1. 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) 3.2Amplitude Modulation 1. Am 1)Sinusoidal carrier wave c(t)=A c cos(2  f c t) 2) AM signal s(t) =A c [1+k a m(t)] cos(2  f c t) m(t) baseband m(t)cos(w c t) passband  cos(w c t) carrier frequency carrier amplitude message signal amplitude sensitivity

2. CNU Dept. of Electronics D. J. Kim2 Lecture on Communication Theory 3) s(t) 의 envelop 이 m(t) 와 똑같은 shape 이 될 조건 a) | K a m(t) | < 1 for all t b) f c >> W where W is message BW

3. CNU Dept. of Electronics D. J. Kim3 Lecture on Communication Theory 4) 주파수상에서의 표현 ex1) Single-Tone Modulator message m(t)=A m cos(2  f m t ) AM s(t)=A c [1+  cos(2  f m t)]cos(2  f c t) Where  = k a A m ; Modulation factor 100  = 100 k a A m ; percentage Modulation B T =2W

4. CNU Dept. of Electronics D. J. Kim4 Lecture on Communication Theory

5. CNU Dept. of Electronics D. J. Kim5 Lecture on Communication Theory 2. Switching Modulation v 1 (t) = A c cos( 2  (t)) + m(t)) If  m(t)   A c v 2 (t)  v 1 (t), c(t) > 0 0, c(t) <0  v 2 (t)  [A C cos(2  (t)) + m(t))] g To (t) where T 0 =1/f c m(t) BPF[v 2 (t)]

6. CNU Dept. of Electronics D. J. Kim6 Lecture on Communication Theory Diode function By Fourier series onoff

7. CNU Dept. of Electronics D. J. Kim7 Lecture on Communication Theory 3. Envelope Detector : AM radio receiver Charging time constant = (  f + R S ) C For Rapid charge (  f + R S )C << 1/f c Discharging time constant =

8. CNU Dept. of Electronics D. J. Kim8 Lecture on Communication Theory

9. CNU Dept. of Electronics D. J. Kim9 Lecture on Communication Theory 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. Limitations 1) Wasteful of power carrier power 2) Wasteful of BW 1/2 로 줄일 수 있다. LSB 와 USB 가 symmetry. 3. Modifications of AM 1) DSB-SC modulation : no carrier 2) VSB modulation : BW 를 약 1/2 로 3) SSB modulation : BW 를 1/2 로

10. CNU Dept. of Electronics D. J. Kim10 Lecture on Communication Theory 3.4 DSB - SC Modulation 1. DSB - SC signal

11. CNU Dept. of Electronics D. J. Kim11 Lecture on Communication Theory 2. Ring Modulator c(t) > 0 s(t)=m(t) c(t) < 0 s(t)= -m(t) + -

12. CNU Dept. of Electronics D. J. Kim12 Lecture on Communication Theory c(t) = BPF[s(t)] =BPF[c(t)m(t)]  f=f c = m(t) ( 주의점 ) Transformers are perfectly balanced and diodes are identical  no leakage of modulation frequency into modulator output 2W2W 2W2W -fc-fc fcfc 3fc3fc -3f c w M(f) S(f)

13. CNU Dept. of Electronics D. J. Kim13 Lecture on Communication Theory 3. Coherent detection or synchronous demodulation frequency coherent detection LPF Local Osc = +

14. CNU Dept. of Electronics D. J. Kim14 Lecture on Communication Theory Coherent Detection 특징 : perfect demodulation but 복잡 cost 4. Costas Receiver V(f) 2w2w f -2f c 2fc2fc 2w2w

15. CNU Dept. of Electronics D. J. Kim15 Lecture on Communication Theory 빠른 주파수 늦은 주파수 정상주파수 s(t) OSC 45 0 - 45 0

16. CNU Dept. of Electronics D. J. Kim16 Lecture on Communication Theory 5. Quadrature-Carrier Multiplexing or QAM In-phase Quadrature

17. CNU Dept. of Electronics D. J. Kim17 Lecture on Communication Theory Key points> Correct phase & frequency  Costas 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

18. CNU Dept. of Electronics D. J. Kim18 Lecture on Communication Theory 1.BPF 의 LSB 와 USB 가 symmetric 할 경우 2. BPF 의 LSB 와 USB 가 unsymmetric 할 경우 H(f) -fc-fc fcfc f LPF m(t) s(t) 0 -fc-fc fcfc FILTER H Q (T) FILTER H i (T) m(t)

19. CNU Dept. of Electronics D. J. Kim19 Lecture on Communication Theory H(f) 와 H I (f) H Q (f) 간의 관계는 ? 또한

20. CNU Dept. of Electronics D. J. Kim20 Lecture on Communication Theory SSB & VSB fcfc H I (f) jH Q (f) -fc-fc fcfc  H I (f) : symmetric component  -fc-fc fcfc  +jH Q (f)

21. CNU Dept. of Electronics D. J. Kim21 Lecture on Communication Theory 3.6 Vestigial Side-Band Modulation 1. Filtering 1) f c 를 중심으로 odd-symmetry  LSB(or USB) 의 vestige 만 보냄. 2) USB or LSB 0.5 1 1 f f f c +W fcfc f c -f v fc-Wfc-W fcfc f c +f v HIHI HQHQ HIHI HQHQ

22. CNU Dept. of Electronics D. J. Kim22 Lecture on Communication Theory 2.Television Signals 1)TV 신호의 특징 a)Video 신호가 large BW  대부분의 energy 가 low-frequency 에 b) 수신기가 간단, cheap  use envelope detection 2) 주파수 특성 color 3.58 MHz

23. CNU Dept. of Electronics D. J. Kim23 Lecture on Communication Theory 3. 0.75 MHz (25%) 의 LSB 를 full scale 로 보내는 이유  Envelope 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 방법 a) k a 를 줄인다. b) Vestigial sideband 의 폭을 늘인다. 3)TV 신호에서의 해법 a) 100% percentage modulation b) 0.75MHz 의 LSB due to cheap negligible distortion

24. CNU Dept. of Electronics D. J. Kim24 Lecture on Communication Theory 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)

25. CNU Dept. of Electronics D. J. Kim25 Lecture on Communication Theory 5. Pass-band 에서 BPF 로 구현 BPF : highly selective filters ( 예 : Crystal resonator) Multiple modulation 으로 구현 m(t)  BPF USB f fcfc f c +W 0 -f1-f1 f2f2 f1f1 -f2-f2 0 f 2 +f 1 easy BPF

26. CNU Dept. of Electronics D. J. Kim26 Lecture on Communication Theory 6. Time Domain Description of SSB (Baseband 에서 구현 ) Hartley modulator jH Q (f) H I (f)  H.T  -90 0 OSC m(t) s(t)

27. CNU Dept. of Electronics D. J. Kim27 Lecture on Communication Theory 7. Demodulation of SSB signal 1) 구현 2) Coherent detector : both in phase & in frequency a) Low-power 의 pilot carrier 를 전송 b) Highly stable oscillator 사용  still phase error 3) Phase error  가 있을 경우  Phase distortion Voice  insensitive to phase error  Donald Duck voice effect Music or Video  unacceptable   -90 0 s(t) LPF

28. CNU Dept. of Electronics D. J. Kim28 Lecture on Communication Theory 3.8 Frequency Translation f 3 = f 2 + f 1 f 5 = f 4 + f 3 = f 4  (f 2  f 1 ) = f 4  (f 2 -f 1 ) f 4  (f 2 +f 1 ) Upward Downward ex) f 1 = 0M f 2 = 44M  f 3 = 44M f 4 = 66M  f 5 = 110M, 22M ex) f 1 =110M f 2 = 1030M  f 3 = 920M, 1140M f 4 = 876M  f 5 = 44M, 1796M f 6 = 44M  f 7 = 0M, 88M   f3f3 f2f2 f4f4 f1f1 f5f5 TV DTV

29. CNU Dept. of Electronics D. J. Kim29 Lecture on Communication Theory 3.9 Frequency-Division Multiplexing ex2) Voice BW= 4kHz, SSB Basic Groups=12 Voice, f c =60+4nkHz. n=1~12 Super Groups= 5Basic Groups, f c =372+48nkHz. n=1~5 Master Group Very Large Group w 1 w 2 w 3 wnwn f w1w1 w2w2 wnwn w1w1 w2w2 wnwn

30. CNU Dept. of Electronics D. J. Kim30 Lecture on Communication Theory 3.4, 3.6, 3.8, 3.16, 3.21

31. CNU Dept. of Electronics D. J. Kim31 Lecture on Communication Theory 3.10 Angle Modulation 1. 장점 : better discrimination against noise and interference than AM 단점 : increased BW 2. Basic Definitions 1) PM 2) FM

32. CNU Dept. of Electronics D. J. Kim32 Lecture on Communication Theory 3) AM 과 다른점 a) AM 은 zero crossing 이 주기적, PM 과 FM 은 비주기적 b) AM 은 envelope 이 변화, PM 과 FM 은 constant carrier m(t) AM PM FM

33. CNU Dept. of Electronics D. J. Kim33 Lecture on Communication Theory 4) PM 과 FM 의 관계 : 미적분의 관계 4.11 Frequency Modulation 1. FM signal 1) 특징 : nonlinear modulation analysis is more difficult than AM

34. CNU Dept. of Electronics D. J. Kim34 Lecture on Communication Theory 2) FM signal

35. CNU Dept. of Electronics D. J. Kim35 Lecture on Communication Theory 2. Narrow-Band Frequency Modulation 1) 2)  = 2f m 3) 식 (1) 의 구현 (1) (2) (3)

36. CNU Dept. of Electronics D. J. Kim36 Lecture on Communication Theory 4) (2) (3) 식의 그림상에서 비교 문제 :envelope 이 변한다   0.3 radians  negligible 3. Wide-band FM 1) FM wave

37. CNU Dept. of Electronics D. J. Kim37 Lecture on Communication Theory FM wave

38. CNU Dept. of Electronics D. J. Kim38 Lecture on Communication Theory 2) Properties of Bessel function. a) For n even For n odd b) For n odd c)

39. CNU Dept. of Electronics D. J. Kim39 Lecture on Communication Theory 3) Observations. a) Spectrum, f c  nf m, n=0,1,2,…... b) for small , spectrum at f c,  f m  narrow-band FM c) Amplitude of carrier component J 0 (  ) varies with  example 3. Fixed freq (f m ) & varying amplitude (i, e,  f) Varing freq(f m ) & fixed amplitude (i, e,  f)

40. CNU Dept. of Electronics D. J. Kim40 Lecture on Communication Theory 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 2f m Wide band : BW  order of 2  f 2) Carson’s rule Approximate BW of FM by single tone f m 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 = 2n max f m where n max =largest value of integer n that satisfies the requirement  2n max 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

41. CNU Dept. of Electronics D. J. Kim41 Lecture on Communication Theory Universal curve 4) General case Highest frequency W  worst case tone f m Deviation ratio D : maximum possible amplitude   Ex4) FM radio in US  f=75KHz W= 15KHz  D= 75 / 15 = 5 By carson’s rule B T =2(75+15)=180KHz By universal curve B T = 3.2  75=240KHz 200KHz 사용

42. CNU Dept. of Electronics D. J. Kim42 Lecture on Communication Theory 5. Genetation of FM signals 1) Indirect FM a) Crystal controlled OSC : to provide frequency stability b) Frequency multiplier c) 식.

43. 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 audio f 1 =0.1MHz,  1 =0.2 radians.  100Hz   f 1 =20Hz 15KHz   f 1 =3KHz To make minimum  f=75KHz By solving  &  n 1 =75 n 2 =50 2) Direct FM a) FM f i (t)=f c +k f m(t) VCO 로 구성 (voltage controlled oscillator) VCO f i (t)=f c + k f m(t) m(t)  

44. 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 bias the larger the reverse voltage  the smaller the capacitance c) VCO 를 이용한 wide-band FM

45. 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 f 0 만 control 할 수 있도록 Narrow-band 로 구현 (m(t) 의 BW 에 비해 Narrow 하게 ) 6. Demodulation of FM signals 1) Direct Method frequency discriminator = slope circuit + envelope detector slope circuit

46. CNU Dept. of Electronics D. J. Kim46 Lecture on Communication Theory s(t) s 2 (t) s 1 (t) s o (t)

47. CNU Dept. of Electronics D. J. Kim47 Lecture on Communication Theory

48. 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 factor a) s(t) 의 spectrum 이 BW=B T 밖에서 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

49. CNU Dept. of Electronics D. J. Kim49 Lecture on Communication Theory 7. FM Stereo Multiplexing 1) 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)=[m l (t)+m r (t)]+[m l (t)-m r (t)]cos(4  f c t)+Kcos(2  f c t) where fc=19KHz pilot=19KHz: 8~9% of the peak freq. deviation. m l +m r or m l -m r : DSB-SC 3) 구조

50. CNU Dept. of Electronics D. J. Kim50 Lecture on Communication Theory 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

51. 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 PLL Near phase-lock : 즉  e (t)<0.5 radians. sin[  e (t)]   e (t)

52. CNU Dept. of Electronics D. J. Kim52 Lecture on Communication Theory BW of h(t)=BW of m(t)  1 (t)  v(t)

53. 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

54. 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

55. CNU Dept. of Electronics D. J. Kim55 Lecture on Communication Theory (a) (d) (c) (b) (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.

56. CNU Dept. of Electronics D. J. Kim56 Lecture on Communication Theory 3.13 Nonlinear Effect in FM system 1. Nonlinearties 1) 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

57. CNU Dept. of Electronics D. J. Kim57 Lecture on Communication Theory 3.14. The Superheterodyne Receiver 1. Tasks of receiver 1) Carrier-frequency tuning 2) Filtering 3) Amplification 2. Superheterodyne : RF IF  Detection(Demodulation) 3.28, 3.30, 3.45 BPF1 BPF2 LPF   50~860M LO 44M 55.25 - 11.25 = 44 image frequency  37.25 + 11.25 = 44 IF LO 