells can also overlap between adjacent
cells and large cells can be divided into smaller cells .
The frequency reuse factor is the rate at which the same frequency can be used in the
network. It is 1/K (or K according to some books) where K is the number of cells which
cannot use the same frequencies for transmission. Common values for the frequency reuse
factor are 1/3, 1/4, 1/7, 1/9 and 1/12 (or 3, 4, 7, 9 and 12 depending on notation).
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 10
In case of N sector antennas on the same base station site, each with different
direction, the base station site can serve N different sectors. N is typically 3. A reuse pattern
of N/K denotes a further division in frequency among N sector antennas per site. Some
current and historical reuse patterns are 3/7 (North American AMPS), 6/4 (Motorola
NAMPS), and 3/4 (GSM).
If the total available bandwidth is B, each cell can only utilize a number of frequency
channels corresponding to a bandwidth of B/K, and each sector can use a bandwidth of
B/NK.
Code division multiple access-based systems use a wider frequency band to achieve
the same rate of transmission as FDMA, but this is compensated for by the ability to use a
frequency reuse factor of 1, for example using a reuse pattern of 1/1. In other words, adjacent
base station sites use the same frequencies, and the different base stations and users are
separated by codes rather than frequencies. While N is shown as 1 in this example, that does
not mean the CDMA cell has only one sector, but rather that the entire cell bandwidth is also
available to each sector individually.
Depending on the size of the city, a taxi system may not have any frequency-reuse in
its own city, but certainly in other nearby cities, the same frequency can be used. In a big city,
on the other hand, frequency-reuse could certainly be in use.
Chapter 2
Basic Components of a mobile network
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 11
2.1 Directional antennas
Fig 2.1Cellular telephone frequency reuse pattern.
Although the original 2-way-radio cell towers were at the centers of the cells and were
omni-directional, a cellular map can be redrawn with the cellular telephone towers located at
the corners of the hexagons where three cells converge. Each tower has three sets of
directional antennas aimed in three different directions and receiving/transmitting into three
different cells at different frequencies. This provides a minimum of three channels for each
cell. The numbers in the illustration are channel numbers, which repeat every 3 cells. Large
cells can be subdivided into smaller cells for high volume areas.
2.2 Sectorisation
By using directional antennae on a base station, each pointing in different directions,
it is possible to sectorise the base station so that several different cells are served from the
same location. Typically these directional antennas have a beamwidth of 65 to 85 degrees.
This increases the traffic capacity of the base station (each frequency can carry eight voice
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 12
channels) whilst not greatly increasing the interference caused to neighboring cells (in any
given direction, only a small number of frequencies are being broadcast). Typically two
antennas are used per sector, at spacing of ten or more wavelengths apart. This allows the
operator to overcome the effects of fading due to physical phenomena such as multipath
reception. Some amplification of the received signal as it leaves the antenna is often used to
preserve the balance between uplink and downlink signal
2.3 Broadcast messages and paging
Practically every cellular system has some kind of broadcast mechanism. This can be
used directly for distributing information to multiple mobiles, commonly, for example in
mobile telephony systems, the most important use of broadcast information is to set up
channels for one to one communication between the mobile transceiver and the base station.
This is called paging.
The details of the process of paging vary somewhat from network to network, but
normally we know a limited number of cells where the phone is located (this group of cells is
called a Location Area in the GSM or UMTS system, or Routing Area if a data packet session
is involved). Paging takes place by sending the broadcast message to all of those cells. Paging
messages can be used for information transfer. This happens in pagers, in CDMA systems for
sending SMS messages, and in the UMTS system where it allows for low downlink latency in
packet-based connections.
2.4 Movement from cell to cell and handover
In a primitive taxi system, when the taxi moved away from a first tower and closer to
a second tower, the taxi driver manually switched from one frequency to another as needed.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 13
If a communication was interrupted due to a loss of a signal, the taxi driver asked the base
station operator to repeat the message on a different frequency.
In a cellular system, as the distributed mobile transceivers move from cell to cell
during an ongoing continuous communication, switching from one cell frequency to a
different cell frequency is done electronically without interruption and without a base station
operator or manual switching. This is called the handover or handoff. Typically, a new
channel is automatically selected for the mobile unit on the new base station which will serve
it. The mobile unit then automatically switches from the current channel to the new channel
and communication continues.
The exact details of the mobile system's move from one base station to the other
varies considerably from system to system (see the example below for how a mobile phone
network manages handover).
Chapter 3Mobile Network: a cellular network
3.1 Example of a cellular network:
The most common example of a cellular network is a mobile phone (cell phone)
network. A mobile phone is a portable telephone which receives or makes calls through a cell
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 14
site (base station), or transmitting tower. Radio waves are used to transfer signals to and from
the cell phone.
Modern mobile phone networks use cells because radio frequencies are a limited, shared
resource. Cell-sites and handsets change frequency under computer control and use low
power transmitters so that a limited number of radio frequencies can be simultaneously used
by many callers with less interference.
A cellular network is used by the mobile phone operator to achieve both coverage and
capacity for their subscribers. Large geographic areas are split into smaller cells to avoid line-
of-sight signal loss and to support a large number of active phones in that area. All of the cell
sites are connected to telephone exchanges (or switches) , which in turn connect to the public
telephone network.
In cities, each cell site may have a range of up to approximately ½ mile, while in rural areas,
the range could be as much as 5 miles. It is possible that in clear open areas, a user may
receive signals from a cell site 25 miles away.
Since almost all mobile phones use cellular technology, including GSM, CDMA, and AMPS
(analog), the term "cell phone" is in some regions, notably the US, used interchangeably with
"mobile phone". However, satellite phones are mobile phones that do not communicate
directly with a ground-based cellular tower, but may do so indirectly by way of a satellite.
There are a number of different digital cellular technologies, including: Global System for
Mobile Communications (GSM), General Packet Radio Service (GPRS), Code Division
Multiple Access (CDMA), Evolution-Data Optimized (EV-DO), Enhanced Data Rates for
GSM Evolution (EDGE), 3GSM, Digital Enhanced Cordless Telecommunications (DECT),
Digital AMPS (IS-136/TDMA), and Integrated Digital Enhanced Network (iDEN).
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 15
3.2 GSM
Structure of a 2G cellular network
A simple view of the cellular mobile-radio network consists of the following:
A network of Radio base stations forming the Base station subsystem.
The core circuit switched network for handling voice calls and text
A packet switched network for handling mobile data
The Public switched telephone network to connect subscribers to the wider telephony
network
This network is the foundation of the GSM system network. There are many functions that
are performed by this network in order to make sure customers get the desired service
including mobility management, registration, call set up, and handover.
Any phone connects to the network via an RBS in the corresponding cell which in turn
connects to the MSC. The MSC allows the onward connection to the PSTN. The link from a
phone to the RBS is called an uplink while the other way is termed downlink.
Radio channels effectively use the transmission medium through the use of the following
multiplexing schemes: frequency division multiplex (FDM), time division multiplex (TDM),
code division multiplex (CDM), and space division multiplex (SDM). Corresponding to these
multiplexing schemes are the following access techniques: frequency division multiple access
(FDMA), time division multiple access (TDMA), code division multiple access (CDMA),
and space division multiple access (SDMA).
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 16
3.3 Cellular handover/handoff in mobile phone networks
As the phone user moves from one cell area to another cell whilst a call is in progress, the
mobile station will search for a new channel to attach to in order not to drop the call. Once a
new channel is found, the network will command the mobile unit to switch to the new
channel and at the same time switch the call onto the new channel.
With CDMA, multiple CDMA handsets share a specific radio channel. The signals are
separated by using a pseudonoise code (PN code) specific to each phone. As the user moves
from one cell to another, the handset sets up radio links with multiple cell sites (or sectors of
the same site) simultaneously. This is known as "soft handoff" because, unlike with
traditional cellular technology, there is no one defined point where the phone switches to the
new cell.
In IS-95 inter-frequency handovers and older analog systems such as NMT it will typically be
impossible to test the target channel directly while communicating. In this case other
techniques have to be used such as pilot beacons in IS-95. This means that there is almost
always a brief break in the communication while searching for the new channel followed by
the risk of an unexpected return to the old channel.
If there is no ongoing communication or the communication can be interrupted, it is possible
for the mobile unit to spontaneously move from one cell to another and then notify the base
station with the strongest signal. Cellular frequency choice in mobile phone networks
Chapter 4
GSM frequency bands
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 17
Fig 4.1
The effect of frequency on cell coverage means that different frequencies serve better for
different uses. Low frequencies, such as 450 MHz NMT, serve very well for countryside
coverage. GSM 900 (900 MHz) is a suitable solution for light urban coverage. GSM 1800
(1.8 GHz) starts to be limited by structural walls. UMTS, at 2.1 GHz is quite similar in
coverage to GSM 1800.
Higher frequencies are a disadvantage when it comes to coverage, but it is a decided
advantage when it comes to capacity. Pico cells, covering e.g. one floor of a building, become
possible, and the same frequency can be used for cells which are practically neighbours.
Cell service area may also vary due to interference from transmitting systems, both within
and around that cell. This is true especially in CDMA based systems. The receiver requires a
certain signal-to-noise ratio. As the receiver moves away from the transmitter, the power
transmitted is reduced. As the interference (noise) rises above the received power from the
transmitter, and the power of the transmitter cannot be increased any more, the signal
becomes corrupted and eventually unusable. In CDMA-based systems, the effect of
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 18
interference from other mobile transmitters in the same cell on coverage area is very marked
and has a special name, cell breathing.
One can see examples of cell coverage by studying some of the coverage maps provided by
real operators on their web sites. In certain cases they may mark the site of the transmitter, in
others it can be calculated by working out the point of strongest coverage.
Chapter 5
CELLULAR TRAFFIC
This article discusses the mobile cellular network aspect of telegraphic measurements.
Mobile radio networks have traffic issues that do not arise in connection with the fixed line
PSTN. Important aspects of cellular traffic include: quality of service targets, traffic capacity
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 19
and cell size, spectral efficiency and sectorization, traffic capacity versus coverage, and
channel holding time analysis.
Teletraffic engineering is a necessary field in telecommunications network planning to ensure
that network costs are minimized without compromising the quality of service delivered to
the user of the network. This field of engineering is based on probability theory and can be
used to analyze mobile radio networks, as well as other telecommunications networks.
A mobile handset which is moving in a cell will record a signal strength that varies. Signal
strength is subject to slow fading, fast fading and interference from other signals, resulting in
degradation of the carrier-to-interference (C/I) ratio. A high C/I ratio yields quality
communication. A good C/I ratio is achieved in cellular systems by using optimum power
levels through the power control of most links. When carrier power is too high, excessive
interference is created, degrading the C/I ratio for other traffic and reducing the traffic
capacity of the radio subsystem. When carrier power is too low, C/I is too low and QoS
targets are not met.
5.1Quality of Service targets
At the time that the cells of a radio subsystem are designed, Quality of Service (QoS) targets
are set, for: traffic congestion and blocking, dominant coverage area, C/I, dropped call rate,
handover failure rate, overall call success rate.
5.2 Traffic load and cell size
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 20
The more traffic generated, the more base stations will be needed to service the customers.
The number of base stations for a simple cellular network is equal to the number of cells. The
traffic engineer can achieve the goal of satisfying the increasing population of customers by
increasing the number of cells in the area concerned, so this will also increases the number of
base stations. This method is called cell splitting (and combined with sectorization) is the
only way of providing services to a burgeoning population. This simply works by dividing
the cells already present into smaller sizes hence increasing the traffic capacity. Reduction of
the cell radius enables the cell to accommodate extra traffic. The cost of equipment can also
be cut down by reducing the number of base stations through setting up three neighbouring
cells, with the cells serving three 120° sectors with different channel groups.
Mobile radio networks are operated with finite, limited resources (the spectrum of
frequencies available). These resources have to be used effectively to ensure that all users
receive service, that is, the quality of service is consistently maintained. This need to
carefully use the limited spectrum brought about the development of cells in mobile
networks, enabling frequency re-use by successive clusters of cells. Systems that efficiently
use the available spectrum have been developed e.g. the GSM system. Walke defines spectral
efficiency as the traffic capacity unit divided by the product of bandwidth and surface area
element, and is dependent on the number of radio channels per cell and the cluster size
(number of cells in a group of cells):
Where Nc is the number of channels per cell, BW is the system bandwidth, and Ac is Area of
cell.
Sectorization is briefly described in traffic load and cell size as a way to cut down
equipment costs in a cellular network. When applied to clusters of cells sectorization also
reduces co-channel interference, according to Walke. This is because the power radiated
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 21
backward from directional base antennas (directional) is greater than that of omnidirectional
antennas by a factor which is the number of sectors per cell (or cell cluster).
5.3 Traffic capacity versus coverage
Cellular systems use one or more of four different techniques of access (TDMA, FDMA,
CDMA, SDMA). See Cellular concepts. Let a case of Code Division Multiple Access be
considered for the relationship between traffic capacity and coverage (area covered by cells).
CDMA cellular systems can allow an increase in traffic capacity at the expense of the quality
of service.
In TDMA/FDMA cellular radio systems, Fixed Channel Allocation (FCA) is used to allocate
channels to customers. In FCA the number of channels in the cell remains constant
irrespective of the number of customers in that cell. This results in traffic congestion and
some calls being lost when traffic gets heavy.
A better way of channel allocation in cellular systems is Dynamic Channel Allocation (DCA)
which is supported by the GSM, DCS and other systems. DCA is a better way not only for
handling bursty cell traffic but also in efficiently utilising the cellular radio resources. DCA
allows the number of channels in a cell to vary with the traffic load, hence increasing channel
capacity with little costs. Since a cell is allocated a group of frequency carries (e.g. f 1-f7) for
each user, this range of frequencies is the bandwidth of that cell, BW. If that cell covers an
area Ac, and each user has bandwidth B then the number of channels will be BW/B. The
density of channels will be. This formula shows that as the coverage area Ac is increased, the
channel density decreases.
5.4 Channel holding time
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 22
Important parameters like the carrier to interference (C/I) ratio, spectral efficiency and reuse
distance determine the quality of service of a cellular network. Channel Holding Time is
another parameter that can affect the quality of service in a cellular network, hence it is
considered when planning the network. It must be mentioned that it is not an easy task to
calculate the channel holding time. (This is the time a Mobile Station (MS) remains in the
same cell during a call). Channel holding time is therefore less than call holding time if the
MS travels more than one cell as handover will take place and the MS relinquishes the
channel. Practically, it is not possible to determine exactly the channel holding time. As a
result, different models exists for modelling the channel holding time distribution. In
industry, a good approximation of the channel holding time is usually sufficient to determine
the network traffic capability.
One of the papers in Key and Smith defines channel holding time as being equal to the
average holding time divided by the average number of handovers per call plus one. Usually
an exponential model is preferred to calculate the channel holding time for simplicity in
simulations. This model gives the distribution function of channel holding time and it is an
approximation that can be used to obtain estimates channel holding time. The exponential
model may not be correctly modelling the channel holding time distribution as other papers
may try to prove, but it gives an approximation. Channel holding time is not easily
determined explicitly, call holding time and user's movements have to be determined in order
to implicitly give channel holding time. The mobility of the user and the cell shape and size
cause the channel holding time to have a different distribution function to that of call duration
(call holding time). This difference is large for highly mobile users and small cell sizes. Since
the channel holding time and call duration relationships are affected by mobility and cell size,
for a stationary MS and large cell sizes, channel holding time and call duration are the same.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 23
Chapter 6
GSM Architecture
The GSM architecture consists of three subsystems
1. Base station subsystem
2. Network Station subsystem
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 24
3. Operating station Subsystem
6.1 Base station subsystem(BSS)
The base station subsystem (BSS) is the section of a traditional cellular telephone network
which is responsible for handling traffic and signaling between a mobile phone and the
network switching subsystem. The BSS carries out transcoding of speech channels, allocation
of radio channels to mobile phones, paging, transmission and reception over the air interface
and many other tasks related to the radio network.
Base transceiver station
The base transceiver station, or BTS, contains the equipment for transmitting and receiving
radio signals (transceivers), antennas, and equipment for encrypting and decrypting
communications with the base station controller (BSC). Typically a BTS for anything other
than a picocell will have several transceivers (TRXs) which allow it to serve several different
frequencies and different sectors of the cell (in the case of sectorised base stations).
A BTS is controlled by a parent BSC via the "base station control function" (BCF). The BCF
is implemented as a discrete unit or even incorporated in a TRX in compact base stations.
The BCF provides an operations and maintenance (O&M) connection to the network
management system (NMS), and manages operational states of each TRX, as well as
software handling and alarm collection.
The functions of a BTS vary depending on the cellular technology used and the cellular
telephone provider. There are vendors in which the BTS is a plain transceiver which receives
information from the MS (mobile station) through the Um (air interface) and then converts it
to a TDM (PCM) based interface, the Abis interface, and sends it towards the BSC. There are
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 25
vendors which build their BTSs so the information is preprocessed, target cell lists are
generated and even intracell handover (HO) can be fully handled. The advantage in this case
is less load on the expensive Abis interface.
The BTSs are equipped with radios that are able to modulate layer 1 of interface Um; for
GSM 2G+ the modulation type is GMSK, while for EDGE-enabled networks it is GMSK and
8-PSK.
Antenna combiners are implemented to use the same antenna for several TRXs (carriers), the
more TRXs are combined the greater the combiner loss will be. Up to 8:1 combiners are
found in micro and pico cells only.
A TRX transmits and receives according to the GSM standards, which specify eight TDMA
timeslots per radio frequency. A TRX may lose some of this capacity as some information is
required to be broadcast to handsets in the area that the BTS serves. This information allows
the handsets to identify the network and gain access to it. This signalling makes use of a
channel known as the broadcast control channel (BCCH).
6.2 CELL SITE
A cell site is a term used to describe a site where antennas and electronic communications
equipment are placed on a radio mast or tower to create a cell in a cellular network. A cell
site is composed of a tower or other elevated structure for mounting antennas, and one or
more sets of transmitter/receivers transceivers, digital signal processors, control electronics, a
GPS receiver for timing (for CDMA2000 or IS-95 systems), regular and backup electrical
power sources, and sheltering.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 26
A synonym for "cell site" is "cell tower", although many cell site antennas are mounted on
buildings rather than as towers. In GSM networks, the technically correct term is Base
Transceiver Station (BTS), and colloquial British English synonyms are "mobile phone mast"
or "base station". The term "base station site" might better reflect the increasing co-location
of multiple mobile operators, and therefore multiple base stations, at a single site. Depending
on an operator's technology, even a site hosting just a single mobile operator may house
multiple base stations, each to serve a different air interface technology (CDMA or GSM, for
example). Preserved treescapes can often hide cell towers inside an artificial tree or preserved
tree. These installations are generally referred to as concealed cell sites or stealth cell sites.
Operation Range
The working range of a cell site - the range within which mobile devices can connect to it
reliably is not a fixed figure. It will depend on a number of factors, including
The frequency of signal in use (i.e. the underlying technology).
The transmitter's rated power.
The transmitter's size.
The array setup of panels may cause the transmitter to be directional or omni-
directional.
It may also be limited by local geographical or regulatory factors and weather
conditions.
Generally, in areas where there are enough cell sites to cover a wide area, the range of each
one will be set to:
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 27
Ensure there is enough overlap for "handover" to/from other sites (moving the signal
for a mobile device from one cell site to another, for those technologies that can
handle it - e.g. making a GSM phone call while in a car or train).
Ensure that the overlap area is not too large, to minimize interference problems with
other sites.
In practice, cell sites are grouped in areas of high population density, with the most potential
users. Cell phone traffic through a single cell mast is limited by the mast's capacity; there is a
finite number of calls that a mast can handle at once. This limitation is another factor
affecting the spacing of cell mast sites. In suburban areas, masts are commonly spaced 1-2
miles apart and in dense urban areas, masts may be as close as ¼-½ mile apart. Cell masts
always reserve part of their available bandwidth for emergency calls.
Objects intruding into the fresnel zone between radio transmitters and receivers can greatly
affect signal strength.
The maximum range of a mast (where it is not limited by interference with other masts
nearby) depends on the same circumstances. Some technologies, such as GSM, have a fixed
maximum range of 40km (23 miles), which is imposed by technical limitations. CDMA and
iDEN have no built-in limit, but the limiting factor is really the ability of a low-powered
personal cell phone to transmit back to the mast. As a rough guide, based on a tall mast and
flat terrain, it is possible to get between 50 to 70 km (30-45 miles). When the terrain is hilly,
the maximum distance can vary from as little as 5 kilometres (3.1 mi) to 8 kilometres (5.0 mi)
due to encroachment of intermediate objects into the wide center fresnel zone of the signal.
Depending on terrain and other circumstances, a GSM Tower can replace between 2 and 50
miles of cabling for fixed wireless networks.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 28
Chapter 7Channel Reuse and signal Strength
7.1Channel reuse
The concept of "maximum" range is misleading, however, in a cellular network. Cellular
networks are designed to create a mass communication solution from a limited amount of
channels (slices of radio frequency spectrum necessary to make one conversation) that are
licensed to an operator of a cellular service. To overcome this limitation, it is necessary to
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 29
repeat and reuse the same channels at different locations. Just as a car radio changes from one
local station to a completely different local station with the same frequency when you travel
to another city, the same radio channel gets reused on a cell mast only a few miles away. To
do this, the signal of a cell mast is intentionally kept at low power and many cases tilting
downward to limit its area. The area sometimes needs to be limited when a large number of
people live, drive or work near a particular mast; the range of this mast has to be limited so
that it covers an area small enough not to have to support more conversations than the
available channels can carry. Due to the sectorized arrangement of antennas on a tower, it is
possible to vary the strength and angle of each sector depending on the coverage of other
towers in view of the sector.
A cellphone may not work at times, because it is too far from a mast, but it may also not work
because the phone is in a location where there is interference to the cell phone signal from
thick building walls, hills or other structures. The signals do not need a clear line of sight but
the more interference will degrade or eliminate reception. Too many people may be trying to
use the cell mast at the same time, e.g. a traffic jam or a sports event, then there will be a
signal on the phone display but it is blocked from starting a new connection. The other
limiting factor for cell phones is the ability of the cell phone to send a signal from its low
powered battery to the mast. Some cellphones perform better than others under low power or
low battery, typically due to the ability to send a good signal from the phone to the mast.
The base station controller (a central computer that specializes in making phone connections)
and the intelligence of the cellphone keeps track of and allows the phone to switch from one
mast to the next during conversation. As the user moves towards a mast it picks the strongest
signal and releases the mast from which the signal has become weaker; that channel on that
mast becomes available to another user.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 30
7.2 Cell phone tower power emission
The U.S. government agency, the FCC, says:
"For example, measurement data obtained from various sources have consistently indicated
that "worst-case" ground-level power densities near typical cellular towers are on the order of
1 µW/cm2 or less (usually significantly less)."
That is 0.01 Watt per square meter. There is no temptation to use more power. The entire idea
of a "cell" phone system is to create small "cells" that don't interfere with each other.
The average energy received over the entire earth is about 250 Watts per square meter over a
24 hour day, ignoring clouds. So, on a day with no clouds, the average electromagnetic
energy received from the Sun is 25,000 times that received near a cell phone tower.
7.3 Signal strength
In telecommunications, particularly in radio, signal strength refers to the magnitude of the
electric field at a reference point that is a significant distance from the transmitting antenna. It
may also be referred to as received signal level or field strength. Typically, it is expressed in
voltage per length or signal power received by a reference antenna. High-powered
transmissions, such as those used in broadcasting, are expressed in dB-millivolts per metre
(dBmV/m). For very low-power systems, such as mobile phones, signal strength is usually
expressed in dB-microvolts per metre (dBµV/m) or in decibels above a reference level of one
milliwatt (dBm). In broadcasting terminology, 1 mV/m is 1000 µV/m or 60 dBµ (often
written dBu).
Examples
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 31
100 dBµ or 100 mV/m: blanketing interference may occur on some receivers
60 dBµ or 1.0 mV/m: frequently considered the edge of a radio station's protected
area in North America
40 dBµ or 0.1 mV/m: the minimum strength at which a station can be received with
acceptable quality on most receivers
Chapter 8
Reasons for weak signal
8.1 Rural areas
In many rural areas the housing density is too low to make construction of a new base station
commercially viable. In these cases it is unlikely that the service provider will do anything to
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 32
improve reception, due to the high cost of erecting a new tower. As a result, the only way to
obtain strong cell phone signal in these areas is usually to install a home cellular repeater. In
flat rural areas the signal is unlikely to suffer from multipath interference, so will just be
heavily attenuated by the distance. In these cases the installation of a cellular repeater will
generally massively increase signal strength just due to the amplifier, even a great distance
from the broadcast towers.
8.2 Building construction material
Some construction materials very rapidly attenuate cell phone signal strength. Older
buildings, such as churches, which use lead in their roofing material will very effectively
block any signal. Any building which has a significant thickness of concrete or amount of
metal used in its production will attenuate the signal. Concrete floors are often poured onto a
metal pan which completely blocks most radio signals. Some solid foam insulation and some
fiberglass insulation used in roofs or exterior walls has foil backing, which can reduce
transmittance. Energy efficient windows and metal window screens are also very effective at
blocking radio signals. Some materials have peaks in their absorption spectra which
massively decrease signal strength.
8.3 Building size
Large buildings, such as warehouses, hospitals and factories, often have no cellular reception
further than a few meters from the outside wall. Low signal strength is also often the case in
underground areas such as basements and in shops and restaurants located towards the centre
of shopping malls. This is caused by both the fact that the signal is attenuated heavily as it
enters the building and the interference as the signal is reflected by the objects inside the
building. For this reason in these cases an external antenna is usually desirable.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 33
8.4 Multipath interference
Even in urban areas which usually have strong cellular signals throughout, there are often
dead zones caused by destructive interference of waves which have taken different paths
(caused by the signal bouncing off buildings etc.) These usually have an area of a few blocks
and will usually only affect one of the two frequency ranges used by cell phones. This is
because the different wavelengths of the different frequencies interfere destructively at
different points. Directional antennas are very helpful at overcoming this since they can be
placed at points of constructive interference and aligned so as not to receive the destructive
signal. See Multipath interference for more.
8.5 Diffraction and general attenuation
The longer wavelengths have the advantage of being able to diffract to a greater degree so are
less reliant on line of sight to obtain a good signal, but still attenuate significantly. Because
the frequencies which cell phones use are too high to reflect off the ionosphere as shortwave
radio waves do, cell phone waves cannot travel via the ionospohere.
8.6 Different operating frequencies
Repeaters are available for all the different GSM frequency bands, some repeaters will handle
different types of network such as multi-mode GSM and UMTS repeaters however dual- and
tri-band systems cost significantly more. Repeater systems are available for certain Satellite
phone systems, allowing the satphones to be used indoors without a clear line of sight to the
satellite.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 34
Chapter 9
CODE DIVISION MULTIPLE ACCESS
Code division multiple access (CDMA) is a channel access method utilized by various radio
communication technologies. It should not be confused with the mobile phone standards
called cdmaOne and CDMA2000 (which are often referred to as simply CDMA), which use
CDMA as an underlying channel access method.
9.1 CDMA basics
One of the basic concepts in data communication is the idea of allowing several transmitters
to send information simultaneously over a single communication channel. This allows several
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 35
users to share a bandwidth of different frequencies. This concept is called multiplexing.
CDMA employs spread-spectrum technology and a special coding scheme (where each
transmitter is assigned a code) to allow multiple users to be multiplexed over the same
physical channel. By contrast, time division multiple access (TDMA) divides access by time,
while frequency-division multiple access (FDMA) divides it by frequency. CDMA is a form
of spread-spectrum signaling, since the modulated coded signal has a much higher data
bandwidth than the data being communicated.
An analogy to the problem of multiple access is a room (channel) in which people wish to
communicate with each other. To avoid confusion, people could take turns speaking (time
division), speak at different pitches (frequency division), or speak in different languages
(code division). CDMA is analogous to the last example where people speaking the same
language can understand each other, but not other people. Similarly, in radio CDMA, each
group of users is given a shared code. Many codes occupy the same channel, but only users
associated with a particular code can communicate.
9.2 Steps in CDMA Modulation
CDMA is a spread spectrum multiple access technique. A spread spectrum technique is one
which spreads the bandwidth of the data uniformly for the same transmitted power. Spreading
code is a pseudo-random code which has a narrow Ambiguity function unlike other narrow
pulse codes. In CDMA a locally generated code runs at a much higher rate than the data to be
transmitted. Data for transmission is simply logically XOR (exclusive OR) added with the
faster code. The figure shows how spread spectrum signal is generated. The data signal with
pulse duration of Tb is XOR added with the code signal with pulse duration of Tc. (Note:
bandwidth is proportional to 1 / T where T = bit time) Therefore, the bandwidth of the data
signal is 1 / Tb and the bandwidth of the spread spectrum signal is 1 / Tc. Since Tc is much
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 36
smaller than Tb, the bandwidth of the spread spectrum signal is much larger than the
bandwidth of the original signal. The ratio Tb / Tc is called spreading factor or processing gain
and determines to a certain extent the upper limit of the total number of users supported
simultaneously by a base station.
Each user in a CDMA system uses a different code to modulate their signal. Choosing the
codes used to modulate the signal is very important in the performance of CDMA systems.
The best performance will occur when there is good separation between the signal of a
desired user and the signals of other users. The separation of the signals is made by
correlating the received signal with the locally generated code of the desired user. If the
signal matches the desired user's code then the correlation function will be high and the
system can extract that signal. If the desired user's code has nothing in common with the
signal the correlation should be as close to zero as possible (thus eliminating the signal); this
is referred to as cross correlation. If the code is correlated with the signal at any time offset
other than zero, the correlation should be as close to zero as possible. This is referred to as
auto-correlation and is used to reject multi-path interference.
In general, CDMA belongs to two basic categories: synchronous (orthogonal codes) and
asynchronous (pseudorandom codes).
9.3 Code division multiplexing (Synchronous CDMA)
Synchronous CDMA exploits mathematical properties of orthogonality between vectors
representing the data strings. For example, binary string 1011 is represented by the vector (1,
0, 1, 1). Vectors can be multiplied by taking their dot product, by summing the products of
their respective components. If the dot product is zero, the two vectors are said to be
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 37
orthogonal to each other (note: if u = (a, b) and v = (c, d), the dot product u·v = ac + bd).
Some properties of the dot product aid understanding of how W-CDMA works. If vectors a
and b are orthogonal, then and:
Each user in synchronous CDMA uses a code orthogonal to the others' codes to modulate
their signal. An example of four mutually orthogonal digital signals is shown in the figure.
Orthogonal codes have a cross-correlation equal to zero; in other words, they do not interfere
with each other. In the case of IS-95 64 bit Walsh codes are used to encode the signal to
separate different users. Since each of the 64 Walsh codes are orthogonal to one another, the
signals are channelized into 64 orthogonal signals. The following example demonstrates how
each users signal can be encoded and decoded.
9.4 USES
A CDMA mobile phone
One of the early applications for code division multiplexing is in GPS. This predates
and is distinct from cdmaOne.
The Qualcomm standard IS-95, marketed as cdmaOne.
The Qualcomm standard IS-2000, known as CDMA2000. This standard is used by
several mobile phone companies, including the Globalstar satellite phone network.
CDMA has been used in the OmniTRACS satellite system for transportation
logistics.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 38
Chapter 10
The Future of Mobile Networking
10.1 Future evolution: Broadband Fourth generation (4G)
The recently released 4th generation, also known as Beyond 3G, aims to provide broadband
wireless access with nominal data rates of 100 Mbit/s to fast moving devices, and 1 Gbit/s to
stationary devices defined by the ITU-R 4G systems may be based on the 3GPP LTE (Long
Term Evolution) cellular standard, offering peak bit rates of 326.4 Mbit/s. It may perhaps
also be based on WiMax or Flash-OFDM wireless metropolitan area network technologies
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 39
that promise broadband wireless access with speeds that reaches 233 Mbit/s for mobile users.
The radio interface in these systems is based on all-IP packet switching, MIMO diversity,
multi-carrier modulation schemes, Dynamic Channel Assignment (DCA) and channel-
dependent scheduling. A 4G system should be a complete replacement for current network
infrastructure and is expected to be able to provide a comprehensive and secure IP solution
where voice, data, and streamed multimedia can be given to users on a "Anytime, Anywhere"
basis, and at much higher data rates than previous generations. Sprint in the US has claimed
its WiMax network to be "4G network" which most cellular telecoms standardization experts
dispute repeatedly around the world. Sprint's 4G is seen as a marketing gimmick as WiMax
itself is part of the 3G air interface. The officially accepted, ITU ratified standards-based 4G
networks are not expected to be commercially launched until 2011.
10.2 Comparison to similar systems
Car phone A type of telephone permanently mounted in a vehicle, these often have more
powerful transmitters, an external antenna and loudspeaker for hands free use. They usually
connect to the same networks as regular mobile phones.
Cordless telephone (portable phone)
Cordless phones are telephones which use one or more radio handsets in place of a
wired handset. The handsets connect wirelessly to a base station, which in turn
connects to a conventional land line for calling. Unlike mobile phones, cordless
phones use private base stations (belonging to the land-line subscriber), which are not
shared.
Professional Mobile Radio
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 40
Advanced professional mobile radio systems can be very similar to mobile phone
systems. Notably, the IDEN standard has been used as both a private trunked radio
system as well as the technology for several large public providers. Similar attempts
have even been made to use TETRA, the European digital PMR standard, to
implement public mobile networks.
Radio phone
This is a term which covers radios which could connect into the telephone network.
These phones may not be mobile; for example, they may require a mains power
supply, or they may require the assistance of a human operator to set up a PSTN
phone call.
Satellite phone
This type of phone communicates directly with an artificial satellite, which in turn
relays calls to a base station or another satellite phone. A single satellite can provide
coverage to a much greater area than terrestrial base stations. Since satellite phones
are costly, their use is typically limited to people in remote areas where no mobile
phone coverage exists, such as mountain climbers, mariners in the open sea, and news
reporters at disaster sites.
IP Phone
This type of phone delivers or receives calls over internet, LAN or WAN networks
using VoIP as opposed to traditional CDMA and GSM networks. In business, the
majority of these IP Phones tend to be connected via wired Ethernet, however
wireless varieties do exist. Several vendors have developed standalone WiFi phones.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 41
Additionally, some cellular mobile phones include the ability to place VoIP calls over
cellular high speed data networks and/or wireless internet.
II
MICROWAVE MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 42
ENGINEERING
Chapter 1
INTRODUCTION
1.1 Microwave Frequencies
The descriptive term microwaves is used to describe electromagnetic waves with
wavelengths ranging from 1 cm to 1 m. The corresponding frequency range is 300 MHz up to
30 GHz for 1-cm-wavelength waves. Electromagnetic waves with wavelengths ranging from
1 to 10 mm are called millimeter waves. The infrared radiation spectrum comprises
electromagnetic waves with wavelengths in the range 1 am (10 6 m) up to 1 mm. Beyond the
infrared range is the visible optical spectrum, the ultraviolet spectrum, and finally x-rays.
Several different classification schemes are in use to designate frequency bands in the
electromagnetic spectrum. These classification schemes are summarized in Tables 1.1 and
1.2. The radar band classification came into use during World War II and is still in common
use today even though the new military band classification is the recommended one. In the
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 43
UHF band up to around a frequency of 1 GHz, most communications circuits are constructed
using lumped-parameter circuit componenta. In the frequency range from 1 up to 100 GHz.
lumped circuit elements are usually replaced by transmission-line and waveguide
components. Thus by the term microwave engineering we shall mean generally the
engineering and design of information-handling systems in the frequency range from 1 to 100
GHz corresponding to wavelengths as long as 30 cm and as short as 3 mm. At shorter
wavelengths we have what can be called optical engineering since many of the techniques
used are derived from classical optical techniques. The characteristic feature of microwave
engineering is the short wavelengths involved, these being of the same order of magnitude as
the circuit elements and devices employed.
The Table 1.1 shows the various bands of Microwave frequencies, their designations
and general applications of each and every band in modern field of Science and Technology
Table 1.1 Different bands of Frequencies and their applications
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 44
Microwave freq.
The short wavelengths involved in turn mean that the propagation time for electrical
effects from one point in a circuit to another point is comparable with the period of the
oscillating currents and charges in the system. As a result, conventional low-frequency circuit
analysis based on Kirchhoffs laws and voltage-current concepts no longer suffices for an
adequate description of the electrical phenomena taking place. It is necessary instead to cany
out the analysis in terms of a description of the electric and magnetic fields associated with
the device. In essence, it might be said, microwave engineering is applied electromagnetic
fields engineering. For this reason the successful engineer in this area must have a good
working knowledge of electromagnetic field theory.
Table 1.2 represents modern labelling of frequency bands according to IEEE
standards.
Table 1.2 IEEE Frequency band Designation
There is no distinct frequency boundary at which lumped-parameter circuit elements
must be replaced by distributed circuit elements. With modern technological processes it is
possible to construct printed-circuit inductors that are so small that they retain their lumped-
parameter characteristics at frequencies as high as 10 GHz or even higher. Likewise, optical
components, such as parabolic reflectors and lenses, are used to focus microwaves with
wavelengths as long as 1 m or more. Consequently, the microwave engineer will frequently
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 45
employ low-frequency lumped-parameter circuit elements, such as miniaturized inductors
and capacitors, as well as optical devices in the design of a microwave system.
1.2 Microwave History of Development
The great interest in microwave frequencies arises for a variety of reasons. Basic
among these is the ever-increasing need for more radio-frequency-spectrum space and the
rather unique uses to which microwave frequencies can be applied. When it is noted that the
frequency range 109 to 1012 Hz contains a thousand sections like the frequency spectrum from
0 to 109 Hz, the value of developing the microwave band as a means of increasing the
available usable frequency spectrum may be readily appreciated.
In more recent years microwave frequencies have also come into widespread use in
communication links, generally referred to as microwave links. Since the propagation of
microwaves is effectively along line-of-sight paths, these links employ high towers with
reflector or lens-type antennas as repeater stations spaced along the communication path.
Such links are a familiar sight to the motorist traveling across the country because of their
frequent use by highway authorities, utility companies, and television networks. A further
interesting means of communication by microwaves is the use of satellites as microwave
relay stations. The first of these, the Telstar, launched in July 1962, provided the first
transmission of live television programs from the United States to Europe.
At the present time most communication systems are shifting to the use of digital
transmission, i.e., analog signals are digitized before transmission. Microwave digital
communication system development is progressing rapidly. In the early systems simple
modulation schemes were used and resulted in inefficient use of the available frequency
spectrum. The development of 64-state quadrature amplitude modulation (64-QAM) has
made it possible to transmit 2,016 voice channels within a single 30-MHz RF channel. This is
competitive with FM analog modulation schemes for voice.
1.3 Microwave Applications
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 46
Even though such uses of microwaves are of great importance, the applications of
microwaves and microwave technology extend much further, into a variety of areas of basic
and applied research, and including a number of diverse practical devices, such as microwave
ovens that can cook a small roast in just a few minutes
Waveguides periodically loaded with shunt susceptance elements support slow waves
having velocities much less than the velocity of light, and are used in linear accelerators.
These produce high-energy beams of charged particles for use in atomic and nuclear
research. The slow-traveling electromagnetic waves interact very efficiently with charged-
particle beams having the same velocity, and thereby give up energy to the beam. Another
possibility is for the energy in an electron beam to be given up to the electromagnetic wave,
with resultant amplification
Sensitive microwave receivers are used in radio astronomy to detect and study the
electromagnetic radiation from the sun and a number of radio stars that emit radiation in this
band. Such receivers are also used to detect the noise radiated from plasmas (an
approximately neutral collection of electrons and ions, e.g., a gas discharge). The information
obtained enables scientists to analyze and predict the various mechanisms responsible for
plasma radiation. Microwave radiometers are also used to map atmospheric temperature
profiles, moisture conditions in soils and crops, and for other remote-sensing applications as
well.
The development of the laser, a generator of essentially monochromatic (single-
frequency) coherent-light waves, has stimulated a great interest in the possibilities of
developing communication systems at optical wavelengths. This frequency band is
sometimes referred to as the ultra-microwave band. With some modification, a good deal of
the present microwave technology can be exploited in the development of optical systems.
For this reason, familiarity with conventional microwave theory and devices provides a good
background for work in the new frontiers of the electromagnetic spectrum.
The domestic microwave oven operates at 2,450 MHz and uses a magnetron tube with
a power output of 500 to 1000 W. For industrial heating applications, such as drying grain,
manufacturing wood and paper products, and material curing, the frequencies of 915 and
2,450 MHz have been assigned. Microwave radiation has also found some application for
medical hyperthermia or localized heating of tumours
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 47
Chapter 2
WAVEGUIDES –I
2.1 Modes of Propogation
For a large variety of waveguides of practical interest it turns out that all the boundary
conditions can be satisfied by fields that do not have all components present. Specifically, for
transmission lines, the solution of interest is a transverse electromagnetic wave with
transverse components only, that is, Ez = Hz = 0, whereas for waveguides, solutions with Ez =
0 or Hz = 0 are possible. Because of the widespread occurrence of such field solutions, the
following classification of solutions is of particular interest.
1. Transverse electromagnetic (TEM) waves. For TEM waves, Ez = Hz = 0. The electric
field may be found from the transverse gradient of a scalar function *(x,y), which is a
function of the transverse coordinates only and is a solution of the two-dimensional
Laplace equation.
2. Transverse electric (TE), or H, modes. These solutions have Ez = 0, but Hz ¥= 0. All the
field components may be derived from the axial component Hz of magnetic field.
3. Transverse magnetic (TM), or E, modes. These solutions have Hz = "» but Ez ¥= 0. The
field components may be derived from Ez.
In some cases it will be found that a TE or TM mode by itself will not satisfy all the
boundary conditions. However, in such cases linear combinations of TE and TM modes may
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 48
be used, since such linear combinations always provide a complete and general solution.
Although other possible types of wave solutions may be constructed, the above three types
are the most useful in practice and by far the most commonly used ones.
The appropriate equations to be solved to obtain TEM, TE, or TM modes will be
derived below by placing E, and Hz, Ez, and Hz. respectively, equal to zero in Maxwell's
equations.
2.2 Rectangular vs Circular Waveguides
Hollow-pipe waveguides do not support a TEM wave. In hollow-pipe waveguides the waves
are of the TE and TM variety. The waveguide with a rectangular cross section is the most
widely used one. It is available in sizes for use at frequencies from 320 MHz up to 333 GHz.
The WR-2300 waveguide for use at 320 MHz has internal dimensions of 58.42 in by 29.1 in
and is a very large duct. By contrast, the WR-3 waveguide for use at 333 GHz has internal
dimensions of 0.034 in by 0.017 in and is a very miniature structure. The standard WR-90 X-
band waveguide has internal dimensions of 0.9 in by 0.4 in and is used in the frequency range
of 8.2 to 12.5 GHz. The rectangular waveguide is widely used to couple transmitters and
receivers the antenna. For high-power applications the waveguide is filled with j inert gas
such as nitrogen and pressurized in order to increase the voltage breakdown rating.
Circular waveguides are not as widely used as rectangular waveguides but are
available in diameters of 25.18 in down to 0.239 in to cover tn frequency range 800 MHz up
to 116 GHz.
2.3 Rectangular Waveguides
Fig 2.3 Rectangular Waveguide
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 49
The rectangular waveguide with a cross section as illustrated in Fig. 3.36 is an example
of a wave guiding device that will not support a TEM wave. Consequently, it turns out that
unique voltage and current waves do not exist, and the analysis of the waveguide properties
has to be carried out as a field problem rather than as a distributed-parameter-circuit problem.
In a hollow cylindrical waveguide a transverse electric field can exist only if a time-
varying axial magnetic held is present. Similarly, a transverse magnetic field can exist only if
either an axial displacement current or an axial conduction current is present, as Maxwell's
equations show. Since a TEM wave does not have any axial field components and there is no
center conductor on which a conduction current can exist, a TEM wave cannot be propagated
in a cylindrical waveguide.
The types of waves that can be supported (propagated) in a hollow empty waveguide are
the TE and TM modes discussed in Sec. 3.7. The essential properties of all hollow cylindrical
waveguides are the same, so that an understanding of the rectangular guide provides insight
into the behavior of other types as well. As for the case of the transmission line, the effect of
losses is initially neglected. The attenuation is computed later by using the perturbation
method given earlier, together with the loss-free solution for the currents on the walls.
The essential properties of empty loss-free waveguides, which the detailed analysis to follow
will establish, are that there is a double infinity of possible solutions for both TE and TM
waves. These waves, or modes, may be labeled by two identifying integer subscripts n and m,
for example, TEmn.
The integers n and in pertain to the number of standing-wave interference maxima
occurring in the field solutions that describe the variation of the fields along the two
transverse coordinates. It will be found that each mode has associated with it a characteristic
cutoff frequency fc „m below which the mode does not propagate and above which the mode
does propagate
TE10 mode is the most dominant mode in Rectangular waveguides
For a rectangular waveguide with a width a equal to twice the height ft, the maximum
bandwidth of operation over which only the dominant TE10 mode propagates is a 2:1 band.
For some system applications it is necessary to have a waveguide that operates with only a
single mode of propagation over much larger bandwidths. A transmission line supporting
only a TEM mode can fulfill this requirement but must then have cross-sectional dimensions
that are small relative to the shortest wavelength of interest. A coaxial transmission line will
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 50
support higher-order TE and TM modes in addition to the TEM mode. Thus, to avoid
excitation of a higher-order mode of propagation, the outer radius must be kept small relative
to the wavelength. The small cross section implies a relatively large attenuation; so some
other form of waveguide is needed. The ridge waveguide illustrated in Fig. 3.46 was
developed to fulfill this need for a single-mode waveguide capable of operating over a very
broad band. Physically, it is easy to understand why the ridge waveguide has a very large
frequency band of operation. The center section of width W and spacing S functions very
much like a parallel-plate transmission line and consequently the ridge waveguide has a much
lower cutoff frequency for the same width and height as does the conventional rectangular
waveguide. Operation over bandwidths of 5 to 10 times more is possible.
Chapter 3
WAVEGUIDE COMPONENTS-1
3.1 ATTENUATORS
Attenuators may be of the fixed or the variable type, The first is used only if a fixed
amount of attenuation is to be provided. For bridge setups used to measure transmission
coefficients, the variable attenuator is used. There are many ways of constructing a variable
attenuator; only one type, the rotary attenuator, is considered
A simple form 0f consists of a thin tapered resistive card, of the type used for mat t
whose depth of penetration into the waveguide is adjustable
Perhaps the most satisfactory precision attenuator developed for AI • the rotary
attenuator, which we now examine in some detail. The h components of this instrument
consist of two rectangular-to-circular wa\ guide tapered transitions, together with an
intermediate section of circular waveguide that is free to rotate,. A thin tapered resistive card
is placed at the output end of each transition section and oriented parallel to the broad walls
of the rectangular guide. A similar resistive card is located in the intermediate circular-guide
section. Tlie incoming TE;o mode in ike rectangular guide is transformed into the TEn mode
in the circular guide with negligible reflection by means of the tapered transition. The
polarization of the TEn mode is such that the electric field is perpendicular to the thin res
card in the transition section. As such, this resistive card has a negligible effect on the TEn
mode. Since the resistive card in the center section can be rotated, its orientation relative to
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 51
the electric field of the incoming TEn mode can be varied so that the amount by which this
mode is attenuated: adjustable.
3.2 Electronically Controlled Attenuators
For applications in various microwave systems, it is desirable to have an attenuator
whose attenuation can be controlled by the application of a suitable signal, such as a dc
voltage or a bias current. Two devices thai are suitable for use in an electronically controlled
attenuator are the PIN dioc and a field-effect transistor. These devices can be used as variable
resi=toi whose resistance is controlled by the applied signal.
3.3 PHASE SHIFTERS
A phase shifter is an instrument that produces an adjustable change in the phase angle of the
wave transmitted through it. Ideally, it should perfectly matched to the input and output lines
and should produce zero attenuation. These requirements can be met to within a reasonable
deg of approximation. There are a variety of designs for phase shifters mechanically
adjustable type. The rotary phase shifter is the best in class
Phase shifters are used to change the transmission phase angle (phase of S21) of a network.
Ideal phase shifters provide low insertion loss, and equal amplitude (or loss) in all phase
states. While the loss of a phase shifter is often overcome using an amplifier stage, the less
loss, the less power that is needed to overcome it. Most phase shifters are reciprocal
networks, meaning that they work effectively on signals passing in either direction. Phase
shifters can be controlled electrically, magnetically or mechanically. Most of the phase
shifters described on this web site are passive reciprocal networks; we will concentrate
mainly on those that are electrically-controlled.
While the applications of microwave phase shifters are numerous, perhaps the most important
application is within a phased array antenna system (a.k.a. electrically steerable array, or
ESA), in which the phase of a large number of radiating elements are controlled to force the
electro-magnetic wave to add up at a particular angle to the array. The total phase variation of
a phase shifter need only be 360 degrees to control an ESA of moderate bandwidth. Networks
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 52
that stretch phase more than 360 degrees are often called line stretchers, and are constructed
similar to the switched line phase shifters to be described below.
Analog versus digital phase shifters
Phase shifters can be analog or digital. Analog phase shifters provide a continuously variable
phase, perhaps controlled by a voltage. Electrically controlled analog phase shifters can be
realized with varactor diodes that change capacitance with voltage, or non-linear dielectrics
such as barium strontium titanate, or ferro-electric materials such as yttrium iron garnet. A
mechanically-controlled analog phase shifter is really just a mechanically lengthened
transmission line, often called a trombone line. Analog phase shifters are a mere side-show
and will not be covered here in depth at this time. If you are interested in more information
on any of these analog phase shifter topics, let us know and we will try to accommodate you.
Most phase shifters are of the digital variety, as they are more immune to noise on their
voltage control lines. Digital phase shifters provide a discrete set of phase states that are
controlled by two-state "phase bits." The highest order bit is 180 degrees, the next highest is
90 degrees, then 45 degrees, etc, as 360 degrees is divided into smaller and smaller binary
steps. A three bit phase shifter would have a 45 degree least significant bit (LSB), while a six
bit phase shifter would have a 5.6 degree least significant bit. Technically the latter case
would have a 5.625 degree LSB, but in the microwave world it is best to ignore precision that
you cannot obtain. If you can't comprehend this point, you might want to consider a different
career such as accounting.
The convention followed for phase shifters is that the shortest phase length is the reference or
"off" state, and the longest path or phase length is the "on" state. Thus a 90 degree phase
shifter actually provides minus ninety degrees of phase shift in its "on" state.
Applications of phase shifters
Frequency translators
Phased arrays
Residual phase noise measurement
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 53
3.4 DIRECTIONAL COUPLERS
A directional coupler is a four-port microwave junction with the properties discussed below.
With reference to Fig. 3.1, which is a schematic illustration of a directional coupler, the ideal
directional coupler has the property that a wave incident in port 1 couples power into ports 2
and 3 but not into port 4. Similarly, power incident in port 4 couples into ports 2 and 3 but
not into port 1. Thus ports 1 and 4 are uncoupled. For waves incident in port 2 or 3, the
power is coupled into ports 1 and 4 only, 80 that ports 2 and 3 are also uncoupled. In
addition, all four ports are matched. That is. if three ports are terminated in matched loads,
the fourth port appears terminated in a matched load, and an incident wave in this port suffers
no reflection.
Fig 3.1 Directional Coupler as a 4 port device
Directional couplers are widely used in impedance bridges for microwave measurements and
for power monitoring. For example, if" a radar transmitter is connected to port 1, the antenna
to port 2. a microwave crystal detector to port 3. and a matched load to port 4. the power
received in port 3 is proportional to the power flowing from the transmitter to the antenna in
the forward direction only. Since the reflected wave from the antenna, if it exists, is not
coupled into port 3, the detector monitors the power output of the transmitter.
If the coupler is designed for 3-dB coupling, then it splits the input power in port 2 into equal
powers in ports 2 and 3. Thus a 3-dB directional coupler serves as a power divider.
Directional couplers with 3-dB coupling are also called hybrid junctions and are widely used
in microwave mixers and as input, and output couplers in balanced microwave amplifier
circuits. There are many available designs and configurations for directional couplers, hybrid
junctions, and power dividers.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 54
Fig 3.2 Directional Couplar showing input and out put ports
Chapter 4
WAVEGUIDE COMPONENTS _II
4.1 HYBRID JUNCTIONS - Magic T
A waveguide hybrid junction, known as a magic T, is illustrated in Fig. 6.32. When a
TE10 mode is incident in port 1, the electric field within the junction is like that sketched in
Fig. 6.326. This electric field has even symmetry about the midplane and hence cannot excite
the TE1U mode in arm 4 since this mode must have an electric field with odd symmetry
(shown dashed in Fig. 6.326). Thus there is no coupling between ports 1 and 4. The coupling
between ports 1 and 2, and 1 and 3, is clearly the same, as may be seen from the symmetry
involved.
For a TE10 mode incident in arm 4. the electric field within the junction is sketched in
Fig. 4.1. Symmetry again shows that there is no coupling into port 1 (this is required by
reciprocity as well). The coupling from port 4 into ports 2 and 3 is equal in magnitude but
180" out of phase. since S,3 = S13, So,, = -S34, from symmetry.
Matching elements that do not destroy the symmetry of the junction may be placed in
the E-plane and //-plane arms so as to make S,, = S44 = 0. For a lossless structure we may then
show that the unitary properties of the scattering matrix require that S.J2 = S,;i = 0, so that all
ports are matched. In addition, S23 = 0; so ports 2 and 3 as well as ports 1 and 4 are
uncoupled. The hybrid T now becomes a directional coupler with 3-dB coupling, and is often
called a magic T, even though there is nothing magic about its operation. The magic T is
commonly used in waveguide balanced mixers and in bridge networks.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 55
Fig 4.1 Magic Tee
The Scattering matrix for a magic T is
0 1 1 0
1 0 0 1
S= 1 0 0 -1
0 1 -1 0
4.2 Hybrid ring or Rat Race
Applications of rat-race couplers are numerous, and include mixers and phase shifters.
The rat-race gets its name from its circular shape, shown below. The circumference is 1.5
wavelengths. For an equal-split rat-race coupler, the impedance of the entire ring is fixed at
1.41xZ0, or 70.7 ohms for a 50 ohm system. For an input signal V in, the outputs at ports 2 and
4 are equal in magnitude, but 180 degrees out of phase. The coupling of the two arms is
shown in the figure below, for an ideal rat-race coupler centered at 10 GHz (10,000 MHz).
An equal power split of 3 dB occurs at only the center frequency. The 1-dB bandwidth of the
coupled port (S41) is shown by the markers to be 3760 MHz, or 37.6 percent.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 56
Fig 4.2 Hybrid Ring
Chapter 5
MICROWAVE PROPAGATION IN FERRITES
5.1 MICROWAVE DEVICES EMPLOYING FARADAY ROTATION
The development of ferrite materials suitable for use at microwave frequencies has
resulted in a large number of microwave devices. A number of them have nonreciprocal
electrical properties; i.e., the transmission coefficient through the device is not the same for
different directions of propagation
5.2 Gyrator
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 57
A gyrator is defined as a two-port device that has a relative difference in phase
shift of 180° for transmission from port 1 to port 2 as compared the phase shift for
transmission from port 2 to Port1.
The phase shift may be obtained by employing the nonreciprocal property of
Faraday rotation. It consists of a rectangular guide with a 90° twist connected to a circular
guide, which in turn connected to another rectangular guide at the other end. The two
rectangular guides have the same orientation at the input ports. The circular guide
contains a thin cylindrical rod of ferrite with the ends tapered to reduce reflections. A
static axial magnetic field is applied so as to produce 90' Faraday rotation of the TE,,
dominant mode in the circular guide. Consider a wave propagating from left to right. In
passing through the twist the plane of polarization is rotated by 90° in a counter-
clockwise direction. If the ferrite produces an additional 90° of rotation, the total angle of
rotation will be 180°, as indicated in Fig. 6.45. For a wave propagating from right to left.
the Faraday rotation is still 90° in the same sense. However, in passing through the twist,
the next 90° of rotation is in a direction to cancel Faraday rotation. Thus, for transmission
from port 2 to port 1, there net rotation of the plane of polarization. The 180° rotation for
transmission from port 1 to port 2 is equivalent to an additional 180° of phase shift since
it reverses the polarization of the field. It is apparent, then, that the device just described
satisfies the definition of a gyrator.
If the inconvenience of having the input and output rectangular guides oriented at 90°
can be tolerated, a gyrator without a 90" twist section can be built. With reference to Fig.
6.46, it is seen that if the ferrite produces 90° of rotation and the output guide is rotated by
90" relative to the input guide, the emerging wave will have the right polarization to
propagate in the output guide. When propagation is from port 2 to port 1, the wave arriving in
guide 1 will have its polarization changed by 180°, as shown in Fig. 6.46. Hence a
differential phase shift of 180° is again produced.
The solution for wave propagation in a circular guide with a longitudinal magnetized cylinder
placed in the center can be carried out exactly.t However, the solution requires a great deal of
algebraic manipulation, and it is very laborious to compute numerical values from the
resultant transcendental equations for the propagation constants. The solution does verify that
Faraday rotation takes place as would be expected, by analogy with propagation in an infinite
ferrite medium.
5.3 ISOLATOR
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 58
The isolator is similar to the gyrator in construction except that it employs a 45° twist
section and 45° of Faraday rotation. In addition, thin resistive cards are inserted in the input
and output guides to absorb the field that is polarized, with the electric vector parallel to the
wide side of the guide, as shown in Fig. 6.47. The operation is as follows: A wave
propagating from port 1 to port 2 has its polarization rotated 45° counter clockwise by the
twist section and 45° clockwise by the Faraday rotator. It will emerge at port 2 with the
correct polarization to propagate in the output guide. A wave propagating from port 2 to port
1 will have its plane of polarization rotated by 90c and will enter the guide at port 1 with the
electric field parallel to the resistance card, and hence be absorbed. Without the resistance
card, the wave would be reflected from port 1 because of the incorrect
polarization, which cannot propagate in the guide constituting port 1. However, multiple
reflections within the isolator will lead to transmission in both directions, and this makes it
necessary to use resistance cards in both the input and output guides for satisfactory
performance. Typical performance figures for an isolator are forward transmission loss of
less than l dB, reverse attenuation of 20 to 30 dB, and bandwidth of operation approaching 10
percent-
5.4 OTHER FERRITE DEVICES
The devices utilizing ferrites for their operation described in the preced" sections
represent only a small number of the large variety of devices th-! have been developed. In
addition to the above, there are other forms of isolators, both reciprocal and nonreciprocal
phase shifters, electronically controlled (by varying the current in the electromagnet that
supplies the static biasing field) phase shifters and modulators, electronic switches and power
limiters, etc. The nonlinear property of ferrites for high signal levels has also been used in
harmonic generators, frequency mixers, and parametric amplifiers. A discussion of these
devices, together with design considerations, performance data, and references to the original
literature, contained in the book by Lax and Button, listed in the references at the end of this
chapter. The recent article by Rodriquez gives a good survey of the present status of ferrite
devices.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 59
Chapter 6
MICROWAVE TUBES
Microwave tubes are the prime signal sources in high-power radar systems. The
magnetron is the tube most frequently used and can provide many kilowatts of continuous-
wave (CW) output power and a megawatt or more of peak power with pulsed operation.
Magnetrons are also used for industrial heating applications and in microwave ovens for
consumer use. The traveling-wave-tube amplifier with power outputs up to 10 W or more is
the workhorse in satellite communications. The klystron tube can function as an oscillator or
as an amplifier. It can be designed for either low or high output power applications. In low-
power applications the klystron was once widely used as the local oscillator in microwave
receivers but has now been replaced by solid-state oscillators. Solid-state oscillators are
replacing n crowave tubes in many low-power transmitter applications also. Even thoug
many of the applications for microwave tubes have been taken over solid-state devices, the
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 60
requirements for high power can only be me microwave tubes, so they are an essential device
for many systems.
Conventional low-frequency tubes, such as triodes, fail to operate at microwave
frequencies because the electron transit time from the cat the grid becomes an appreciable
fraction of the period of the sinu ^ signal to be amplified. In other words, propagation time
becomes short , and the same limitations that are inherent in low-frequencies are present in
low-frequency tubes also. Microwave tubes must be to utilize the wave-propagation
phenomena to best advantage.
Broadly speaking, there are two basic types of microwave tubes, one that employ
electromagnetic cavities (klystrons and some magnetron) and the other those that apply
those that employ slow-wave circuits (travelling-wave tubes)
Both types of tubes utilize an electron beam on which space-charge waves and cyclotron waves can be excited.
The space-charge waves are primarily longitudinal oscillations of the electrons and interact with the
electromagnetic fields in cavities and slow-wave circuits to give amplification.
6.1 Klystron Amplifier
A klystron is a specialized linear-beam vacuum tube (evacuated electron tube).
Klystrons are used as amplifiers at microwave and radio frequencies to produce both low-
power reference signals for super heterodyne radar receivers and to produce high-power
carrier waves for communications and the driving force for modern particle accelerators.
Klystron amplifiers have the advantage (over the magnetron) of coherently amplifying a
reference signal so its output may be precisely controlled in amplitude, frequency and phase.
Many klystrons have a waveguide for coupling microwave energy into and out of the device,
although it is also quite common for lower power and lower frequency klystrons to use
coaxial couplings instead. In some cases a coupling probe is used to couple the microwave
energy from a klystron into a separate external waveguide.
The name klystron comes from the stem form κλυσ- (klys) of a Greek verb referring to
the action of waves breaking against a shore, and the end of the word electron
Working
Klystrons amplify RF signals by converting the kinetic energy in a DC electron beam
into radio frequency power. A beam of electrons is produced by a thermionic cathode (a
heated pellet of low work function material), and accelerated by high-voltage electrodes
(typically in the tens of kilovolts). This beam is then passed through an input cavity. RF
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 61
energy is fed into the input cavity at, or near, its natural frequency to produce a voltage which
acts on the electron beam. The electric field causes the electrons to bunch: electrons that pass
through during an opposing electric field are accelerated and later electrons are slowed,
causing the previously continuous electron beam to form bunches at the input frequency. To
reinforce the bunching, a klystron may contain additional "buncher" cavities. The RF current
carried by the beam will produce an RF magnetic field, and this will in turn excite a voltage
across the gap of subsequent resonant cavities. In the output cavity, the developed RF energy
is coupled out. The spent electron beam, with reduced energy, is captured in a collector.
6.2 Two Cavity Klystron
Fig 6.1 Two Cavity Klystron
In the two-chamber klystron, the electron beam is injected into a resonant cavity. The
electron beam, accelerated by a positive potential, is constrained to travel through a
cylindrical drift tube in a straight path by an axial magnetic field. While passing through the
first cavity, the electron beam is velocity modulated by the weak RF signal. In the moving
frame of the electron beam, the velocity modulation is equivalent to a plasma oscillation.
Plasma oscillations are rapid oscillations of the electron density in conducting media such
as plasmas or metals.(The frequency only depends weakly on the wavelength). So in a quarter
of one period of the plasma frequency, the velocity modulation is converted to density
modulation, i.e. bunches of electrons. As the bunched electrons enter the second chamber
they induce standing waves at the same frequency as the input signal. The signal induced in
the second chamber is much stronger than that in the first. The figure below is that of a two
cavity klystron amplifier.
6.3 Reflex klystron
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 62
Fig 6.1 Reflex Klystron
In the reflex klystron (also known as a 'Sutton' klystron after its inventor), the electron beam
passes through a single resonant cavity. The electrons are fired into one end of the tube by
an electron gun. After passing through the resonant cavity they are reflected by a negatively
charged reflector electrode for another pass through the cavity, where they are then collected.
The electron beam is velocity modulated when it first passes through the cavity. The
formation of electron bunches takes place in the drift space between the reflector and the
cavity. The voltage on the reflector must be adjusted so that the bunching is at a maximum as
the electron beam re-enters the resonant cavity, thus ensuring a maximum of energy is
transferred from the electron beam to the RF oscillations in the cavity. The voltage should
always be switched on before providing the input to the reflex klystron as the whole function
of the reflex klystron would be destroyed if the supply is provided after the input. The
reflector voltage may be varied slightly from the optimum value, which results in some loss
of output power, but also in a variation in frequency. This effect is used to good advantage
for automatic frequency control in receivers, and in frequency modulation for transmitters.
The level of modulation applied for transmission is small enough that the power output
essentially remains constant. At regions far from the optimum voltage, no oscillations are
obtained at all. This tube is called a reflex klystron because it repels the input supply or
performs the opposite function of a klystron.
There are often several regions of reflector voltage where the reflex klystron will oscillate;
these are referred to as modes. The electronic tuning range of the reflex klystron is usually
referred to as the variation in frequency between half power points—the points in the
oscillating mode where the power output is half the maximum output in the mode. The
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 63
frequency of oscillation is dependent on the reflector voltage, and varying this provides a
crude method of frequency modulating the oscillation frequency, albeit with accompanying
amplitude modulation as well.
Modern semiconductor technology has effectively replaced the reflex klystron in most
applications.
6.4 Cavity Magnetron
Fig 6.3 Magnetron
The cavity magnetron is a high-powered vacuum tube that
generates microwaves using the interaction of a stream of electrons with a magnetic field.
The 'resonant' cavity magnetron variant of the earlier magnetron tube was invented
by Randall and Boot in 1940. The high power of pulses from the cavity magnetron made
centimetre-band radar practical. Shorter wavelength radars allowed detection of smaller
objects. The compact cavity magnetron tube drastically reduced the size of radar sets so that
they could be installed in anti-submarine aircraft and escort ships. At present, cavity
magnetrons are commonly used in microwave ovens and in various radar applications.
The basic structure of a magnetron is a number of identical reason arranged in a
cylindrical pattern around a cylindrical cathode, as show, °*' Fig. 9.19. A permanent magnet
is used to produce a strong magnetic fi T normal to the cross section. The anode is kept at a
high positive voltage v relative to the cathode. Electrons emitted from the cathode are
accelerator toward the anode block, but the presence of the magnetic field BQ produce a force
~evrB„ in the azimuthall direction which causes the electron trajectory to be deflected in the
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 64
same direction. If the cathode radius is a and the anode radius is 6, the potential at any radius
r is V(r) = V0Un(r/a)]/lln(b/a)].
6.5 OTHER TYPES OF MICROWAVE TUBES
In addition to the main types of microwave tubes already discussed the are a variety of
others as well. In one form of travelling-wave tube the resistance-wall amplifier, the helix is
replaced by a circular guide lined with a resistive material. The resistive lining enables a slow
wave to propagate in the guide, a wave that is highly attenuated in the absence of a beam If
an electron beam is present, amplification takes place with a growth constant aB large enough
to offset the attenuation due to the resistive lining. Thus a net overall amplification is
obtained,
In another form of travelling-wave tube, the double-stream amplifier. two parallel
electron beams are used. In this tube one of the beams provides the slow-wave structure, or
circuit, for the other beam.
It is also possible to amplify the space-charge waves directly by passing the beam
through a succession of accelerating and decelerating regions. This type of tube is called a
velocity-jump amplifier because the beam velocity v{l is periodically changed, or jumped, to
new values.
For both the O-type and M-type travelling-wave tubes, it is possible to adjust the beam
velocity so that it is equal to the phase velocity of any one of the spatial harmonics making up
the Bloch wave that can propagate along the periodic structure used for the slow-wave
circuit. In particular, interaction between the beam and one of the backward-propagating
spatial harmonics is possible
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 65
Chapter 7
THE GUNN EFFECT AND ITS APPLICATIONS
7.1 The Gunn Effect
In some materials (III-V compounds such as GaAs and InP), after an electric field in
the material reaches a threshold level, the mobility of electrons decrease as the electric field
is increased, thereby producing negative resistance. A two-terminal device made from such a
material can produce microwave oscillations, the frequency of which is primarily determined
by the characteristics of the specimen of the material and not by any external circuit. The
Gunn Effect was discovered by J. B. Gunn of IBM in 1963.
7.2 The Gunn Diode
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 66
In certain semiconductors, notably GaAs, electrons can exist in a high-mass low
velocity state as well as their normal low-mass high-velocity state and they can be forced
into the high-mass state by a steady electric field of sufficient strength. In this state they form
clusters or domains which cross the field at a constant rate causing current to flow as a series
of pulses. This is the Gunn effect and one form of diode which makes use of it consists of an
epitaxial layer of n-type GaAs grown on a GaAs substrate. A potential of a few volts applied
between ohmic contacts to the n-layer and substrate produces the electric field which causes
clusters. The frequency of the current pulses so generated depends on the transit time
through the n-layer and hence on its thickness. If the diode is mounted in a suitably tuned
cavity resonator, the current pulses cause oscillation by shock excitation and r.f. power up to
1 W at frequencies between 10 and 30 GHz is obtainable.
7.3 Gunn Diode Theory
The Gunn diode is a so-called transferred electron device. Electrons are transferred
from one valley in the conduction band to another valley. In order to understand the nature of
the transferred electron effect exhibited by Gunn diodes, it is necessary to consider the
electron drift velocity versus electric field (or current versus voltage) relationship for GaAs
(seeFigure 2). Below the threshold field, E th , of approximately 0.32 V/mm, the device acts
as a passive resistance. However, above E th the electron velocity (current) decreases as the
field (voltage) increases producing a region of negative differential mobility, NDM
(resistance, NDR). This is the essential feature that leads to current instabilities and Gunn
oscillations in an active device and is due to the special conductance band structure of direct
band gap semiconductors such as GaAs
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 67
Fig 7.1 Gunn Effect
The energy-momentum relationship contains two conduction band energy levels, G
and L (also known as valleys) with the following properties:
l In the lower G valley, electrons exhibit a small effective mass and very high
mobility, µ 1 . l In the satellite L valley, electrons exhibit a large effective mass and very low
mobility, µ
2 . l The two valleys are separated by a small energy gap, D E, of approximately 0.31
eV. In equilibrium at room temperature most electrons reside near the bottom of the lower G
valley. Because of their high mobility (~ 8000 cm 2V -1s-1), they can readily be accelerated
in a strong electric field to energies in the order of the G -L intervalley separation, D E.
Electrons are then able to scatter into the satellite L valley, resulting in a decrease in the
average electron mobility, µ, as given below:
µ = (n 1 µ 1 + n 2 µ 2 ) / (n 1 + n 2 ( where n 1 = electron density in G valley, n 2 =
electron density in L valley
Above the high field, E H , most electrons reside in the L valley and the device
behaves as a passive resistance (of greater magnitude) once again. In a practical Gunn diode,
electrons are accelerated from the cathode by the prevailing electric field. When they have
acquired sufficient energy, they begin to scatter into the low mobility satellite valley and
slow down.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 68
The question of exactly how the NDR phenomenon in GaAs results in Gunn-
oscillations can now be answered with the aid of Figure 4. A sample of uniformly doped n-
type GaAs of length L is biased with a constant voltage source V=0
The electrical field is therefore constant and its magnitude given by E . 0 =V 0 /L.
From the bottom graph in Figure 4 it is clear that the electrons flow from cathode to anode
with constant velocity v3
7.4 Applications
Gunn diodes are reliable, relatively easy to install and the lower output power levels fall well
below the safety exposure limits. They are ideally suited for use in low noise sources such as
local oscillators, locking oscillators, low and medium power transmitter applications and
motion detection systems. Higher power varieties can be used in phase-locked oscillators or
as reflection amplifiers in point-to-point communication links and telemetry systems.
Microwave sources have the advantages over ultrasonic detectors of size and beam width,
and over optical systems of working in dusty and adverse environments. The low voltage
requirements of Gunn oscillators mean that battery or regulated mains supplies may be used,
(battery drain can be reduced by using low current devices or by operation in a pulsed
mode). However, microwaves are reflected from metal surfaces and partially reflected from
many others e.g. brick, Tarmac and concrete, and they are attenuated by oxygen, water or
water vapour. The range of application of Gunn sensors for industrial and commercial use is
extensive and the following is only a brief list:
Collision avoidance radar
Vehicle ABS
Traffic analyser sensors
`Blind spot' car radar
Pedestrian safety systems
Elapsed distance meters
Automatic identification
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 69
Presence/absence indicators
Movement sensors
Distance measurements
Chapter 8
TRANSMISSION LINES AND CHARACTERISTIC IMPEDANCE
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 70
Transmission line is any conducting structure that supports an electromagnetic wave
"in captivity". Most transmission lines use two conductors, where one is considered ground.
This includes coax (the outer conductor is ground), micro strip and strip line. The
transmission line that does not use a pair of conductors is waveguide. By the way, we are
talking about lossless transmission lines here, or at least near-lossless.
When microwave engineers talk about a "fifty-ohm system", what does that mean? A
common misconception is that if you placed an ohmmeter across the ground and conductor of
a fifty-ohm coax cable, you would always read 50 ohms. This is not the case, here's what
we're talking about: transmission lines have two important properties that depend on their
geometry, their inductance per unit length, and their capacitance per unit length. The
"characteristic impedance" of a system is calculated from the ratio of these two:
Z=sqrt(L'/C')
Where L' is the inductance per unit length and C' is the capacitance per unit length. Note that
higher inductance translates to higher impedance, and higher capacitance translates to lower
impedance. Notice also that the units of length don't matter, since they are "lost in the sauce".
The units of inductance and capacitance must be self-consistent, such as Pico-henries/foot
and Pico-farads/foot.
Let's start with coax cable. The inductance per unit length is mainly attributed to the
diameter of the centre conductor. Decrease this diameter (keeping everything else the same)
and you will increase the inductance. This also raises the characteristic impedance, referring
to the equation above. Filling the cable with a material of higher relative dielectric raises the
unit capacitance, and lowers the line impedance.
Another example: micro strip. Here unit capacitance and inductance are inexorably linked
together; widening the micro strip line decreases its inductance while it increases it
capacitance. Hence, wide lines are always lower in impedance than narrow lines for a given
substrate height. As with coax, the dielectric constant of the substrate has a big effect on
capacitance; using a higher dielectric substrate will yield a lower impedance line, all other
things being equal. So it is important not to mix up your Rogers Droid materials, once your
circuit is etched it is pretty hard to judge the dielectric constant from color and texture alone!
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 71
8.1Impedance matching
Impedance matching of source and load is important to get maximum power transfer. If you
have a 75 ohm load, you don't want to drive it with a 50 ohm source, because it is inefficient.
You can learn more about the simple math behind maximum power transfer by clicking here.
Simple impedance transformation can be done using quarter wave transformers. Click here to
go to our main page on quarter-wave tricks!
8.2 Dielectric constant and effective dielectric constant
"Dielectric constant" is another way to say "relative permittivity". Check out our separate
page on permittivity for more info on this subject. Although some people use the phrase
"relative dielectric constant", this is incorrect, akin to saying "deja vu again".
Remember back to your physics class, when you learned that dielectric constant is used to
calculate the value of a capacitor? The higher the dielectric constant, the higher the capacitor
value. For an ideal parallel plate capacitor, the capacitance is calculated by:
C=( 0x RxA)/D
where 0 is the permittivity of free space (thanks, Maarten!), R is the relative permittivity
(the dielectric constant) of the material between the plates, A is the area of the parallel plates,
and D is the distance they are separated. Technically for this expression to be 100% accurate,
the material surrounding the plates must be of the same relative dielectric constant R, but
this induces only a small error in the calculation under most circumstances. 0 is equal to
8.854x10-12 Farads per meter (you should commit this to memory). Most often it is the
dielectric constant R that is most important in microwaves.
For electromagnetic radiation, the permittivity of the medium that the wave is propagating in
is equal to R 0. In a vacuum or in dry air, R is equal to unity, and the signal travels at the
speed of light. All electromagnetic energy, from 60 Hertz power that your electric company
sells you, to signals that the latest Mars satellite returns to earth, travels really, really fast. In a
vacuum, the speed of light, denoted "c" in textbooks, is 2.998 x 1010 centimeters/second
(thanks, Jared!) , or 2.998 x 108 meters per second, or about 186,000 miles per second, which
puts the moon about 1.5 seconds away by radio.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 72
The dielectric constant of a material can be used to quantify how much a material "slows" an
electromagnetic signal. The velocity of the signal within any transmission line that is 100%
filled with a material of dielectric constant R is computed by:
v=c/sqrt( R)
So if your strip line or coax transmission line is fabricated on a material with dielectric
constant 2.2, the velocity of propagation is only 67% of the speed of light in free space.
Similarly, because wavelength is proportional to velocity, the length of a quarter-wave
transformer is also 67% of what it would be in free space. Thus one of the tricks of reducing
the size of microwave components is revealed; by using materials of higher dielectric
constant, distributed structures can be made smaller. One of the advantages of using GaAs for
microwave ICs (known in the industry as MMICs) is its dielectric constant of 12.9, which is
appreciably higher than ceramics such as alumina, and most soft substrates.
A very good rule of thumb is that electromagnetic radiation in free space travels about
one foot in one nanosecond; a more exact value is 0.983571 feet per nanosecond. This slows
to about 8 inches per nanosecond for coax cables filled with PTFE (almost all coax cables are
filled with PTFE, or a combination of PTFE and air.) For more information please see our
discussion of group delay.
This brings us to the subject of "effective dielectric constant". In transmission lines
realized in micro strip media, most of the electric fields are constrained within the substrate,
but a fraction of the total energy exists within the air above the board. The effective dielectric
constant takes this into account. The effective dielectric constant of a fifty-ohm transmission
line on ten mil alumina is a number somewhere around 7, which is less than the dielectric
constant of the substrate bulk material (9.8). Another example of an effective dielectric
constant is if you were to create a strip line circuit using two sheets of substrates with
different dielectric constants. To a first order, the effective dielectric constant would be the
average of the two materials' dielectric constants. A third example is coplanar waveguide
transmission lines with air above the substrate. Here the effective dielectric constant is very
nearly the average of the substrate dielectric constant and one (the dielectric constant of
air=1). Thus the effective dielectric constant of CPW circuits on GaAs ( R=12.9) is
approximately
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 73
8.3Lumped elements versus distributed elements
When the behaviour of a resistor, capacitor, or inductor can be fully described by a
simple linear equation, microwave engineers refer to it as a lumped element. For example, a
50-ohm resistor at low frequencies will obey Ohm's law (V=IxR). Put five volts across it and
it will draw 100 milliamps of current. "Lumped element hood" is restricted to components
that are operate at frequencies where they are physically much smaller than a quarter-
wavelength. For example, axial-leaded components perform well up to 10s of MHz, but at
one GHz, chances are that an axial-leaded resistor is closer to an open circuit, or a lousy
inductor, rather than an ideal resistor. This is why you will rarely be asked the resistor color
code as a microwave engineer!
At microwave frequencies, other factors must be considered. To accurately calculate the
behaviour of that same 50-ohm resistor, you need to consider its length, width, and thickness
of metal (due to the skin effect), and its proximity to the ground plane. This is when we must
consider it as a distributed element.
By designing really tiny parts, you can often consider them lumped elements, even at
microwave frequencies. You must keep the critical dimensions (such as length and width of a
thin-film resistor) small compared to an electrical quarter wavelength. For example, if you
are designing a 50 ohm micro strip load resistor at X-band, on an alumina substrate (dielectric
constant 9.8), a quarter wavelength is approximately 120 mils. You'd better keep both the
length and width of the resistor to less than 40 mils, or you else you have to spend some time
with a EDA simulation tool such as Agilent ADS or Eagleware Genesis evaluating the
performance. Where else but microwave engineering can you make a project out of designing
a stupid fifty-ohm resistor?!
At low frequencies, the metal that connects components together is treated as an ideal
connection, with no loss, no characteristic impedance, and no transmission phase angle.
When interconnects become an appreciable fraction of the signal wavelength, these
interconnections themselves must be treated as distributed elements or transmission lines. An
extreme example of the need to consider the distributed properties of transmission lines is
when we are dealing with a quarter-wavelength. At this electrical length (90 degrees), an
open circuit is transformed to a short circuit, and a short-circuit is transformed to an open
circuit! Think about this: a short-circuited 90 degree "stub" hanging in shunt off of a
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 74
transmission line will be invisible to signals propagating down the transmission line, while an
open circuited 90 degree stub shunting a transmission line will cause a short circuit and the
propagating signal will get hosed! A whole lot of microwave engineering exploits this
concept, so you'd better understand it.
One "classic" distributed element is the quarter-wave transformer (we've written an entire
chapter on this and other quarter wave tricks! The quarter wave transformer is used to shift
the impedance of a circuit by the following simple formula:
Z2=sqrt(Z0ZL)
where Z2 is the characteristic impedance of the transformer, ZL is the load impedance, and Z0
is the characteristic impedance of the system you are trying to maintain. Do you detect a
pattern? Most of the equations on this page use the square-root function... perhaps they put
that button on your Casio calculator for a reason!
8.4 VSWR and return loss
VSWR stands for voltage standing wave ratio. It is a measure of how well a network is
matched to it's intended characteristic impedance (Z0), which is almost always 50 ohms in
microwave engineering. Return loss is just another way to express the same thing. Both are
used in microwave engineering, that's just to keep you on your toes.
VSWR dates back to the days when a "standing wave meter" was an important piece of lab
equipment. Long before you could buy s network analyzer for measuring how well a part is
impedance matched, the standing wave meter was used by engineers to evaluate the same
problem. A small probe was inserted into a waveguide, the output of which was rectified,
producing a current or voltage proportional to the electric field with the waveguide. The
engineer would pull the probe longitudinally along the waveguide, in search of local maxima
and minima readings. These are due to the standing wave within the transmission line. The
ratio of the maximum to the minimum voltage recorded was known as the voltage standing
wave ratio (VSWR). To this day VSWR is often used to quantify how well a part is
impedance matched. Always expressed as a ratio to unity, a VSWR of 1.0:1 indicates
perfection (there is no standing wave). A VSWR of 2:1 means the maxima are twice the
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 75
voltage of the minima. A high VSWR such as 10:1 usually indicates you have a problem,
such as a near open or near short circuit.
Chapter 9
MICROWAVE MEASUREMENTS
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 76
9.1Bandwidth
Bandwidth is a measure of how much spectrum your microwave system can respond to.
Bandwidth is often given in megahertz or gigahertz, calculated from from a low frequency FL
to an high frequency FH, the bandwidth is given by (FU-FL). Bandwidth is expressed a number
of other ways, which we will define here:
Three-dB bandwidth: for a network that has a non-ideal frequency response (which includes
all physical networks), the three-dB bandwidth is where the transmission coefficient S21 falls
off from its highest peak by three dB. Similarly, you could describe a network by its two-dB
or one-dB bandwidths.
Percentage bandwidth: for a system that works from a low frequency FL to an high
frequency FH, the percentage bandwidth is given by 100%x(FH-FL)/FC. FC is the center
frequency, equal to (FH+FL)/2. Note that it is possible to have more than 100% bandwidth by
this definition; an amplifier that works from 100 MHz to 10 GHz has a bandwidth of 200%.
Instantaneous bandwidth: this is a measure of how wide a spectrum a system can respond
to, without any type tuning. Using the analogy of radio, the IF bandwidth in an American FM
receiver is about 200 kHz, which is necessary to pass the full spectrum of a broadcast FM
signal. The demodulator processes this bandwidth to obtain the approximately 18 kHz
baseband bandwidth. The "dispreading" effect of this processing results in the superior signal
to noise ratio enjoyed by FM transmission. (Thanks for the correction, Miles!)
Tuneable bandwidth: tuneable bandwidth is a measure of how wide a spectrum a system
can respond to with the user allowed to change settings such as local oscillator frequency. For
a receiver, the tuneable bandwidth is almost always more than the instantaneous bandwidth.
An AM radio has a tuneable bandwidth of 540 kHz to 1600 kHz, or over one MHz of
bandwidth. This is about 100X its instantaneous bandwidth.
What does octave bandwidth mean? It implies that the the upper frequency of operation is
double the lower frequency of operation, for example, an amplifier that works from 2 to 4
GHz has one octave bandwidth. The origin of the word octave goes back to music theory,
where an octave is an interval of eight notes in the major scale. For reference, the interval
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 77
from middle C to high C on a piano is an octave; high C is double the audio frequency of
middle C.
A device with an octave bandwidth always has 67% bandwidth (do the math for homework!)
9.2 Frequency conversion
A fundamental problem in electromagnetics is that for a signal to be radiated into free space,
an antenna must be on the order of 1/10 or more of a wavelength. Thus transmitting voice
without some type of upconversion would require a 30 kilometer antenna for a 10 kHz signal!
Thus, baseband signals need to ride on carrier waves, which are at RF and microwave
frequencies. Mixers are the devices that are used to convert from one frequency to another.
Upconversion means you are increasing the frequency of your signal, and downconversion
means you are decreasing it.
9.3 Harmonic frequencies
A harmonic frequency is 2X, 3X, 4X, etc. the frequency of a signal. Why is it called a
harmonic? Because in music, harmonic frequencies of 2X, 3X, 4X sound good together (they
are harmonious, like the Del Vikings). 2X and 4X frequencies are octaves, 3X is an octave
plus a perfect fifth.
A sub harmonic frequency is one that is 1/2, 1/3, 1/4 of a signal.
9.4 DECIBLES
This is simply the same logarithmic calculation but instead of comparing two power levels to
each other, you are comparing one power level to 1 mill watt. 10 dBm is the same at 10 mW,
20 dBm is the same as 100 mw, 30 dBm is the same as 1000 mw (or one watt).
How do you "think" in decibels compared to linear units? Just remember a few key
conversions and you will be all set to impress your friends with quick approximations of
some heavy multiplication and division (that is, if they are easily impressed). By the way, we
rounded these off so they will be easier to remember, if you need an exact answer, get a
calculator!
30 dB is an increase of 1000X in power
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 78
20 dB is an increase of 100X in power
dB is an increase of 10X in power
6 dB is an increase of 4X in power
3 dB is an increase of 2X in power
2 dB is an increase of 1.6X in power
1 dB is an increase of 1.25X in power
0 dB is no increase or decrease in power
-1 dB is a decrease of 20% in power
-2 dB is a decrease of 37% in power (roughly a decrease of 1/3)
-3 dB is a decrease of 50% in power
-6 dB is a decrease of 75% in power
-10 dB is a decrease of 90% in power
-20 dB is a decrease of 99% in power
-30 dB is a decrease of 99.9% in power
When you input a 5 milliwatt signal into a power amplifier that has 12 dB of gain, the output
is 80mW. You can easily do the math in your head. Break down the 12 dB into 6 dB + 6 dB,
and remember that each 6 dB increases power by 4X, so you have an increase of 16X ( equal
to 4x4). Sixteen times five is eighty.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 79
III
DIGITAL
COMMUNICATION
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 80
Chapter 1
BASICS OF DIGITAL COMMUNICATION
1.1 Introduction
In the simplest form, a transmission-reception system is a three-block system,
consisting of a) a transmitter, b) a transmission medium and c) a receiver. If we think of a
combination of the transmission device and reception device in the form of a ‘transceiver’
and if (as is usually the case) the transmission medium allows signal both ways, we are in a
position to think of a both-way (bi-directional) communication system. For ease of
description, we will discuss about a one-way transmission-reception system with the implicit
assumption that, once understood, the ideas can be utilized for developing / analyzing two-
way communication systems. So, our representative communication system, in a simple
form, again consists of three different entities, viz. a transmitter, a communication channel
and a receiver.
Fig 1.1
A digital communication system has several distinguishing features when compared with an
analog communication system. Both analog (such as voice signal) and digital signals (such as
data generated by computers) can be communicated over a digital transmission system. When
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 81
the signal is analog in nature, an equivalent discrete-time-discrete-amplitude representation is
possible after the initial processing of sampling and quantization. So, both a digital signal and
a quantized analog signal are of similar type, i.e. discrete-time-discrete-amplitude signals.
A key feature of a digital communication system is that a sense of ‘information’, with
appropriate unit of measure, is associated with such signals. This visualization, credited to
Claude E. Shannon, leads to several interesting schematic description of a digital
communication system. For example, consider Fig.1.1 which shows the signal source at the
transmission end as an equivalent ‘Information Source’ and the receiving user as an
‘Information sink’. The overall purpose of the digital communication system is ‘to collect
information from the source and carry out necessary electronic signal processing such that the
information can be delivered to the end user (information sink) with acceptable quality’. One
may take note of the compromising phrase ‘acceptable quality’ and wonder why a digital
transmission system should not deliver exactly the same information to the sink as accepted
from the source. A broad and general answer to such query at this point is: well, it depends on
the designer’s understanding of the ‘channel’ (Fig. 1.1) and how the designer can translate his
knowledge to design the electronic signal processing algorithms / techniques in the ’Encoder’
and ‘decoder’ blocks in Fig. 1.1. We hope to pick up a few basic yet good approaches to
acquire the above skills. However, pioneering work in the 1940-s and 1950-s have
established a bottom-line to the search for ‘a flawless (equivalently, ‘error-less’) digital
communication system’ bringing out several profound theorems (which now go in the name
of Information Theory) to establish that, while error-less transmission of information can
never be guaranteed, any other ‘acceptable quality’, arbitrarily close to error-less
transmission may be possible. This ‘possibility’ of almost error-less information transmission
has driven significant research over the last five decades in multiple related areas such as, a)
digital modulation schemes, b) error control techniques, c) optimum receiver design, d)
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 82
modelling and characterization of channel and so forth. As a result, varieties of digital
communication systems have been designed and put to use over the years and the overall
performance have improved significantly.
It is possible to expand our basic ‘three-entity’ description of a digital communication
system in multiple ways. For example, Fig. 1.1 shows a somewhat elaborate block diagram
explicitly showing the important processes of ‘modulation-demodulation’, ‘source coding-
decoding’ and ‘channel encoding – decoding’. A reader may have multiple queries relating to
this kind of abstraction. For example, when ‘information’ has to be sent over a large distance,
it is a common knowledge that the signal should be amplified in terms of power and then
launched into the physical transmission medium. Diagrams of the type in Figs. 1.1 and 1.2
have no explicit reference to such issues. However, the issue here is more of suitable
representation of a system for clarity rather than a module-by-module replication of an
operational digital communication system.
Fig 1.2
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 83
Chapter 2
PULSE CODE MODULATION
Pulse-code modulation (PCM)
PCM is a method used to digitally represent sampled analogy signals, which was invented
by Alec Reeves in 1937. It is the standard form for digital audio in computers and
various Blu-ray, Compact Disc and DVD formats, as well as other uses such as
digital telephone systems. A PCM stream is a digital representation of an analog signal, in
which the magnitude of the analogue signal is sampled regularly at uniform intervals, with
each sample being quantized to the nearest value within a range of digital steps.
PCM streams have two basic properties that determine their fidelity to the original analog
signal: the sampling rate, which is the number of times per second that samples are taken; and
the bit depth, which determines the number of possible digital values that each sample can
take.
Fig 2.1 PCM Block Diagram
2.1Modulation
In the diagram, fig 2.2 a sine wave (red curve) is sampled and quantized for pulse
code modulation. The sine wave is sampled at regular intervals, shown as ticks on the x-axis.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 84
For each sample, one of the available values (ticks on the y-axis) is chosen by some
algorithm. This produces a fully discrete representation of the input signal (shaded area) that
can be easily encoded as digital data for storage or manipulation. For the sine wave example
at right, we can verify that the quantized values at the sampling moments are 7, 9, 11, 12, 13,
14, 14, 15, 15, 15, 14, etc. Encoding these values as binary numbers would result in the
following set of nibbles: 0111, 1001, 1011, 1100, 1101, 1110, 1110, 1111, 1111, 1111, 1110,
etc. These digital values could then be further processed or analyzed by a purpose-
specific digital signal processor or general purpose DSP. Several Pulse Code Modulation
streams could also be multiplexed into a larger aggregate data stream, generally for
transmission of multiple streams over a single physical link. One technique is called time-
division multiplexing, or TDM, and is widely used, notably in the modern public telephone
system. Another technique is called Frequency-division multiplexing, where the signal is
assigned a frequency in a spectrum, and transmitted along with other signals inside that
spectrum. Currently, TDM is much more widely used than FDM because of its natural
compatibility with digital communication, and generally lower bandwidth requirements.
There are many ways to implement a real device that performs this task. In real systems, such
a device is commonly implemented on a single integrated that lacks only the clock necessary
for sampling, and is generally referred to as an ADC (Analog-to-Digital converter). These
devices will produce on their output a binary representation of the input whenever they are
triggered by a clock signal, which would then be read by a processor of some sort.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 85
Fig 2.2
Demodulation
To produce output from the sampled data, the procedure of modulation is applied in
reverse. After each sampling period has passed, the next value is read and a signal is shifted
to the new value. As a result of these transitions, the signal will have a significant amount of
high-frequency energy. To smooth out the signal and remove these
undesirable aliasing frequencies, the signal would be passed through analog filters that
suppress energy outside the expected frequency range (that is, greater than the Nyquist
frequency fs / 2). Some systems use digital filtering to remove some of the aliasing,
converting the signal from digital to analog at a higher sample rate such that the analog filter
required for anti-aliasing is much simpler. In some systems, no explicit filtering is done at all;
as it's impossible for any system to reproduce a signal with infinite bandwidth, inherent losses
in the system compensate for the artifacts — or the system simply does not require much
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 86
precision. Thesampling theorem suggests that practical PCM devices, provided a sampling
frequency that is sufficiently greater than that of the input signal, can operate without
introducing significant distortions within their designed frequency bands.
The electronics involved in producing an accurate analog signal from the discrete data are
similar to those used for generating the digital signal. These devices are DACs (digital-to-
analog converters), and operate similarly to ADCs. They produce on their output
a voltage or current (depending on type) that represents the value presented on their inputs.
This output would then generally be filtered and amplified for use.
2.2 Limitations
There are two sources of impairment implicit in any PCM system:
Choosing a discrete value near the analog signal for each sample leads to quantization
error, which swings between -q/2 and q/2. In the ideal case (with a fully linear ADC) it
is uniformly distributedover this interval, with zero mean and variance of q2/12.
Between samples no measurement of the signal is made; the sampling
theorem guarantees non-ambiguous representation and recovery of the signal only if it has
no energy at frequency fs/2 or higher (one half the sampling frequency, known as
the Nyquist frequency); higher frequencies will generally not be correctly represented or
recovered.
As samples are dependent on time, an accurate clock is required for accurate reproduction. If
either the encoding or decoding clock is not stable, its frequency drift will directly affect the
output quality of the device. A slight difference between the encoding and decoding clock
frequencies is not generally a major concern; a small constant error is not noticeable. Clock
error does become a major issue if the clock is not stable, however. A drifting clock, even
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 87
with a relatively small error, will cause very obvious distortions in audio and video signals,
for example.
Extra information: PCM data from a master with a clock frequency that can not be influenced
requires an exact clock at the decoding side to ensure that all the data is used in a continuous
stream without buffer underrun or buffer overflow. Any frequency difference will be audible
at the output since the number of samples per time interval can not be correct. The data speed
in a compact disk can be steered by means of a servo that controls the rotation speed of the
disk; here the output clock is the master clock. For all "external master" systems like DAB
the output stream must be decoded with a regenerated and exact synchronous clock. When
the wanted output sample rate differs from the incoming data stream clock then a sample rate
converter must be inserted in the chain to convert the samples to the new clock domain.
Digitization as part of the PCM process
In conventional PCM, the analog signal may be processed (e.g., by amplitude compression)
before being digitized. Once the signal is digitized, the PCM signal is usually subjected to
further processing (e.g., digital data compression).
PCM with linear quantization is known as Linear PCM (LPCM).[1]
Some forms of PCM combine signal processing with coding. Older versions of these systems
applied the processing in the analog domain as part of the A/D process; newer
implementations do so in the digital domain. These simple techniques have been largely
rendered obsolete by modern transform-based audio compression techniques.
DPCM encodes the PCM values as differences between the current and the predicted
value. An algorithm predicts the next sample based on the previous samples, and the
encoder stores only the difference between this prediction and the actual value. If the
prediction is reasonable, fewer bits can be used to represent the same information. For
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 88
audio, this type of encoding reduces the number of bits required per sample by about 25%
compared to PCM.
Adaptive DPCM (ADPCM) is a variant of DPCM that varies the size of the
quantization step, to allow further reduction of the required bandwidth for a given signal-
to-noise ratio.
Delta modulation is a form of DPCM which uses one bit per sample.
In telephony, a standard audio signal for a single phone call is encoded as 8,000 analog
samples per second, of 8 bits each, giving a 64 kbit/s digital signal known as DS0. The
default signal compression encoding on a DS0 is either μ-law (mu-law) PCM (North America
and Japan) or A-law PCM (Europe and most of the rest of the world). These are logarithmic
compression systems where a 12 or 13-bit linear PCM sample number is mapped into an 8-bit
value. This system is described by international standard G.711. An alternative proposal for
a floating point representation, with 5-bit mantissa and 3-bit radix, was abandoned.
Where circuit costs are high and loss of voice quality is acceptable, it sometimes makes sense
to compress the voice signal even further. An ADPCM algorithm is used to map a series of 8-
bit µ-law or A-law PCM samples into a series of 4-bit ADPCM samples. In this way, the
capacity of the line is doubled. The technique is detailed in the G.726 standard.
Later it was found that even further compression was possible and additional standards were
published. Some of these international standards describe systems and ideas which are
covered by privately owned patents and thus use of these standards requires payments to the
patent holders.
Some ADPCM techniques are used in Voice over IP communications.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 89
Chapter 3
DIGITAL MODULATION TECHNIQUES I
There are three major classes of digital modulation techniques used for transmission
of digitally represented data:
Amplitude-shift keying (ASK)
Frequency-shift keying (FSK)
Phase-shift keying (PSK)
All convey data by changing some aspect of a base signal, the carrier wave (usually
a sinusoid), in response to a data signal. In the case of PSK, the phase is changed to represent
the data signal. There are two fundamental ways of utilizing the phase of a signal in this way:
By viewing the phase itself as conveying the information, in which case
the demodulator must have a reference signal to compare the received signal's phase
against; or
By viewing the change in the phase as conveying information
— differential schemes, some of which do not need a reference carrier (to a certain
extent).
A convenient way to represent PSK schemes is on a constellation diagram. This shows the
points in the Argand plane where, in this context, the real and imaginary axes are termed the
in-phase and quadrature axes respectively due to their 90° separation. Such a representation
on perpendicular axes lends itself to straightforward implementation. The amplitude of each
point along the in-phase axis is used to modulate a cosine (or sine) wave and the amplitude
along the quadrature axis to modulate a sine (or cosine) wave.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 90
In PSK, the constellation points chosen are usually positioned with uniform angular spacing
around a circle. This gives maximum phase-separation between adjacent points and thus the
best immunity to corruption. They are positioned on a circle so that they can all be
transmitted with the same energy. In this way, the moduli of the complex numbers they
represent will be the same and thus so will the amplitudes needed for the cosine and sine
waves. Two common examples are "binary phase-shift keying" (BPSK) which uses two
phases, and "quadrature phase-shift keying" (QPSK) which uses four phases, although any
number of phases may be used. Since the data to be conveyed are usually binary, the PSK
scheme is usually designed with the number of constellation points being a powerof 2.
3.1 Amplitude-shift keying (ASK) is a form of modulation that represents digital data as
variations in the amplitude of a carrier wave.
The amplitude of an analog carrier signal varies in accordance with the bit stream
(modulating signal), keeping frequency and phase constant. The level of amplitude can be
used to represent binary logic 0s and 1s. We can think of a carrier signal as an ON or OFF
switch. In the modulated signal, logic 0 is represented by the absence of a carrier, thus giving
OFF/ON keying operation and hence the name given.
Like AM, ASK is also linear and sensitive to atmospheric noise, distortions, propagation
conditions on different routes in PSTN, etc. Both ASK modulation and demodulation
processes are relatively inexpensive. The ASK technique is also commonly used to
transmit digital data over optical fiber. For LED transmitters, binary 1 is represented by a
short pulse of light and binary 0 by the absence of light. Laser transmitters normally have a
fixed "bias" current that causes the device to emit a low light level. This low level represents
binary 0, while a higher-amplitude lightwave represents binary 1.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 91
3.2 Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing,
or modulating, the phase of a reference signal (the carrier wave).
Any digital modulation scheme uses a finite number of distinct signals to represent digital
data. PSK uses a finite number of phases, each assigned a unique pattern of binary digits.
Usually, each phase encodes an equal number of bits. Each pattern of bits forms
the symbol that is represented by the particular phase. The demodulator, which is designed
specifically for the symbol-set used by the modulator, determines the phase of the received
signal and maps it back to the symbol it represents, thus recovering the original data. This
requires the receiver to be able to compare the phase of the received signal to a reference
signal — such a system is termed coherent (and referred to as CPSK).
Alternatively, instead of using the bit patterns to set the phase of the wave, it can instead be
used to change it by a specified amount. The demodulator then determines the changes in the
phase of the received signal rather than the phase itself. Since this scheme depends on the
difference between successive phases, it is termed differential phase-shift keying (DPSK).
DPSK can be significantly simpler to implement than ordinary PSK since there is no need for
the demodulator to have a copy of the reference signal to determine the exact phase of the
received signal (it is a non-coherent scheme). In exchange, it produces more erroneous
demodulations. The exact requirements of the particular scenario under consideration
determine which scheme is used.
3.3 Differential Phase-shift keying (DPSK) is a digital modulation scheme that
conveys data by changing, or modulating, the phase of a reference signal (the carrier wave).
Any digital modulation scheme uses a finite number of distinct signals to represent digital
data. PSK uses a finite number of phases, each assigned a unique pattern of binary digits.
Usually, each phase encodes an equal number of bits. Each pattern of bits forms
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 92
the symbol that is represented by the particular phase. The demodulator, which is designed
specifically for the symbol-set used by the modulator, determines the phase of the received
signal and maps it back to the symbol it represents, thus recovering the original data. This
requires the receiver to be able to compare the phase of the received signal to a reference
signal — such a system is termed coherent (and referred to as CPSK).
Alternatively, instead of using the bit patterns to set the phase of the wave, it can instead be
used to change it by a specified amount. The demodulator then determines the changes in the
phase of the received signal rather than the phase itself. Since this scheme depends on the
difference between successive phases, it is termed differential phase-shift keying (DPSK).
DPSK can be significantly simpler to implement than ordinary PSK since there is no need for
the demodulator to have a copy of the reference signal to determine the exact phase of the
received signal (it is a non-coherent scheme). In exchange, it produces more erroneous
demodulations. The exact requirements of the particular scenario under consideration
determine which scheme is used.
3.4 BPSK(Binary Phase shift keying)
BPSK (also sometimes called PRK, Phase Reversal Keying, or 2PSK) is the simplest form of
phase shift keying (PSK). It uses two phases which are separated by 180° and so can also be
termed 2-PSK. It does not particularly matter exactly where the constellation points are
positioned, and in this figure they are shown on the real axis, at 0° and 180°. This modulation
is the most robust of all the PSKs since it takes the highest level of noise or distortion to
make the demodulatorreach an incorrect decision. It is, however, only able to modulate at 1
bit/symbol (as seen in the figure) and so is unsuitable for high data-rate applications when
bandwidth is limited.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 93
In the presence of an arbitrary phase-shift introduced by the communications channel, the
demodulator is unable to tell which constellation point is which. As a result, the data is
often differentially encoded prior to modulation.
3.5 QPSK
Sometimes this is known as quaternary PSK, quadriphase PSK, 4-PSK, or 4-QAM.
(Although the root concepts of QPSK and 4-QAM are different, the resulting modulated radio
waves are exactly the same.) QPSK uses four points on the constellation diagram, equispaced
around a circle. With four phases, QPSK can encode two bits per symbol, shown in the
diagram with gray coding to minimize the bit error rate (BER) — sometimes misperceived as
twice the BER of BPSK.
The mathematical analysis shows that QPSK can be used either to double the data rate
compared with a BPSK system while maintaining the same bandwidthof the signal, or
to maintain the data-rate of BPSK but halving the bandwidth needed. In this latter case, the
BER of QPSK is exactly the same as the BER of BPSK - and deciding differently is a
common confusion when considering or describing QPSK.
Given that radio communication channels are allocated by agencies such as the Federal
Communication Commission giving a prescribed (maximum) bandwidth, the advantage of
QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth
than BPSK does - at the same BER. The engineering penalty that is paid is that QPSK
transmitters and receivers are more complicated than the ones for BPSK. However, with
modern electronicstechnology, the penalty in cost is very moderate.
As with BPSK, there are phase ambiguity problems at the receiving end, and differentially
encoded QPSK is often used in practice.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 94
Fig 3.1 QPSK Transmitter
Fig 3.2 QPSK Reciever
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 95
3.6 Frequency Shift Keying - FSK
The two binary states, logic 0 (low) and 1 (high), are each represented by an analogue
waveform. Logic 0 is represented by a wave at a specific frequency, and logic 1 is
represented by a wave at a different frequency.
.
Fig 3.2 FSK Representation
With binary FSK, the centre or carrier frequency is shifted by the binary input data.
Thus the input and output rates of change are equal and therefore the bit rate and baud
rateequal.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 96
Chapter 4
DELTA MODULATION
Delta modulation (DM or Δ-modulation) is an analog-to-digital and digital-to-analog
signal conversion technique used for transmission of voice information where quality is not
of primary importance. DM is the simplest form of differential pulse-code
modulation (DPCM) where the difference between successive samples is encoded into n-bit
data streams. In delta modulation, the transmitted data is reduced to a 1-bit data stream.
Its main features are:
the analog signal is approximated with a series of segments
each segment of the approximated signal is compared to the original analog wave
to determine the increase or decrease in relative amplitude
the decision process for establishing the state of successive bits is determined by
this comparison
only the change of information is sent, that is, only an increase or decrease of the
signal amplitude from the previous sample is sent whereas a no-change condition
causes the modulated signal to remain at the same 0 or 1 state of the previous
sample.
To achieve high signal-to-noise ratio, delta modulation must use oversampling techniques,
that is, the analog signal is sampled at a rate several times higher than the Nyquist rate.
Derived forms of delta modulation are continuously variable slope delta modulation, delta-
sigma modulation, and differential modulation. The Differential Pulse Code Modulation is
the super set of DM. The block diagram of Delta modulation is given below in diagram 4.1
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 97
Fig 4.1 Block Diagram of Delta modulation
4.1Principle
Rather than quantizing the absolute value of the input analog waveform, delta
modulation quantizes the difference between the current and the previous step, as shown in
the block diagram in Fig. 4.1
The modulator is made by a quantizer which converts the difference between the
input signal and the average of the previous steps. In its simplest form, the quantizer can be
realized with a comparator referenced to 0 (two levels quantizer), whose output is 1 or 0 if the
input signal is positive or negative. It is also a bit-quantizer as it quantizes only a bit at a time.
The demodulator is simply an integrator (like the one in the feedback loop) whose output
rises or falls with each 1 or 0 received. The integrator itself constitutes a low-pass filter.
4.2 Adaptive delta modulation
Adaptive delta modulation (ADM) or continuously variable slope delta modulation (CVSD)
is a modification of DM in which the step size is not fixed. Rather, when several consecutive
bits have the same direction value, the encoder and decoder assume that slope overload is
occurring, and the step size becomes progressively larger. Otherwise, the step size becomes
gradually smaller over time. ADM reduces slope error,at the expense of increasing quantizing
error.This error can be reduced by using a low pass filter.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 98
Chapter 5
INFORMATION THEORY
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 99
Coding theory is one of the most important and direct applications of information theory. It
can be subdivided into source coding theory and channel codingtheory. Using a statistical
description for data, information theory quantifies the number of bits needed to describe the
data, which is the information entropy of the source.
Data compression (source coding): There are two formulations for the compression
problem:
1. lossless data compression : the data must be reconstructed exactly;
2. lossy data compression : allocates bits needed to reconstruct the data, within a
specified fidelity level measured by a distortion function. This subset of Information
theory is called rate–distortion theory.
Error-correcting codes (channel coding): While data compression removes as
much redundancy as possible, an error correcting code adds just the right kind of
redundancy (i.e., error correction) needed to transmit the data efficiently and faithfully
across a noisy channel.
This division of coding theory into compression and transmission is justified by the
information transmission theorems, or source–channel separation theorems that justify the
use of bits as the universal currency for information in many contexts. However, these
theorems only hold in the situation where one transmitting user wishes to communicate to
one receiving user. In scenarios with more than one transmitter (the multiple-access channel),
more than one receiver (the broadcast channel) or intermediary "helpers" (the relay channel),
or more general networks, compression followed by transmission may no longer be
optimal. Network information theory refers to these multi-agent communication models.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 100
5.1 Source theory
Any process that generates successive messages can be considered a source of information. A
memoryless source is one in which each message is an independent identically-distributed
random variable, whereas the properties of ergodicity and stationarity impose more general
constraints. All such sources are stochastic. These terms are well studied in their own right
outside information theory.
5.2 Information Rate
Information rate is the average entropy per symbol. For memory less sources, this is merely
the entropy of each symbol
5.3Channel Capacity
Communications over a channel—such as an Ethernet cable—is the primary motivation of
information theory. As anyone who's ever used a telephone (mobile or landline) knows,
however, such channels often fail to produce exact reconstruction of a signal; noise, periods
of silence, and other forms of signal corruption often degrade quality. How much information
can one hope to communicate over a noisy (or otherwise imperfect) channel?
Consider the communications process over a discrete channel. A simple model of the process
is shown below:in fig 5.1
Fig 5.1 Channel Capacity
Here X represents the space of messages transmitted, and Y the space of messages received
during a unit time over our channel. Let p(y | x) be the conditional probability distribution
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 101
function of Ygiven X. We will consider p(y | x) to be an inherent fixed property of our
communications channel (representing the nature of the noise of our channel). Then the joint
distribution of X and Y is completely determined by our channel and by our choice of f(x), the
marginal distribution of messages we choose to send over the channel. Under these
constraints, we would like to maximize the rate of information, or the signal, we can
communicate over the channel. The appropriate measure for this is the mutual information,
and this maximum mutual information is called the capacity and is given by:
Chapter 6
SHANNON – HARTLEY THEORM
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 102
In information theory, the Shannon–Hartley theorem (also known as Shannon's law)
is an application of the noisy channel coding theorem to the archetypal case of a continuous-
time analog communications channel subject to Gaussian noise. The theorem establishes
Shannon's channel capacity for such a communication link, a bound on the maximum amount
of error-free digital data (that is, information) that can be transmitted with a
specified bandwidth in the presence of the noise interference, assuming (a) the signal power
is bounded; (b)the Gaussian noise process is characterized by a known power or power
spectral density. The law is named after Claude Shannon and Ralph Hartley.
6.1Statement of the theorem
Considering all possible multi-level and multi-phase encoding techniques, the
Shannon–Hartley theorem states the channel capacity C, meaning the theoretical tightest
upper bound on the information rate (excluding error correcting codes) of clean (or arbitrarily
low bit error rate) data that can be sent with a given average signal power S through an analog
communication channel subject to additive white Gaussian noise of power N, is:
where
C is the channel capacity in bits per second;
B is the bandwidth of the channel in hertz (passband bandwidth in case of a
modulated signal);
S is the total received signal power over the bandwidth (in case of a modulated signal,
often denoted C, i.e. modulated carrier), measured in watt or volt2;
N is the total noise or interference power over the bandwidth, measured in watt or
volt2; and
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 103
S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the
communication signal to the Gaussian noise interference expressed as a linear power
ratio (not as logarithmic decibels).
6.2 Nyquist rate
In 1927, Nyquist determined that the number of independent pulses that could be put through
a telegraph channel per unit time is limited to twice the bandwidth of the channel. In symbols,
where fp is the pulse frequency (in pulses per second) and B is the bandwidth (in hertz). The
quantity 2B later came to be called the Nyquist rate, and transmitting at the limiting pulse
rate of 2B pulses per second as signalling at the Nyquist rate. Nyquist published his results in
1928 as part of his paper "Certain topics in Telegraph Transmission Theory."
6.3 Noisy channel coding theorem and capacity
Claude Shannon's development of information theory during World War II provided
the next big step in understanding how much information could be reliably communicated
through noisy channels. Building on Hartley's foundation, Shannon's noisy channel coding
theorem (1948) describes the maximum possible efficiency of error-correcting
methods versus levels of noise interference and data corruption.[5][6] The proof of the theorem
shows that a randomly constructed error correcting code is essentially as good as the best
possible code; the theorem is proved through the statistics of such random codes.
Shannon's theorem shows how to compute a channel capacity from a statistical description of
a channel, and establishes that given a noisy channel with capacity C and information
transmitted at a line rate R, then if
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 104
there exists a coding technique which allows the probability of error at the receiver to be
made arbitrarily small. This means that theoretically, it is possible to transmit information
nearly without error up to nearly a limit of C bits per second.
The converse is also important. If
the probability of error at the receiver increases without bound as the rate is increased. So no
useful information can be transmitted beyond the channel capacity. The theorem does not
address the rare situation in which rate and capacity are equal.
6.4 Shannon–Hartley theorem
The Shannon–Hartley theorem establishes what that channel capacity is for a finite-
bandwidth continuous-time channel subject to Gaussian noise. It connects Hartley's result
with Shannon's channel capacity theorem in a form that is equivalent to specifying the M in
Hartley's line rate formula in terms of a signal-to-noise ratio, but achieving reliability through
error-correction coding rather than through reliably distinguishable pulse levels.
If there were such a thing as an infinite-bandwidth, noise-free analog channel, one could
transmit unlimited amounts of error-free data over it per unit of time. Real channels,
however, are subject to limitations imposed by both finite bandwidth and nonzero noise.
So how do bandwidth and noise affect the rate at which information can be transmitted over
an analog channel?
Surprisingly, bandwidth limitations alone do not impose a cap on maximum information rate.
This is because it is still possible for the signal to take on an indefinitely large number of
different voltage levels on each symbol pulse, with each slightly different level being
assigned a different meaning or bit sequence. If we combine both noise and bandwidth
limitations, however, we do find there is a limit to the amount of information that can be
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 105
transferred by a signal of a bounded power, even when clever multi-level encoding
techniques are used.
In the channel considered by the Shannon-Hartley theorem, noise and signal are combined by
addition. That is, the receiver measures a signal that is equal to the sum of the signal
encoding the desired information and a continuous random variable that represents the noise.
This addition creates uncertainty as to the original signal's value. If the receiver has some
information about the random process that generates the noise, one can in principle recover
the information in the original signal by considering all possible states of the noise process. In
the case of the Shannon-Hartley theorem, the noise is assumed to be generated by a Gaussian
process with a known variance. Since the variance of a Gaussian process is equivalent to its
power, it is conventional to call this variance the noise power.
Such a channel is called the Additive White Gaussian Noise channel, because Gaussian noise
is added to the signal; "white" means equal amounts of noise at all frequencies within the
channel bandwidth. Such noise can arise both from random sources of energy and also from
coding and measurement error at the sender and receiver respectively. Since sums of
independent Gaussian random variables are themselves Gaussian random variables, this
conveniently simplifies analysis, if one assumes that such error sources are also Gaussian and
independent.
Chapter 7
Linear Block Codes
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 106
In coding theory, a linear code is an error-correcting code for which any linear
combination of codewords is another codeword of the code. Linear codes are traditionally
partitioned into block codes andconvolutional codes, although Turbo codes can be seen as a
hybrid of these two types[1]. Linear codes allow for more efficient encoding and decoding
algorithms than other codes (cf. syndrome decoding).
Linear codes are used in forward error correction and are applied in methods for transmitting
symbols (e.g., bits) on a communications channel so that, if errors occur in the
communication, some errors can be detected by the recipient of a message block. The "codes"
in a linear block code are blocks of symbols which are encoded using more symbols than the
original value to be sent. A linear code of length n transmits blocks containing n symbols. For
example, the "(7,4)" Hamming code is a linear binary code which represents 4-bit values each
using 7-bit values. In this way, the recipient can detect errors as severe as 2 bits per block.
[2] As there are 16 distinct 4-bit values expressed in binary, the size of the (7,4) Hamming
code is sixteen.
7.1 Formal definition
A linear code of length n and rank k is a linear subspace C with dimension k of
the vector space where is the finite field with q elements. Such a code with
parameter q is called a q-ary code (e.g., when q = 5, the code is a 5-ary code). If q = 2
or q = 3, the code is described as a binary code, or a ternary code respectively.
7.2Generator matrix and parity check matrix
Because the linear code could be considered as a linear subspace C of (and therefore a
codeword is a vector in this linear subspace), any codeword could be represented as a
linear combination of a set of basis vectors such
that
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 107
,
where is the message and is thegenerator matrix.
On another hand, for any linear subspace , there is a dimension n − k null
space such that . The basis vectors of the null
space form another matrix such that , where is
called parity check matrix.
7.2Hamming codes
As the first class of linear codes developed for error correction purpose, famous Hamming
codes has been widely used in digital communication systems. For any positive
integer , there exists a [2r − 1,2r − r − 1,3]2 Hamming code. Since d = 3, this Hamming
code can correct 1-bit error.
Example : The linear block code with the following generator matrix and parity check matrix
is a [7,4,3]2 Hamming code.
:
7.3 Hadamard codes
Hadamard code is a [2r,r,2r – 1]2 linear code and is capable of correcting many errors.
Hadamard code could be constructed column by column : the ith column is the bits of the
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 108
binary representation of integer I, as shown in the following example. Hadamard code has
minimum distance 2r – 1 and therefore can correct 2r – 2 – 1 errors.
Example : The linear block code with the following generator matrix is a [8,3,4]2 Hadamard
code: .
Hadamard code is a special case of Reed-Muller code If we take the first column (the all-zero
column) out from , we get [7,3,4]2 simplex code, which is the dual code of Hamming
code. Let be the parity check matrix of C, then the code generated by is called
the dual code of C.
Reference
1. W.C.Y. Lee, Mobile cellular communications, Tata McGraw Hill, 2nd
Edition, 2006.
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 109
2. Gordon L.stuber, Principles Of Mobile Communications, Springer
international 2nd edition,2007
3. Samuel Y.Liao - Microwave Devices And Circuits, 3rd Edition 1994.
4. Herbert J.Reich, J.G Skalnik, P.F.Ordung And H.L. Krauss – Microwave
Principles, CBS Publishers And Distributors, New Delhi,2004
5. Simon Haykin, John Wiley – Digital Communication,2005
6. H.Tabu And D.Schilling – Principles Of Communication Systems, THM,
2003
MAHAVEER INSTITUTE OF SCIENCE AND TECHNOLOGY Page 110