chapter 3. continuous-wave modulation

CNU Dept. of Electronics

D. J. Kim1

Lecture on Communication Theory

Chapter 3. Continuous-wave modulation

3.1 Introduction

modulation: the process by which some characteristic of a carrier is varied in accordance with a

modulating wave(signal)

3.2 Amplitude Modulation

1. Am1) Sinusoidal carrier wave

c(t)=Ac cos(2fct)

2) AM signal

s(t) =Ac [1+ka m(t)] cos(2fct)

m(t)baseband

m(t)cos(wct)passband

cos(wct)

carrier frequencycarrier amplitude

message signalamplitude sensitivity


D. J. Kim2


3) s(t) 의 envelop 이 m(t) 와 똑같은 shape 이 될 조건a) | Kam(t) | < 1 for all t

b) fc >> W where W is message BW


D. J. Kim3


4) 주파수상에서의 표현

ex1) Single-Tone Modulator

message m(t)=Am cos(2f m t )

AM s(t)=Ac [1+cos(2f m t)]cos(2fc t)

Where = kaAm ; Modulation factor

100 = 100 kaAm ; percentage Modulation

)] (M ) ([M2

Ak )] ( ) ( [

2

A S(f) cac

cccc ffffffff

BT=2W


D. J. Kim4


modulation 100%1 if

power total

power band side total

3

1

2 2

2

A 8

1 power frequency -side-Lower

A 8

1 power frequency -side-Upper

A2

1 power Carrier

2c

2

2c

2

2c


D. J. Kim5


2. Switching Modulation

v1(t) = Accos(2(t)) + m(t))

If m(t) Ac

v2(t) v1(t), c(t) > 0

0, c(t) <0

v2(t) [AC cos(2(t)) + m(t))] gTo(t)

where T0=1/fc

m(t)

BPF[v2(t)]


D. J. Kim6


Diode function

By Fourier series

1n2tf2cos1n2

1

2

1c

1n

1n

2

(t)gTo

signal AM

(t)vBPF

)cos(6 )cos(4

2

cff2 )tf2cos()t(mA

41

2

A

)tf()tf(

)t(m2

1)tf2cos()t(m

A

41

2

A

1n2tf2cos1n2

1

2

1)t(mtf2cosA)t(v

cc

c

cc

cc

c

c1n

1n

cc2

on off


D. J. Kim7


3. Envelope Detector : AM radio receiver

Charging time constant = (f + RS ) C

For Rapid charge (f + RS )C << 1/fc

Discharging time constant =

BW message Wwhere

W

1CR

f

1l

c

CRl


D. J. Kim8



D. J. Kim9


3.3 Virtues, Limitations , and Modifications of AM

1. Virtues 1) easy modulator: switching mod, square-law modulator

demodulator: envelop detector, square-law detector

2) relatively cheap

2. Limitations1) Wasteful of power carrier power

2) Wasteful of BW 1/2 로 줄일 수 있다 .

LSB 와 USB 가 symmetry.

3. Modifications of AM1) DSB-SC modulation : no carrier

2) VSB modulation : BW 를 약 1/2 로3) SSB modulation : BW 를 1/2 로


D. J. Kim10


3.4 DSB - SC Modulation

1. DSB - SC signal

)t(m)tf2cos(A

)t(m)t(c)t(s

cc

)ff(M)ff(MA2

1)f(S ccc


D. J. Kim11


2. Ring Modulator

c(t) > 0 s(t)=m(t)

c(t) < 0 s(t)= -m(t)

+ -


D. J. Kim12


c(t) =

BPF[s(t)] =BPF[c(t)m(t)] f=fc

= m(t)

( 주의점 ) Transformers are perfectly balanced and diodes are identical

no leakage of modulation frequency into modulator output

]1n2tf2cos[1n2

)1(4c

1n

1n

tf2cos4

c

2W2W

-fcfc 3fc-3fc

w

-3fc

M(f)

S(f)


D. J. Kim13


3. Coherent detection or synchronous demodulation

frequency coherent detection

'ffcc

null quadrature

;0)t(v90if

)t(m2

1'AA

2

1)t(v45if

)t(m'AA2

1)t(v0if

)t(m]cos['AA2

1)t(v

0

0

cc0

0

cc0

cc0

LPF

)t'f2cos('A)t(c cc Local Osc

)(0 tv)t(s

)t(m]t)'ff(2cos['AA2

1)]t(v[LPF)t(v cccc0

)t(m)tf2cos(A)t'f2cos('A)t(v cccc

)t(mt)'ff(2cos'AA2

1cccc

)t(mt)'ff(2cos'AA2

1cccc

=

+

)t(v


D. J. Kim14


Coherent Detection 특징 : perfect demodulation

but 복잡 cost

4. Costas Receiver

)t(m'AA2

1)t(v

0,'ff

cc0

cc

: coherent phase &frequency

00Q

)t(mI

: torDiscrimina Phase

real : m(t)

근거구현

V(f)

2wf-2fc 2fc

2w


D. J. Kim15


sin

1

sin

)t(mcos

)t(msin,

φφsin

1φcos ,

channel I

channel Q small for

빠른 주파수

늦은 주파수 정상주파수

s(t)

OSC

450

- 450


D. J. Kim16


5. Quadrature-Carrier Multiplexing or QAM

)tf2sin()t(mA)tf2cos()t(mA)t(s c2cc1c

In-phase Quadrature


D. J. Kim17


Key points> Correct phase & frequencyCostas Receiver 사용

Send a pilot signal outside the passband of the modulated signal

Pilot : Low power sinusoidal tone whose frequency and phase are related to c(t)

Add pilot signal of small carrier

3.5 Filtering of side-bands

)t(m2

1)t(r

)t(m2

1)t(r

)tf4sin()t(m2

1)tf4cos()t(m)t(m

2

1

)tf2cos()tf2sin()t(m)tf2cos()tf2cos()t(m

)tf2cos()t(s)t(r

22

11

c2c1

cc2cc1

c

LPF

LPF

<Band pass filtering>


D. J. Kim18


1.BPF 의 LSB 와 USB 가 symmetric 할 경우

2. BPF 의 LSB 와 USB 가 unsymmetric 할 경우

H(f)

-fcfc

f

LPFm(t) s(t)

)tf2cos(A cc

0

-fc fc

FILTERHQ(T)

FILTERHi(T)

m(t)


D. J. Kim19


H(f) 와 HI(f) HQ(f) 간의 관계는 ?

또한

)tf2sin()t(s)tf2cos()t(s)t(scQcI

)ff(S)ff(Sj2

1)ff(S)ff(S

2

1)f(S

)f(H)ff(M)ff(M2

A)f(

cQcQcIcI

ccc

LPF

S

BPF

식

식

,

)cff(H)cff(H)f(IH

Wf)ff(H)ff(H)f(M2

A

Wf),ff(S)ff(S)f(S

)f2f(S)f(Sj2

1)f2f(S)f(S

2

1)ff(S

)f(S)f2f(Sj2

1)f(S)f2f(S

2

1)ff(S

ccc

ccI

cQQcIIc

QcQIcIc

,

)cff(H)cff(Hj)f(QH

Wf)ff(H)ff(H)f(M2

Aj

Wf)],ff(S)ff(S[j)f(S

ccc

ccQ


D. J. Kim20


SSB & VSB

fc

HI(f)

jHQ(f)

-fc fc

HI(f) : symmetric component

-fc fc

+jHQ(f)

component

symmetric-anti ; )ff(H)ff(H)f(jH ccQ


D. J. Kim21


3.6 Vestigial Side-Band Modulation

1. Filtering

1) fc를 중심으로 odd-symmetry

LSB(or USB) 의 vestige 만 보냄 .

2) USB or LSB

0.5

0.5

1

1

f

f

fc+Wfc

fc-fv

fc-W fc fc-fv

fc+fv

fc+fv

HI

HQ

HI

HQ


D. J. Kim22


2.Television Signals1)TV 신호의 특징

a)Video 신호가 large BW

대부분의 energy 가 low-frequency 에b) 수신기가 간단 , cheap use envelope detection

2) 주파수 특성

color

3.58 MHz


D. J. Kim23


3. 0.75 MHz (25%) 의 LSB 를 full scale 로 보내는 이유Envelope detection 에서 waveform distortion 을 줄이기

위해

1) Waveform distortion

add carrier component to apply envelope detector

Envelop detector output

2) m’(t) 에 의한 distortion 을 줄이는 방법a) ka를 줄인다 .

b) Vestigial sideband 의 폭을 늘인다 .

3) TV 신호에서의 해법a) 100% percentage modulation

b) 0.75MHz 의 LSB

due to cheap

)tf2sin()t('mAk2

1)tf2cos()t(mk

2

11A)t(s ccacac

21

2

a

a

ac

21

2

a

2

ac

)t(mk2

11

)t('mk2

1

1)t(mk2

11A

)t('mk2

1)t(mk

2

11A)t(a

negligibledistortion


D. J. Kim24


3.7 SSB

1. 방법 : USB 나 LSB 만 전송

2. 이유 : Message m(t) 가 실수 M(f) 는 conjugate symmetric

3. 문제점 : LSB 나 USB 가 붙어 있을 경우 filtering 이 어렵다 .

4. 적용분야 : Message spectrum 이 origin 에서 energy gap 이 있을 때

ex) Voice (-3400 ~ -300) (300 ~ 3400Hz)

)f(H

f


D. J. Kim25


5. Pass-band 에서 BPF 로 구현

BPF : highly selective filters ( 예 : Crystal resonator)

Multiple modulation 으로 구현

m(t) BPF

USB

ffc fc+W0

)tf2cos( c

-f1

f2

f1

-f2

0

f2+f1

easy BPF


D. J. Kim26


6. Time Domain Description of SSB (Baseband 에서 구현)

Hartley modulator

jH Q(f)

HI(f)

)fsgn(j)f(H, Q 즉

)tf2sin()t(m̂A2

1)tf2cos()t(mA

2

1)t(s

)tf2sin()t(m̂A2

1)tf2cos()t(mA

2

1)t(s

cccc

cccc

LSB

USB

H.T

-900

OSC

)tf2cos( c

)tf2sin( c

(t)m̂

m(t)

s(t)


D. J. Kim27


7. Demodulation of SSB signal1) 구현

2) Coherent detector : both in phase & in frequencya) Low-power 의 pilot carrier 를 전송b) Highly stable oscillator 사용 still phase error

3) Phase error 가 있을 경우

Phase distortionVoice insensitive to phase error Donald Duck voice effect

Music or Video unacceptable

-900

)tf2cos( c

)tf2sin( c

s(t)

(t)m̂

m(t)LPF

LPF

0f),jexp()f(M'AA4

1

0f),jexp()f(M'AA4

1

)f(V

)f(M)fsgn(j)f(M̂

sin)f(M̂cos)f(M'AA4

1)f(V

sin)t(m̂cos)t(m'AA4

1)t(v

cc

cc

0

cc0

cc0

여기서


D. J. Kim28


3.8 Frequency Translation

f3 = f2 + f1

f5 = f4 + f3= f4 (f2 f1)

= f4(f2-f1)

f4(f2+f1)

Upward

Downward

ex) f1= 0M f2= 44M f3 = 44M

f4= 66M f5 = 110M, 22M

ex) f1=110M f2= 1030M f3 = 920M, 1140M

f4= 876M f5 = 44M, 1796M

f6= 44M f7 = 0M, 88M

f3

f2f4

f1 f5

TV

DTV


D. J. Kim29


3.9 Frequency-Division Multiplexing

ex2) Voice BW= 4kHz, SSB

Basic Groups=12 Voice, fc=60+4nkHz. n=1~12

Super Groups= 5Basic Groups, fc=372+48nkHz. n=1~5

Master Group

Very Large Group

w1 w2 w3 wnf

w1

w2

wn

w1

w2

wn


D. J. Kim30


<HW #3> 3.4, 3.6, 3.8, 3.16, 3.21


D. J. Kim31


3.10 Angle Modulation

1. 장점 : better discrimination against noise and interference than AM

단점 : increased BW

2. Basic Definitions

1) PM

2) FM

dt

)t(d

2)t(f

)]t(cos[A)t(s

)t(

ii

ic

i

1 frequency ousinstantane

wavemodulated Angle

m(t) of function a angle, : Let

signal, modulated-frequency

ysensitivitfrequency

t0fcc

t0fci

fc

dt)t(mk2tf2cosA)t(s

dt)t(mk2tf2)t(

)t(mkf)t(f i

signal, modulated-phase

y sensitivit phase

)t(mktf2cosA)t(s

)t(mktf2)t(

pcc

pci


D. J. Kim32


3) AM 과 다른점a) AM 은 zero crossing 이 주기적 , PM 과 FM 은 비주기적b) AM 은 envelope 이 변화 , PM 과 FM 은 constant

carrier

m(t)

AM

PM

FM


D. J. Kim33


4) PM 과 FM 의 관계 : 미적분의 관계

4.11 Frequency Modulation

1. FM signal1) 특징 : nonlinear modulation

analysis is more difficult than AM


D. J. Kim34


2) FM signal

f - f :min

ff :max

deviation)frequency where

c

c

(Akf

)tf2cos(ff

)tf2cos(Akf)t(f

mf

mc

mmfci

tf2

tf2

tπf2)t(

f

Δf

t)πf2(sintπf2

t)πf2(sinf

Δftπf2

dt)t(f2)t(

c

c

c

m

mc

mm

c

t0 ii

: min

:max

angle the from angle the of departure maximum ;

index modulation ; where

phase

i

radian : FM band-wide

radian : FM band-narrow

signal FM

1

1

)tf2sin(tf2cosA)t(s mcc

)tf2cos(Am(t) mm consider

frequency ousinstantane


D. J. Kim35


2. Narrow-Band Frequency Modulation

1)

2) < BW of Narrow band FM > < BW of AM > = 2fm

3) 식 (1) 의 구현

tff2costff2cosA2

1tf2cosA)t(s

tff2costff2cosA2

1tf2cosA

)tf2sin(tf2sinAtf2cosA)t(s

)tf2sin()tf2sin(sin

1)tf2sin(cos

)tf2sin(sintf2sinA)tf2sin(costf2cosA

)tf2sin(tf2cosA)t(s

mmccccAM

mmccc

mcccc

mm

m

mccmcc

mcc

case AM

)180

57( radians. 1 : Band-Narrow

0

π

(1)

(2)

(3)


D. J. Kim36


4) (2) (3) 식의 그림상에서 비교문제 : envelope 이 변한다

0.3 radians negligible

3. Wide-band FM1) FM wave

m

mc

c

mcc

fts

tf2jAts

tf2jts

tf2jtf2jAts

withfunctionperiodic :

where

)(~sinexp)(~

exp)(~Re

sinexpRe)(


D. J. Kim37


FM wave

-nnc

n

n

)exp(JA(t)s

J 2

1)(J

kind first the of function Bessel order nth

xlet

where

series Fouriercomplex by Expand

tnf2j~

)(Ac

dxnxxsinjexp

dxnxxsinjexp2

Ac

tf2

dttnf2jtf2sinjexpAf

dttnf2jexp)t(s~fc

tnf2jexpc)t(s~

)t(s~

m

cn

cn

m

mmf2

1

f2

1cm

mf2

1

f2

1mn

nmn

m

m

m

m

nmcnc

nmcnc

tnff2cos)(JA

tnff2jexp)(JReA)t(s

mcmcnn

c nfffnfff)(J2

A)f(S

T.F


D. J. Kim38


)(J)(J

)(J)(J

nn

nn

n all for )(J)1()(J nn

n

2n,02

)(J

)(J

1)(J

n

1

0

n

2n 1)(J

2) Properties of Bessel function.

a) For n even For n odd

b) For n odd

c)


D. J. Kim39


3) Observations.a) Spectrum, fcnfm, n=0,1,2,…...

b) for small , spectrum at fc, fm narrow-band FM

c) Amplitude of carrier component J0() varies with

example 3.

Fixed freq (fm) & varying amplitude (i, e, f)

Varing freq(fm) & fixed amplitude (i, e, f)

2

cn

2

n

2

cA

2

1)(JA

2

1P

index moduiation : mf

f


D. J. Kim40


4. Transmission Bandwidth of FM signals.

1) BW of FM 의 개념 .

실제 FM: infinite number of side freq.

Effectively finite number of side freq.

Single tone FM case.

Narrow band : BW order of 2fm

Wide band : BW order of 2f

2) Carson’s rule

Approximate BW of FM by single tone fm

3) BW of FM the separation between the two freq beyond which none of the frequencies is greater

than

1% of the unmodulated carrier amplitude

= 2nmax fm

where nmax=largest value of integer n that satisfies the

requirement

m

mT

f)1(2

11f2f2f2B

def

01.0)(Jn

2nmax

Carson’s rule

0.1 0.3 0.5 1.0 2.0 5.0 10.0 20.0 30.0 2 4 4 6 8 16 28 50 70

2.2 2.6 3 4 6 12 22 42 62


D. J. Kim41


Universal curve

4) General case

Highest frequency W worst case tone fm

Deviation ratio D : maximum possible amplitude

Ex4) FM radio in US f=75KHz

W= 15KHz

D= 75 / 15 = 5

By carson’s rule BT=2(75+15)=180KHz

By universal curve BT= 3.275=240KHz

정결서에이사 curve universal

rule sCarson’

200KHz 사용

mTT

T ff

Bf

f

BB )()(


D. J. Kim42


5. Genetation of FM signals1) Indirect FM

a) Crystal controlled OSC : to provide frequency stability

b) Frequency multiplier

c) 식 .

t

0fcc

n

n

3

3

2

21

t

0fcc

dt)t(mnk2tnf2cos'A)t('s

)t(sa......)t(sa)t(sa)t(sa)t(v

dt)t(mk2tf2cosA)t(s


D. J. Kim43


d) Freq. Multiplier 2 개를 사용한 예

Ex5). ( 목적 ) fc=100MHz, minimum of f = 75kHz

m(t) : 100Hz~15KHz audio

f1=0.1MHz, 1=0.2 radians.

100Hz f1=20Hz

15KHz f1=3KHz

To make minimum f=75KHz

By solving & n1=75

n2=50

2) Direct FM

a) FM fi(t)=fc+kfm(t)

VCO 로 구성 (voltage controlled oscillator)

VCO fi(t)=fc+ kfm(t)m(t)

21

2112c

1

nn1059100

nfnff

375020

75000

Hz20f

f

..

min

nn 21

그리고


D. J. Kim44


b) Oscillator 의 구현 예

c(t) : (varactor or varicap) + fixed capacitance

ex) p-n junction diode in reverse bias

the larger the reverse voltage

the smaller the capacitance

c) VCO 를 이용한 wide-band FM

00

m0i

m

0

0

021

0

2

1

m

0

0i

m0

21

i

f

f

c2

c

tf2fftf

tf2c2

c1f

cLL2

1tf

tf2c

c1ftf

tf2cctc

tcLL2

1tf

where

where

cos)(

cos)(

cos)(

cos)(

)()(


D. J. Kim45


d) VCO 를 이용한 FM 에서 주파수 안정화를 위한 feedback scheme

가정 m(t) is zero mean

LPF 는 f0 만 control 할 수 있도록 Narrow-band 로 구현

(m(t) 의 BW 에 비해 Narrow 하게 )

6. Demodulation of FM signals1) Direct Method frequency discriminator

= slope circuit + envelope detector

slope circuit

otherwise , 0

2

Bff

2

Bf,

2

Bffa2j

2

Bff

2

Bf,

2

Bffa2j

)f(H Tc

Tc

Tc

Tc

Tc

Tc

1


D. J. Kim46


t0fc

T

f

cT

c1

t0f

T

f

cT

T1

TTT

11

TTT

1

t0fc

t0fcc

2dt)t(mk2tf2cos)t(m

B

k21aAB

)tf2jexp()t(s~Re)t(s

dt)t(mk2jexp)t(mB

k21aABj

)t(s~Bjdt

)t(s~da)t(s~

02

Bf

2

B)f(S

~

2

Bfa2j

)f(S~

)f(H~

2

1)f(S

~

02

Bf

2

B

2

Bfa4j

)f(H~

dt)t(mk2jexpA)t(s~s(t)

dt)t(mk2tf2cosA)t(s

otherwise ,

,

otherwise

of envelopecomplex

s(t) s2(t)

s1(t)

so(t)

)(~ ts1

)(~ ts2

< Balanced frequency discriminator >


D. J. Kim47


)()(~

)(

tmB

k21aABts

1tmB

k2

T

f

cT1

T

f

detector envelope usemay wet, all for If

)t(maAk4)t(s~)t(s~)t(s

)t(mB

k21aAB)t(s~

)f(H~

)f(H~

cf210

T

f

cT2

12


D. J. Kim48


2) Circuit diagram 으로 구현

각각의 Resonator 의 3-dB BW=2B 일 때 3B separation 이 ideal.

위 회로의 distortion factora) s(t) 의 spectrum 이 BW=BT밖에서 완전히 0 이 아니다 .

b) Tuned filter 가 완전히 band limit 되어 있지 않다 .

c) Tuned filter 특성이 모든 FM 대역에서 완전히 linear 하지 않다

cycle per dissipatedenergy

cycle one during circuit the in storedenergy Maximum2

circuit RLC for BW 3dB

)(f freq. Resonantfactor Q c


D. J. Kim49


7. FM Stereo Multiplexing1) FM stereo 의 조건

a) The Tx has to operate within the allocated FM channels

b) Compatible with monophonic radio receivers

2) Multiplexed signal

m(t)=[ml(t)+mr(t)]+[ml(t)-mr(t)]cos(4fct)+Kcos(2 fct)

where fc=19KHz

pilot=19KHz: 8~9% of the peak freq. deviation.

ml+mr or ml-mr : DSB-SC

3) 구조


D. J. Kim50


3.12 PLL

1. 용도 : Synchronization, frequency division / multiplication

indirect frequency demodulation.

2. PLL 의 구조

Locking 조건

다른 응용 : Coherent detection 용 clock generation

t

0v2

2cv

t

0f1

1cc

dt)t(vk2)t(where

)t(tf2cosA)t(r

dt)t(mk2)t(where

)t(tf2sinA)t(s

90 Phase

0차이는동일주파수

v

f

21 k

k)t(m)t(v)t()t(if


D. J. Kim51


3. Nonlinear Model of PLL

여기서 sin( ) : nonlinear function difficult to analyze

4. Linear Model of the PLLNear phase-lock : 즉 e(t)<0.5 radians.

sin[e(t)] e(t)

parameter gain-loop : k where

filter loop : e wher

gain multiplier; here W

0 vcvm

e01e

t

0v1

21e

m

evcm

AAkk

d)t(h)(sinK2dt

)t(d

dt

)t(d

)t(h)t(h)t(e)t(v

dt)t(vk2)t(

)t()t()t(

k

)t(sinAAk)t(e

dt

tdthtK2

dt

td 1e0

e )()()(

)(


D. J. Kim52


BW of h(t)=BW of m(t)

PLL of function transfer loop-open ; wherejf

)f(HKL(f)

)f()f(L1

1)f(

0

1e

)t(mk

k

dt

)f(d

k2

1)t(v

)f(k

jf)f(V1)f(LIf

)f()f(L1

)f(L

k

jf

)f()f(Lk

jf)f()f(H

k

K)f(V

v

f1

v

1

v

1

v

e

v

e

v

0

output

1(t) dt

d v(t)

vk2

1


D. J. Kim53


5. PLL 의 BW 와 Lock Range

1) 1st-order H(s)=1

2) 2nd-order

)(

)(

)(

)(

)()()(

)()(

)(

)()(

)()(

)(

sHKs

sHK

s

ss2

1sHK2ss

K2KssHKs

ss

jf

fHKfL

ffL1

1f

L

L

1

2

Le2

0L1

L

e

0

1e

where

RadianBW

W Range Lock

stable

0

L

L

L

L

L

1

2

K

K

0K

Ks

K

s

s

)(

)(

)s(

)s(log20

1

2

LKlog )log(

decade/dB20

2

1

Ks

KssH

)(

0K, KKK

KKsKKs

KKsK

s

s

K

KK0HKw

1LL2

1L2L2

1LL

1

2

2

1LL

if stable

Range Lock

)(

)(

)(


D. J. Kim54


(a) |z| < |p|

(b) |z| = |p|

즉 BW 과 Lock Range 을 별도 조절 가능

Computer Experiment II Acquisition Mode

a) acquisition

tracking

1L KK

2

1L K

KK

best 0.707

0.125Hz of step freq a for

이

0.1,707.0,3.0

Hz2

1f,Hz

2

50K n0

)(

)(log

s

s20

1

2

)wlog(1Klog

1L KKlog

1L KKlog1L KKlog

1Klog


D. J. Kim55


(a)

(d)(c)

(b)

3

2f)d(

12

7f)c(5.0f)b(Hz325.0f)a(

(b), (c), (d) 의 경우 Cycle slipping : Phase error of 2 radians a slip by one cycle

b) Variations in the instantaneous frequency of the PLL’s VCO for varying frequency step f.


D. J. Kim56


3.13 Nonlinear Effect in FM system

1. Nonlinearties1) Strong nonlinearity : square-law modulators, limiters,

frequency multiplier

2) Weak nonlinearity : due to imperfections.

2. Weak Nonlinearity 의 경우

( 결론 ) FM 은 Channel 로 전송 중 생기는 Amplitude Nonlinearity 에 의한 영향이 없다 .

Microwave radio, satellite communication system 에 사용 .

이 채널에서는 highly nonlinear Amp 와 power transmitter 를 사용한다 왜냐하면 maximum power 을 내는 것이 중요하기 때문 .

( 단점 ) Extremely sensitive to phase nonlinearities

wff

wffwff

ttfAa

ttfAattfAaAaAatv

dttmkt

ttfAtv

tvatvatvatv

c

cc

cc

cccccc

t

f

cci

iii

23

22

)(36cos4

1

)(24cos2

1)(2cos

4

3

2

1)(

)(2)( where

)(2cos)( input

)()()()(

3

3

2

2

3

31

2

20

0

3

3210

2

조건주파수

)(cos)( ttf2Aa4

3Aatv c

3

c3c1w2f2BW

ff0 c


D. J. Kim57


3.14. The Superheterodyne Receiver

1. Tasks of receiver1) Carrier-frequency tuning

2) Filtering

3) Amplification

2. Superheterodyne : RF IFDetection(Demodulation)

<HW #4> 3.28, 3.30, 3.45

757.25M

ch69

11.25M

ch2 LO

Tuning Channel

44MHzIF

801.25

806~800

ch69

55.25

60~54

ch2

RF ;TV ex)

FRLOLORFIF

fforfff

BPF1 BPF2 LPF 50~860M LO 44M

44M

55.25 - 11.25 = 44image frequency 37.25 + 11.25 = 44

IF

LO

chapter 3. continuous-wave modulation

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