- , - , . , , , . .
, , - , s(t). . , , u(t) = f(t; a1, a2, am). ai . ai . s(t), .. s(t) ( ), u(t) . , s(t). u(t) , (carrier), (modulation). s(t) (modulating signal), (modulated signal). (demodulation).
:
u(t) = U×cos(wt+j),
: U, w j. , , (), () () . , , - (angle modulation). , .
(, ) , , ( ) . : , , .
, . . , , ( ) .
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5.1 5.1 /
(amplitude modulation, ) , . ( ) . .
s(t) Þ U(t) w j. U(t) . - :
u(t) = U(t)×cos(wot+jo), (5.1.1)
U(t) = Um×[1+M×s(t)], (5.1.2)
Um () s(t),
. , So, =So/Um. 0 1 . <1 s(t), . 5.1 ( s(t) = sin(wst)). (<<1) , .. , .
. 5.1. . 5.2.
. 5.2 , M 1 s(t). : M = (Umax - Um)/Um, : M = (Um - Umin)/Um, %.
(=1) , ( U(t) ).
>1 , . 5.3. , , .
. 5.3. . . 5.4. .
. W:
u(t) = Um[1+M×cos(Wt)]×cos(wot). (5.1.3)
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, , .
cos(x)×cos(y) = (1/2)[cos(x+y)+cos(x-y)] (5.1.3) :
u(t) = Umcos(wot) + (UmM/2)cos[(wo+W)t] + (UmM/2)cos[(wo-W)t] (5.1.4)
, W wo , wo, (wo+W) - , (wo-W) - (.5.4 , . 5.1). , 100%- . (5.1.4) , : , . .
-.
- (5.1.4):
u(t) = u(t) + u(t) + u(t).
p(t)=u2(t)=
=u2(t)+u2(t)+u2(t)+2u(t)u(t)+2u(t)u(t)+2u(t)u(t) (5.1.5)
p(t):
Pu =
( ), :
Pu = + + = Um2/2 + (UmM)2/4 (5.1.6)
:
( + )/ = 2/2, (5.1.7)
.. 50% 100%- .
, , .. . (. 5.1.5):
. 5.5.
h = (Um2 M2/4) /Pu = M2/(2+2) (5.1.8)
. 5.5, =1 33%, 20%.
Pmax. -:
Pmax = Um2 (1+M)2.
. , , , :
s(t) = an cos(Wnt+Fn), (5.1.9)
an Fn Wn . (5.1.9) (5.1.2) Man () Mn = Man, - :
u(t) = Um[1+ ncos(Wnt+Fn)]×cos(wot+jo). (5.1.10)
u(t) = Umcos(wot+jo) + (Um/2) Mncos[(wo+Wn)t+jo +Fn] +
+ (Um/2) Mncos[(wo-Wn)t+jo -Fn] (5.1.11)
. 5.6. .
. 5.6 - . wo, . , - .
:
1 0-200 . 5-5000 . ?
, .. 50 . 2×5 = 10 1 , .. 11 . : (200-50+5)/11 = 14 .
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-:
Bu(t) = u(t) u(t-t) dt. (5.1.12)
C , , u(t)=U(t)cos wot :
cos wot cos wo(t-t) = 0.5 cos wot + 0.5 cos wo(2t-t).
Bu(t) = U(t) U(t-t) dt + 0.5 U(t) U(t-t) cos wo(2t-t) dt. (5.1.13)
- U(t)U(t-t) 2wo, . U(t). :
Bu(t) @ BU(t). (5.1.14)
:
Bu(0) @ (1/2) BU(0).
:
Bu(t) = (5.1.15)
- .
( ) .
. 5.7 - ( ). : 30 , 3 , =1.
, 2wo 5 . ( 4/5) . . =1 , =0 ( ) .
. 5.7.
2-, 3- (.. {117, 120, 123} , {177, 180, 183} ..), . 2%, . , .
, .
. . :
y(t) = u(t) cos(wot) =
=U(t) cos(wot) cos(wot) = ½ U(t) + ½ U(t) cos(2wot). (5.1.16)
.5.8.
, , , 2w. . 5.8 , . , , . , : 2w , wo , 2 . , .. 1.
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-.
Dw :
y(t) = U(t) cos(wot) cos(wot-Dj) = ½ U(t) cos(-Dj) + ½ U(t) cos(2wot-Dj).
, Dw=p/2 .
:
y(t) = U(t) cos(wot) cos(wot-Dw) = ½ U(t) cos(-Dwt) + ½ U(t) cos((2wo-Dw)t),
(beat ) Dw.
.