А27402 Афанасьева НА Булат ЛП Электротехника и электроника Учебн пособие

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Методы по электротехнике

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.. , ..

-

3

-

.. , ..

- , : 260100 ; 260200 ( -: 260202 , , 260204 ); 260500 ( : 260504 , 260501 - ); 260300 ( : 260301 94 , 260303 )

- 2005

621.3 31.2+32.85 94 .., ..4

: . . .: , 2005. 178 .ISBN 5-89565-117-8

, , , , , . . , , : 260100, 260200, 2260300, 260500 , . - , - . - .

621.3 31.2+32.85 -- (. . , . .. ) . .. , . , . .. - ISBN 5-89565-117-8

- , 2005

5

, : 260100 ; 260200 (: 260202 , , 260204 ); 260500 (: 260504 , 260501 ); 260300 (: 260301 , 260303 ). - . 15 9 14 , 68 . , , - . , . : . . ., . .. , ..., . .. , ..., . .. , ..., . .. , . ..., . .. , .. .

6

, . - : , , , , , . . XVIII . , , . 70- XIX . - . . 7080 . XIX , . 90- XIX . ; . , , , . -- . , , , . , XVIIIXIX . , , , .

7

: . -, . () , , , , , . . () : , , . . , . , , , . , , . , . () . 1001500 . . , , , .

8

1. 1.1. . . (, , , .) . (. 1, ). , . (. 1, ).

a I E E I

I E E E

I R

9

, , . . . . , , , I, U, R. , , (. 2): S ( ); E ( ); HL ( ); ; pV ; R1, R2 : 1, 2, 3, 4 ; I, II 1 3 HL R1 HL E SS 3. 2

2

4 R2

II

II

4

, , . , . , , . . , , , . , (. 2, 13 12, 24). (. 2, 1, 2, 3, 4).10

. 1 2, (1 2) - R1. 3 4 , 3 = 4, , . , , (, . 2: 1 2 43 = 1). , (, . 2 I II). 1.2. () . . , , R = const, . , (. 3, ). U : I = , R . R , (. 3, ). , , .a

R U I

Rt U I

11

: (. 4, ) (. 4, ). R1 E R2 E R2 R3 R1

(. 5). . , , , (. 6). R1 E1 R2 E2 U R1 R2

1.3. . . , . . R 12

(). , () I 2, P R = . I2 , . , , R . . , . ( ), . - (. 7, ) (. 7, ) U = E + R I, R . U R I 0 I U E

; . , . , - , , .13

, , , . 1.4. , (. 8), , . Ub = a b, a b a b. I = Uab / R, Uab = IR. a I R Uab

b

, , I II . I , , . I , , (. 9). I : , , , . , , , , , , .

14

I3 I2 I1. 9k =1

Ik

n

= 0,

n , ; k . I1 I2 I3 = 0 II , . II , . II : , . + , , (. 10).

15

k =1

U k

m

= 0,

m .

k =1

Ek = Rk I k ,k =1

n

m

m ; n . I (R 1 + R 2) = E. 2. , , . R1 E I , I II . : ; ; (); ( ); . R2

16

2.1. . . , . : , , ( ); (, , , ); II ; , , , , I , : n = q 1, q ; II ; , , , . , .11, 5 3 . 11 , ; I : R1 R2 E1 E2 2 R6 3 R5 1 R3 E3 1 R4

17

1: I 1 I 2 I 3 I 4 = 0, 2: I 5 + I 2 I 1 = 0. , II , I, II, III: I: R1 I1 +R2 I2 = E1 E2, II: R3 I3 + R6 I5 R2 I2 = E2, III: (R4 + R5 ) I4 R3 I3 = E3. I1; I2; I3; I4; I5. , , , . : EI = RI 2. , . , + , , . , , , . . 2.2. , . , II -

18

, . I, II, III , . 11. , : I11; I22; I33. . , , : I1 = I11; I4 = I33; I5 = I22. : I 2 = I11 I22; I3 = I22 I33. , . , . 11, II : I: (R1 + R2) I11 R2 I22 = E 1 E2; II: (R2 + R3 + R 6) I22 R 2I11 R3I33 = E2; III: (R 3 + R4 + R5) I33 R 3I22 = E3. , ( ). . : R11I11 R12I22 + R13I33 = E11; R21I11 + R22I22 R23I33 = E22; R31I11 R32I22 + R33I33 = E33, R11; R22; R33 ; E11; E22; E33 . R11 = R 1 + R 2; R22 = R 2 + R 3 +R 6; R33 = R 3 + R 4 + R 5. E11 = E1 E 2; E22 = E2; E33 = E3 .

:19

R12 = R21 = R 2; R23 = R32 = R 3. : R11 R21 R31 R12 R22 R32 R13 R23 R33 I 11 E11 I 22 = E22 [ R] [ I ] = [ E ] , I 33 E33

[ R] ; [ I ] ; [ E ] . 1 1 [ I ] = [ R] [ E ] , [ R] , [ R ] . , , , . n , n. n In : In = E11 E 2 2 E + ++ n n ;

; 1n , k- m- (1) k + m, k , m . R11 R12 R21 R22

=

R1n R2n

Rn1 Rn2

Rnn

20

2.3. () , . , . , , . . [1]. 2.4. ( ) . , , , . . Ek, Ik, Rk , k . I =K

Ek U ab , Rk

Uab ( a b); . 1 gk = , Rk Ik = (Ek Uk) gk. I :

21

I1 + I2 +..+ Ik + ... + In =

k=1

I k = 0,

n

k =1

( Ek U ab ) gk = 0, Ek g k g kk =1 n n

n

Uab = .k =1

. [1]. 2.5. , . - , . , ( ) . , . , , , ( ) . , . , , E

22

R; , , . [1].

23

3. . , 1876 . .. " " , . . . , , , . , . , , , , . ( ) 50 , . 3.1. , , . , , . , . . 1. , , i, u, e. 2. , , Im, Um, Em.24

3. , , (T / 2). I, U, E : I = 2I m 2 m U 2Em , U = , E = .

4. , , T . I, U, E : I= U E Im ; U = m; E = m. 2 2 2

(. 12), i = I m sin (t + i) I m i Im ; ; i , t (t = 0); i = 2f , f = 1/T T . . 12 (e, u, i) . . = u i. , , , , .

25

3.2. , : , : i = I m sin (t ); u = U m sin (t + ); e = E m sin t; (. 13);u, e, i

u

e

i

t u i . 13. 13

; . . (. 14) Am . - - y t = 0: a = a 0 = A m sin a; t1: a1 = A m sin (t1 + a). a , 1 = + t1; 2 = + t2. . 14 , t - y. , () -, , x .26

. 14

-, , . . , , . . +j, -, Im (. . 14) A a2 , . x (+1, Re), y a (+j, Im) . 15. a1 +1, Re A , - 1 -j , . 15 , :

27

1) : A = a + ja ; 1 2 2) : A = A (cos + jsin ), a a2 2 A = a1 + a2 ( ); ( ), = arctg 2 /1;

3) : A = Ae+ j a , e . , , A = Ae j a ,

A = a ja , A = A ( cos jsin ) 1 2 a a

A . . . , . 3.3. , . . . . , R . R , , , : P = I 2R , . R- : u= Um sin (t + u).28

. 16, . (. 16, ) (. 16, ). i i u

R u t

U

I

. 16 1 6 : u = Ri, , -

, . . i= u Um = sin (t + u) = Im sin (t + i). R R

, . : Z= Um Im

=

U m j ( u i ) e = R e 0 = R. Im

Z = R , . . , R. . . L , . L i Li 2 Wm = = , 2 2 L .

29

L- , . . I = Im sin ( t + i), L = Li = LImsin (t + i). eL d Ldi = = LI mcos( t + i ) = E L msin( t + i ) . dt dt 2 eL = u = eL = U msin( t + i + ) = U msin( t + u ) . 2 L = 2fL = xL (); u = i + . = u i = , 2 2 . , L- ; , . 2 L- . 17, ; . 17, 17, . , .

30

u i i L u

Z= Um Im

=

Um Im

e

j ( u i )

= xL e

j

2

= jx L ,

xL = L = 2fL , Z = jxL , . . L-, , x L. L- , . , QL : Q L = UL I L = x L I L2 = UL2 / xL. : - ( ). . . C , qu Cu2 W= , = 2 2 q , Cu.

31

- u = Um sin (t + u). i, i= dq du =C = CU m cos(t + u ) = CU m sin(t + u + ) = dt dt 2 = I m sin(t + i ), i = u + ; 2 1 , = u i = ; C = xC 2

I m = CU m; xC =

1 ( 2fC ). , . , . 2 C- . 18, ; . 18, 18, .

i C u

i

u

32

Z=

Um Im

j j ( ) U = m e u i = xC e 2 = jxC , Im

Z = jxC , . . - , xC . - , . QC, , Q ().2 2 QC = U C I C = xC I C = U C / xC .

, , , , . , , . 3.4. . , . I : .k=1

ik = 0,

n

n , .

33

: , - , .k=1

I k = 0.

n

II : .k=1

uk = 0,

m

m . , (, , ) , II : . II : U k = Ek .k=1 n

m

k=1

3.5. R-, L- . (. 19) i = I m sin (t + i ). . II : R U = U R +U L +UC , L ( ): U = R I ; U = jx I ; R L L U C = jxC I .

C

34

: U = I ( R + jxL jxC ) , R + j (xL xC ) = Z c . : U =IZ. R, L : Z = R + jx L jxc . : I= U R + ( xL xC )2 2

;

Z = R2 + ( xL xC )2 .

. - , , , . () , . , ( xL > xC ). (. 20, ). (. 20, ). () (. 20, ).

35

UL U

U UL I UR

Z

R

x

UR UC

cos = R/Z. 20

3.6. , . , . : L = 1 C xL = xC

. 21, , ( ) (. 21, ):

UL

I

U R =U UC

I

= 0, cos = 1 .

C. 21

C

36

, : ; = 0, . . , ; cos = 1; ape L- - ( ), L- - ( U C = U L + ) . , ; . 3.7. , , . 22. u = U m sin t. . I : I = I + I , 1 2 : I 1 = U ; I 2 = U . Z1 Z2

I R1 R2 C

:

U U , I= + Z1 Z 2

Z1 = R1 + jxL ; Z 2 = R2 jxC . :37

U

I1

L

. 22

1 1 I =U + Z Z , 1 2

1 1 = Y 1; = Y 2 . Z1 Z2 : Y= 1 = g jb , Z

g , ; b , ( bL bC ). R- L- - I =UY I = U g2 + b2 , Y = y = g2 + b2 () . . , . 22, R1 jxL R2 + jxC 1 1 1 1 = I =U + 2 Z + Z = U R + jx + R jx = U 2 2 2 1 2 1 L 2 C R1 + xL R2 + xC R1 xC xL R2 = U ( g1 + g2 jbL + jbC ) = U [ g j ( bL bC ) ] . =U 2 j 2 + 2 + j 2 Z Z1 Z2 Z2 1

, , bL; , bC. g .38

g=

R Z2

=

x x 1 ; bL = L ; bC = C . R Z2 Z2

. ( ) , . , (bC > bL) . 23. y

I22

I

II 1R I 2R

IR

U

..

.

IL. 23

g

b

. (bL > bC), . 3.8. R-, L- C- b L = b C. . 24, ,

39

( ) , . 24, . , . , , .

IC

I2

I

I 1R IL

I 2R,

I

Ucos = g IR = =1 y I

C

C

I1

. 24

: I = U g 2 + ( bL bC ) 2 , bL = bC , I = U g; ( = 0), cos = 1; , . . , . 3.9. P , . . 40

. ( ). P = U I cos ; P = I 2 R = U 2 g. Q . ( ). Q = U I sin ; Q = I 2 x = U 2 b. S , (S). (). S = U I;

S = I 2Z= U 2 Y.

S = U I , I . U = Ue S = UIe j( ui ) = UIe j = Sej , = u i ; S = Sej = P jQ. , , , . , > 0, , S = P + jQL ,

j u

;

I = Ie ji ,

41

< 0, , S = P jQC . (. . 20, ), , (. . 23), . . 25 . +j , Im S = P2 + Q2; S Q P. 25

P = sin = Scos Q= SScos ;;

+1 , Re

Q = S sin ; P os = . S

(cos = P/S) , , (, , , , . .). cos , . , . , , , .

42

4. , , , . . : --, , - . . : ( 25 %); , , ; : U U . .. -, , , . . (. 26): A A A A e X A X Y Z Y e Z B B B C C eA eA e eCC X Y ZX Y Z eB eB B B

eC C C

43

A , , : e A = E m sin t ; 2 e B = E m sin t ; 3 4 2 eC = E m sin t = E m sin t + . 3 3 : EA = E; E B = Ee

j j

2 3 4 3

; = Eej 2 3 .

E C = Ee

(. 27): e

eA

eB

eC

t T/3

T. 27

44

(. 28):

EB

EB . 28

: A , B , C , , . 4.1. : ( ), . (. 29) , . . X, Y, Z N, () . , , . , , , . U U A , U B , U C . U ( ) U AB; U BC ; U CA .

45

, , , , . AEA

UA

U AB

U CA

NEC

EB

UBB

UC

C

U BC

. 29

, , . . (UA = UB = UC = U). (UAB = UBC = UCA= U). e II . U AB = U A U B ; U BC = U B U C ; U CA = U C U A . , : U = 3 U I = I.

46

4.2. , (. 30). (a, b, c) , A, B, C. A a x B b y C c z A a x n

B b y

C c z

, (x , y , z) n, (). , . 4.2.1. (. 31) A aZa

Nc B C

Zc

n

Zbb

. 31

47

Z a = Zb = Z c = Zej Z a Zb Z c . U a = U b = U c () . To : Ua Ub Ia = ; Ib = ; Za Zb

Uc Ic = ; Zc

Ia = Ib = Ic .

: I = I. (. 32). a cnd

U ca Ucc 30

U a U ab n Ubd b

U bc 3. = U c cos 30 = U c 2 2 : U = 3U

U bc

. 32

: I a + I b + I c = I N ( I n ). I N n = 0 (. . 33), . . . ( = 0).

48

( -) (. 33). a

U ca U a Uc c Ic

Ia

U ab

Ib U bc

Ub b

. 33

Z a Zb Z c . ( Za Zb Zc ), , . . ( a b c ). I a I b I a . U Nn. ( ) U Nn =

YaU A +YbU B+YcUC , Y a + Y b + Y c + Y Nn

U A , U B , U C ; Y a , Y b , Y c ; Y Nn . , Y Nn . II : U a = U A U Nn; U b = U B U Nn; U c = U C U Nn, U a , U b, U c .

49

. . 34. (. ....