CNU Dept. of Electronics D. J. Kim 1 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) 3.2Amplitude Modulation 1. Am 1) Sinusoidal carrier wave c(t)=A c cos(2f c t) 2) AM signal s(t) =A c [1+k a m(t)] cos(2f c t) m(t) baseband m(t)cos(w c t) passband cos(w c t ) carrier frequency carrier amplitude message signal amplitude sensitivity
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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
CNU Dept. of Electronics
D. J. Kim2
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim3
Lecture on Communication Theory
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 ) ([M2Ak )] ( ) ( [
2A S(f) cac
cccc ffffffff
BT=2W
CNU Dept. of Electronics
D. J. Kim4
Lecture on Communication Theory
modulation 100%1 if
power totalpower band side total
31
2 2
2
A 81 power frequency -side-Lower
A 81 power frequency -side-Upper
A21 power Carrier
2c
2
2c
2
2c
CNU Dept. of Electronics
D. J. Kim5
Lecture on Communication Theory
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)]
CNU Dept. of Electronics
D. J. Kim6
Lecture on Communication Theory
Diode function
By Fourier series
1n2tf2cos1n2
121
c1n
1n
2 (t)gTo
signal AM
(t)vBPF
)cos(6 )cos(4
2
cff2 )tf2cos()t(mA41
2A
)tf()tf(
)t(m21)tf2cos()t(m
A41
2A
1n2tf2cos1n2
121)t(mtf2cosA)t(v
cc
c
cc
cc
c
c1n
1n
cc2
on off
CNU Dept. of Electronics
D. J. Kim7
Lecture on Communication Theory
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
W1CR
f1
l
c
CRl
CNU Dept. of Electronics
D. J. Kim8
Lecture on Communication Theory
CNU Dept. of Electronics
D. J. Kim9
Lecture on Communication Theory
3.3 Virtues, Limitations , and Modifications of AM
4) General caseHighest frequency W worst case tone fm
Deviation ratio D : maximum possible amplitude
Ex4) FM radio in US f=75KHz W= 15KHz D= 75 / 15 = 5By 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
fB
B )()(
CNU Dept. of Electronics
D. J. Kim42
Lecture on Communication Theory
5. Genetation of FM signals1) Indirect FM
a) Crystal controlled OSC : to provide frequency stability
b) Frequency multiplier
c) 식 .
t
0fcc
nn
33
221
t
0fcc
dt)t(mnk2tnf2cos'A)t('s
)t(sa......)t(sa)t(sa)t(sa)t(v
dt)t(mk2tf2cosA)t(s
CNU Dept. of Electronics
D. J. Kim43
Lecture on Communication Theory
d) Freq. Multiplier 2 개를 사용한 예
Ex5). ( 목적 ) fc=100MHz, minimum of f = 75kHz m(t) : 100Hz~15KHz audiof1=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
nn1059100nfnff
375020
75000Hz20f
f
..
min
nn 21
그리고
CNU Dept. of Electronics
D. J. Kim44
Lecture on Communication Theory
b) Oscillator 의 구현 예
c(t) : (varactor or varicap) + fixed capacitance
ex) p-n junction diode in reverse biasthe larger the reverse voltage the smaller the capacitance
c) VCO 를 이용한 wide-band FM
00
m0i
m0
0
021
0
21
m0
0i
m0
21
i
ff
c2c
tf2fftf
tf2c2c1f
cLL21tf
tf2c
c1ftf
tf2cctc
tcLL21tf
where
where
cos)(
cos)(
cos)(
cos)()(
)(
CNU Dept. of Electronics
D. J. Kim45
Lecture on Communication Theory
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
2Bff
2Bf,
2Bffa2j
2Bff
2Bf,
2Bffa2j
)f(H Tc
Tc
Tc
Tc
Tc
Tc
1
CNU Dept. of Electronics
D. J. Kim46
Lecture on Communication Theory
t0fc
T
fcT
c1
t0f
T
fcT
T1
TTT
11
TTT
1
t0fc
t0fcc
2dt)t(mk2tf2cos)t(m
Bk2
1aAB
)tf2jexp()t(s~Re)t(s
dt)t(mk2jexp)t(mBk2
1aABj
)t(s~Bjdt
)t(s~da)t(s~
02
Bf
2B
)f(S~2
Bfa2j
)f(S~)f(H~21)f(S~
02
Bf
2B
2B
fa4j)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 >
CNU Dept. of Electronics
D. J. Kim47
Lecture on Communication Theory
)()(~
)(
tmBk2
1aABts
1tmBk2
T
fcT1
T
f
detector envelope usemay wet, all for If
)t(maAk4)t(s~)t(s~)t(s
)t(mBk2
1aAB)t(s~
)f(H~)f(H~
cf210
T
fcT2
12
CNU Dept. of Electronics
D. J. Kim48
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim49
Lecture on Communication Theory
7. FM Stereo Multiplexing1) FM stereo 의 조건
a) The Tx has to operate within the allocated FM channelsb) Compatible with monophonic radio receivers
2) Multiplexed signalm(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
CNU Dept. of Electronics
D. J. Kim50
Lecture on Communication Theory
3.12 PLL
1. 용도 : Synchronization, frequency division / multiplicationindirect 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
0차이는
동일주파수
v
f21 k
k)t(m)t(v)t()t(if
CNU Dept. of Electronics
D. J. Kim51
Lecture on Communication Theory
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(ddt
)t(d)t(h)t(h)t(e)t(v
dt)t(vk2)t(
)t()t()t(k
)t(sinAAk)t(e
dt
tdthtK2
dttd 1
e0e )(
)()()(
CNU Dept. of Electronics
D. J. Kim52
Lecture on Communication Theory
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(mkk
dt)f(d
k21)t(v
)f(kjf)f(V1)f(LIf
)f()f(L1
)f(Lkjf
)f()f(Lkjf)f()f(H
kK
)f(V
v
f1
v
1v
1v
ev
ev
0
output
1(t) dtd
v(t)
vk21
CNU Dept. of Electronics
D. J. Kim53
Lecture on Communication Theory
5. PLL 의 BW 와 Lock Range
1) 1st-order H(s)=1
2) 2nd-order
)()(
)()(
)()()(
)()(
)(
)()(
)()(
)(
sHKssHK
ss
s21sHK2ss
K2KssHKs
ss
jffHKfL
ffL1
1f
L
L
1
2
Le2
0L1L
e
0
1e
where
RadianBW
W Range Lock
stable
0
L
L
L
L
L
1
2
K
K
0K
KsK
ss
)()(
)s()s(log20
1
2
LKlog )log(
decade/dB20
2
1
KsKs
sH
)(
0K, KKK
KKsKKsKKsK
ss
KK
K0HKw
1LL2
1L2L2
1LL
1
2
2
1LL
if stable
Range Lock
)()(
)(
CNU Dept. of Electronics
D. J. Kim54
Lecture on Communication Theory
(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
Hz21f,Hz
250K n0
)()(
logss
201
2
)wlog(1Klog
1L KKlog
1L KKlog1L KKlog
1Klog
CNU Dept. of Electronics
D. J. Kim55
Lecture on Communication Theory
(a)
(d)(c)
(b)
32f)d(
127f)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.
CNU Dept. of Electronics
D. J. Kim56
Lecture on Communication Theory
3.13 Nonlinear Effect in FM system
1. Nonlinearties1) Strong nonlinearity : square-law modulators, limiters, frequency multiplier2) 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
wffwffwff
ttfAa
ttfAattfAaAaAatv
dttmktttfAtvtvatvatvatv
c
cc
cc
cccccc
t
f
cci
iii
23 22
)(36cos41
)(24cos21)(2cos
43
21)(
)(2)( where
)(2cos)( input)()()()(
3
3
2
2
3
31
2
20
0
3
3210
2
조건주파수
)(cos)( ttf2Aa43Aatv c
3c3c1
w2f2BWff0 c
CNU Dept. of Electronics
D. J. Kim57
Lecture on Communication Theory
3.14. The Superheterodyne Receiver
1. Tasks of receiver1) Carrier-frequency tuning2) Filtering3) Amplification