Principles of CommunicationsLecture 3: Analog Modulation Techniques (1)

Chih-Wei Liu 劉志尉National Chiao Tung Universitycwliu@twins.ee.nctu.edu.tw

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Outlines

Linear Modulation

Angle Modulation

Interference

Feedback Demodulators

Analog Pulse Modulation

Delta Modulation and PCM

Multiplexing

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Types of Modulation

Analog modulation and Digital modulationA process to translate the information data to a new spectral location depending on the intended frequency for transmission.

Modulation, historically, is done on the RF transmission system. Thus, the conversion from message signals to RF signals is called modulation.

Analog modulation: continuous-wave modulation and pulse modulation (sampled data)

Continuous-wave modulation: linear modulation (AM) and angle modulation (FM)

m(t) xc(t)

modulated carrier

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Linear Modulation

General form:

Ac(t): 1-to-1 correspondence to the message m(t)

cos(ωct): carrier (ωct is fixed)

DSB (Double-Sideband) Suppressed Carrier (SC)

ttAtx ccc ωcos)()( =

)(21)(

21)(X

cos)()(

C CCCC

cCc

ffMAffMAf

ttmAtx

−++=⇔

= ω

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DSB-SC

Upper sideband (USB)

Lower sideband (LSB)

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DSB-SC

Coherent (Synchronous) Demodulator (Detector): The receiver knows exactly the phase and frequency of the carrier in the received signal.

ttmAtmAtttmAttxtd

cCC

ccCcc

ωωωω

2cos)()( cos2]cos)([cos2)()(

+=⋅=⋅=

Message m(t) is recovered!

desired part High freq. noise

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What if the receiver reference is not coherent? -- A phase error occurs (θ(t), unknown, random, time-varying, …)

2cos(ωct+θ(t))

xc(t) d(t)

))(2cos()()(cos)( ))(cos(cos)(2)(

tttmAttmAttttmAtd

cCC

ccC

θωθθωω

++=+⋅=

1)(cos1 ),(cos)()( ≤≤−= tttmtyD θθIt is time-varying !!

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Carrier Recovery

Carrier recovery: Regenerate the carrier (fc and θ(t)) at the receiver site

Example: Square circuit

( )2 NarrowbandBPF at 2fc 2÷fxr(t)

cos2ωct cosωct

ttmAtmAttmAtx cCCcCr ωω cos2)(21)(

21cos)()( 22222222 +==

Carrier (2xf)!DC

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Carrier Recover (2)

How to extract the carrier? It becomes clearer when we examine it in the frequency domain.FT of xr2(t):

0 2fc-2fc

FT(m2(t))

Narrow BPF

f

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Remarks

The spectrum of DSB signal does not contain a discrete spectral component at the carrier frequency unless m(t) has a DC component.DSB systems with no carrier frequency component present are often referred to as suppressed carrier (SC) systems.If the carrier frequency is transmitted along with DSB signal, the demodulation process can be rather simplified. Alternatively, let’s see the following amplitude modulation (AM) scheme.

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Amplitude Modulation

A DC bias A is added to m(t) prior to the modulation process

The result is that a carrier component is present in the transmitted signal

DefinitionttamA

tAtmAtx

cnc

ccc

ωω

cos)](1[ cos)]([)(

+=

′+=

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Amplitude Modulation (AM): DSB with carrier

Normalized message 1+mn(t)>=0

AM

mn(t): the normalized message

A

tma t

)(min= a: the modulation index (had better be less than 1)

ttamAtx cnCc ωcos)](1[)( +=

,)(min

)()(tm

tmtmt

n =m(t): the original message

A: the DC bias

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Envelope Detection

The modulation index is defined such that if a=1, the minimum value of Ac[1+amn(t)] is zero

a 0 for all tIn AM, all the information is just the envelop.The envelop detection is a simple and straightforward technique

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Over-modulation: modulation index a > 1DC bias: the shifted level of the zero-value message

AM (2)

mn(t)m(t)

mmin

mn(t)+1/am(t)+A

-1

A

mmax

1/a

x 1/mmin→

↓ dc bias ↓ dc bias

x 1/mmin→

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-fc fc0 0

AM

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AM Demodulation

Coherent detection: precise but requires carrier recovery circuit.

Incoherent detection, envelope detection: simple receiver (LPF) but requires sufficient carrier power (a < 1) and fc >> W. (In theory, fc>W is sufficient, but a “good”LPF is needed.)

Impulse response of RC circuit:

1( ) ( )tRCh t e u t

RC−=

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Remarks

The time constant RC of the envelop detector is an important design parameter.The appropriate RC time constant is related to the carrier frequency fc and to the bandwidth W of the original signal m(t)

1/fc

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Power Efficiency of AM

Suppose that m(t) has zero mean, then the total power contained in the AM modulator output is

The power efficiency : the power ratio of the input information to the transmitted signal

])([21

])()(2[21

2cos)()]([21)()]([

21

cos)()]([)(

222

222

2222

2222

tmAA

tmtmAAA

tAtmAAtmA

tAtmAtx

C

C

cCC

cCc

+′=

++′=

′++′+=

′+=

ω

ω

%100)(1

)(%100

)(

)(Efficiency

22

22

22

2

×+

=×+

≡≡tma

tma

tmA

tmE

n

n

〈⋅〉 denotes the time average value

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Power Efficiency Example

If the signal has symmetrical value, i.e. |minm(t)|=|maxm(t)|,then |mn(t)|≤1 and hence 〈mn2(t)〉≤1.

If a≤1, the maximum efficiency is 50%, e.g. the square wave-type

For a sine wave, 〈mn2(t)〉=1/2, for a=1, the efficiency is 33.3%If we allow a>1,

Efficiency can exceed 50%, (a→∞, the efficiency=100%)

But, the envelope detector is precluded.

%)100()(1

)(%)100(

)(

)(22

22

22

2

tma

tma

tmA

tmEfficiencyE

n

n

+=

+≡≡

,)(min

)()(tm

tmtmt

n =

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Remarks

The main advantage of AM:A coherent reference is not necessary for demodulation as long as a≤1

The disadvantage of AM:The power efficiency The DC value of the message signal m(t) cannot be accurately recovered. (mixed with carrier)

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Single Sideband (SSB) Modulation

Why SSB? In DSB, either the USB and the LSB have equal amplitude and odd phase symmetry about the carrier frequency

Send only “half” signal (USB & LSB symmetric);Good power efficiency; Good bandwidth utilizationBasis of more advanced modulations

Methods to generate SSB signalsMethod 1: Sideband (BPF) filtering Easy to understand, but difficult to implement. Method 2: Phase-shift modulation

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Sideband Filtering

Sideband filtering

An ideal passband filter is necessaryThe (very) low frequency component will be encapulated

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SSB Modulation

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DSB signal: ( ) ( ) ( )2 2

1LPF: ( ) [sgn( ) sgn( )]2

( ) ( ) ( )1 [ ( )sgn( ) ( )sgn( )]41 [ ( )sgn( ) ( )sgn( )]4

C CDSB c c

L c c

c DSB L

C c c c c

C c c c c

A AX f M f f M f f

H f f f f f

X f X f H f

A M f f f f M f f f f

A M f f f f M f f f f

= + + −

= + − −

= ⋅

= + + + − +

− + − + − −

[ ( ) ( )] part-A4

[ ( )sgn( ) ( )sgn( )] part-B4

Cc c

Cc c c c

A M f f M f f

A M f f f f M f f f f

= − + +

+ + + − − −

SSB Signal Generation

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2 21

2 2

ˆ ˆ{part-B} [ ( ) ( ) ]4

1ˆ ˆ ( )[ ( )] ( )sin2 2 2

c c

c c

j f t j f tC

j f t j f tC Cc

A jm t e jm t e

A Am t j e e m t t

π π

π π ω

−−

−

ℑ = −

= − =

SSB Signal Generation (2)

1

Part-A (FT of) DSB signal: ( )cos2

ˆPart-B: Let ( ) { sgn( ) ( )}

Cc

A m t t

m t j f M f

ω

−

↔

≡ ℑ − ⋅

-jsgn(f)( )m t ˆ ( )m t

ˆThus, ( ) sgn( ) ( )M f j f M f= − ⋅2ˆ ˆ( ) ( ) cj f tcM f f m t eπ− ↔

Define Hilbert Transform:

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Phase-shift SSB Modulator

ˆLower-Side Band: ( ) ( )cos ( )sin2 2C C

c c cA Ax t m t t m t tω ω= +

ttmAttmAtx cCcCc ωω sin)(ˆ2cos)(

2)( +=

ttmAttmAtx cCcCc ωω sin)(ˆ2cos)(

2)( −=

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Phase-shift SSB Modulator (2)

ˆUpper-Side Band: ( ) ( )cos ( )sin2 2C C

c c cA Ax t m t t m t tω ω= −