振幅変調（1） - ist.aichi-pu.ac.jp

1 AM Amplitude Modulation FM (Frequency Modulation) PM (Phase Modulation)FM,PM AM AM Carrier C(t)=Accos( ) Ac S(t) Ac A[1+ks(t)] A s(t)=s0s1(t) AM(t)=A{1+ks0s1(t)}cos( ct+ c) s1(t) ma =ks0 AM(t)=A{1+ mas1(t)}cos( ct+ c)ma ma<1ma 1 ma= AM(t)/A={1+ mas1(t)}cos( ct+ c)AM cos mt m: modulating signal c=0 AM(t)=A{1+macos m }cos c = Acos c +Amacos m cos c = Acos ct+(Ama/2)cos( m+ c)t+(Ama/2)cos( m- c)t c ( m+ c) ( )( c- m) mma c- mAma/2A c c+ mAma/2 m- mAma/2 AAma/2 A ej ct Ama/2ej( c+ m)t Ama/2ej( c- m)t m- mAma/2 AAma/2 A ej ct+Ama/2ej( c+ m)t+Ama/2ej( c- m)t AM(t)=Re[A ej ct{1+ma /2 ej mt+ma/2 e-j mt] m 1~ 2 mma c- mAma/2A c c+ mAma/2 1 2 c c+ 1 c- 1 1~ 2 S( ) AM(t)= A{1+ks(t)}cos( ct) = Acos ct +Aks(t)cos ct=Acos c +Ak(1/2 ) + - S( )ej td (1 /2){ej ct+e-j ct }=Acos c +Ak(1/4 ) + - S( )ej( + c)td +Ak(1/4 ) + - S( )ej( - c)td =Acos c +Ak(1/4 ) + - S( - c)}

2 Ej td +Ak(1/4 ) + - S( + c)ej td 1~ 2 S( ) ej AM(t)= Acos c +Ak(1/4 ) + - S( ) ej{( + c)t+ } } d + Ak(1/4 ) + - S( ) ej{( - c)t+ } } d S( ) S(- ) - = - [- 2 - 1] [ 1 2] 2 AM(t) + - S( ) ej{( + c)t+ } } d = - 1- 2 S( ) ej{( + c)t+ } } d + 2 1 S( ) ej{( + c)t+ } } d AM 1 2 c c + 1 c - 1 =( c+ 2)-( c- 2)=2 2 c+ 2 c- 2 Pc=(A/ 2)2=A2/2 Ps=2{ Ama/2 / 2}2=ma 2A2/4 ma=1 Ps=A2/4 Ps/(Ps+Pc)=1/3 P(t)=A2(1+macos mt)2/2 Pmax=A2(1+ma)2/2 ma=1 Pmax=A222/2=2A2 ma=0 Pmax=A2/2 AM(t)=A{1+ macos mt}cos( ct) cos ct AM(t)=A{1+ macos mt}cos2 ct= A{1+ macos mt}(cos2 ct+1)/2= A/2{1+ macos mt} + A/2{1+ macos mt}(cos2 ct) cos mt =( c+ 2)-( c- 2)=2 2 1 2 c c + 1 c - 1 c+ 2 c- 2 2- c+ 1, c+ 2 maA/2 cos( c+ m)t A cos ct s(t)= A cos ct+ maA/2 cos( c+ m)t s(t)= A cos( ct)+ maA/2cos( c+ m)t | s(t)|= {A 2 +(maA/2)2-A maAcos( - mt)}= {A 2 +(maA/2)2+A maAcos mt} = ct+tan-1((maA/2)sin mt/(A +maA/2cos mt))A >>maA/2 = ct+(maA/(2A ))sin mt ct mt s(t)= {A 2 +(maA/2)2+A maAcos mt}cos A >>maA/2 ( ct= )| s(t)|= A (1+Ama/(2A )cos mt) = ct+(maA/2A )sin mt s(t)= | s(t)|cos mt ct DSB 3/4 A2 1/2+1/8+1/8 SSB.

3 1/8A2 1/6 1/2 1 2 c c + 1 c - 1 c+ 2 c- 2 1 2 c 1/21 g(x)=c0+c1x+c2x2+c3x3+.. s(t)+Acos ct x (X4 )g(x)=c0+c1(s(t)+Acos ct)+c2(s(t)+Acos ct)2+ c3(s(t)+Acos ct)3 cos 0 ct cos 1 ct cos 2 ct cos 3 ct Acos cts(t) cos ct g(x)=A(c1+3c3A2)cos ct+2c2As(t)cos ct+3c3As(t)2cos ct+..c=c1+3c3A2 g(x)=Ac{1+2c2s(t)/c+3c3s(t)2/c+..}cos ct c3 s(t) Acos ct +s(t) c=c1+3c3A2 g1(x)=Ac{1+2c2s(t)/c+3c3s(t)2/c}cos ctAcos ct -s(t) g2(x)=Ac{1-2c2s(t)/c+3c3s(t)2/c}cos ct g1(x)-g2(x) s(t) XY Acos ct X-Y Acos ct -s(t)Acos ct + s(t) s(t)+Acos ct c AM OO s(t) B AA CC B s(t) B C AA C C B s(t) B AA C C B C s (t)-s (t) c c c c n=- cnein ct c AM SSB - fading 190 90 2 2+ 1(t)= (Ama/2)cos{( m+ c)t+ c}+(Ama/2)cos{( m- c)t+ c} 2(t)= (Ama/2)cos{( m+ c)}

4 T- + c} +(Ama/2)cos{( m- c)t+ c} 1(t)+ 2(t)= Amacos{( m- c)t+ c} 1(t)- 2(t)= Amacos{( m+ c)t+ c} AM AM(t)=A{1+ks(t)}cos( ct+ c) c cos( ct) ed(t)= A{1+ks(t)}cos( ct) cos( ct) = A{1+ks(t)} {cos(2 ct)+1}/2= A/2{1+ks(t)}+A/2{1+ks(t)} cos(2 ct) s(t) ed(t)= A{1+ks(t)}cos( ct) cos( ct+ ) cos( ct) cos( ct+ ) = {cos(2 ct+ )+cos( )}/2 = 1/2{cos(2 ct)cos -sin(2 ct)sin )+cos( )}=1/2 {cos(2 ct)+1}cos -1/2 sin(2 ct)sin cos ct cos mtcos ctcos ct= cos mt(cos2 ct +1)/2 g(x)=c0+c1x+c2x2+..x AM A{1+ks(t)}cos ct g(x)=c2A2ks(t)+c2A2k2s(t)2/2s(t) 1 2 n 12n 1 2 n 12n 1 n (kHz) 122460728496f (kHz)