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CT0004NI – L.03 – Telecommunications Systems - pp 1/50 Telecommunications Telecommunications Systems Systems Saroj Regmi Saroj Regmi Lecture 03 Lecture 03 CT0004NI CT0004NI Principles of Comms Systems Principles of Comms Systems By: Dr. N. Ioannides (Feb. 2010)

CT0004NI – L.03 – Telecommunications Systems - pp 1/50 Telecommunications Systems Saroj Regmi Lecture 03 CT0004NI Principles of Comms Systems By: Dr. N

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Page 1: CT0004NI – L.03 – Telecommunications Systems - pp 1/50 Telecommunications Systems Saroj Regmi Lecture 03 CT0004NI Principles of Comms Systems By: Dr. N

CT0004NI – L.03 – Telecommunications Systems - pp 1/50

Telecommunications Telecommunications SystemsSystems

Saroj RegmiSaroj Regmi

Lecture 03Lecture 03

CT0004NICT0004NIPrinciples of Comms SystemsPrinciples of Comms Systems

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 2/50

Last Lecture: 02Last Lecture: 02Analogue & Digital SignalsAnalogue & Digital Signals

• Signals.

• Voltage, Resistance and Current.

• Open and Closed Circuits.

• Analogue vs Digital Signals.

• Analogue Signal Characteristics.

• Digital Signal Characteristics.

• Digital Binary Codes.

• Data Coding Noise Immunity.

• Morse and ASCII Codes.

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 3/50

Today’s Lecture: 03Today’s Lecture: 03Telecommunications SystemsTelecommunications Systems

• Systems and System Specifics,

• Telecommunications Systems,

• Fundamental Blocks of Communication,

• Bandwidth in Analogue & Digital Systems,

• Transmission Media,

• Attenuation,

• The Decibel,

• Noise in Analogue & Digital Systems,

• Multiplexing Techniques (FDM, WDM & TDM),

• Modulation (AM & FM).

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 4/50

• A system is a process which receives an input, processes it and gives an output.

• All systems regardless of their nature may be represented as a black box.

SystemsSystems

InputInput OutputOutput

Black Box

By: Dr. N. Ioannides (Feb. 2010)

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• Any system consists of three main parts:

Input: the initial trigger,

Output: the result,

Processing: the relationship between the output and input.

• Systems are differentiated by:

the form that the input(s) and output(s) take,

the nature of their processing on the input(s) in order to generate the output(s).

• System classification is based on the nature of its input(s) and output(s).

Examples: ‘Hi-Fi System’, ‘PC System’, ‘Banking System’, ‘Economic System’, ‘Analogue System’, ‘Digital System’, Telecommunications System, and many more.

System SpecificsSystem Specifics

By: Dr. N. Ioannides (Feb. 2010)

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• In electronics, system inputs and outputs are referred to as Signals.

• Signals can be either Analogue or Digital:

Analogue Signals: Current or Voltage variations in a wire (or light in a fibre) whose amplitude changes continuously.

The fundamental components of Analogue Systems are Resistors, Capacitors, Inductors, Diodes, etc.

Digital Signals: Current or Voltage variations in a wire (or light in a fibre) that have only two distinct levels. These are either HIGH (5V or 1) or LOW (0V or 0).

The fundamental components of Digital Systems are Digital Logic Gates.

Electronic SignalsElectronic Signals

By: Dr. N. Ioannides (Feb. 2010)

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• Electronic Systems are classified based on the type of signals that they can accept as input and the type of signals they can produce as output.

Analogue System: When the input and output signals of a system are both analogue.

Digital System: When the input and output signals of a system are both digital.

• Larger Systems, however, are made out of both analogue and digital sub-systems where the corresponding type of signal is used to produce an overall output, or outputs.

• A clear understanding of the various processing elements of each class of system is extremely important.

Electronic SystemsElectronic Systems

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 8/50

• Telecommunications is the systems and techniques used to

transmit and receive information via any kind of transmission

media, like:

Electrical - (using wires and cables),

Optical- (using optical fibres),

Free Space - (using electromagnetic waves).

Definition of TelecommunicationsDefinition of Telecommunications

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 9/50

• All communication systems comprise six fundamental blocks:

Information Signal: All forms of intelligence to be transmitted from one point to another: sound, images, data, etc.

Input Transducer or Source: Converts the input information signal into electrical form.

Transmitter: Converts the electrical signal from the transducer into a form suitable for transmission to the required destination and transmits.

Transmission Medium: Guided or Unguided.

Receiver: Accepts signals from the medium and presents them in electrical form to the output transducer.

Output Transducer or Destination: Converts the received signal into its original form or into a form required by the recipient.

Fundamental Blocks of CommunicationFundamental Blocks of Communication

By: Dr. N. Ioannides (Feb. 2010)

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Bandwidth (BW) in Analogue Bandwidth (BW) in Analogue SystemsSystems

• The range of frequencies that a telecommunications system must be able to support.

• The range of frequencies that can be carried across a given transmission medium.

• Examples of Bandwidth:

Telephone Voice Channel: BW = 3 kHz,

Hi-Fi Music: BW = 15 kHz,

CD Stereo Player: BW = 22 kHz,

AM Radio Station: BW = 10 kHz

FM Radio Station: BW = 200 kHz,

TV Channel on CATV: BW = 6 MHz.

By: Dr. N. Ioannides (Feb. 2010)

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Bandwidth (BW) in Digital SignalsBandwidth (BW) in Digital Signals

• Binary Digital Systems:

Bit Rate: The number of bits transmitted per second.

bpsRateBit 1

• Other (Non-Binary) Digital Systems:

Baud Rate: The number of symbols transmitted per second.

Each symbol is composed of more than 1 bit.

By: Dr. N. Ioannides (Feb. 2010)

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Transmission MediaTransmission Media

• Media are used to enable the propagation of signals (information) from transmitter (source) to receiver (destination).

All media suffer from problems (such as attenuation and noise) to some degree.

• It is important to understand the characteristics of each media type in order to be able to select the most appropriate type of medium for the application at hand.

• There are two broad classes of Transmission Media:

Conducted or Guided or Wired.

Radiated or Unguided or Wireless.

By: Dr. N. Ioannides (Feb. 2010)

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• Conducted (Guided) Media: The electrical information signals are conveyed by transmission lines.

Wires, Twisted pair, Cables of bundled twisted pairs (2 up to 2000 pairs),

Coaxial cables,

Fibre optic cable.

• Radiated (Unguided) Media: Antennas radiate electromagnetic waves into free-space (air or space).

Radio frequency,

Microwave frequency, Satellite (microwave frequency),

Infrared.

Transmission Media ClassesTransmission Media Classes

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 14/50

Distance of TransmissionDistance of Transmission

• Acoustic means:

Very short distance of communication (tens of meters),

Very poor data rates (bps).

• Electromagnetic means:

Much longer distance of communication (tens of kilometres),

Very good data rates (hundreds of Mbps).

• State of the art electromagnetic (microwave) communications:

Very long distances (thousands of kilometres),

Very good data rates (Gbps).

• State of the art optical fibre communications:

Long distances (hundreds of kilometres)

Extremely good data rates (tens of Tbps).

By: Dr. N. Ioannides (Feb. 2010)

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• Signals attenuate (weaken) as they travel away from the source.

They arrive with less strength than when they started.

• All transmission media weaken, or attenuate, the strength of the signal.

Signal Attenuation (Signal Attenuation (αα))

By: Dr. N. Ioannides (Feb. 2010)

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• Not all of the transmitted signal arrives at the receiver since all transmission media weaken, or attenuate, the strength of the signal.

• As the signal travels down the medium:

Some part is dispersed as heat,

Some part is absorbed by the transmission medium.

• The longer the distance that the signal travels, the greater will be the attenuation that the signal suffers.

If the medium is too long, no signal will arrive at the end, or the signal will be so small that it cannot be used (buried in noise).

• Attenuation is measured in decibels (dB).

Signal Attenuation (Signal Attenuation (αα) (…2)) (…2)

By: Dr. N. Ioannides (Feb. 2010)

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Decibels (dB)Decibels (dB)

• The decibel is a means of logarithmically expressing the ratio between two signal levels.

It is a way of stating the amount of gain or loss of power, voltage or current that occurs in a circuit or system.

• Decibels are expressed as:

Amplification: Gain or + (only one is used, never both).

Weakening: Loss or – (only one is used, never both).

• The resultant numbers will be based on the ratio of a final value (signal strength) to another reference value (input signal or noise value).

By: Dr. N. Ioannides (Feb. 2010)

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Decibel (dB) EquationsDecibel (dB) Equations

)()(log20 dBB

AdB

)()(log10 dBD

CdB

• The equations used to measure decibel (dB) quantities depend on the quantity being measured.

If Voltage or Current signal strength is measured:

Where: A = Output Voltage or Current signal strength

B = Input or Noise Voltage or Current signal strength

If Power signal strength is being measured:

Where: C = Output Power signal strength

D = Input or Noise Power signal strengthBy: Dr. N. Ioannides (Feb. 2010)

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Power vs Voltage Decibel (dB) ValuesPower vs Voltage Decibel (dB) Values

dB dB Gain/LossGain/Loss

Gain Power Gain Power RatioRatio

Loss Power Loss Power RatioRatio

Voltage Voltage GainGain

Voltage Voltage LossLoss

0 1.00 1.00 1.00 1.001 1.26 0.79 1.12 0.892 1.58 0.63 1.26 0.793 2.00 0.50 1.41 0.714 2.51 0.40 1.58 0.635 3.16 0.32 1.78 0.566 3.98 0.25 2.00 0.507 5.01 0.20 2.24 0.458 6.31 0.16 2.51 0.409 7.94 0.13 2.82 0.35

10 10.00 0.10 3.16 0.3220 100.00 0.01 10.00 0.1030 1000.00 0.001 31.62 0.0340 10000.00 0.0001 100.00 0.0150 100000.00 0.00001 316.23 0.00360 1000000.00 0.000001 1000.00 0.001

By: Dr. N. Ioannides (Feb. 2010)

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)()(log20 dBV

V

in

out

)()(log20 dBI

I

in

out

Vout = Signal amplitude at outputin Volts (Voltage)

Vin = Signal amplitude at inputin Volts (Voltage)

Iout = Signal amplitude at outputin Amps (Current)

Iin = Signal amplitude at inputin Amps (Current)

• Attenuation is measured in decibels (dB).

Attenuation (Attenuation (αα) Measurements) Measurements

If half the signal voltage or current is lost by the time it reaches the destination then it has suffered a 6 dB loss.

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 21/50

)()(log10 dBP

P

in

out Pout = Signal amplitude at output

in Watts (Power)

Pin = Signal amplitude at inputin Watts (Power)

If half the signal power is lost by the time it reaches the destination then it has suffered a 3 dB loss.

Attenuation (Attenuation (αα) Measurements (…2)) Measurements (…2)

By: Dr. N. Ioannides (Feb. 2010)

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Noise in Analogue SignalsNoise in Analogue Signals

• Noise: A usually interferential random frequency current or voltage signal extending over a considerable frequency spectrum and having no useful purpose.

• Noise Level: The amplitude of ambient electrical noise generated in or outside an electronic circuit.

• Types of Noise:

White Noise,

Pink Noise,

Shot Noise,

Thermal Noise.

• Signal to Noise Ratio: The ratio of signal amplitude to noise amplitude.

Measured in decibels (dB).By: Dr. N. Ioannides (Feb. 2010)

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• If the transmitting electronics are not properly shielded then signals of other frequency could be superimposed on the signal of interest. This will also be a form of noise.

• Noise added to the analogue signal can greatly affect the accuracy of the information.

• Noise is always unwanted and efforts are always taken to minimise its effect but limiting the level of noise is not an easy or inexpensive process.

Noise in Analogue Signals (…2)Noise in Analogue Signals (…2)

By: Dr. N. Ioannides (Feb. 2010)

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Signal to Noise Ratio (SNR)Signal to Noise Ratio (SNR)

• Signal to Noise Ratio: The ratio of signal amplitude to noise amplitude.

)()(log20 dBV

V

N

S

N

S

)()(log10 dBP

P

N

S

N

S

VS = Signal amplitude in Volts (Voltage)

VN = Noise amplitude in Volts (Voltage)

PS = Signal amplitude in Watts (Power)

PN = Noise amplitude in Watts (Power)

)()(log20 dBI

I

N

S

N

S IS = Signal amplitude in Amperes (Current)

IN = Noise amplitude in Amperes (Current)

By: Dr. N. Ioannides (Feb. 2010)

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Bit Error Rate (BER)Bit Error Rate (BER)

• BER relates to the number of possible erroneous bits received.

• Shows the quality of a particular communications link.

dTransmitteBitsofNumberTotal

ReceivedBitsErroneousofNumberBER

• BER values for a digital transmission system are normally specified and depend on the Signal-to-Noise Ratio (SNR) of the detection system.

• A typical BER requirements is in the region of 10-9.

• BER is an error probability defined as:

By: Dr. N. Ioannides (Feb. 2010)

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Bit Error Rate (BER): ExampleBit Error Rate (BER): Example

• Example: What is the BER of a transmission consisting of 5Gb if the erroneous bits received are 3?

109

1060000000006.0105

3

BER

By: Dr. N. Ioannides (Feb. 2010)

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MultiplexingMultiplexing

• The Multiplexer combines the different signals allocating each signal a self-contained channel or slot thus preventing the signals from interfering with each other during transmission.

• The Multiplexed signals are then transmitted along a common transmission medium (conducted or radiated).

• The Demultiplexer separates the received multiplexed signals out of the multiplexed package.

• The process of sharing and simultaneously using a common transmission medium to transmit several independent channels of information.

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 28/50

• Frequency Division Multiplexing (FDM),

• Wavelength Division Multiplexing (WDM),

• Time Division Multiplexing (TDM).

Multiplexing TechniquesMultiplexing Techniques

By: Dr. N. Ioannides (Feb. 2010)

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• When the available bandwidth of the system is divided up into non-overlapping frequency slots with each modulated carrier confined to its own slot.

Guard Bands

Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. n

FrequencyAvailable Bandwidth

Ch. …

The slots are separated by guard bands to allow for filtering the individual channels in practical multiplexer / demultiplexer circuits.

Frequency Division Multiplexing (FDM)Frequency Division Multiplexing (FDM)

By: Dr. N. Ioannides (Feb. 2010)

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• The various channels:

Occupy their own frequency range within the allocated bandwidth,

Are separated by guard bands to avoid crosstalk.

FDM SpectrumFDM Spectrum

By: Dr. N. Ioannides (Feb. 2010)

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Wavelength Division Multiplexing (WDM)Wavelength Division Multiplexing (WDM)

• Allows many separate channels of data to be carried by a different colour of light in a single fibre optic cable thus increasing the bandwidth considerably.

23 4 5 6

• Multiple beams of light at different frequency,

• Each colour of light (wavelength) carries separate data channel,

• Carried by optical fibre,

• WDM is a form of FDM – same general architecture.

By: Dr. N. Ioannides (Feb. 2010)

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Time Division Multiplexing (TDM)Time Division Multiplexing (TDM)

• When the transmission time is divided into time slots and only one signal occupying the common medium during its allocated slot time.

• Extensively used for:

multi-channel digital signal transmission of data,

pulse code modulation transmission of speech (PCM telephony).By: Dr. N. Ioannides (Feb.

2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 33/50

Guard Times

Ch

. …

Ch

. 1

Ch

. 2

TimeFrame 1

Ch

. 3

Ch

. n

Ch

. 1

Ch

. 2

Ch

. 3

Ch

. …

Ch

. n

Ch

. 1

Ch

. 2

Ch

. 3

Ch

. …

Ch

. n

Frame 2 Frame n

TDM (…2)TDM (…2)

• Each signal channel uses the time space on a round-robin basis, and it is only transmitted in its allocated time slot in successive frames.

• A single transmission may utilise the whole available bandwidth.

By: Dr. N. Ioannides (Feb. 2010)

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Sinusoidal Carrier ModulationSinusoidal Carrier Modulation

• The process by which the signal which is to be transmitted (modulating or information signal) modifies a property of another sinusoidal signal of higher frequency.

• The two signals are:

Carrier Wave: The higher frequency sinusoidal signal.

Modulating Signal: The lower frequency signal, i.e. the information to be transmitted.

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 35/50

Modulator Demodulator

Modulatedcarrier wave

Carrier wave

Modulatingsignal

Recoveredmodulatingsignal

• The carrier wave and the modulating signal are combined together using a modulator.

• Demodulation: The process by which the modulating signal is recovered.

The listener adjusts the frequency of reception of his / hers receiver to be the same as that of the carrier wave which carries the signal which the listener would like to receive.

Sinusoidal Carrier Modulation (…2)Sinusoidal Carrier Modulation (…2)

By: Dr. N. Ioannides (Feb. 2010)

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Modulation (Review)Modulation (Review)

• Modulation allocates each station its own carrier of specified frequency upon which the information is impressed.

• Enables the selection and separation of the many hundreds of transmissions that could easily be present through multiplexing in a conducted or radiated transmission medium.

• Without modulation only one transmitting station could operate in a given area.

• By tuning a receiver to the carrier frequency of the required station this particular station is selected and all others are rejected.

• Modulation enables the choice of high frequency carriers which decrease the size of the antenna required to a practical size for both transmission and reception.

• Certain types of modulation also minimise the effects of interference and noise thus offering a better sound quality, i.e. FM.

By: Dr. N. Ioannides (Feb. 2010)

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• The allocation of carrier frequencies is a process administered by governments in full compliance with international agreements.

• The International Telecommunications Union (ITU) administers carrier frequency allocation licenses helped by information gathered at periodic Regional and Worldwide Administrative Radio Conferences (RARC and WARC).

• Operating licences are provided to potential users but they usually include restrictions as to the permissible radiated power, type of modulation and sometimes the hours of operation of a station.

Carrier Frequency AllocationCarrier Frequency Allocationfor One-Way Radio Service (Broadcasting)for One-Way Radio Service (Broadcasting)

By: Dr. N. Ioannides (Feb. 2010)

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CT0004NI – L.03 – Telecommunications Systems - pp 38/50

Analogue Radio Frequency RangesAnalogue Radio Frequency Ranges

Broadcasting

Frequency Range

Bandwidth Channels

AM 535 - 1605 kHz 10 kHz 107

FM 88 - 108 MHz 200 kHz 100

By: Dr. N. Ioannides (Feb. 2010)

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Amplitude Modulation (AM)Amplitude Modulation (AM)

• In AM the amplitude of the carrier wave is increased or decreased in direct relation to the instantaneous amplitude of the modulating signal.

By: Dr. N. Ioannides (Feb. 2010)

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• AM results in the outline, or envelope, of the carrier taking the shape of the modulating signal on both its positive and negative peaks.

• The AM process superimposes the signal on a higher frequency carrier thus lifting the signal information content to a higher frequency range suitable for efficient transmission at a desired carrier frequency.

• AM translates the information signal and places it on either side of the carrier frequency thus creating the upper and lower sideband frequencies.

• When both upper and lower sideband frequencies are transmitted the process is called double sideband AM (DSB-AM).

AM (…2)AM (…2)

By: Dr. N. Ioannides (Feb. 2010)

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Frequency Spectrum ofFrequency Spectrum ofthe Frequencies Involved in AMthe Frequencies Involved in AM

• The bandwidth of the AM carrier wave can be found from:

)Hz(f2)ff()ff(BW mmcmc Where:

fm: the modulating signal frequency.fc: the carrier signal frequency.

By: Dr. N. Ioannides (Feb. 2010)

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Frequency Spectrum for AM Voice TransmissionFrequency Spectrum for AM Voice Transmission

• The range of frequencies (bandwidth) needed to transmit voice is between 300 Hz and 3400 Hz.

• The bandwidth (BW) involved is:

kHz8.6Hz800,6400,32)400,3f()400,3f(BW cc • In multi-channel telephony where several hundred telephone

channels may be transmitted over the same cable, only one sideband per channel is used thus halving the bandwidth to 4 kHz (SSB-AM).By: Dr. N. Ioannides (Feb.

2010)

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Frequency Modulation (FM)Frequency Modulation (FM)

• In FM the frequency of the carrier wave is varied in sympathy with the amplitude of the modulating signal.

ff f ff f

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FM (…2)FM (…2)

• In frequency modulation the amplitude of the carrier wave is held constant and the information signal is impressed on the carrier by changing its frequency.

• The variation of the frequency of the carrier wave depends on the signal strength of the modulating signal.

• The frequency of the carrier wave remains constant when no modulating wave is applied.

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• The bandwidth of a frequency modulated communications system will depend on:

the minimum and maximum frequencies which the carrier wave is arranged to vary to (frequency deviation, fd),

the bandwidth of the modulating signal.

• The FM bandwidth can approximately be found by Carson’s Rule: )()(2

maxmaxHzffBW mdFM

BWFM: bandwidth of the FM communications system,

fdmax: peak frequency deviation from carrier unmodulated frequency,

fmmax: bandwidth of modulating signal.

Frequency Modulation BandwidthFrequency Modulation Bandwidth

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Comparison Between AM and FMComparison Between AM and FM

• AM can transmit longer distances than FM.

• AM requires less bandwidth than FM.

• AM is cheaper to implement than FM.

• FM offers far superior quality of sound than AM.

• FM has far superior immunity against noise and interferencethan AM.

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SummarySummary

• Systems and System Specifics,

• Telecommunications Systems,

• Fundamental Blocks of Communication,

• Bandwidth in Analogue & Digital Systems,

• Transmission Media,

• Attenuation,

• The Decibel,

• Noise in Analogue & Digital Systems,

• Multiplexing Techniques (FDM, WDM & TDM),

• Modulation (AM & FM).

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1. Calculate the ratio in dBs for the following and determine whether the resultant signal was amplified or attenuated:

(a) Pin = 10 W; Pout = 100 W (b) Pin = 20 W; Pout = 40 W

(c) Pin = 1 W; Pout = 10 mW (d) Pin = 10 mW; Pout = 500 μW

(e) Vin = 2 V;Vout = 6 V (f) Vin = 5 V; Vout = 2.5 V

(g) Vin = 1 μV; Vout = 10 mV (h) Iin = 7 A; Iout = 14 A

(i) Iin = 7 A; Iout = 3.5 A (j) Iin = 1 mA; Iout = 1 nA

• What is the attenuation that a voltage signal has suffered if it started as 6 V and reached the end of the cable as 2 V?

• What is the attenuation that a power signal has suffered if it started as 15 W and reached the end of the cable as 7 W?

• What is the signal to noise ratio of a communications system if the signal is 5 V and the noise is 5 mV (5 x 10-3 V)?

• What is the signal to noise ratio of a communications system if the signal is 5 W and the noise is 5 mW (5 x 10-3 W)?

Tutorial QuestionsTutorial Questions

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Tutorial Questions (…2)Tutorial Questions (…2)

6. What is the BER of a transmission consisting of 157 Gb if the erroneous bits received are:

a. 5, b. 9, c. 11, d. 13, e. 20, f. 28.

7. What is the BER of a transmission if the erroneous bits received are 15 for the total transmissions shown below:

a. 15 kbps, b. 150 kbps, c. 1.5 Mbps, d. 15 Mbps,

e. 22 kbps, f. 350 Mbps g. 1 Tbps h. 150 bps

8. What would the bandwidth of an AM communications system be if the modulating signal had a frequency range of:

a. 100 Hz < fm < 10725 Hz b. 150 Hz < fm < 12000 Hz

c. 300 Hz < fm < 3400 Hz d. 20 Hz < fm < 20000 Hz

e. 5000 Hz < fm < 15 kHz f. 275 < fm < 12 kHz

g. 10 kHz < fm < 10500 Hz h. 1 MHz < fm < 1275 kHz

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9. Estimate, using Carson’s rule, the channel bandwidth for FM transmission of sound limited to the baseband range 0 - 5 kHz, at 50 MHz and where the rated system deviation is 30 kHz.

10. What would the required bandwidth of an FM communications system be if the peak frequency deviation of the modulated carrier wave was 75kHz and the bandwidth of the modulating signal was 15 kHz?

11. A digital transmission lasts for 15 minutes and 27 seconds. The transmission (bit) rate was 56.6 kbps. Find the BER if the erroneous bits received are:

a. 2, b. 7, c. 19, d. 131, e. 210, f. 528.

12. A communications system uses frequency division multiplexing. Each channel occupies 4 kHz and a guard band of 1 kHz is employed between adjacent channels to protect from crosstalk. How many channels can be accommodated if the total bandwidth of the communications system is:

a. 1500 kHz, b. 12 MHz, c. 7.5 MHz, d. 50 kHz.

Tutorial Questions (…3)Tutorial Questions (…3)

By: Dr. N. Ioannides (Feb. 2010)