Analog Modulation Techniques

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Communication Systems

• Basic structure

• Information sources•Message signal m(t) is the information source to be sent•Possible information sources include voice, music, images, video, and data, which are baseband signals•Baseband signals have power concentrated near DC

Transmitter

• Signal processing conditions the message signal– Lowpass filtering to make sure that the message signal

occupies a specific bandwidth, e.g. in AM and FM radio, each station is assigned a slot in the frequency domain.

– In a digital communications system, we might add redundancy to the input bit stream

• Carrier circuits– Convert baseband signal into a frequency band

appropriate for the channel– Uses analog and/or digital modulation

Channel

• Transmission media:– Wireline (twisted pair, coaxial, fiber optics)– Wireless (indoor/air, outdoor/air, underwater,

space)

• Propagating signals experience a gradual degradation over distance

• Boosting improves signal and reduces noise, e.g. repeaters

Wireline Channel Impairments• Attenuation: linear distortion that is dependent on the

frequency response of the channel.• Spreading: the finite extent of each transmitted pulse

increases, i.e. pulse widens due to– Transmit pulse length T s– Channel impulse response length T h– Resulting waveform due to convolution has duration T s +

T h• Phase jitter: the same sinusoid experiences different phase

shifts in the channel• Additive noise: arises from many sources in the transmitter,

channel, and receiver

Wireless Channel Impairments

• Same as wireline channel impairments plus

others• Fading: multiplicative noise

– Example: talking on a cellular phone while driving a car when the reception fades in and out

• Multiple propagation paths– Multiple ways for transmitted signal to arrive

atreceiver

Receiver and Information Sinks

• Receiver– Carrier circuits undo effects of carrier circuits in

transmitter, e.g. demodulate from a bandpass signal to a baseband signal

– Signal processing subsystem extracts and enhances the baseband signal

• Information sinks– Output devices such as computer screens,

speakers,and TV screens

Hybrid Communication Systems• Mixed analog and digital signal processing in the

transmitter and receiver– Ex: message signal is digital but broadcast over an

analog channel (compressed speech in digital cell phones)

• Signal processing in the transmitter

• Signal processing in the receiver

Baseband and Bandpass signalsThe Bandpass communication signal is obtained by modulating a baseband analog or digital signal onto a carrier

Definitions:• Baseband

– A baseband waveform has a spectral magnitude that is nonzero for frequencies in the vicinity of the origin (i.e., f = 0) and negligible elsewhere.

• Bandpass– A bandpass waveform has a spectral magnitude that is nonzero

for frequencies in some band concentrated about a frequency f = ± fc , where fc>>0. fc is called the “carrier frequency “.

• Modulation– Modulation is the process of imparting the source information

onto a bandpass signal with a carrier frequency fc by the introduction of amplitude or phase perturbations or both.

The bandpass signal is called the modulated signal s(t), and The baseband source signal is called the modulating signal m(t).

REPRESENTATION OF MODULATED SIGNALS

Modulated signal is just a special application of the bandpass representation.

Modulated signal is given by: tj cetgts )(Re

cc f 2

)()( tmgtg The complex envelope g(t) is a function of the modulating signal & is given by:

where

g tm- performs a mapping operation on

Modulation is the process of encoding the source information m(t) (modulating signal) into a bandpass signal s(t) (modulated Signal)

It is possible to use any type of g[m] functions

Most commonly used g[m] functions are…

1. g[m] functions that are easy to implement and that will give desirable spectral properties

2. g[m] functions should suppress as much noise as possible

Complex envelope functions

Where:

• AM- Amplitude Modulation • DBS-SC - Double-sideband Suppressed Carrier• PM- Phase Modulation • FM - Frequency Modulation • SSB-AM-SC- Single-sideband AM Suppressed

Carrier • SSB-PM - Single-sideband PM• SSB-SQ - Single-sideband Square-law

Detectable• QM - Quadrature Modulation .

Amplitude Modulation

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.5

0

0.5

1

t

m(t

)

0 0.5 1 1.5 2 2.5 3 3.5 4-2

-1

0

1

2

t

v(t) (solid) |g(t)| (dotted)

ttmAts cc cos)](1[)(

Generation of AM

Amount of Modulation

If m(t) has a peak positive values of +1 and a peak negative value of -1

AM signal 100% modulated

100)(max100max

tmA

AA

c

c

100)(min100min

tmA

AA

c

c

100

2

)(min)(max100

2minmax

tmtm

A

AA

c

]0 [i.e., modulation of absence in the envelope AM of Level -

)](1[ of valueMinimum -

)](1[ of valueMaximum -

min

max

m(t)A

tmAA

tmAA

c

c

c

Definition:

The percentage of positive modulation on an AM signal is

The percentage of negative modulation on an AM signal is

The percentage of overall modulation is

Amount of Modulation

Under modulated (<100%) 100% modulated Over modulated ( > 100%)

Envelope detector distorted

Amax = 1.5Ac

Amin = 0.5 Ac

% of positive modulation= 50%% of negative modulation =50%Overall Modulation = 50%

Effect of Over Modulation

Effect of Over Modulation

0 0.5 1 1.5 2 2.5 3 3.5 4-2

0

2

4

t

m(t) (solid) |g(t)| (dotted)

0 0.5 1 1.5 2 2.5 3 3.5 4-2

0

2

4

t

v(t)

Normalized Average Power of AM signals

tmAtmAA

tmtmA

tmAtgts

ccc

c

c

2222

22

2222

2

1

2

1

212

1

12

1

2

1

2

1

2

1 2222 tmAAts cc

The normalized average power of the AM signal is

If the modulation contains no dc level, then

The normalized power of the AM signal is

Discrete

carrier powerSideband power

0tm

Peak Envelope Power (PEP)• Another type of power rating, called the peak envelope power (PEP),

is useful for transmitter specification.• Definition:

The peak envelope power (PEP) is the average power that would be obtained if |g(t)| were to be held constant at its peak value.

• THEOREM. The normalized PEP is given by

• PEP is useful for specifying the power capability of AM, SSB, and television transmitters.

22

max12

tmA

P cPEP

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

Highest efficiency for a 100% AM signal : 50% - square wave modulation

Voltage Spectrum of the AM signal:

Translated version of message signal

ccccc ffMffffMff

AfS

2)(

Carrier line spectral component

Example : Power of an AM signalThe FCC rates AM broadcast band transmitters by their average carrier power; this rating system is common in other AM audio applications as well. Suppose that a 5000-W AM transmitter is connected to a 50 ohm load;

V 707000,5502

1 2

cc A

Athen the constant Ac is given by No modulation

If the transmitter is then 100% modulated by a 1000-Hz test tone , the total

(carrier + sideband) average power will be

WAc 500,750005.1502

15.1

2

The peak voltage (100% modulation) is (2)(707) = 1414 V across the 50 ohm load.

The peak envelope power (PEP) is

WAc 000,2050004502

14

2

The modulation efficiency would be 33% since <m2(t)>=1/2

2

1

2

1 2222 tmAAts cc =

modulation 100%for 21 2 tm

Generation of AM Waves

• AM waves generated using nonlinear device

m(t)+

Accos(2fct+

Squareror Switch BPF

s(t)

Double sideband with carrier Signal

Disadvantage of DSB/WC– Transmitting extra power– Disaster for power-hungry cell phones

Advantages of DSB/WC:– Very simple demodulation circuit– Important in early to mid 1900’s

Double Side Band Suppressed Carrier

Power in a AM signal is given by

2

1

2

1 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 ffMffM

AfS

2)(

Since no power is wasted in carrier the efficiency is

Power

2

1 222 tmAts c

%1001002

2

tm

tmE

Double Sideband Suppressed Carrier (DSBSC)

• Remove inefficient constant term

• Modulated signal is s(t)=Ac m(t) cos(2fct)

• Generated by a Product modulator/ Balanced Modulator

AMModulator

+

AMModulator-m(t)

m(t)

Accos(2fct) s(t)+

-

DSBSC Disadvantage:

• Disadvantage:– Less information about the carrier will be

delivered to the receiver.– Needs a coherent carrier detector at receiver

Single Sideband SignalSingle sideband:• The DSBSC signal also contains the same information twice in the two sidebands

• All the useful information can be conveyed by one sideband only

•BW is half of DSBSC and same as that of the modulating signal

•SSB used in systems where

•Power saving is essential eg. Mobile systems where power and weight required is low

•Bandwidth is at premium

Note: Normally SSB refers to SSB-AM type of signal

USSB LSSB

Single Sideband Signal

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t

x(t) (solid) y(t) (dotted) |g(t)| (dashed)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.5

0

0.5

1

t

cos(

wc*

t)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.5

0

0.5

1

t

v(t)

UPPER SSB

SSB - PowerThe normalized average power of the SSB signal

SSB signal power is

tmAts c222

The normalized peak envelope (PEP) power is

Power gain factor Power of the modulating signal

Generation of SSB• SSB Can be generated using two techniques1. Phasing method

2. Filter Method

• Phasing method

Generation of SSBFilter Method The filtering method is a special case in which RF processing (with

a sideband filter) is used instead of using baseband processing The filter method is the most popular method because excellent

sideband suppression can be obtained when a crystal oscillator is used for the sideband filter.

Crystal filters are relatively inexpensive when produced in quantity at standard IF frequencies

Only limitation is the sharp change in attenuation reqd. in a small freq. band specially if carrier is very high. Then carrier is up-converted after modulation

Advantages of SSB

Superior detected signal-to-noise ratio compared to that of AM

SSB has one-half the bandwidth of AM or DSB-SC signals

Power saving

TRANSMITTERS AND RECEIVERS

Generalized Transmitters– Transmitters generate the modulated signal at the carrier frequency fc , from

the modulating signal m(t). – Any type of modulated signal could be represented by

TransmitterModulating

signalModulated

signal

g(t) is a function of the modulating signal m(t) .

The particular relationship that is chosen for g(t) in terms of m(t) defines the type of modulation that is used, such as AM, SSB, or FM.

)( : PM

)](1[ : AM

g(m) Modulation of Type

tmjDc

c

peA

tmA

Generalized Receiver• The receiver has the job of extracting the

source information from the received modulated signal that may be corrupted by noise.

• Often, it is desired that the receiver output be a replica of the modulating signal that was present at the transmitter input.

• There are two main classes of receivers: 1. The Tuned Radio-Frequency (TRF) receiver

and2. The Superheterodyne receiver.

• Most receivers employ the Superheterodyne receiving technique.

Super Heterodyne Receiver

• The technique consists of either down-converting or up-converting the input signal to some convenient frequency band, called the intermediate frequency (IF) band, and then extracting the information (or modulation) by using the appropriate detector.

• This receiver is used for the reception of all types of bandpass signals, such as television, FM,AM, satellite, cellular, and radar signals

Receiver Parameters

• Sensitivity– The voltage that must be applied to the Rx I/P to give

a standard O/P• Selectivity

– Ability of the receiver to reject adjacent unwanted signals

• Image Frequency Rejection– Rejection of the frequency which would generate the

same IF when mixed with the LO frequency fsi=fs+2fi = fo+fi

Detection of AM Waves• Entails tradeoff between performance and

complexity (cost)

• 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 receiver)

• Envelope detector detects envelope of s(t)– Simple circuit (resistors, capacitor, diode)– No distortion.– Non-coherent

Angle ModulationAngle Modulation

• Phase Modulation

• Frequency Modulation

Angle Modulation

We have seen that an AM signal can be represented as

ttmAts c ccos )](1[)(

Now we will see that information can also be carried in the angle of the signal as

where the amplitude of signal carries information.

ttAts cc cos

where the amplitude remains constant.

Angle Modulation

The alternative to the amplitude modulation involves using the message to vary either the Phase or the Frequency of the carrier signal.

Phase Modulation and Frequency Modulation are special cases of Angle Modulation

• Representation of PM and FM signals:

• The complex envelope is given by tjceAtg

• θ(t) - linear function of the modulating signal m(t)

• The angle-modulated signal in time domain is given by

ttAts cc cos

Angle Modulation: Basic Definitions

Angle Modulation Analysis

Example: Sinusoidal Modulating Signal

Spectrum of Angle-Modulated Signal

• Output consists of a carrier and apparently an infinite

number of pairs of sidebands with J coefficients

FM with sinusoidal modulating signal

Bessel functions of the first kind

J0(β)=0 at β=2.4, 5.52 & so on

Bessel functions of the first kind

Spectrum: Examples

Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted.

Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side.

Carson’s rule

(1+fm

Carson’s rule

Therefore the bandwidth required is given by

BBT 12 β – phase modulation index/ frequency modulation index

B – bandwidth of the modulating signal

For sinusoidal modulation

mT fB 12

mfB Carson’s rule : Bandwidth of an FM signal is given by

Bandwidth of Angle-Modulated Signal

Narrowband Angle Modulation

Wideband Angle Modulation

• Modulation index is high• The signal bandwidth is:

• Different for PM and FM!• Wideband FM: the bandwidth is twice the frequency deviation. Does not depend on the modulating frequency.• Wideband PM: the bandwidth depends on modulating frequency.• Modulation index is bandwidth expansion factor.

PM Modulator

FM Modulator

Narrowband Angle Modulator

Indirect Wideband Angle Modulator

FM Demodulators

FM Slope Detector

Balanced Discriminator:Block Diagram

Balanced Discriminator:Circuit Diagram

Modulating Techniques Analog data to digital signal

• Pulse code modulation (PCM)• Delta modulation (DM)

Once analog data have been converted to digital signals,

the digital data:• can be transmitted using NRZ-L• can be encoded as a digital signal using a code

other than NRZ-L• can be converted to an analog signal, using

previously discussed techniques

Reasons for Growth of Digital Techniques

Growth in popularity of digital techniques for sending analog data

– Repeaters are used instead of amplifiers• No additive noise

– TDM is used instead of FDM• No inter-modulation noise

– Conversion to digital signaling allows use of more efficient digital switching techniques

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