Communications I Amplitude Modulations and Demodulationssite.iugaza.edu.ps/tskaik/files/Com1-Chapter4-part1.pdf · Communications I Amplitude Modulations and Demodulations ... Amplitude

EELE 3370

Communications I

Amplitude Modulations and Demodulations

Dr. Talal Skaik 2016

Islamic University of Gaza

Electrical Engineering Department

1

Introduction

2

Modulation is a process that moves the message signal into

a specific frequency band that is dictated by the physical

channel.

We will study classic analog modulations:

Amplitude modulation and Angle modulation

Communication systems that does not use modulation –

baseband communications

Communication systems that use modulation –

carrier communications

Dr. Talal Skaik IUG 2016

Baseband vs Carrier Communications

3

Baseband Communications

The baseband is the frequency band of the original signal.

Example: Telephones: 300–3700 Hz

Baseband signals such as audio and video contain

significant low-frequency content.

They cannot be effectively be transmitted over radio

(wireless) link.

Baseband communication usually requires wire (single,

twisted pair, coax).


Baseband vs Carrier Communications

4

Carrier Communications oCarrier communication uses modulation to shift spectrum of signal. oWireless communication requires frequencies higher than baseband. oIn carrier communication, the signal modulates a sinusoidal carrier. oThe signal modifies the amplitude, frequency, or phase of carrier.

s(t) = A(t) cos(ωct +φ (t))

◮ Amplitude modulation: A(t) is proportional to m(t) ◮ Frequency modulation: frequency is proportional to m(t) ◮ Phase modulation: φ(t) is proportional to m(t)

Frequency and phase modulation are called angle modulation.


Double Sided Amplitude Modulation

5

The carrier amplitude is changed in proportional to the message

signal.

At the same time, angular frequency ωc and the phase θc remains

constant ( assume phase θc = 0).

If carrier amplitude A is made directly proportional to the

modulating signal m(t), then modulated signal is:

m(t) cos ωct (shifts spectrum of m(t) to carrier frequency

If

1

22

c c c

m( t ) M ( f )

then

m( t ) cos( f t ) M ( f f ) M ( f f )



6 Dr. Talal Skaik IUG 2016

• If the bandwidth of m(t) is B Hz, then the modulated signal has a

bandwidth of 2B Hz.

• The modulated signal spectrum centered at ±fc (or ωc rad/s)

consists of two parts:

a portion that lies outside ±fc and is know as upper sideband (USB)

A portion that lies inside ±fc is known as Lower Sideband (LSB)

• The modulated signal does not contain a discrete component of the

carrier frequency fc.

• This modulation process does not introduce sinusoid at fc and as a

result, it is called Double-sideband, suppressed-carrier (DSB-SC

modulation).



• The relationship of B to fc is of interest:

• From fig c, if fc ≥ B, thus avoiding overlap of modulated spectra

centered at ±fc .

• If fc < B, the two copies of message spectra overlap and the

information of m(t) is distorted during modulation. This will make

it impossible to recover m(t) from m(t)cos ωct.


8

Examples: ◮ AM radio: B = 5 KHz, 550 ≤ fc ≤ 1600 KHz

◮ FM: B = 200 KHz, 87.7 ≤ fc ≤ 108.0 MHz

◮ US television: B = 6 MHz, 54 ≤ fc ≤ 862 MHz


• DSB-SC modulation shifts spectrum to right and left by fc.

• To recover original signal m(t) from the modulated signal, it is necessary to retranslate the spectrum to its original position (Demodulation)

• If modulated signal spectrum in fig c (previous figure) is shifted to the left and to the right by fc and multiplied by half, we obtain:

• The figure contains the desired baseband spectrum plus and unwanted spectrum at ±2fc.

• The unwanted spectrum can be suppressed by a low-pass filter.

DSB-SC Demodulation


• Demodulation consists of multiplication of the incoming modulated signal m(t)cos ωct by a carrier cosωct followed by a low pass filter.

• This can be verified in the time domain by observing e(t):

DSB-SC Demodulation

10

2 12

2

1 12 2

2 4

c c

c c

e( t ) m( t ) cos t m( t ) m( t ) cos t

E ( f ) M ( f ) M ( f f ) M ( f f )


• The spectrum of the second component in E(f), being a signal with

carrier frequency 2fc, is centered at ±2fc.

• This component is suppressed by low-pass filter.

• On the other hand, the desired component (1/2)M(f), being a low-pass

spectrum (centered at f = 0) passes through the filter unharmed, resulting

in (½)m(t).

• You can get rid of the inconvenient fraction ½ in the output by using a

carrier 2cosωct instead of cosωct

• This method of recovering the baseband signal is called synchronous

detection or coherent detection where we use a carrier of exactly the

same frequency(same phase) as the carrier used for modulation.

Demodulation

11

1 1

2 22 4

c cE ( f ) M ( f ) M ( f f ) M ( f f )

For a baseband signal: m(t) = cos ωmt = cos 2πfmt

Find the DSB-SC signal, and sketch its spectrum. Identify the upper

and lower sidebands (USB and LSB). Verify that the DSB-SC

modulated signal can be demodulated by the demodulator shown

previously (synchronous detection or coherent detection)

[This case is called tone modulation because the modulating signal is a

pure sinusoid or tone, cos ωmt ]

Example


Example


Example



Multiplier Modulators

• Modulation is achieved directly by using an analog multiplier

whose output is proportional to the product of two signals m(t)

and cos ωct.

• Typically, the multiplier is obtained from a variable-gain

amplifier in which the gain parameter is controlled by one of

the signals e.g m(t).

• When cos ωct is applied to the input of the amplifier, the output

is proportional to m(t)cos ωct.

Modulators


Non-Linear Modulator

Modulation is achieved through nonlinear devices such as a

semiconductor diode or a transistor.

• Let the input-output characteristics of either of the nonlinear

elements be approximated by a power series:

y(t) = a x(t) + b x2(t)

• where x(t) and y(t) are the input and output of the nonlinear element.

Modulators


Modulators


Non-Linear Modulator

• Passing z(t) through a bandpass filter tuned to ωc, the signal

am(t) is suppressed and the desired modulated signal

4bm(t)cosωct can pass through the system without distortion

• Because the cos ωct does not appear at the z(t), this setup is

called balanced circuit.

• The nonlinear modulator is an example of a class of modulators

known as balanced modulator.

• Because m(t) appears in z(t), it is called single balance

modulator, however, m(t) is removed through bandpass filter.

Modulators


Switching Modulators • multiplication operation for modulation is replaced by a simple

switching operation.

• Multiplication of the signal by a sinusoid can be replaced by multiplication the signal by any periodic signal w(t) with fundamental radian frequency ωc.

• The periodic signal can be expressed as:

• Hence

Modulators

20

0

n c n

n

w ( t ) C cos( n t )

0

n c n

n

m( t ) w ( t ) C m(t) cos( n t )


• This shows that the spectrum of the product m(t)w(t) is the spectrum

M(f) shifted to ±fc, ±2fc, ……… ±nfc….

• Passing the signal through bandpass filter of bandwidth 2B Hz and

tuned to fc will result c1m(t) cos(ωct+θ1).

• For a square wave centered at t = 0. Then

• Then m(t) w(t) is given by

Switching Modulators

21

0

n c n

n

m( t ) w ( t ) C m(t) cos( n t )

1 2 1 13 5

2 3 5c c cw ( t ) cos t cos t cos t

1 2 1 13 5

2 3 5c c cm(t)w ( t ) m( t ) m( t ) cos t m( t ) cos t m( t ) cos t


• The signal m(t)w(t) consists of m(t) and an infinite number of modulated signals with angular frequency ωc, 3ωc, 5ωc…..

• Spectrum of m(t)w(t) consists of m(t) shifted by ±fc, ±3fc ….. (with decreasing relative weight).

• We are only interested in m(t)cosωct, hence the signal m(t)w(t) is passed through a bandpass filter of bandwidth 2B Hz centered at ±fc

• This will suppress all spectra components not centered at ±fc to yield the desired modulated signal (2/π)m(t)cos ωct as shown in fig (d).


22

1 2 1 13 5

2 3 5c c cm(t)w ( t ) m( t ) m( t ) cos t m( t ) cos t m( t ) cos t






• The advantage of this scheme is that multiplication of a signal by a

square pulse train is in reality a switching operation.

• It involves switching the signal m(t) on and off periodically and can

be implemented using simple switching element.

• Example is the diode bridge modulator driven by a sinusoid

Acos ωct to produce the switching action.


25

•When the signal cos ωct is of a

polarity that will make terminal c

positive with respect to d, all diodes

conduct.

•terminals a and b have the same potential and are effectively shorted.


• During the next half-cycle, terminal d is positive with respect to c and all four diodes off, thus opening terminal a and b.

• This therefore acts as a switch.

• Terminals a and b open and close periodically with carrier frequency fc when a sinusoid A cos ωct is applied across c and d.



• To obtain m(t)cos wct, terminals a and b are connected in series or across (parallel) to m(t) as shown below:

• This is called series bridge diode modulator and the shunt bridge diode modulator.

• The switching on and off periodically with fc results in switched signal m(t)w(t) which when bandpassed yields modulated signal (2/π)m(t)cosωct



• This another switching modulator.

• During the positive half-cycles of the carrier, diodes D1 and D3

conduct and D2 and D4 are off.

• Terminal a is therefore connected to c and terminal b to d.

Ring Modulators


• During negative half-cycles of the carrier, D1 and D3 are off, D2 and

D4 are conducting

• Terminal a and d are connected and so is b and c.

• Output is proportional to m(t) during positive half-cycle and to –m(t)

during the negative half-cycle.

Ring Modulators


• In effect, m(t) is multiplied by a square pulse w0(t) shown below:

Ring Modulators


• The Fourier series of w0(t) is given by:

• When m(t)w0(t) is passed through a bandpass filter tuned to ωc, the filter output will be (4/π)m(t)cos ωct.

Ring Modulators

31

4 1 13 5

3 5c c cw ( t ) cos t cos t cos t

4 1 13 5

3 5

i 0

c c c

and v (t) = m(t)w ( t )

m( t ) cos t m( t ) cos t m( t ) cos t


• The Ring modulator circuit has two inputs: m(t) and cos ωct

• The input to the bandpass filter does not contain either of these inputs

• As a result, this circuit is an example of a double balanced modulator.

Ring Modulators


• Frequency mixer or converter: is used to change the carrier angular

frequency of a modulated signal m(t)cos ωct from ωc to ωI

• This is achieved by multiplying m(t) cos ωct by 2cos ωmixt, where

ωmix = ωc+ ωI or ωc-ωI and bandpass filtering the product.

• The product x(t) is:-

Frequency Mixer or Converter

33

2 c mix

c mix c mix

x ( t ) m( t ) cos t cos t

m( t ) cos t cos t


• If ωmix = ωc-ωI then

• If ωmix = ωc+ωI then


34

c mix c mixx ( t ) m( t ) cos t cos t

2I c Ix ( t ) m( t ) cos t cos t

2I c Ix ( t ) m( t ) cos t cos t


• When a bandpass filter tuned to ωI is applied at the output,

m(t) cos ωIt will be passed and the other spectra will be suppressed.

• As a result, carrier frequency ωc has been translated to ωI from ωC.

• The operation of frequency mixing/conversion is known as

heterodyning.



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Communications I Amplitude Modulations and Demodulationssite.iugaza.edu.ps/tskaik/files/Com1-Chapter4-part1.pdf · Communications I Amplitude Modulations and Demodulations ... Amplitude