, . , , .

, , , . . , .

, F(w t) , .. , ,

F(wt) = A0 + A1sin(wt+y 1) + A2sin(2wt+y 2) + + Aksin(kwt+y k)+ =

A0 + B1sinwt + B2sin2wt + + Bksinkwt+

+ C1coswt + C2cos2wt + + Ckcoskwt + =

A0+a1+a2+ + ak+ ,

(1)

ac/image251.gif.

A0 . A1sin(wt+y 1) F(wt) ( - ). Aksin(kwt+y k) k . k , .. , ..

(1) , - Bksinkwt Ckcoskwt. Bk Ck .

ac/sac_12_1.gif

, . , , . , , , . Ak y k , Bk Ck - . , (. 1). .1 u(t)=10+20sin(500t-p /6)+5sin(1500t+p /4)+7sin(2500t+2p /3).

wt = a . F(a ), 2p ,

F(a ) = A0 + B1sina + B2sin2a + + Bksinka +

+ C1cosa + C2cos2a + + Ckcoska + =

= A0 + A1sin(a +y1) + A2sin(2a +y2) + + Aksin(ka +yk)+ .

ac/image252.gif.

(2)


, , , . , . (2). . , , .. .

ac/sac_12_2.gif

, , , .

(. 2 )), .. , F(a) = - F(a +p) F(a)+F(a +p)=0, . ,

F(a)+F(a +p)=A0 + A1sin(a +y1) + A2sin(2a +y2) + + Aksin(ka +yk)++ A0 - A1sin(a +y1) + A2sin(2a +y2) + + Aksin(ka +yk)+=0 , , .. k sin(ka +kp ) = - sin(ka ).

A0 + A2sin(a +y1) + A4sin(2a +y2) + + A2ksin(2ka +yk)+=0,

.

(. 2 )) F(a) = - F(- a) F(a) +F(- a)=0. ,

F(a ) +F(- a )= A0 + B1sina + B2sin2a + + Bksinka +

+ C1cosa + C2cos2a + + Ckcoska ++

+ A0 - B1sina - B2sin2a - - Bksinka +

+ C1cosa + C2cos2a + + Ckcoska +=

=2( A0 +C1cosa + C2cos2a + + Ckcoska +)=0 ,

, .

. 2 ) , , .. F(a ) = F(- a ), .


, .

I

ac/image253.gif.

,

i= I0 + I1sin(a +y 1) + I2sin(2a +y 2) + + Iksin(ka +y k)+ ,

ac/image254.gif.

ac/image255.gif,

ac/image256.gif

(3)

, .

,

ac/image257.gif

(4)


P .

ac/image258.gif.

, ,

ac/image259.gif

p q ,

(5)

(5) , .

S = UI,

P/(UI) cosφ.

ac/image261.gif , I U. P. , , , φ, . , φ .

(5) , , . .

Q = U1I1sinφ 1 + U2I2sinφ 2 + + UkIksinφ k +

, , , .. ac/image262.gif.


, .. , , .

, , .. :

. 3, u(t)=10+20sin(1000t- 30 )+5sin(3000t+45 ) , R = 20 , C = 50 L = 5 .

, .

. k-

,

xL1 = w 1L= 5 xC1 = 1/(w 1C) = 20 - . . xL0 = 0, xC0 = , , .

k-

ac/image264.gif.

k = 0, 1, 3, Z0 = 20 ; Z1 = 10- j5 ; Z3 = 2+j9 . , .

- I0 = U0/Z0 = 10/20 = 0.5 ; I1 = U1/Z1 = 20e- j30 /(10- j5) = 1.78e- j3.4 ; I3 = U3/Z3 = 5e j45 /(2+j9) = 0.54e- j32.4 .

i = 0.5+1.78sin(1000t- 3.4 )+0.54sin(1000t- 32.4 ) .

ac/image265.gif


, , . , .. , .

kf , kA kd.

, , ..

.

kf » 1.11.

kA = Um/U 1.414 ( 2).

, .. kd = U1/U.

, . , , 5%. 12.


( 20 )

, ?
( , - , , , , ( ) . , .
, , , , . , , . " ", , , , , "", . , . FAQ .


 13.06.2019 - 05:11: - Ecology -> ר - _.
12.06.2019 - 09:05: , - War, Politics and Science -> - _.
11.06.2019 - 18:05: - Experimental Physics -> Ѹ - _.
11.06.2019 - 18:03: , , - Upbringing, Inlightening, Education -> - _.
11.06.2019 - 13:23: , , - Upbringing, Inlightening, Education -> - _.
11.06.2019 - 13:18: , , - Upbringing, Inlightening, Education -> - _.
11.06.2019 - 06:28: - Astrophysics -> 110 - _.
10.06.2019 - 21:23: , , - Upbringing, Inlightening, Education -> - _.
10.06.2019 - 19:27: - Conscience -> - _.
10.06.2019 - 19:24: , - War, Politics and Science -> - _.
10.06.2019 - 19:14: - Conscience -> - _.
10.06.2019 - 08:40: - Economy and Finances -> - _.
Bourabai Research Institution home page

   - Bourabai Research Bourabai Research Institution