Communication SystemsLecture 5

Dong In KimSchool of Info/Comm EngineeringSchool of Info/Comm Engineering

Sungkyunkwan University

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A li d d l i (A )Amplitude Modulation (AM) Definition: Definition:

Assumption: m(t) has zero DC component.( ) [ ( )]cos( )x t A A m t tw¢ +

A carrier component is transmitted.C i i i if h t d d l ti i d

( ) [ ( )]cos( )c c cx t A A m t tw= +

Carrier recovery is easier if coherent demodulation is used Carrier recovery is not needed at all if the system is designed properlyproperly. Price paid: Lower efficiency (carrier carries no information)

|Xc(f)|

2ffc-fc

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A li d d l i (A )Amplitude Modulation (AM)

Normalized format:( ) [ ( )]cos( )c c cx t A A m t tw¢= +

( ) [1 ( )]cos( )c c n cx t A am t tw= +

( ) [ ( )] ( )c c c

Modulation index

a x 100%: Percent modulation

min ( ) /a m t A=

a 00%: e ce t odu at o

( ) ( ) / min ( )nm t m t m t= Normalized message with min value = -1.

Derivation:Derivation:

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A lAM Example ( ) [1 ( )]cos( )c c n cx t A am t tw= +( ) cos( ) ( )m t t m tw0( ) cos( ) ( )nm t t m tw= =

0.5a = 1a =

1.5a =

Observation: if a ≤ 1: the envelope contains the message.4

Observation: if a ≤ 1: the envelope contains the message.

a ≥ 1: envelope is not the message (over-modulation).

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A l DAM Envelope Detector( ) [1 ( )] ( )t A t t+( ) [1 ( )]cos( )c c n cx t A am t tw= +

If a £ 1, m(t) can be extracted by envelope detector Can be implemented by simple circuit Much easier than coherent demodulation Used in standard AM radios

The diode: only allows the positive part to pass.5

The diode: only allows the positive part to pass.The lowpass RC circuit: tracks the envelope

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A l DAM Envelope DetectorTh i f t b l h > 10 BW f (t) The carrier freq. must be large enough: > 10 BW of m(t) Otherwise too much error.

The RC time constant must be set carefully The RC time constant must be set carefully too large: won’t track too small: tracks the carrier

RC too large

too small: tracks the carrier

RC too smallGood RC

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A1 1 2 2( ) [ ( ) ( )]y t a x t a x t= +H

AM 1 1 2 2[ ( )] [ ( )]a x t a x t= +H H

Strictly speaking, AM is not a linear system:[1 ( ( ) ( ))]cos( )A a m t m t tw+ +1 2

1 1

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

c c

c c c c

A a m t m t tA am t t A am t t

ww w

+ +

¹ + + +

but AM is generally considered as linear any way.

However, DSB-SC is a linear system:( ) ( )cos( )x t A m t tw=( ) ( )cos( )c c cx t A m t tw=

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ffi i f AEfficiency of AM

Ratio of the sideband power to the total powermPE mffT

EP

=

( ) [1 ( )] ( )t A t t+( ) [1 ( )]cos( )c c n cx t A am t tw= +

2 21lim ( ) ( )T

TP x t dt x t= ò 2 2 2[1 ( )] cos ( )A am t tw= +lim ( ) ( )2T c cT TP x t dt x tT¥ -ò [1 ( )] cos ( )c n cA am t tw= +

Trigonometric identity again: 21cos ( ) [1 cos(2 )]2c c

t tw w= +

2 2 2 21 1[1 ( )] [1 ( )] cos(2 )2 2T c n c n c

P A am t A am t tw= + + +2

8≈ 0 if carrier changes much faster than m(t)

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cont …1 2 2A A

( ) [1 ( )]cos( )c c n cx t A am t tw= +

2 21 [1 ( )]2T c n

P A am t= +2 2

2 2 2

2 2

( ) ( )2 2

c cc n n

A AA a m t a m t

A A

= + +

2 22 2 ( )

2 2c c

nA A a m t= +

(2nd term is 0 because we assume m(t) has zero DC)(2 term is 0 because we assume m(t) has zero DC).

2 2 ( )na m tE2 21 ( )ff n

Ea m t

=+

Better efficiency for larger a a : Eff 1 (DSB SC!)

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a : Eff 1 (DSB-SC!) But no envelope detector if a > 1.

l2 2 ( )n

ff

a m tE =

Examples 2 21 ( )ff nE

a m t+

0 35 0 5

0.25

0.3

0.35

m(t) is sinusoidal0.35

0.4

0.45

0.5

m(t) is square wave

0.15

0.2

Effi

cien

cy

0.2

0.25

0.3

Effi

cien

cy

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 10

0.05

0.1

0

0.05

0.1

0.15

If m(t) is sinusoidal, the max Eff is 33%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Modulation Index

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Modulation Index

If m(t) is sinusoidal, the max Eff is 33%

If m(t) is square wave, the max Eff is 50%.10

Measurement of Modulation Index

How to measure the modulation index from oscilloscope display? (Part of Lab 1)p p y ( )

( ) [1 ( )]cos( )c c n cx t A am t tw= +

-EminE E

If mn(t) in [-1, 1], then

-Emaxmax min

max min

.E EaE E

Proof:

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Measurement of Modulation Index How to measure the modulation index from Spectrum How to measure the modulation index from Spectrum

Analyzer (SA) display? (Part of Lab 1) SA usually measures power in dBm unit: 10 log Px SA usually measures power in dBm unit: 1010 log 1mW

x P1

P

: carrier power (dBm)

: sideband power (dBm)P2 : sideband power (dBm)

1 2 202 10 for sinusoidal m(t)

P P

a

202 10 for sinusoidal m(t).a

Proof:2 2A A 2 2 ( )

2 2c c

T nA AP a m t= +

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SSummary

Topics in Amplitude Modulation DSB-SC AM (with carrier) envelope detection envelope detection efficiency Measurement of modulation index

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