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Dar es Salaam institute of Technology (DIT)

ETU 07123

Introduction to Communication System

Ally, J

jumannea@gmail.com

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Analogue Modulation

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Introduction to Modulation Definitions

Analog modulation

Both the message signal and the transmitted signal are analog signals

Two classes: amplitude modulation, angle modulation

Three signals:

Message signal: the information signal to be modulated and transmitted

Carrier signal c(t) : high frequency sinusoidal signal

Modulated signal: the signal to be transmitted, or the signal obtained after modulation

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Modulation It is the process of facilitating the transfer of

information over a medium.

This is done by changing one or more the parameters of a signal including power, frequency, phase and amplitude depending on the requirement of the transmission system.

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Baseband, Passband

Baseband: refers to the signals and systems before modulation, which have frequencies/bandwidth much lower than the carrier frequency

Passband: refers to the signals and systems after (including) modulation, which have frequencies/bandwidth around the carrier frequency

Baseband signal: is usually the message signal

Passband signal: is usually the modulated signal, or transmitted signal

Baseband and Passband signals

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Baseband and Bandpass Signals Baseband signal is the original signal having the original

frequencies when delivered by transmitters.

In Baseband communication, signals are transmitted without modulation.

Bandpass signal is a signal which is modulated by one of the modulation schemes.

Demodulation is the process of extracting the baseband message from the carrier so that it may be processed and interpreted by the intended receiver

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Message signal m(t) modifies: Amplitude: AM linear modulation Phase: PM Frequency: FM Example Compare signal waveforms

( )A t

( ) ( )f t d t dtNon-linear modulation)(t

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Concept of Modulation

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Checkpoints for studying each modulation

Modulated signal (time-domain)

Spectrum (frequency-domain)

Parameters: bandwidth, power, etc

Modulator and demodulator (Principles, block diagrams or circuits)

Major properties (advantages/disadvantages over other modulations)

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List of modulation methods we will learn

Amplitude modulation methods and applications1. AM (amplitude modulation): AM radio, short wave

radio broadcast, 2. DSBSC (double sideband suppressed carrier AM):

data modem, Color TV’s color signals 3. SSB (single sideband AM): telephone4. VSB (vestigial sideband AM): TV picture signal

Angle modulation methods and applications1. FM (frequency modulation): FM radio broadcast, TV

sound signal, analog cellular phone2. PM (phase modulation): not widely used, except in

digital communication systems (but that is different)

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Amplitude Modulation (AM) AM (conventional amplitude modulation)

Amplitude Modulation (AM) is the one which the amplitude of a sinusoidal carrier is varied in accordance with an incoming message signal

Modulated signal Carrier: Message signal: m(t) AM modulated signal

where ka, is a constant called the amplitude

sensitivity of the modulator responsible forthe generation of the modulated signal s(t).

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Time-Domain descriptionThe standard form of an AM wave is defined by

The amplitude of the time function multiplying is called the envelope of AM wave s(t).

The envelope of s(t) has essentially the same shape as the baseband signal m(t) provided that two requirements are satisfied:

1. The amplitude of is always less than unity, that is, for all t 2. The carrier frequency fc, is much greater than the highest frequency

component W (message bandwidth) of the message signal m(t), that is

(a) Baseband signal m(t) (b) AM wave for (c) AM wave for

tf c2cos

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Frequency-Domain descriptionThe Fourier transform of the AM wave s(t) is given by

(a) Spectrum of baseband signal

(b) Spectrum of AM wave

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Generation of AM Waves Multipliers difficult to build in hardware AM waves typically generated using a nonlinear device to obtain the

desired multiplication Square law modulator sums carrier c(t) and information m(t) signals,

then squares them using a nonlinear device. Unwanted terms are filtered out with a bandpass filter.

Switched modulation sums c(t) and m(t) then passes sum through a switch, which approximately multiplies it by a periodic square wave. This generates the desired signal plus extra terms that are filtered out.

m(t)

+

Accos(2fct+

Squareor Switch BPF

s(t)

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Modulation IndexThe degree of modulation is an important parameter and is known as the modulation index. It is the ratio of the peak amplitude of the modulating signal, Am to the peak amplitude of the carrier signal, Ac

(a) Under Modulation (ka < 1)

(b) Ideal Modulation (ka = 1)

(c) Over Modulation (ka > 1)

c

ma A

Ak

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Over Modulation http://www.williamson-labs.com/480_am.htm

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Detection of AM waves There are two devices for the detection of AM waves, namely, the

square-law detector and the envelope detector

Square law detector, squares signal and then passes it through a LPF Residual distortion proportional to m2(t) Non-coherent (carrier phase not needed in RX) Envelope detection simple alternative method

+ Square-law devices

Square-law devicesBPF LPFm(t)

tfA cc 2cos

S(t) m’(t)

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Explanation

Diode D1 cut the negativeportion of AM signal s(t)

When signal after D1 is positive,C is charged.When signal after D2 is 0,C is discharged.

Overall effect: y(t) remains approximatelyas the envelope of s(t)

m(t) can be detected from y(t)using capacitor to remove d.c.1.

Very important: this isEnvelope Detector.

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Bandwidth of AM signal BT = 2W

AM signal’s bandwidth is twice message bandwidth

This is also transmitted signal bandwidth, or required minimum channel bandwidth Bc

Negative frequency contents of m(t) becomes visible in positive frequency

Upper sideband (USB):

Lower sideband (LSB):

Transmission power: PT = PM + Pcarrier

= PUSB + PLSB + Pcarrier

Wfff cc

cc ffWf

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AM Power Distribution In any electrical circuit, the power dissipated is

equal to the voltage squared divided by the resistance.

Mathematically, power in an unmodulated carrier:

The upper and lower sideband powers is given by:

The total power in AM wave is equal to:

RAP c

c 2

2

482

2/ 2222ccc

lsbusbP

RA

RAPP

21

244

2222 c

cc

ccclsbusbct PPPPPPPPPP

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AM – Modulation EfficiencyDefinition : The modulation efficiency is the percentage of the total power of the modulated signal that conveys information.

Only “Sideband Components” – Convey information

Modulation Efficiency:

1001 2

2

tm

tmE

Voltage Spectrum of the AM signal:

Translated version of message signal

ccccc ffMffffMffA

fS 2

)(

Carrier line spectral component

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Major Properties of AM Advantages

Simplicity in implementation, especially in receiver and transmitter The major reason that AM was the first & most popular

broadcasting methods during early days Disadvantages

Waste power and bandwidth Carrier components wastes a major portion power, but

carrier does not have message information Both USB and LSB are transmitted, which carry the same

message information

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Ways for AM improvement

To enhance power efficiency Reduce/remove carrier: DSB-SC Remove one/partial sideband: SSB, VSB

To enhance bandwidth efficiency Remove one/partial sideband: SSB, VSB Multiplex two message signals together: QAM

Cost for the improvement More expensive implementation The simple envelope detector is no longer applicable

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Double-Sideband Suppressed-carrier (DSB-SC) In the standard form of Amplitude Modulation (AM), the carrier wave

c(t) is completely independent of the message signal m(t), which means that the transmission of the carrier wave represents a waste of power.

To overcome this shortcoming , we may suppress the carrier component from the modulated wave, resulting in double-sideband suppressed carrier (DSB-SC) modulation.

Thus, by suppressing the carrier, we obtain a modulated wave that is proportional to the product of the carrier wave and the message signal.

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Time-Domain Description The standard form of a DSB-SC wave is defined by

This modulated wave undergoes a phase reversal whenever the message signal m(t) crosses zero, as illustrated in figure below

(a) Baseband signal (b) DSB-SC modulated wave

tmtcts

tmtfAts cc 2cos

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The Fourier transform of the DSB-SC wave s(t) is given by

(a) Spectrum of message signal

(b) Spectrum of DSB-SC modulated wave

Frequency-Domain Description

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Generation of DSB-SC Waves A DSB-SC modulated wave consists simply of the product of the

message signal and the carrier wave. A device achieving this requirement is called a Product Modulator.

Remove inefficient constant term

Modulated signal is

Can also use ring modulator: diodes and inductors

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Coherent Detection of DSB-SC Modulated Wave The baseband signal m(t) can be uniquely recovered from a DSB-

SC wave s(t) by first multiplying s(t) with a locally generated sinusoidal wave and then low-pass filtering the product

It is assumed that the local oscillator output is exactly coherent or synchronized, in both frequency and phase, with the carrier wave c(t) used in the product modulator to generate s(t).

This method of demodulation is known as coherent detection or synchronous detection.

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Coherent Detection of DSB-SC Modulated Wave-2 We find that the product modulator output is:

The first term represents a DSB-SC modulated signal with a carrier frequency 2fc, whereas the second term is proportional to the baseband signal m(t).

the first term is removed by the low-pass filter, this requirement is satisfied by choosing fc > W. At the filter output we then obtain a

signal given by

The demodulated signal is therefore proportional to m(t) when the phase error is a constant.

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Coherent Detection of DSB-SC Modulated Wave-3 The amplitude of this demodulated signal is maximum when and it is minimum (zero) when

As long as the phase error is constant, the detector provides an undistorted version of the original baseband signal m(t).

In practice, however, we usually find that the phase error varies randomly with time, due to random variations in the communication channel. The result is that at the detector output, the multiplying factor also varies randomly with time, which is obviously undesirable.

Therefore, provision must be made in the system to maintain the local oscillator in the receiver in perfect synchronism, in both frequency and phase, with the carrier wave used to generate the DSB-SC modulated signal in the transmitter.

The resulting system complexity is the price that must be paid for suppressing the carrier wave to save transmitter power.

cos

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Costas Loop (DSB-SC Demodulator)Goal: Maintain

-90o

Phase-shifter

Product Modulator

Product Modulator

VoltageControlled Oscillator

Low-passfilter

Low-passfilter

Phasediscriminator

tmtfA cc 2cos

tfc2cos

tfc2sin

tmsin21

tmcos21

I-channel

Q-channel

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Costas Loop One method of obtaining a practical synchronous receiver system, suitable

for demodulating DSB-SC waves, is to use the Costas loop.

This receiver consists of two coherent detectors supplied with the same input signal, namely, the incoming DSB-SC wave Accos(2πfct)m(t), but with individual local oscillator signals that are in phase quadrature with respect to each other.

The frequency of the local oscillator is adjusted to be the same as the carrier frequency fc, which is assumed known a priori.

The detector in the upper path is referred to as the in-phase coherent detector or I-channel, and that in the lower path is referred to as the quadrature-phase coherent detector or Q-channel.

These two detectors are coupled together to form a negative feedback system designed in such a way as to maintain the local oscillator synchronous with the carrier wave.

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Double Side Band Suppressed CarrierPower in a AM signal is given by

21

21 2222 tmAAts cc

Discrete carrier power Sideband power

Discrete carrier power can be eliminated (Suppressing carrier )if m(t) is assumed to have a zero DC level

Then ttmAts cc cos)()(

Spectrum

ccc ffMffMAfS

2)(

Since no power is wasted in carrier the efficiency is

Power

21 222 tmAts c

%1001002

2

tm

tmE

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Noise in AM Receivers

Power in s(t) is 0.5Ac2Pm

Power in n(t) is N0B

SNR=Pm/Pn= Ac2Pm/(2N0B)= Ps/(N0B) (SNR at the receiver input)

Power in m(t) is 0.25Ac2Pm (half the power in s(t))

Power in n(t) is 0.5N0B (PSD 0.25N0 over BW 2B)

SNR=Pm´/Pn´= Ac2Pm/(2N0B)= Ps/(N0B) (SNR at the receiver output)

ProductModulato

r

m´(t)+ n´(t)

Accos(2fct+

s(t)=Accos(2fct+m(t) +

n(t)LPF1

White Gaussian noise (AWGN)

-B B

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Single-SideBand (SSB) Modulation Standard AM and DSB-SC Modulation are wasteful of

bandwidth because they both require a transmission bandwidth equal to twice message the message bandwidth.

This means that insofar as the transmission of information is concerned, only one sideband is necessary, and no information is lost.

Thus the channel needs to provide only the same bandwidth as the message signal, a conclusion that is intuitively satisfying.

When only one sideband is transmitted, the modulation is referred to as single-sideband modulation

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Single Sideband Modulation(2) Only transmits upper or lower sideband of AM and DSBSC The transmitted signal can be written in terms m(t) and the

Hilbert Transform of m(t) Use same demodulator as DSBSC SSB has half the SNR of DSBSC for half the transmit

power: no SNR gain SSB can introduce significant distortion at DC where the

sidebands meet: not good for TV signals

USB LSBM(f)

0 fc-fcB-B

USB

LSB)]2sin()()2cos()([

2)( tftmtftmAts chc

c

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Baseband Representation of Modulated Signals

Baseband signal representation is a compact way to represent passband signals.

All passband signals at carrier frequency fc can be written as s(t) = sI(t) cos(2fct) + sQ(t) sin(2fct).

sI(t) is called the in-phase signal component; sQ(t) is called the quadrature signal component.

The sine and cosine are orthogonal signals, can be used to separate out the in-phase and quadrature components from s(t).

We define as the baseband signal representation. Then which is a compact way to represent and analyze passband signals.

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Generating of SSB modulated wave by phase discrimination method

The phase discrimination method of generating an SSB modulated wave involves two separate simultaneous modulation processes and subsequent combination of the resulting modulation products.

The system uses two product modulators, I and Q, supplied with carrier waves in phase quadrature to each other.

The incoming baseband signal m(t) is applied to product modulator I, producing a modulated DSBSC wave that contains reference phase sidebands symmetrically spaced about carrier frequency fc.

The hilbert transform mh(t) of m(t) is applied to product modulator Q, producing DSBSC modulated wave that containssideband having identical amplitude spectra to those of modulator I, but with phase spectra such that vector addition or subtraction of the two modulator outputs results in cancellation of one setof sidebands and reinforcement of the other set.

The use of plus sign yields SSB wave with only the upper sideband, whereas the use of minus sign yields SSB wave with only upper sideband.

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Block diagram for generating of SSB modulated wave by phase discrimination method

-90o

Phase-shifter

I

Q

Oscillator

In-phase path

Quadrature path

Wide-band

-90o

Phase-shifter

tfA cc 2cos

tfA cc 2sin

ModulatingWave m(t)

Hilbert transform m~(t)

+

+-

SSB wave

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Demodulation of SSB wave To recover the baseband signal m(t) from the SSB wave s(t), we

have to shift the spectrum by the amounts so as to convert the transmitted sideband back into the baseband signal.

This can be accomplished using coherent detection, which involves applying the SSB wave s(t), together with locally generated carrier , assumed to be of unit amplitude for convenience, to a product modulator and then low-pass filtering the modulator output.

cf

tfc2cos

,

Product Modulator

Low-pass filter

SSB waves(t)

tfc2cos

v(t) vo(t)

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Demodulation of SSB wave (2) The product modulator output is given by

The first term is the desired message signal. The second term represents an unwanted components in the product modulator output that is removed by low-pass filtering.

The detection of SSB modulated waves assume perfect synchronization between the local carrier and that in the transmitter both in frequency and phase. The effect of a phase error Ф in the locally generated carrier wave is to modify the detector output as follows

tstftv c2cos

tftmtftmAtmA

tftmtftmtfA

cccc

cccc

4sin~4cos41

41

2sin~2cos2cos21

sin~41cos

41 tmAtmAtv cco

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Demodulation of SSB wave (3) Owing to the phase error Ф, the detector output

vo(t) contains not only the message signal m(t) but also its Hilbert transform mh(t).

Consequently, the detector output suffers from phase distortion. This phase distortion is usually not serious with voice communications because the human ear is relatively insensitive to phase distortion.

In the transmission of music and video signals, on the other hand, phase distortion in the form of a constant phase difference in all components can be intolerable.

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Vestigial Side-Band (VSB) Modulation Single-sideband modulation is well-suited for the

transmission of voice because of the energy gap that exists in the spectrum of voice signals between zero and a few hundred hertz.

When the message signal contains significant components at extremely low frequencies i.e. television signals, the upper and lower sidebands meet at the carrier frequency. This means SSB modulation is inappropriate for the transmission of television signals.

This difficulty suggests another scheme known as vestigial sideband modulation (VSB), which is a compromise between SSB and DSBSC modulation.

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Vestigial Sideband VSB is similar to SSB but it retains a small portion (a vestige) of the

undesired sideband to reduce DC distortion. Transmits USB or LSB and vestige of other sideband

Reduces bandwidth by roughly a factor of 2

VSB signals are generated using standard AM or DSBSC modulation, then passing modulated signal through a band-pass filter i.e. it is the special design of the band-pass filter that distinguishes VSB modulation from SSB modulation.

Demodulation uses either standard AM or DSBSC demodulation

VSB used for image transmission in TV signals

USB

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Generation of VSB modulated wave The transmission bandwidth of VSB modulation is given by

where W is the message bandwidth, and f, is the width of the vestigial sideband

To generate a VSB modulated wave, we pass a DSBSC modulated wave through a sideband shaping filter.

The exact design of this filter depends on the desired spectrum of the VSB modulated wave.

the VSB modulated wave is described in the time domain as

This is the desired representation representation for a VSB modulated wave containing a vestige of the lower sideband. The component 0.5Acm(t) constitutes the in-phase component of this VSB modulated wave, and 0.5AcmQ(t) constitutes the quadrature components.

tftmA

tftmA

ts cQc

cc 2sin

22cos

2

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Scheme for generation and demodulation of a VSB modulated wave

Block diagram of VSB modulator

Block diagram of VSB demodulator

ProductModulator

SidebandShaping

filter

tfA cc 2cos

m(t) DSBSC VSB waves(t)

ProductModulator

Low-passfilter

tfA cc 2cos

v(t)VSB waves(t)

tvo

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Envelope detection of a VSB wave plus carrier

In commercial television broadcasting, a sizable carrier is transmitted together with the modulated wave.

This makes it possible to demodulate the incoming modulated wave by an envelope detector in the receiver.

In commercial television broadcasting, the vestigial

sideband occupies a width of about 1.25 MHz, or about one-quarter of a full sideband.

This has been determined empirically as the width of vestigial sideband required to keep the distortion due to mQ(t) within tolerable limits when when the percentage modulation is nearly 100.