Chapter 2: ContinuousWave Modulation

1 Chapter 2 ContinuousWave Modulation 2.1 Introduction2 2.2 Amplitude Modulation The output of the modulator Where m(t) is the baseband signal , ka is the amplitude sensitivity. : carrier frequency : carrier amplitude ( ) cos(2 ) (2.1) c c c c A f c t  A f t s(t)  Ac1 kam(t)cos(2fct) (2.2) where is the hightest freqency of ( ) 2. (2.4) 1. ( ) 1, for all t (2.3) W m t f W k m t a c   X 1+k am(t) S(t) A ccos(2fct)3 Recall 1.Negative frequency component of m(t) becomes visible. 2.fcW  M(f)  fc lower sideband fc  M(f)  fc+W upper sideband 3.Transmission bandwidth B T=2W s(t)  Accos(2fct)  Ackam(t)cos(2fct) (2.2)         where ( ) is the Fourier Transform of ( ) ( ) ( ) (2.5) 2 ( ) ( ) 2 ( ) ( ) ( ) 1 2 ( )cos(2 ) ( ) ( ) 1 2 cos(2 ) M f m t s f A f f f f k A M f f M f f m t f t M f f M f f f t f f f f c c a c c c c c c c c c c                      4 Virtues and Limitations of Amplitude Modulation Transmitter Receiver Major limitations 1.AM is wasteful of power. 2.AM is wasteful of bandwidth.5 2.3 Linear Modulation Schemes Linear modulation is defined by Three types of linear modulation: 1.Double sidebandsuppressed carrier (DSBSC) modulation 2.Single sideband (SSB) modulation 3.Vestigial sideband (VSB) modulation ( ) Quadrature component ( ) In phasecomponent ( ) ( )cos(2 ) ( )sin(2 ) (2.7)     s t s t s t s t f t s t f t I Q I  c Q  c6 Notes: 1.s I(t) is solely dependent on m(t) 2.s Q(t)is a filtered version of m(t). The spectral modification of s(t) is solely due to sQ(t).7 Double SidebandSuppressed Carrier (DSBSC) Modulation The Fourier transform of S(t) is s(t)  Acm(t)cos(2fct) (2.8) ( ) ( ) (2.9) 1 2 s( f )  Ac  M f  fc  M f  fc   8 Coherent Detection (Synchronous Detection) The product modulator output is Let V(f) be the Fourier transform of v(t) cos( ) ( ) (2.10) 1 2 cos(4 ) ( ) 1 2 cos(2 )cos(2 ) ( ) ( ) cos(2 ) ( ) A A f t m t A A m t A A f t f t m t v t A f t s t c c c c c c c c c c c                cos ( ) (2.11) 1 2 v0(t)  AcAc  m t filtered out (Low pass filtered)9 Costas Receiver Ichannel and Qchannel are coupled together to form a negative feedback system to maintain synchronization The phase control signal ceases with modulation. 1 4 2 2 2 2 2 2 0 1 1 cos sin ( ) ( )sin(2 ) 4 8 ( ) (sin2 2 ) c c c A m t A m t A m t            (multiplier + very narrow band LF)10 QuadratureCarrier Multiplexing (or QAM) Two DSBSC signals occupy the same channel bandwidth, where pilot signal (tone ) may be needed. s(t)  Acm1(t)cos(2fct)  Acm2(t)sin(2fct)11 SingleSideband Modulation (SSB) The lower sideband and upper sideband of AM signal contain same information . The frequencydiscrimination method consists of a product modulator (DSBSC) and a bandpass filter. The filter must meet the following requirements: a.The desired sideband lies inside the passband. b.The unwanted sideband lies inside the stopband. c.The transition band is twice the lowest frequency of the message. To recover the signal at the receiver, a pilot carrier or a stable oscillator is needed (Donald Duck effect ).12 Vestigial Sideband Modulation (VSB) When the message contains near DC component The transition must satisfy (2.14) ( ) ( ) 1 for (2.13) b.The phaseresponseis linear : a. ( ) ( ) 1 B W f H f f H f f W f W H f f H f f T ν c c c c             Consider the negative frequency response: H f     f W c   f f c v  fc   f f c v f f c v  fc f f c v  f W c  Here, the shift response │H(ffc)│ is H f f   c  2 W  fv 0 fv f f c v  2 fc 2 f f c v  2 f W c  13and │H(f+fc)│ is H f f   c    2 f W c   2 f f c v 2 fc   2 f f c v  fv 0 fv W 14So, we get │H(ffc)│ +│ H(f+fc)│ is H f f   c  2 W  fv 0 fv f f c v  2 fc 2 f f c v  H f f   c    2 f f c v 2 fc   2 f f c v  fv 0 fv W 15Consider –W fm =w pre de FM o T c o T c N B A N B A 2 2 2 2   BT For the purpose of comparing different CW modulation systems, we define The average power of the modulated signal (SNR)c= The average power of channel noise in the message band Message signal with LP filter the same power as output modulated wave noise n(t) The equivalent baseband transmission model. with bandwidth wSupplements More precisely, we may express the DSBSC as m(t) S‘(t) cos(2πfc t+θ) θ is uniformly distributed over ﹝ 0, 2π﹞ S(t)=Ac m(t) cos(2πfc t+θ) At the receiver we may write S(t)=C Ac m(t) cos(2πfc t+θ)                         w w m m c m c c c c c x s s R P S f df C A R C A P C A E f t E m t E CA m t f t S f df P E S t R (0) ( ) (0) 2 2 cos (2 ) ( ) ( ( )cos(2 )) ( ) ( ) (0) 2 2 2 2 2 2 2 2 2 2     The average noise power in –w (t) increases or decreases 2 The discriminator output is equal to 1 ( ) ) ( ) 2 c P r t A t     nQ(t) r(t) x(t) A c P 1 0  P2 n I(t) 74Figure 2.44 Illustrating impulselike components in  (t)  d (t)dt produced by changes of 2 in  (t); (a) and (b) are graphs of (t) and  (t), respectively. 75A positivegoing click occurs , when , , 0 A negativegoing click occurs when , , 0 The carrierto noise ratio is defin ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) c c d t r t A t t d t dt d t r t A t t d t dt                      ed by (2.154) The output signaltonoise ratio is calculated as 1. The average output signal power is calculated assuming a sinusoidal modulation which produces . (noise free) 2. 2 0 2 c T T A B N B f     The average output noise power is calculated when no signal is present (The carrier is unmodulated). 76 2threshold effects may be avoided 20 (2.155), 2 20 or 2 When 0 2 0 2 A B N B N A T c c T     Figure 2.45 Dependence of output signaltonoise ratio on input carriertonoise ratio for FM receiver. In curve I, the average output noise power is calculated assuming an unmodulated carrier. In curve II, the average output noise power is calculated assuming a sinusoidally modulated carrier. Both curves I and II are calculated from theory. 77The procedure to calculate minimum 1. Given and W, determine (using Figure 2.26 or Carsons rule) 2. Given , we have 20 Capture Effect: The receiv 2 0 0 ( 20) 2 c T c T A B A N B N     er locks onto the stronger signal and suppresses the weaker one. 78FM Threshold Reduction (tracking filter) • FM demodulator with negative feedback (FMFB) • Phase locked loop Figure 2.46 FM threshold extension. Figure 2.47 FM demodulator with negative feedback. 79Preemphasis and Deemphasis on FM Figure 2.48 (a) Power spectral density of noise at FM receiver o (b) Power spectral density of a typical message signal. Figure 2.49 Use of preemphasis and deemphasis in an FM system. 80(2.162) 3 ( ) 2 The improvement factor is ( ) (2.158) power withde emphsis Average outputnoise (2.157) 2 ( ) ( ) ( ) , (2.146) 2 ( ) , The PSD at thediscriminator outputis , (2.156) ( ) 1 ( ) w w 2 2 3 2 de 2 0 2 2 2 de 2 2 0 de 2 2 0 pe de                      f H f df W I I f H f df N A B H f f A N f H f S f B f A N f S f W f W H f H f de W W c T c N T c N d d 81(2.161) 3 ( ) tan ( ) ( ) 1 ( ) 3 1 2 1 ( ) A de emphsis filter responseis ( ) 1 A simple pre emphsis filter responseis 0 1 0 3 0 2 0 2 3 0 de 0 pe             W f W f f W f f f df W I f H f j f f j f H f W W Example 2.6 Figure 2.50 (a) Preemphasis filter. (b) Deemphasis filter. 82 The main difference between FM and PM is in the relationship between frequency and phase. f = (12).ddt.  A PM detector has a flat noise power (and voltage) output versus frequency (power spectral density). This is illustrated in Figure 938a.  However, an FM detector has a parabolic noise power spectrum, as shown in Figure 938b. The output noise voltage increases linearly with frequency.  If no compensation is used for FM, the higher audio signals would suffer a greater SN degradation than the lower frequencies. For this reason compensation, called emphasis, is used for broadcast FM. Preemphasis for FM 83Figure 938. Detector noise output spectra for (a). PM and (b). FM. Preemphasis for FM 84 A preemphasis network at the modulator input provides a constant increase of modulation index mf for highfrequency audio signals.  Such a network and its frequency response are illustrated in Figure 939. Preemphasis for FM Fig. 939. (a)Premphasis network, and (b) Frequency response. 85 With the RC network chosen to give  = R1C = 75s in North America (150s in Europe), a constant input audio signal will result in a nearly constant rise in the VCO input voltage for frequencies above 2.12 kHz. The largerthannormal carrier deviations and mf will preemphasize highaudio frequencies.  At the receiver demodulator output, a lowpass RC network with  = RC = 75s will not only decrease noise at higher audio frequencies but also deemphasize the highfrequency information signals and return them to normal amplitudes relative to the low frequencies.  The overall result will be nearly constant SN across the 15 kHz audio baseband and a noise performance improvement of about 12dB over no preemphasis. Phase modulation systems do not require emphasis. Preemphasis for FM 86Preemphasis and deemphasis: (a) schematic diagrams; (b) attenuation curves Preemphasis and Deemphasis on FM 87Example of SN without preemphasis and deemphasis. Preemphasis and Deemphasis on FM 88Example of SN with preemphasis and deemphasis. Preemphasis and Deemphasis on FM 89Dolby dynamic preemphasis 90Figure 2.55 Comparison of the noise performance of various CW modulation systems. Curve I: Full AM,  = 1. Curve II: DSBSC, SSB. Curve III: FM,  = 2. Curve IV: FM,  = 5. (Curves III and IV include 13dB preemphasis, deemphasis improvement.) 91In making the comparison, it is informative to keep in mind the transmission bandwidth requirement of the modulation systems in question. Therefore, we define normalized transmission bandwidth as B W B T n  Table 2.4 Values of B n for various CW modulation schemes FM AM, DSBSC SSB B n   2   5 2 1 8 16 92李家同教授我的恩師

1

Chapter 2 Continuous-Wave Modulation

2.1 Introduction

2

2.2 Amplitude Modulation

The output of the modulator

Where m(t) is the baseband signal , k a is the amplitude sensitivity

frequency carrier

:

amplitude carrier

:

(2.1)

) 2 cos( ) ( c c c c f A t f A t c    1 ( )  cos( 2 ) (2.2) ) ( t A k m t f t s  c  a  c ) ( of freqency hightest the is where (2.4)

2 (2.3)

t

all for ,

1 )

(

1

t m W

W f

t m

k

c

a





X

A ccos(2f c t)

)

2 cos(

) ( )

2 cos(

the is ) ( where

(2.5)

) (

)

( 2

) (

)

( 2

)

(

) (

)

( 2

1 )

2 cos(

)

(

) (

)

( 2

1 )

2 cos(

t m f

M

f f

M f

f M A k f

f f

f M t

f t

m

f f

f f t

f

c c

c a c

c c

c c

c

c c

1.AM is wasteful of power

2.AM is wasteful of bandwidth

5

2.3 Linear Modulation Schemes

Linear modulation is defined by

Three types of linear modulation:

1.Double sideband-suppressed carrier (DSB-SC) modulation 2.Single sideband (SSB) modulation

3.Vestigial sideband (VSB) modulation

component Quadrature

) (

component phase

In )

-(

(2.7)

) 2

sin(

) ( )

2 cos(

) ( )

t s

t f t

s t

f t

s t

s

Q

I

c Q

c

6

Notes:

1.sI(t) is solely dependent on m(t)

2.sQ(t)is a filtered version of m(t)

The spectral modification of s(t) is solely due to sQ(t)

)

2 cos(

) ( )

(2.9)

) (

)

( 2

1 )

( f  AcM f  fc  M f  fc 

s

8

Coherent Detection (Synchronous Detection)

The product modulator output is Let V(f) be the Fourier transform of v(t)

(2.10)

) ( ) cos( ' 2 1 ) ( ) 4 cos( ' 2 1

) ( ) 2 cos( ) 2 cos( '

) ( ) 2 cos( ' ) ( t m A A t m t f A A t m t f t f A A t s t f A t v c c c c c c c c c c c                (2.11)

)

( cos

' 2

1

)

(

filtered out

(Low pass filtered)

9

Costas Receiver

I-channel and Q-channel are coupled together to

form a negative feedback system to maintain synchronization

10

Quadrature-Carrier Multiplexing (or QAM)

Two DSB-SC signals occupy the same channel

bandwidth, where pilot signal (tone ) may be

needed

) 2

sin(

) ( )

2 cos(

) ( )

11

Single-Sideband Modulation (SSB)

The lower sideband and upper sideband of AM signal

contain same information

The frequency-discrimination method consists of a

product modulator (DSB-SC) and a band-pass filter

The filter must meet the following requirements:

a.The desired sideband lies inside the passband

b.The unwanted sideband lies inside the stopband

c.The transition band is twice the lowest frequency of

the message

To recover the signal at the receiver, a pilot carrier or a stable oscillator

is needed (Donald Duck effect )

12

Vestigial Sideband Modulation (VSB)

When the message contains near DC component

The transition must satisfy (2.14)

(2.13)

for

1 ) ( ) ( : linear is response phase b.The 1

) (

) (

.

a

f W

B

W f

W f

f H f

f H

f f

H f

f H

ν T

c c

c c



























Consider the negative frequency response:

Consider –W<f<W we get:

v f v

± corresponds to upper or lower sideband

(2.15)

) 2

sin(

) (

' 2

1 )

2 cos(

)

( 2

1 )

18

Television Signals (NTSC)

20

2.5 Frequency-Division Multiplexing (FDM)

21

2.6 Angle Modulation

Basic Definitions:

Better discrimination against noise and interference

(expense of bandwidth)

The instantaneous frequency is

 ( )  (2.19) cos

)

constant is

where

(2.22)

2 )

(

is ) ( carrier, d

unmodulate an

For

(2.21)

) ( 2 1

2 ) ( ) ( lim

) ( lim ) (

0 Δ Δ 0 Δ c c c i i i i i t

t t

i

t f t

t dt

t d

t

t t

t

t f t

f



















































modulator the

of

y sensitivitphase

:

)(2

)

(

t m k t

f A

s(t)

k

t m k t

f t

p c

c p

p c

: Δ

(2.28)

) 2

cos(

) 2

cos(

) (

(2.27)

) 2

cos(

) ( let

m f

m c

m m

f c

i

m m

A k

f

t f f

f

t f A

k f

t f

t f A

t m

24

radian.

one n

larger tha is

FM Wideband

radian.

one an

smaller th is

FM Narrowband

(2.33)

) 2

sin(

2 cos )

(

(2.32)

)

2 sin(

2 )

(

(2.31)

index

M odulation

(2.30)

)

2 sin(

2

) ( 2

) ( (2.25),

f A

t s

t f t

πf t

f f

t

f f

f t

πf

d f

t

m c

c

m

c i

m

m m

c

t i i

sin(

)2

sin(

)2

cos(

)

(

)2

sin(

)2

sin(

sin

1)

2sin(

cos

small,is

Because

)34.2()2

sin(

sin)2

sin(

)2

sin(

cos)

2cos(

)2

sin(

2cos)

(

t f t

f A

t f A

t

s

t f t

f

t f

t f t

f A

t f t

f A

t f t

f A

t

s

m c

c c

c

m m

m

m c

c m

c c

m c

26

The output of Fig 2.21 is

s(t) differs from ideal condition in two respects:

1.The envelope contains a residual AM

(FM has constant envelope)

2 i(t) contains odd order harmonic distortions

For narrowband FM, ≤ 0.3 radians

) 2

sin(

) ( )

2 cos(

! 5

! 3 (sin

7 5

1 ) 2

( cos

) 2

cos(

) 2

( cos )

2 ( cos

(2.2)

)

2 ( cos )

( 1

)

(

) 2

cos(

) ( wave

modulating sinusoidal

with AM

For

(2.36) )

( 2 cos )

( 2

cos 2

1 ) 2

( cos

(2.35)

)

2 )sin(

2 ( sin )

2 ( cos )

t f f

A t

f A

t f t

f A

k t

f A

t f t

m k A

t

s

t f t

m

t f f

t f f

A t

f A

t f t

f A

t f A

t

s

m c

m c

c c

c

m c

c a c

c

c a

c

m

m c

m c

c c

c

m c

c c

) 2

envelope complex

the is

)

(

~

and part

real the

denotes Re

where

(2.38)

)) ( 2

exp(

) (

~ Re

)) 2

sin(

2 exp(

Re )

(

sin cos

exp

(2.33)

)

2 sin(

2 cos )

m c

c

m c

c

m c

c

t nf j

c t

s

t f j

A t

s

t

s

t f j

t s

t f j

t f j

A t

s

x j

x (jx)

t f t

f A

m m

(

is)(ofransform Fourier t

The

(2.48)

)(

2cos)

(

(2.47)

)

(2exp

)(Re

)

(

m c

m c

n c

m c

n c

m c

n c

nf f

f nf

f f

J

A f

S

t s

t nf f

J A

t nf f

j J

2.For small , the FM signal is effectively composed of a carrier and

a single pair of side freqencies at narrowband FM

32

Example 2.2

33

Transmission Bandwidth of FM signals

With a specified amount of distortion , the FM signal is

effectively limited to a finite number of significant side

35

Example 2.3

In north America, the maximum value of frequency deviation is fixed at 75kHz for commercial FM broadcasting by radio If we take the modulation frequency W=15kHz, which is typically the

“maximum” audio frequency of interest in FM transmission, we find that corresponding value of the deviation ratio is

Using Carson’s rule of Equation (2.55) , replacing by D , and

replacing f m by W , the approximate value of the transmission

bandwidth of the FM signal is obtained as

B T=2(75+15)=180kHz

On the other hand , use of the curve of Figure 2.26 gives the

transmission bandwidth of the FM signal to be

BT=3.2 =3.2x75=240kHz

In practice , a bandwidth of 200kHz is allocated to each FM

transmission On this basis , Carson’s rule underestimates the

transmission bandwidth by 10 percent , whereas the universal curve

of Figure 2.26 overestimates it by 20 percent

5 15

36

Generation of FM signals

(2.56) ( )

The frequency multiplier output

(2.58)

Varactor diode VCO FM modulator

32-1

Crosby Direct FM Transmitter

32-2

Demodulation of FM signals

The frequency discrimination consists of a slope circuit

followed by an envelope detector

,

0

22

),2

(2

22

),2

(2)

T c

T c

T c

T c

B f

f

B f

B f

f a j

B f

f

B f

B f

f a j

Appendix 2.3 Hilbert Transform

) ( ˆ

1 )

(

ansform Hilbert tr

inverse The

(A2.31)

) (

1 )

( ˆ

g t

g

d t

g t

j f t

The Fourier transform of is

H(f)

36

Properties of the Hilbert Transform

(time domain operation)

If g(t) is real

) ( ˆ )

g(

0 )

( gˆ ) g(

3.

) ( is

) ( ˆ of transform 2.Hilbert

spectrum magnitude

same the

have )

( and

) (

g

t g t

( )

g t

For a band-pass system , we consider

 

) '

( 2 )

' (

~ ) ( from )

(

~ obtain can

We

(A2.55)

0

) ( 2 )

(

~

with to

limited is

) (

H~

and

) (

)

(

*

real is

) ( Since

(A2.54)

) (

*

~ )

(

~ )

(

2

(A2.53) to

ansform Fourier tr

Apply

(A2.53)

) 2

exp(

) (

*

~ )

2 exp(

) (

~ )

(

2

)

* 2

( have we

(A2.52)

From

functions pass

low are

-) ( h

~ and )

( ,

)

(

(A2.52)

)

2 exp(

) (

~ Re

)

(

) ( of tion representa

complex

The

(A2.51)

) ( )

( )

(

~

response impluse

complex the

Define

c c

c

c c

c c

Q

I

c

Q I

f f H f

H f

H f

H

f f

H f

f

H

f B B

f f

f H

f

H

t h

f f

H f

f H f

H

t f j

t h t

f j

t h t

h

z z v ju

v z

t t

h

t

h

t f j

t h t

h

t h

t

j h t

~ ) (

~ )

2 exp(

Re 2

1

)) (

2 exp(

) (

~ ) 2

exp(

) (

~ Re

2

1

) (

) (

Re 2

1

(A2.59)

) (

Re )

( Re

)

(

becomes (A2.58)

x h

t f j

d t

f j t

x f

j h

d t

x h

d t

x h

t

y

c

c c

42

) (

} {

(1)

) (

2

2 2

2

c

t nf f

j

t f j t

nf j

t nf j

nf f

dt e

dt e

e e

F

c

c c

) (

) (

1

0 ),

(

1

0 ),

(

1

0 ,

1

0 ,

1

0 ,

0 ,

令 , }

{

(2)

) (

2

) (

2

2 2

2 2

2 2

2

c c

c c

k f n

f j

k f n

f j

k n

f j k f j

k n

f j k f j

t f j t nf j t

nf j

nf f

f n

f n

n

f n

f n

n

f n

f n

n dk

e n

n dk

e n

n n

dk e

e

n n

dk e

e

n

dk dt

k nt dt

e e

e

F

c c c

c

c c

=

=

=

43

) 2

exp(

factor he

without t (t)

h

~

and

(t) y

~ (t), x

~ functions lowpass

equivalent

by the

systems and

signals bandpass

represent can

We

(A2.63)

) (

~

* ) (

~ )

)

(

~ ) (

~ )

(

~

2

have we

(A2.61) and

(A2.57) Comparing

t f j

t x t

h t

y

d t

x h

   

(A2.68)

)

( )

( )

( )

( (t)

2y

(A2.67)

)

( )

( )

( )

( (t)

2y

(A2.66)

) (

~ )

(

~ )

(

~

let

(A2.65)

) ( )

( )

( )

(

) ( )

( )

( )

(

(A2.64)

) ( )

( )

( )

( )

h t

x t

h

t x t

h t

x t

h

t y j t

y t

y

t x t

h t

x t

h j

t x t

h t

x t

h

t jx t

x t

jh t

h t

y

Q I

I Q

Q Q

I I

Q I

Q I

I Q

Q Q

I I

Q I

Q I

Procedure for evaluating the response

( 4

) (

~

* ) (

~ )

(

~ 2 Obtain .

3

) 2

exp(

) (

~ Re )

( 2

) 2

exp(

) (

~ Re

) (

) (

~

by )

( Replace 1.

t f j

t y t

y

t x t

h t

y

t f j

t h t

h

t f j

t x t

x

t x t

x

c

c c

To simplify the analysis

1 shift to the right by to align to the band-pass frequency

2 set , for (2.61) Recall

c

c

T c

(2.65) From (2.63) and (2.65) , we have

 

(2.67)

2

) ( 2

2 cos )

(

2 1

) 2

exp(

) (

~ Re )

(

0

1 1

T

f c

T

c

d m

k t

f t

m B

k aA

B

t f j t

s t

is a hybrid-modulated signal (amplitude , frequency)

However, provided that we choose 1, for all

using an envelope detector, we have

The bias term can be removed by a second frequency

discriminator with 2( ) , where 2( ) 1( ).

(2.71)

)(4

)(

~)

(

~)

(

(2.70)

)(

21)

(

~

(2.69)

)(

~)

(

~

2 1

0 2

1 2

t m aA k

t s t

s t

s

t

m B

k aA

B t

s

f H

f H

c f

T

f c

Let the transfer function of the second branch of Fig 2.30

be (complementary slope circuit)

50

FM Stereo Multiplexing

Two factors which influence FM stereo standards

1.Operation within the allocated FM channels

2.Compatible with monophonic radio receiver.

 ( ) ( )   ( ) ( )  cos( 4 ) cos( 2 ) (2.72) )

51

Figure 9-40 FM stereo generation block diagram

51-1

 In Figure 9-40, audio signals from both left and right

mircrophones are combined in an linear matrixing network

to produce an L+R signal and an L-R signal

 Both L+R and L-R are signals in the audio band and must

be separated before modulating the carrier for transmission

This is accomplished by translating the L-R audio signal

up in the spectrum

 As seen in Figure 9-40, the frequency translation is

achieved by amplitude-modulating a 38-kHz subsidiary

carrier in a balanced modulator to produce DSB-SC

51-2

Stereo FM transmitter using frequency-division multiplexing

51-3

Stereo FM transmitter: (a) block diagram; (b) resulting spectrum

SAC: Subsidiary Communication Authorization

51-4

 The stereo receiver will need a frequency-coherent 38-kHz reference signal to demodulate the DSB-SC

 To simplify the receiver, a frequency- and phase-coherent

signal is derived from the subcarrier oscillator by frequency division (÷2) to produce a pilot

 The 19-kHz pilot fits nicely between the L+R and DSB-SC

L-R signals in the baseband frequency spectrum

51-5

 As indicated by its relative amplitude in the baseband

composite signal, the pilot is made small enough so that

its FM deviation of the carrier is only about 10% of the

total 75-kHz maximum deviation

 After the FM stereo signal is received and demodulated to baseband, the 19-kHz pilot is used to phase-lock an

oscillator, which provides the 38-kHz subcarrier for

demodulation of the L-R signal

 A simple example using equal frequency but unequal

amplitude audio toned in the L and R microphones is used

to illustrate the formation of the composite stereo (without pilot) in Figure 9-41

51-6

Figure 9-41 Development of composite stereo signal The 38 kHz alternately

multiplies L-R signal by +1 and –1 to produce the DSB-SC in the balanced AM

modulator (part d) The adder output (shown in e without piot) will be filtered to reduce higher harmonics before FM modulation

51-7

Spectrum of stereo FM signal

SCA: Subsidiary communication authorization

(commercial-free program)

51-8

51-9

Reference : G M Miller “Modern Electronic Communication” 5th Edition, Prentice Hall

2.8 Nonlinear Effects in FM Systems

1.Strong nonlinearity, e.g., square-law modulators , hard limiter, frequency multipliers

2.Weak nonlinearity, e.g., imperfections

Nonlinear input-output relation

(2.73)

)

( )

( )

( )

Nonlinear Channel (device)

52

1

) ( 2 4

cos 2

1

) ( 2

cos

) 4

3 (

2

1

(2.74)

)

( 2

cos

) ( 2

cos )

( 2

cos )

(

) ( 2

)

(

) ( 2

cos )

(

signal FM

For

3 3

2 2

3 3 1

2 2

3 3

3

2 2

2 1

0

0

t t

f A

a

t t

f A

a

t t

f A

a A

a A

a

t t

f A

a

t t

f A

a t

t f A

a t

v

d m

k t

t t

f A

t

v

c c

c c

c c

c c

c c

c c

c c

t f

c c

W f

f f

rule s

2.9 Super Heterodyne Receiver

(Carrier-frequency tuning , filtering , amplification , and demodulation)

Commercial FM Broadcast、

Allocations and Sidebands

56

2.10 Noise in CW modulation System

1 Channel model: additive white Gaussian noise (AWGN)

2 Receiver model: a band-pass filer followed by an ideal demodulator

(2.81)

(SNR)

(SNR) merit

of

Figure

output

at the noise

of power average

signal d

demodulate the

of power average

)

SNR

(

ratio noise

to - signal output

-The

) ( of power average

) ( of power

average )

SNR

(

ratio noise

to - signal channel

-The

(2.80)

) ( )

( )

(

is

on demodulati for

signal filtered

The

(2.79)

) 2

sin(

) ( )

2 cos(

) ( )

(

: tion representa noise

narrowband

in noise filtered

The

C O O

t s

t n t

s

t

x

t f t

n t

f t

n

t

58