CT1037NCT1037NIntroduction to CommunicationsIntroduction to Communications

Analogue Modulation & Multiplexing

Er. Saroj Sharan Regmi

Lectures 03 & 04

Last Lecture: 02Last Lecture: 02Analogue Signal CharacteristicsAnalogue Signal Characteristics

• Signal Overview and Definitions.

• Voltage, Resistance, Current & Power.

• Characteristics of Sinusoidal Waveforms.

• Electro-Magnetic Spectrum.

• Signal Attenuation.

• Power Budget.

• Noise in Analogue Signals and Types of Noise.

• Periodic Waveforms.

• Bandwidth.

Today’s Lectures: 03 & 04Today’s Lectures: 03 & 04Analogue Multiplexing & ModulationAnalogue Multiplexing & Modulation

• Issues on Communication.

• Problems Affecting Communication.

• Antenna dipole lengths.

• Sinusoidal Carrier Modulation.

• Amplitude Modulation & Demodulation.

• Frequency Modulation & Demodulation.

• Multiplexing in Frequency, Wavelength or Time Division.

CommunicationCommunication

• The transmission of signals / information from a transmitter to a receiver.

• BUT:

Not a process which can easily be put to practice.

Various problems affect the transmission of these signals calling for alternative methods of transmission.

• SOLUTIONS:

Multiplexing:

FDM, WDM, TDM.

Modulation: AM, FM, PAM, PCM, PWM, etc.

Problems AffectingProblems Affectingthe Transmission of Signalsthe Transmission of Signals

• Sharing of Common Transmission Medium:

If all sources of signals were transmitting at the same time in the audible frequency range (20 Hz - 20 kHz) then all the listeners would receive all these transmitted signals simultaneously.

• Distance of transmission:

Acoustical power (sound) cannot travel long distances.

• Antenna Dipole Size:

The size of the antenna dipole required to transmit or receive information is inversely proportional to the wavelength of the signal transmitted.

Solutions to the Problems AffectingSolutions to the Problems Affectingthe Transmission of Signalsthe Transmission of Signals

• Sharing of Common Transmission Medium:

Transmit at different frequencies.

• Distance of transmission:

Transmit using Electromagnetic (EM) waves.

Radio frequency energy travels greater distances when compared to the distances travelled by the same amount of energy but as an acoustical power (sound).

• Antenna Dipole Size:

Use practical sizes of antennas.

• Only possible if:

Modulation and Multiplexing techniques are used.

where: v: the velocity of the wave in free space,

f: frequency of interest,

½: relates to one half wavelength,

0.95: average adjustment value of the calculated length.

AntennasAntennas

Dipole

Reflector

Directors

Antenna Size ( Dipole) =0 .95×ν

2× f(m)

• Are used to pick up the received signal or radiate a transmitted signal.

• Example: A Yagi-Uda array:

• Antenna (dipole) sizes for transmission at various frequencies:

FrequencyFrequency Antenna Size (m)Antenna Size (m)

100 Hz 100 Hz 1,425,000

1,000 Hz 1 kHz 142,500

10,000 Hz 10 kHz 14,250

100,000 Hz 100 kHz 1,425

1,000,000 Hz 1 MHz 142.5

10,000,000 Hz 10 MHz 14.25

100,000,000 Hz 100 MHz 1.425

Example on AntennasExample on Antennas

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).

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.

• A sinusoidal carrier wave can be modulated by the modulating signal in three ways.

Consider the signal s(t) in the following equation which is modelled as a cosine function:

• The amplitude of the carrier wave can be varied in sympathy with the modulating signal (Amplitude Modulation - AM).

• The frequency of the carrier wave can be varied in sympathy with the modulating signal (Frequency Modulation - FM)

• The phase of the carrier wave can be varied in sympathy with the modulating signal (Phase Modulation - PM) – Not really used nowadays.

s ( t ) = A c × cos [ 2πf ( t )+ φ ( t ) ]Ac:amplitude of the carrier

wave,f: frequency of the carrier

wave,t: time, : phase of the carrier wave.

φ

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.

• There are three parameters of a sinusoid (carrier) wave that can be varied in sympathy with the amplitude of the modulating (information) signal:

Types of Sinusoidal ModulationTypes of Sinusoidal Modulation

Amplitude: Amplitude Modulation (AM)

Frequency: Frequency Modulation (FM)

Phase: Phase Modulation (PM)

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.

Broadcasti

ng

Frequency

RangeBandwidth Channels

AM 535 - 1605 kHz 10 kHz 107

FM 88 - 108 MHz 200 kHz 100

• 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)

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.

• 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).

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

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

BW = ( f c + f m )− ( f c − f m ) = 2f m ( H z )

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

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:

BW = ( f c +3, 400 )−( f c− 3, 400 ) = 2 × 3, 400 = 6,800 H z = 6 . 8 kH z

• 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).

Depth of Modulation, Depth of Modulation, mm, in AM, in AM

• Depth of modulation, m, in AM is the degree by which the signal modulates the carrier in the modulator at the transmitter and is quantified as:

m =Am

Ac

Where: Am is the peak deviation of AM carrier about its unmodulated value,

Ac is the peak amplitude of unmodulated carrier.

Overmodulated AM WaveOvermodulated AM Wave

• For successful recovery of the signal at the receiver, m must always be less than 1 (m < 1) otherwise distortion will occur:

Analysis of Amplitude Modulation (AM)Analysis of Amplitude Modulation (AM)

• Let the modulating signal be:υ m = A m sin ω m t

Where:ω m = 2πf m

f m = signal frequency

υ c = A c sin ω c t ω c = 2πf c

f c = carrier frequency

• The Amplitude Modulated signal is then represented as:

υ AM = ( A c + A m sin ω m t ) sin ω c t =

• Let the carrier signal be:

m =Am

Ac

since:

= A c ( 1+ m sin ω m t ) sin ω c t . . . . . eq . 1

= Ac (1+Am

Ac

sin ωm t )sin ωc t =

• Expanding eq. 1:υ AM = A c sin ω c t + mA c sin ω m t sin ω c t

• And using the trigonometric identity:

sin X sin Y =12[ cos( X −Y )−cos( X +Y ) ]

• Then:

υ AM = Acsin ωc t+mAc

2cos (ωc−ωm) t−

mAc

2cos( ωc+ωm) t . . .. . eq . 2

LowerSidebandFrequency

(fc – fm)

CarrierFrequency

(fc)

UpperSidebandFrequency

(fc + fm)

CarrierAmplitude

LSB-AMAmplitude

USB-AMAmplitude

Power in the AM Wave & SidebandsPower in the AM Wave & Sidebands

• The total power in the AM wave is the sum of the carrier power and power contained in the sideband components.

• Since the power in a sinusoidal signal is proportional to the square of its amplitude, the total power (PT) in the AM wave is proportional to:

PT ∝ Ac2+(

mAc

2)2+(

mAc

2)2 = A

c2(1+ m2

2)

• The useful power, PSB, is the power in the sideband as the carrier itself carries no information, therefore:

P SB ∝ (mAc

2)2+(

mAc

2)2 = A

c2m2

2

• And the ratio of the useful to total power is:

PSB

PT

=

m2

2

(1+m2

2)= m2

2+m2

• The maximum useful power occurs when the depth of modulation is:

m = 1

m cannot exceed 1 otherwise distortion will occur.

PSB

PT

= m2

2+m2= 1

3

• The maximum value of the ratio of the useful to total power is:

35

AM DemodulationAM Demodulation

• Demodulation enables the recovering of the original information.

• Consider an AM information signal of 5 kHz modulating a Carrier of 35 kHz:

(a) Generating the AM Signal,

(b) The AM signal in time domain,

(c) The “envelope”,

(d) One sided frequency spectrum of the AM signal (frequency domain).

AM Demodulation (…2)AM Demodulation (…2)

• Simplest demodulating Circuit: Peak-Amplitude Detector or Rectifier. The diode contacts when vin > v0

(the diode cut-in voltage: 0.2 V for Germanium).

The result is simply the positive peaks of the input AM signal.

The AM modulated Carrier Wave:

AM Demodulation (…3)AM Demodulation (…3)

• If a capacitor is added to the rectifier then filtering is provided and also the average value of the demodulated signal is increased thus increasing the efficiency of the demodulator.

The capacitor charges up to the positive peak of the carrier while the diode is conducting and discharges while the diode is not conducting.

AM Demodulation (…4)AM Demodulation (…4)

• The values of R and C at the output of the AM rectifier must be chosen to optimise the demodulation process:

If the capacitor is too large, it will not be able to discharge fast enough for v0 to follow the fast variations of the AM envelope.

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

Frequency Modulation (FM)Frequency Modulation (FM)

• 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 maximum frequency deviation of the carrier is fd.

When the amplitude of the modulating signal increases the frequency of the carrier wave (fc) also increases reaching a maximum of fc + fd at the positive signal peak amplitude.

When the amplitude of the modulating signal decreases the frequency of the carrier wave (fc) also decreases reaching a minimum of fc - fd at the negative signal peak amplitude.

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

Analysis of Frequency Modulation (FM)Analysis of Frequency Modulation (FM)

fc - fd

fc + fd

ModulatingVoltage

Amplitude(Vm)

Frequency

fc

+ Vmax

- Vmax

• The characteristics of an FM modulator:

Where: fc = unmodulated carrier frequency.fd = frequency deviation (system maximum).Vmax = peak value of modulating signal (before distortion).

• The instantaneous frequency of the FM wave output from a modulator:

f i = f c+ kv mWhere: fi = Instantaneous frequency.

k = constant.vm = modulated signal voltage.fc = unmodulated carrier frequency.

• The maximum amplitude of modulating signal allowable before distortion occurs due to non-linearity is limited to +/- Vmax and the corresponding frequency deviation is:

f d max= kvmax so k =

f dmax

v max

Hz /V

• The modulating index, M, is: M =f d max

vmax

• Rated System Deviation is the specified maximum permitted frequency deviation for an FM system.

• The frequency spectrum of an FM wave is considerably more complex than in AM:

Amplitudeof sidebandcomponents

fc

fc+fdfc-fd

fm

Frequency

FM Bandwidth

• During the FM modulation process pairs of sidebands are generated thus making the overall bandwidth required considerably greater than in AM:

f c ± f m , f c ± 2f m , f c± 3f m , f c± 4f m , . . . . . .

• 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: BW FM = 2 ( f d max

+ f mmax) ( Hz )

where: BWFM: bandwidth of the FM communications system,fdmax:peak frequency deviation from carrier unmodulated

frequency,fmmax: bandwidth of modulating signal.

Aim:

• To provide an output signal whose amplitude is linearly proportional to the instantaneous frequency of the input waveform.

FM DemodulationFM Demodulation

• The process of converting a frequency modulated signal back to the original modulating (information) signal.

Procedure:

• Band Pass Filtering,

• Voltage Limiting,

• Low Pass Filtering,

• Offset voltage decoupling,

• Demodulating,

• Regenerating (if digital).

i. A band pass filter is used to eliminate all the noise beyond the signal band of the received FM signal.

At the FM ReceiverAt the FM Receiver

+Vmmax

-Vmmax

• Upon reception of the FM signal the following takes place:

The received signal now looks like this:

iii. A low-pass filter eliminates the higher frequency components from these pulses to obtain a signal which very closely resembles the transmitted FM signal:

ii. A voltage limiter restricts the signal amplitude to the range -Vmmax to +Vmmax. The output is a series of nearly rectangular pulses:+Vmmax

-Vmmax

+Vmmax

-Vmmax

iv. A decoupling capacitor removes any dc offset voltage that may be present.

fc - fd

fc + fd

DemodulatedVoltage

Amplitude(Vm)

Frequency

fc

+ Vmax

- Vmax

FM DemodulationFM Demodulation

• The characteristic curve of a frequency to voltage converter of an FM demodulator:

• Once the added noise has been removed FM demodulation takes place.

• In order to demodulate an FM signal the frequency variations of the frequency modulated carrier wave must be converted into voltage variations.

FM Demodulation (Review)FM Demodulation (Review)

• FM Demodulation: The process of converting a frequency modulated signal back to the original modulating (information) signal.

• Aiming to provide an output signal whose amplitude is linearly proportional to the instantaneous frequency of the input waveform.

• The FM demodulation process starts after the received signal has been:

Band pass filtered to exclude unwanted frequencies,

Voltage limited to remove noise and nonlinear effects,

Low pass filtered to remove the high frequency component of the pulses which resulted from the voltage limiting,

Offset voltage decoupling to remove any dc voltage present,

Demodulation usually with a phase locked loop or zero crossing detection. Other methods also exist.

Regenerating of the signal (if digital) avoiding bias distortion.

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 since it has far superior immunity against noise and interference than AM.

For the same transmitted power FM can offer an improvement of 800 times that of AM in signal-to-noise power ratios.

In FM the signal information is contained in the frequency variation of the carrier therefore noise and interference which affect the carrier envelope can be largely eliminated at the receiver.

For this purpose a limiter circuit is used which when the received signal passes through it the amplitude variations of the signal are removed before demodulation.

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.

• Frequency Division Multiplexing (FDM),

• Wavelength Division Multiplexing (WDM),

• Time Division Multiplexing (TDM).

Multiplexing TechniquesMultiplexing Techniques

• 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)

FDM TransmissionFDM Transmission

• The various channels are:

Allocated their own modulated carrier,

Combined to form the “Composite Baseband Modulating Signal”,

Transmitted as the FDM signal.

• The various channels:

Occupy their own frequency range within the allocated bandwidth,

Are separated by guard bands to avoid crosstalk.

FDM Spectrum of theFDM Spectrum of theComposite Baseband Modulating SignalComposite Baseband Modulating Signal

FDM ReceptionFDM Reception

• At the receiver:

The Composite Baseband Modulating Signal is inputted into bandpass filters which separate each channel,

Each channel is then demodulated,

The result is the original transmitted information signal.

FDM Example 1FDM Example 1

FDM Example 2FDM Example 2

• A voice channel occupies a bandwidth of 4 KHz. Combine three voice channels into a link with a bandwidth of 12 kHz, from 20 to 32 kHz. Show the configuration in frequency domain without using guard bands.

FDM in Analogue Carrier SystemsFDM in Analogue Carrier Systems

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.

WDM EvolutionWDM Evolution

• 1997 Bell Labs:

100 beams (channels),

Each at 10 Gbps,

100 beams * 10 Gbps = 1 Tbps.

• Commercial systems of 160 channels of 10 Gbps now available.

• Lab Systems (Alcatel):

256 beams (channels),

Each at 39.8 Gbps,

256 beams * 39.8 Gbps = 10.1 Tbps,

Over 100km.

1 1

Mu

ltiplexer

Dem

ultip

lexer

n

n

Fibre Fibre

Optical Amplifier

Routing Node

• Number of sources generating laser beams at different frequencies,

• WDM is achieved using optical multiplexers and demultiplexers.

Multiplexer consolidates sources for transmission over single fibre,

Demultiplexer separates channels at the destination.

• Optical amplifiers amplify all wavelengths,

Positioned typically tens of km apart.

WDM OperationWDM Operation

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).

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.

TDM SynchronisationTDM Synchronisation

• Necessary to prevent input and output from getting out of step:

TDM Synchronisation (…2)TDM Synchronisation (…2)

• Added Digit Framing: An extra channel supplies an alternating bit (101010...) to each frame to indicate the slot / frame alignment.

• Framing Search Mode: if synchronization is lost, successive frames are looked at to find the pattern again.

SummarySummary

• Overviewed issues on Communication.

• Identified Problems Affecting Communication.

• Antenna dipole lengths.

• Sinusoidal Carrier Modulation.

• Amplitude Modulation & Demodulation.

• Frequency Modulation & Demodulation.

• Multiplexing in Frequency, Wavelength or Time Division.