情報通信工学2-ocw.dvi

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4 4.1 (Amplitude Modulation) (VSB: 4.1.1 ( ) (AM) m(t) f c s(t) = (1 + m(t)) c(t) =A c (1 + m(t)) cos(2ßf c t + ffi c ) = <[(1 + m(t)) A c e j2ßfct+ffic ] (4.1) c(t) = A c cos(2ßf c t + ffi c ) = = <[A c e j2ßfct+ffic ] (4.2) 4.1 AM(Amplitude Modulation ) DSB-SC SSB-SC AM (4.1) Modulating Signal m(t) AM Signal (1+m(t))cos2πfct 4.1: AM m(t) M(f) S(f) = A c 2 [M(f + f c)e jffic + ffi(f + f c )e jffic +M(f f c )e jffic + ffi(f f c )e jffic ] (4.3) 17

1: AM m(t) =a cos 2ßf m t f m fi f c s(t) = A c (1 + a cos 2ßf m t)cos(2ßf c t + ffi c ) = A c cos(2ßf c t + ffi c )+ A c 2 cos(2ß(f c f m )t + ffi c )+ A c 2 cos(2ß(f c + f m )t + ffi c ) = < 1+ a 2 e j2ßfmt + a 2 ej2ßfmt A c e j2ßfct+fficλ (4.4) S(f) = A c 2 [e jffic ffi(f + f c )+e jffic ffi(f f c )] + A ca 4 fe jffic [ffi(f + f c + f m )+ffi(f + f c f m )] + e jffic [ffi(f f c + f m )+ffi(f f c f m )]g 4.2: AM (1) 2 AM 4.3: AM (2) 18

4.1.2 (DSB-SC) m(t) s(t) = m(t) c(t) =A c m(t) cos(2ßf c t + ffi c ) = <[m(t) A c e j2ßfct+ffic ] (4.5). 4.4 Modulating Signal m(t) DSB-SC Signal m(t)cos2πfct 4.4: DSB-SC m(t) M(f) s(t) S(f) = M(f) Λ A c 2 [e jffic ffi(f + f c )+e jffic ffi(f f c )] = A c 2 [M(f + f c)e jffic + M(f f c )e jffic ] (4.6) ( )A 1 DSB-SC m(t) =a cos 2ßf m t f m fi f c (4.5) S(f) = A ca 4 f e jffic [ffi(f + f c + f m )+ffi(f + f c f m )] + e jffic [ffi(f f c + f m )+ffi(f f c f m )]g (4.7) 4.5: DSB (1) 19

1 DSB-SC 4.6: DSB (2) 4.1.3 (SSB) s(t) = A c m(t) cos(2ßf c t + ffi c ) A c ^m(t) sin(2ßf c t + ffi c ) = < m(t) ± j ^m(t) A c e j2ßfct+fficλ (4.8) ^m(fi) h(fi) = 1 ßfi (4.9) H(f) = ( j; f>0 0; f =0 +j; f<0 = ( e jß=2 ; f > 0 0; f =0 e +jß=2 ; f < 0 (4.10) ( ß=2 m(t) m(t) 1 ^m(fi) ^M(f) (4.8) S(f) = A c 2 [M(f + f c)e jffic + M(f f c )e jffic ] ^M(f) = M(f)H(f) (4.11) j A c 2 [ ^M(f + f c )e jffic ^M(f f c )e jffic ] (4.12) = A c 2 f[m(f + f c) j ^M(f + f c )]e jffic +[M(f f c ) ± j ^M(f f c )]e jffic g (4.13) ( M(f + fc j ^M(f ); f> f c + f c )= 0; f = f c (4.14) M(f f c ); f< f c ( M(f fc j ^M(f ); f>f c f c )= 0; f = f c (4.15) M(f f c ); f<f c (4.12) f >f c ( f< f c M(f f c ) M(f + f c ) USB(upper side-band: 0 <f<f c ( f c <f<0 M(f f c ) M(f + f c ) LSB(lower side-band: 1 h(fi) H(f) 20

1 SSB-SC m(t) =a cos 2ßf m t f m fi f c ^m(t) =asin 2ßf m t s(t) =A c a cos 2ßf m t cos(2ßf c t + ffi c ) A c a sin 2ßf m t sin(2ßf c t + ffi c ) s U (t) =A c a cos(2ß(f c + f m )t + ffi c ) s L (t) =A c a cos(2ß(f c f m )t + ffi c ) 4.7: SSB(LSB) (1) 2 SSB-SC 4.8: SSB(LSB) (2) 21

4.1.4 AM m(t) A c cos(2ßf c t + ffi c ) ( ( f(x) =ffx + fix 2 s(t) s(t) = f(m(t) +A c cos(2ßf c t + ffi c )) = ffm(t) +ffa c cos(2ßf c t + ffi c ) +fim 2 (t) +2fim(t)A c cos(2ßf c t + ffi c )+fia 2 c cos2 (2ßf c t + ffi c ) = A c ff(1 + 2fi ff m(t)) cos(2ßf ct + ffi c ) ffm(t) +fim 2 (t) +fia 2 c cos2 (2ßf c t + ffi c ) f c AM A c ff(1 + 2fi ff m(t)) cos(2ßf ct + ffi c ) (2fi=ff) 4.9 AM m(t) V f c 1X [V + m(t)]ffi(t m=f c ) (4.16) m= 1 (f c ) AM 4.10 m(t) mt )?JELA @ALE?A fc v fc v(t) v vt 4.9: 4.10: DSB-SC 4.11 DSB-SC AM AM DSB-SC 4.12 SSB SSB 4.13 4.14 DSB-SC 22

m(t) Ac[1+m(t)]cos2 AM 2 modulator fct m(t) v out s(t)=acm(t)cos2 Ac 2 cos2 fct m(t) AM modulator Ac[1 m(t)]cos2 fct 2 fct Square-wave carrier (fc ) 4.11: 4.12: m(t) Accos2 fct Hilbert transform s(t) m(t) Highpass Filter s(t) 90 m(t) Acsin2 fct Accos2 fct 4.13: 4.14: DSB-SC 4.1.5 AM AM 4.15 Capacitor voltage, Carrier envelope Carrier in 4 + L c out t 4.15: 4.16: A c (1 + m(t)) cos(2ßf c t + ffi c ) A 2 c [ 1 2 + m(t) (t) +m2 ][1 + cos(2ß2f c t +2ffi c )] (4.17) 2 m(t) m(t) 2 A c (1 + m(t)) cos(2ßf c t + ffi c ) cos(2ßf c t + ψ) 2 m 2 (t)=2 1 2 (A c(1 + m(t))[cos(ffi c ψ) + cos(2ß2f c t + ffi c + ψ)] (4.18) 23

2f c m(t), ffi c ψ =0ffi c ψ = ß=2 3 DSB-SC A c m(t) cos(2ßf c t + ffi c ) C cos(2ßf c t + ffi c ) C(1 + A c C m(t)) cos(2ßf ct + ffi c ) (4.19) Ac C m(t) A c m(t) cos(2ßf c t + ffi c ) cos(2ßf c t + ψ) 1 2 A cm(t)[cos(ffi c ψ) + cos(2ß2f c t + ffi c + ψ)] (4.20) 2f c m(t), ffi c ψ =0ffi c ψ = ß=2 4 SSB-SC SSB-SC DSB-SC ( ) SSB-SC AM DSB-SC ( ) 3, 1 Ac cos(ffic ψ) 4 2 24

4.2 (PM: Phase Modulation),, (FM: Frequency Modulation) FM FM 4.2.1 s(t) = A c cos(2ßf c t + ffi(t)+ffi c ) (4.21) = < e jffi(t) A c e j2ßfct+fficλ ffi(t) f i (t) = 1 d 2ß = f c + 1 2ß dt (2ßf ct + ffi(t)) dffi(t) dt (4.22) ffi(t) m(t) k p ffi(t) =k p m(t) (4.23) ffi max = k p max[jm(t)j] (4.24) (modulation index) m(t) f i (t) =f c + k p dm(t) 2ß dt (4.25) m(t) f i (t) f c = 1 d 2ß dt ffi(t) =k f m(t) (4.26) k f f max = k f max[jm(t)j] (4.27) m(t) W fi f = f max =W m(t) ffi(t) = 2ßk f Z t 1 m(fi)dfi (4.28) 25

4.2.2 (4.25) m(t) dm(t)=dt (4.28) m(t) m(t) 4.17 4.17: m(t) = cos 2ßf m t max[jm(t)j] =1 ffi max = k p f i (t) =f c k p f m sin! m t (4.29) sin! m t k p f m ( k p ) m(t) = cos 2ßf m t k f =f m ( k f ) ffi(t) = 2ßk f 2ßf m sin 2ßf m t (4.30) sin! m t ( ) k f =f m 26

4.2.3 ffi(t) fi 1 (4.22) s(t) = A c cos(2ßf c t + ffi(t)) = A c cos 2ßf c t cos ffi(t) A c sin 2ßf c t sin ffi(t) ß A c cos 2ßf c t A c ffi(t) sin 2ßf c t (4.31) 5 f c A c DSB A c ffi(t)sin2ßf c t (4.31) AM A c (1 + ffi(t)) cos 2ßf c t reffig:pm-am-vectors 6 sin2πf t c sin2πf t c cos2πf t c cos2πf t c modulating signal component 4.18: m(t) = cos 2ßf m t s(t) = A c cos(2ßf c t + k p m(t)) = A c cos(2ßf c t + k p cos 2ßf m t) = +1X J n () n A c J n (k p ) cos(2ß(f c + nf m )t) (4.32) n= 1 J n (fi) = ß +1X k=0 kn p 2 n n! ( 1) k ( kp 2 )n+2k k!(k + n)! (4.33) k p (4.32) f c f m k p PM 98%, W 7 (Carson 2(k p max[jm(t)j] +1)W (4.34) 5 ffi<<1sin ffi ß 0, cos ffi ß 1 6 AM (ffi(t) fi 1) () PM ( (4.31) 7 m(t) =cos2ßf mt 2(k p +1)f m 27

4.2.4 m(t) m(t) Armstrong sin ct 90 phase shift cos ct Carrier signal source sin ct Adder FM signal mt To remainder of oscillator m(t)= sin mt Blanced modulator m(t)sin ct= sin mt sin ct 4.19: ( ) 4.20: (Armstrong ) 4.2.5 ( ) ( ) (Phase Lock Loop:PLL) Loop Filter ( ) A i cos2 f o t A o cos(2 f o t+ ) Frequency selective network (a) Diode Demodulator A o Intput signal Phase comparator Loop filter / B Output signal A o A i R o Linear Section, slope= d(a o A i ) df VCO (b) f f o 4.22: PLL 4.21: 28

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