Mala Skola Elektronike PDF

5/20/2018 Mala Skola Elektronike PDF

1/124

1

1.1

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1.1.1

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2/124

2 1

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1.1.3

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3/124

1.1 3

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1.1.5

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4/124

4 1

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1.1.6

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1.1. ,

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k A B.

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.

N, -

(1.1).


5/124

1.1 5

=

=N

k

kke iup1

(1.1)

, .

, .

m.

, 1.1, -

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.

.

Mem,

Mm. ,

m. -

.

mmm Mp = (1.2)

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. 1.1, . pe, (1.1),

-

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, pe.

1.1.7

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-

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6/124

6 1

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1.2. -

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pe pm,

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pe.

, (-pe) -

(-pm) .

1.2. .

1.2

. -

,


7/124

1.2 7

-

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1.3.

.

(A)-

, ,

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. -.

(B).

, -

-

. -

m, Mm.

, .

(C)

Pm= mMm-

, -.

(D) 0,5

MW 1000 MW. .

.

. ,

. , -

.

, -

u(t).

.

-.

pe= ui.

, -

-

Mem. -

. (-


8/124

8 1

), .

, Mm, , -

, Mem-

. -

.

,

.

1.

()-

. -

6kV 25 kV, 50 Hz 60 Hz.

-

2.

1 19. , , , -. (-) ,. - . ,- . -

, . . - . . . 400 V, -

. 231 V. - -, -.

2 ,

, , . -

. . .


9/124

1.2 9

750 kV,

1000 kV.

(F)

, ,

.

.

10(20) kV,

10(20)/0,4 kV/kV 400 V -

231 V, . -

, -

.(G)

, , , , , -

, , , , , -

, , ,

. -

, , , -

, , , , ,

CD/DVD , . 8% -

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.

(H), 70% -

-

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-

,

, , -

, .

, -

, -

, . -

, -

-

.


10/124

10 1

1.3. .


11/124

1.3 11

1.3

. -

, . -

,

.

()

m. ,

dm/dt= m, . m

.

. , -

, .

-

, -

.

SI , s-1

,

. f = /2 -

(Hz).

,

mm n 54,92

60=

.

(1.3)

Mem

.

-

. Mem-

. Mem

.

F,

, , . 1.4Mem=FD, R=D/2

.

1.4 Mem=

FD, R= D/2 -

.


12/124

12 1

Mem Mm,

.

, Mem>Mm,

. , . -

(1.4).

memm MMJa

t

J ==

d

d

(1.4)

1.4 . .

a= dm/dt-

[rad/s2] .

, . MemMm.

J.

, J=JR+ JRM-

JR

JRM. 5 -


13/124

1.3 13

. -

, R m.

J= mR2.

(1.1):

-

Rm. .

(1.1):

JRM= mR2.

1.5. () (B). (C).

1.3.1

,

(up, ip, pp= upip) -

-

(Up, Ip, Pp= UpIp),

(IEC). -

F, M. -

M

m-

. , .

, s-1

.

. z-

. ,


14/124

14 1

3. ,

uSiS.

, uS iS

. ,

. uSiS

. -

US

IS. [A] A. -

().

sin, cos, rot, div, mod, d ,

, .

, ,

, FHB

,, . ,

B,

H, F.

. , -

.

, -

., (SI)

1954. . .

SI

. , SI -

. , W-

F, l,

4. SI , W[J]

=F[N] l[m], ,

3

. -space vector. . . "V"

.

4W=Fl , .


15/124

1.4 15

1 J = 1 N 1 m. ,

, Fl

. -

. , -

.

.

Vs = Wb, Nmrad/s = W, Nmrad = J, A=V, AH = Wb = Vs,

.

1.4

-

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-

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-

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16/124

16 1

, ,

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,

.

1.4.1

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-

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1.4.2

. - ,

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, () -

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.

1.4.3

,

,

. -

. -

Mem(m) Mem-m. -


17/124

1.4 17

-

.

1.4.4

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. .

-

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-

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(). -

() -

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-

-

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-

.

.

,

, .

,

.


18/124

18 1

1.4.5

-

-

. -

u = Ri+ d/dt,

J dm/dt=MemMm. J

R, m -

().

, , -

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, -

.

,

, .

,

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,

, E-

. , -, -

.

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-

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1.5

-

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19/124

1.5 19

,

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N

, ,

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-

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.


20/124

20 1

,

(), () ().

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5-

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1.5.1

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-

5 , , , . -() . . , .


21/124

1.5 21

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-

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(), . -

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1.5.2

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22/124

22 1

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-

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,

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-

.

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1 kHz. -

-

. -

. -

.

-

.

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.

1 GW. , -

, -

50 Hz. -

, -


23/124

1.5 23

, -

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-

-

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,

.

: -

,

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-

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() -

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.

-

50 Hz,

.

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: -

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.

. -


24/124

24 1

. , .

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-

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:

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P, -

-

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-

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-

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.

(

) .

-

. -


25/124

1.5 25

, -

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-

. ,

-

.

-

,

.


26/124

2

. -

. -

. , -. -

,

.

, .

2.1

. -

, -

.

-

, -

Qv-

.

( )BvQEQF

+= (2.1)

, -

. -

B

. , (2.1)

-

.

2.1 l-

i -

B. F


27/124

28 2

i , l, B-. -

2.1, . -

x, y, z, ,

.

2.1.

.

( )BliFiBB

ill

z

x

=

=

=

,

,

(2.2)

,

F= lBi.

lB.

y y, Wm = Fy.vy, pm=Fvy. , pm

. ,

, pm,

.


28/124

2.2 29

, ,

e. -

ei(pe= ei) -

(pm= Fvy).

,

pepm.

.

2.2

- -

.

,

.

2.2. (A)

. (B) -

. (C) .


29/124

30 2

, 2.1. -

.

,

. ,

.

, -

.

1 A , d= 0,1 m, -

-

.

(2.3).

T102T1,02

1104

2

67

0

=

==

d

IB

(2.3)

-

, -

l= 1 m (2.4).

N102 6== IBlF (2.4)

,

, 1

-,

.

2.3

, . -

1. SB. S C, . S, S-

, = BS.

, S.


30/124

2.3 31

2.3 ,

, . -

l,

vy.

,

Fs. Bz.

-

Eind.

. -

Q, , (2.1),

.

( ) ( ) indEQBvQBvQEQF

==+= (2.5)

, -

QE .

FQ,

B.

BvEind

= (2.6)

2.3. -

.

e -

l. ,


31/124

32 2

Eind.

,

(2.7).

( )BvlEle ind

== (2.7)

, x, -

z, -

y .

(2.8), a

a e = lvB. e

, -l.

lvBEleivBE

ivviBBill

indxind

yzx

===

===

,

,,,

(2.8)

2.4

, 2.3, -

, e, -

R. 2.4. -

, i = e/R. -

, -

R. -

,

. i-Fm

(2.2). Fs ,

Fm. -

2.4, -

Fsvei.

e= lvB, , -

u=Ri, R.

, 2.4, ,

(2.9).

( ) yiilBBliF

== (2.9)


32/124

2.4 33

, Fs

Fm.

.

e,

i= e/R.

2.4. , -

R.

, , -

v, -

.

ilBFFFFFF msmsms ====+

;;0 (2.10)

FsPm=Fsv= ilBv. -

e

Pe= ei= ilBv=Pm. Pe= e2/R> 0, -

. ,

, ,

, (Pe=Pm).(2.1): , 2.4, -

, ?

(2.1): , -

-

, .


33/124

34 2

2.5

e -

. 2.5 -

(Fe>> o),

.

,

.

2.5. , -.

. ,

,

() , ,

. () -

. -

() -

. ,

.

, -. .

.

(2.2):

?


34/124

2.6 35

(2.2):

-

. ,

.

. -

, , .

. -

, -

.

2.6

2.6, -

.

.

-

B, B.

2.6.

.

2.6

.

, .

, -

.


35/124

36 2

, ()

. ,

.

-

,

.

2.7

, -

E, 2.7. -, . -

, -

.

.

. F .

x, Fx.

-

, .

2.7.

.


36/124

2.8 37

2.8

,

, .

2.8, -

= r0. -

0.

r >1

. ,

x = a, . -

, x = 0, . -

0


37/124

38 2

( )[ ]r

re

xxaa

Sd

d

U

Sda

x

d

USd

a

xa

d

UW

+

=

=

+

=

2

0

2

0

2

0

2

1

2

1

2

1

(2.11)

U, -

, Fx Wi = We + Wmeh(2.19).

(2.12).

( )12

1

d

d2

0

== re

a

Sd

d

U

x

WF

(2.12)

F-

.

,

p= we1- we2, we1we2

.

w0= 10(U/d)2,

wd= 1r0(U/d)2, F

(2.13), Sd= bd= Sd/a.

( ) ( )a

Sd

d

USwwF rdd

== 1

2

12

00 (2.13)

(2.3):

. -

Q,

.

(2.3):

. -1/

. U-

.

, EdU,

E=U/d.


38/124

2.8 39

, Dd-

D0 ,

d

UD

d

UD rd 000 , == .

-

,

Dn

= .

, , . ,

,

D, .

2.8, Q-

xDdD0,

( ) ( )

( ) ,0

000

r

rd

xxad

Ub

d

Uxb

d

UbxaDxbDbxaQ

+=

=+=+=

C

( )rxxad

b

U

QC

+== 0 .

, Wmeh= Fx, ,

Wmeh = - We. F = -dWe/dx.

We = 1Q2/C, We= 1CU

2.

Q, U, -

==Cx

Q

x

WF

e 1

d

d

2d

d 2.


39/124

40 2

( )2

0

2

0

2 11

2

1

d

d

2

+=

+=

r

r

r xxab

dQ

xxaxb

dQF

.

,

. Q=

CU,

( ) ( )a

Sd

d

U

d

bUF rr 1

21

2 2

2

00

2

==

,

(2.12) (2.13). x,

.

(2.4):

2.8

. E D

-

?

?

(2.4):

, r

.

wed= 0rE2/2 rwev= 0E

2/2

. -

wevVv+ wedVd, wev wed

, VvVd-

, . -

, Vv-

Vd. wev < wed,

. ,

, -

. -

Q, , E . -

E, -

. -

We(x),


40/124

2.9 41

( ) 0

22

22

1

bxxa

dQ

C

QW

r

e +== ,

, Q,

.

2.9

, , . -

. -

,

,

. , -

, .

-

.

(

).

-

. -, -

.

.

, -

. -

.

. -

-

, .


41/124

42 2

2.9.

-

.

2.10

o

. , - -

. 2.10 -

. , , -

, . , -

.

. -

.

2.10. -

.


42/124

2.11 43

-

50 Hz, -

. -

, -

.

2.11

-

. -

. ,

.

-

-

, 2.11.

(S >> d2), -

E = U/d[V/m],

U. D [As/m2]

E 0.

.

,

. -

.

2.11.1 ,

, -

,E=

U/d. D -

Q/S. D

E (-

) 0.

d

USESQE

S

QD

d

UE 000 ;; ======

(2.14)


43/124

44 2

2.11. -

.

C-

Q U. , -

-

.

d

S

U

QC 0==

(2.15)

-

we.

,

. -

we= 0E2. V=

Sd, W=

CU2= Q

2/C.

( )

C

QCUESd

VEVEDVwWVVV

ee

22

1

2

1

d2

1ddd

222

0

2

0

==

=

=

===

(2.16)


44/124

2.11 45

2.11.2 ,

2.12, -

.

.

,

F. ,

x, Fx. , -We-

.

F

, .

x. ,.

We, .

( )

. 2.12 U

.

, C .

, . , Q = CU ,

Q.

Wi = UQ, Wmeh=Fx. , -

. ,

(2.17).

,

, We= Wmeh= Wi.2.12, ,

.

, D , .

, -

. -

, Wmeh= -We. -, (2.18).


45/124

46 2

( ) ( )xd

SUCUExdSxWe

==

=-22

1

2

1- 0

222

0

(2.17)

( ) ( )S

xdQ

C

QExdSxWe

0

222

0

-

222

1-

==

= (2.18)

2.12. .

2.11.3

. -

,

, -

. 2.12 -. -

Wmeh= Fx Wmeh= -We, Wmeh= Wi. , x, -

.


46/124

2.11 47

, 2.12

. -

, (2.19).

emehemehi

i

WWWWW

QUW

=+=

==

0

(2.19)

F, -

(2.20). Wex-, We/x We(x) x = xx= 0.

0

2

0

2

2

-

2d

d

d

d

S

Q

S

xdQ

xx

WF

x

WF

e

e

=

==

=

(2.20)

, .

, -

(2.21).

eeimehemehi

iei

WWWWWWW

WQUCU

WQUW

==+=

==

==

2

1

2

1

2

;2

(2.21)

F, -

(2.22). Wex-, We/xdWe(x)/dx.

( )

0

2

0

2

0

2

2

02

02

222

-2-2d

d

d

d

S

QS

DS

E

xd

SU

xd

SU

xx

WF e

===

==

=+=

(2.22)

(2.20) (2.22) -

, , -

. ,

, -

C.

,


47/124

48 2

=

==Cx

Q

C

Q

xx

WF e

1

d

d

2

1

2d

d

d

d 22.

, ,

C-

.

,

x

CUC

U

xx

WF e

d

d

22d

d

d

d 22+=

+=+= .

(2.5):

(2.20) F

, (2.22)

.

, Q.

? .

(2.5):

. . -

. -

, -

. -

D, -

E=D/0.

.

2.11.4

,

. , -

Wmeh, Wmeh=-We. , Wi, We= Wmeh= Wi.


48/124

2.11 49

2.13.

.

,

,

. We-

we= 10E2. -

-

. Emax 30 kV/cm., -

, . -

we.

, -We(max). , -

, -

.

, -

, , -

.

-

, , -

, ,

. ,

. -

. -, -

, .

2.13. (A),

(),

.


49/124

50 2

(2.6):

-

. ,

, -

Em = 30 kV/cm.

(2.6):

-

. S, -

d

we(max)=0Em2. -

W= Sd we(max).

(2.7):

f, -

.

(2.7):

fPsr= fW=f Sd we(max).

2.11.5

-.

. -

, -

. -

. -

-

.

-

.

-

. ,

-

.

,

.

-


50/124

2.11 51

. 0 =8,8510-1210-11, 0= 410

-710-6.

wm= 0H2/2 -

we = 0E2/2.

, -

. ,

Emax30 kV/cm 3000 kV/m, HHmaxBmax/01000 kA/m. -

. ,

(103-10

4

) .

2.11.6

-

, -

EH. -

-

-

. -

.

. ,

Wm2. -

.

. -

EH,

.

-

, , -

. , -

-

. , -. ,

. -

, .

. (

)


51/124

52 2

,rott

DJH

+=

(2.23)

D-

H. H

, H-

.

H

.

. ,

, -

.

, .

,

.

.

(),

,rott

BE

=

(2.24)

B(-

) , E.

2.12

. -

.

.

.

.

.


52/124

2.12 53

2.12.1

2.14 -

. -

, , -

U, . -

AB l1

U. AB,

U. -

AB ,

R.

2.14. -

.

, i.

l12.14

AB. ,

B. Fm-

(2.25).

( )BliFm

= 1 (2.25)

l1 , -

Fm= l1iB. 2.14, -. , -

v. Fs,

. ,

, v, -

.

.


53/124

54 2

BilFFFFFF msmsms 1;;0 ====+

(2.26)

,

Eind,

.

, e = eAB

(2.27)

( ) ( )( )BvlEle ind

== 11 (2.27)

,

a a e = l1vB. - e = eAB ,

2.14.

e = eAB > 0 A

B.

, i= (U- e)/R.

, i(t) I=

(U l1vB)/R. Pi= Ui= ei+ Ri2PAB= ei=

l1vBi, P=Ri2. -

.

PAB. -

, FmF

s,

. , -

Pmeh=Fmv= l1iBv. Pmeh-

, -

U, . Pmeh=Fmv=PAB=

ei = l1vBi, Pi

(2.28).

222 RiPRivFRieiUiP mehmi +=+=+== (2.28)

, ,

. -

ePe= e(-i) = -ei< 0. , -

e, -ei= l1vBi, Pmeh= Fmv=

ei. , -

. -

(2.29) .


54/124

2.12 55

vFei m= (2.29)

, P=Ri2. -

, , -

. -

, , -

.

P -.

,

. -

. , -, . ,

, , .

R. ,

, , .

,

2.14 , -

.

2.4 .

2.12.2

,

. ()

2.15. ABCD, DL-, B. ,

2.15, .

mm= dm/dt.

m= 0, -

S=DL.

I. F1 AB CD -

. -

L, F1= LIB. -

BC DA, D,

, . m=/2,


55/124

56 2

BC DA ,

, .

2.15.

.

Mem = DF1. -m= dm/dt,

(t= 0) Pmeh=Memm=DLIBm.

Pmeh-

, I, .

. A1 D1

u= vA1 vD1.

ABCD, u= RI + d/dt,

SR

.

S. ABCD, ,

.

2.15 1.16, n.

, Sm-

.


56/124

2.12 57

2.16. .

2.16, m-

S.

, .

m, Sn1.

, (m)=msin(m) =msin(mt), m=BS

m=/2. ,

u=RI + mmcos(mt).

, m = 0,

(2.30).

222

22

RIPDLIBRIBSIRI

BSIRIIRIuIP

mehmm

mmmi

+=+=+=

=+=+==

(2.30)

, ,

.

m = 0,

Mem= mI=Pmeh/m. m, KF1,

2.16, K=(D/2) cosm. Memm(2.31)

mmem IM cos= (2.31)

(2.31)

. -

2.15


57/124

58 2

. -

, -

.

, -

2.15 ,

.

,

.

2.12.3 -

2.15, e1e2

.

, -

, -

.

2.17. -

.

2.17 ,

A1 D1. -

S.

S, n

2.15 2.16.

I

(ABCD) n.

m, 2.15 S.

S,

, -

. -

. ,

. -


58/124

2.12 59

. 2.17,

.

Req= , e1. , , -

A1 D1

, -

e1.

, -

. ,

.

.

. ,

2.15,

.

e1, (2.32).

t

e

d

d1 =

(2.32)

e1


59/124

60 2

2.15 2.17. e1,

(B) 2.17, -

(2.32). ,

() (2.34). e2= +d/dt

-.

t

ee

d

d12 ==

(2.34)

2.13

-

.

, -

.

, ,

-

. -

, -

(a). 2.18.

2.18 , -.

() .

,

-

(). -

N , .

,

-

. HFe=B/Fe, -H0= B/0. -, -

. Ni =H0,

H0 i=

H0/.B,

i = B/ ( 0). , . -


60/124

2.13 61

-

+lFe, lFe-

. 1+lFe/ . lFe>>, -

. -

. ,

.

-

.

2.18. -

.

. . -

,

.

2.13.1

.

,


61/124

62 2

B(H) .

0d =S

SB

(2.35)

, -

. -. -

, -

, -

. ,

.

. -

. -

, ,

( ) .

. N=N. , -

.

.

,

-

.

(2.36). cS2.19.

= ScSJlH

dd (2.36)


62/124

2.13 63

2.19. Sc.

, , -. -

. , -

J-

S, ,

. (2.36) (2.37).

IlHc

=

d (2.37)

HB-

(2.38).

( )HBB

= (2.38)

, -

. , (2.39). 0 =4107H/m. , B(H) .

, .

, B(H) -B/H-0.

HHB r

0== (2.39)


63/124

64 2

2.13.2

2.19 . -

S, c,

B. ,

.

S. - ,

, -

=N,

S.

2.13.3

. -

B(H)2.20. -

B/H =o, , FeB(H). B-H

H, ,

B

.

. -

.

.

. H, -

, -

. -

.

H,

B = FeHB = 0H.

.


64/124

2.13 65

2.20. . -

, .

2 T, . -

H ,

. -

. ,

, B = 0 H.

2.13.4

-

. . HNi,

N i. Ni/-

.

. ,

, ,

, (


65/124

66 2

).

.

2.21. , ,

.

.

B(H) . -

. ,, -

. -

,

. -

.

(2.37), H

c, 2.21, Ni. F =

Ni , H

. -


66/124

2.13 67

F .

F = Ni-

H, . 2.21,

Fnk,

.

S

. -

,

Hc Ni-

.

,

, = BS.

= N.

. S= S0=

SFe, SBFe= SB0, BFe= B0, B0-

BFe-

. H0= B0/0, -HFe = BFe/Fe= B0/Fe. (2.40), l-

, l0.

NilHlHFe =+ 00 (2.40)

H0 = B0/0HFe = BFe/ Fe = B0/ Fe(2.40), (2.41), BFe=B0.

FNilB

lB

Fe

==+ 00

00

(2.41)

= BS, -

F(2.42).

R

F

Sl

Sl

F

Sl

Sl

Ni

FeFe

=

+

=

+

=

0

0

0

0

(2.42)

,

2.22, E

. -

R = F/R


67/124

68 2

i = E/R .

-

. -

.

F-

c. , i = U/R,

= F/R, R

., -

Ni . -

,

-

. -. , F R

i, U R . (2.42)

"" , .

l,

S R= l/(S). -

.

,

, -

, -

Rk= lk/(Skk), (2.43).

=

=n

k kk

k

S

lR

1

(2.43)

2.22.

.


68/124

2.13 69

S - ,

(2.44), c

. S(x) (x) x,

c, . -

S(x), (x), x, S(x)S(x+x), (x)(x+x). R x/(S). , (2.44).

(2.44) S(x) (x).

( ) ( )=c

xSx

xR

d

(2.44)

N , = N

. (2.45),

.

=

=====k

ii

i

S

lN

RN

RNi

iN

iN

iL

1i

22 (2.45)

2.13.5

wm.

, BH/2.

, -

, V(2.46) -.

( )

===

VVV

me VBHVBHVwW d2

1ddd

(2.46)


69/124

70 2

dV= Sdl,Sdl

, c. -

,

.

,

B/S. -

,

(2.46)

. -

dl, -.

( )

=

===ccc

SV

e lHlHlBHSVBHW

d2

d2

dd2

1d

2

1 (2.47)

,

c

Ni, -

(2.48).

-

.

2

2

1

22d

2Li

iNilHW

c

e ==

=

=

(2.48)

(2.8):

, 2.21, -

.

.

(2.8):

, -R= l0/(So). L= oSN

2/l0.

2.13.6

. -

2.23 ,N1N2.

. -


70/124

2.13 71

-

. , 1,

n12.22,

c, n, -

.

, 1= N1.

n2

c.

Sn, 2

= -N2. ,

-.

2.23. .

1= N12= -N2 , ,

. ,

N1 N2,

1/2. , -

.

N1 N2.


71/124

72 2

-

. , .

, |1 /2|

N1/N2.

k1. , -

1.

2.14

,

. -

() . B

.

.

.

2.24. .

, -

.

2.14.1

-

.

B= f(H) . B-

T, 2.24,

B = f(H) .


72/124

2.14 73

() T-

.

-

. -

.

pH

B=f(H) -

. -

V

HH SVBHVW == d , (2.49)

SHB=f(H) . -

HH SVfP = . (2.50)

HH

H SfV

Pp ==1 .

(2.51)

SH -

Hm Bm. -

BmHm, Bm2,

2

11 mHH Bfp = . (2.52)

H H1

,

2

mHH Bfp = . (2.53)

2.14.2

. -

-

-

. -

-

.


73/124

74 2

2.25 -

BBm.

C, -

SC lC.

, -

RC= lC/(SC).

( ) tBStBStt

e mCmC cossin

d

d

d

d===

(2.54)

2.25. . -

-

.

-

, E Bm2 fBm. , ,IC E/RC2 fBm/RC. , (2.55), -RCIC.


74/124

2.14 75

C

m

C

mCCCC

R

B

R

BRIRP

222

2 ~~~

(2.55)

-

-

.

22

mVV Bfp = , (2.56)

V

.

2.14.3

(2.57). pFe

W/kg. m-

PFe=pFem.

222

mVmHVHFe BfBfppp +=+= (2.57)

, -pFe, -

PFe -

.

2.14.4

-

. , -

.

.

, , .

.

, -

. -

-


75/124

76 2

-

.

-

, , -

. RC

(2.55) .

,

()

,

2.26.

, -

.

2.26.

.

,

.

, -

.

.-

50 Hz -

0,2 mm 0,5 mm.

(, ) -

, -

.


76/124

2.14 77

-

, , -

1 kHz. -

(0.05 0.1mm), -

, , -

.

. -

, 50 m.

. .

.

() , -

.

2.14.5

2.27, ()

. a -

, B(t) =Bmsin t, Bm-. a-

l. , c

2x. xa/2, x


77/124

78 2

( )

tBxxE

tBlxxElldEe

m

m

C

cos)(

,cos22

=

===

(2.58)

2.27. -

.

-E-

J = E. , ,

( ) .cos)( tBxxExJ m ==


78/124

2.14 79

.

,

( ) ( ) .cos)(

)(2

22 tBx

xJxE

V

Pxp mFe

===

=

P1FealH- (2.59).

( ) ( )

( ) 2232223

2

0

2

cos12

cos21

==

===

mm

V

a

mFeFe

BaktBlHa

dxtBxlHdVxpP

(2.59)

kH l,

cos2t, 0,5. (2.59) -

-

a.

2.26()

a=A.

,

(2.59) Phom (2.60).

322 ABkP mhom = (2.60)

N

() a=A/N,

2.26(B). -

a,

, 2.26 ().

P1Fe, (2.59). -

N, PlamA = aN(2.61).

2

222

3

22

N

PaABk

N

ABkNP hommmlam ==

=

(2.61)


79/124

80 2

(2.61) -

N2

N ,

. -

, -

. ,

.

,

a,

.

50 Hz

0,2 mm. -, ,

, ,

-

.

,

,

B. ,

. ,

.

,

, -.

2.15

()

. -

,

. . -

.

, . -,

. -

.


80/124

2.15 81

2.15.1

. -

, ,

.

,

(). ,

.

, -

. -

, .

2.28 .

2.28. . ()

. (B) . (C) -

. (D)

Fem.


81/124

82 2

2.15.2

. m. -

Mem

, m-

Pem=Memm. -

Pem.

.

2.29.

2.29. , -

.

, ,

. m-

em.

, (Mem> 0), -

(, )

, Mm. ,

em>0 , -

m>0 .

.

memm MM

tJ =

d

d

(2.62)

-

.

, .

, em ,

. ,

, Mm

2.29.


82/124

2.15 83

em ,

. -

Pem. -

, Pem

-

.

2.15.3

, , -

, ,

. -

. ,

().

. , -

. .

.

, , , -

.

, . -

(, ).

i aNF=Ni.

R . , -

.

, .

-

.

, . 2.30 () -

.

-

. .-

.

, .

-.

2.30, -

(C) -

. . ,

2.30 (E).


83/124

84 2

2.30. -

. (A) 2

. (B) .

(C) . (D) -

. (E) .

-

,

, .

. -

,

.

2 2.30 -, . -, ..

, --. H-, . BFe< 1,7 T

HFe=BFe/Fe0, , -.


84/124

2.15 85

2.31.

.

2.15.4

,

. , -

2.33.

, , . -

, ,

.

(, ) .

,

, .

, , , -

. -

(),

. 2.32.

,

.


85/124

86 2

2.32. . (A). (B) .(C) .

2.33, (B) 3.

(

2.33). ,

, . ,

, .

2.33,

,

.

2.33. .

3[= slot (eng.), cava (it.) = tooth (eng.) dente (it.)].


86/124

2.15 87

(2.33). -

, .

,

2.33 (D)4. -

(D)

.

-

, (F 2.33). -

(C -

) (D).

. . -

.

.

.

. -

.

NN.

(2.9):

? ?(2.9):

, -

. ,

. ,

,

.

,

.

2.15.5

, , , -

,

. -

4end turns, eng.


87/124

88 2

2.36.

,

, .

-

, . -

,

, . , -

, -

.

. ,

-, ,

.

.

,

. -

, . -

.

.

-

.

-

, . .

-

. ,

HFe. , -

, -

2.34. Ni =

2 Ho.

, , -

, , ,

.

. .

, , -

, ,

.

, -

, .

, -


88/124

2.15 89

-

.

2.34.

, -

.

. , -

(6 ),

.

().

2.34. .

2.15.6

, , -

. -

-.

, -

,

. -

. -

. -


89/124

90 2

-

.

,

PeM= uiM. -

PeMiM-

(). , -

(,PFeM) (,PCuM).

-

Memm.

, PmM.

PmM= Memm-PmM= Mmm-

. , PeM -, PmM, PFeM+PCuM+PmM-

. = PmM/PeM-

, .

2.35.

2.35. .

,

.

2.36. PmG, , , -

.

2.36,

.

( 2.35),

, Pm-


90/124

2.15 91

.

PeG,

iG.

PmG.

.

PmGPmG

.

PCuGPFeG.

. -

PeG = uiG,

.

2.36. .

-

. , -

, .

-

, . ,

. , . , , -

, .

-

.

, -


91/124

92 2

. , -

,

,

-

.

.

,

.

, .

.,

.

2.15.7

,

5.

0,5 mm ,

.

() .

, .

Fe>>0, H , -

je Ho.

H -

(2.63) -

.

==C

HlHNiF 02d

(2.63)

Ho(2.63)

, -

2.38.

5[airgap (eng.) traferro (it.) entrefer (fr.) ]


92/124

2.15 93

2.37. . (A) -

. (B) . (C)

.

2.38. -

.

Ni = 2 Ho, ,


93/124

94 2

. , -

. ,

,

0.5 1 mm, -.

2.15.8 ,

-

. -

. , -

-

.

.

.

2.37 2.38.

. ,

.

. /

, -/. 2.33

-

. -

, -

,

, -

. 2.39, Wi, WmehWm

, -

, . -

2.13.2 .(2.39 ), -

u Nd/dt= 0, -

. , -

, dWmeh= -dWm.

-

. dx-


94/124

2.15 95

dWmeh=Fdx, F

. L(x) -

.

, R,

, . -

dx(2.64),

i.

2.39. , . () -

, = const. (B) , I=

const.

LiLLL

LiWm d2

1d

22d

2

1dd 2

2

222 ==

=

=

(2.64)

dWmeh= -dWm,

(2.65).

== mmeh WxFW ddd

x

LiF

d

d

2

1 2=

(2.65)

(2.39 B), -

I. dx, dWi= uIdt,


95/124

96 2

u= d/dt.

(2.66).

ddd ItIuWi == (2.66)

,

-

(2.67).

im WILILIW d2

1d

2

1d

2

1

2

1dd 22 ===

=

(2.67)

6

dWm= dWmeh= dWi/2.

(2.65),

.

.

, Wm

. ,

, .

-

H B. Wm-

, -

Bmax< (1,7 2) T. , - ( 2.39) (). -

,

.

6 dWm= dWmeh= dWi/2 -, , -. L(x) -

x, /i. , -(2.66) (2.67) dWm= dWmeh= dWi/2. -, B(H) .

, , L= /i =f(x,). , .


96/124

2.15 97

(2.20) (2.22) -

, , -

.

, -

, -

.

,

.

, -

.

. 2.39, -Wm(max) -

. , -

,

Wmeh(1)= 2Wm(max) . () , -

.

Mem

(2Mem).

.

H

.

. , .

Memm,

. , -

, -

.

(2.10):

-

, -

.

(2.10):

-

. V= LD, D-,L. B

.

() -

. -


97/124

98 2

Bmax1,7 T, B-.

1Bmax2/o. -

Wm(max)1LDBmax2/o,

2.

2.16

. -

(), (),

, -

.

-

. -

,

, -

,

. -

. 2.40 Pe, -

Pm, PCu, PFe, -PmWm.

2.40. -.


98/124

2.16 99

2.16.1

-

. -

, ,

. -

, -

, -

, , -

.,

, , ,

.

, -

-

, -

,

.

Pe -

, Pm

() ,

PCu, PFe, Pm-.

2.40.

? ?

,

. -

. ,

. ,

, (

, , ).

,

. , -

. , , -

() . ,

, -


99/124

100 2

, ,

.

, ().

, ,

, . -

, -

. ,

.

.

-

, , -, R, L, C,-

(Ri = u, i = Cdu/dt, u=Ldi/dt). -

, ,

RLC -

,

.

: -

,

, -

,

() . , -

, , .

, . -

. -

, .

-.

-

. -

E = U/d.

, -

, . -


100/124

2.16 101

, -

dV/dt. ,

, -

. , -

, -

E = U/d(

). ,

, -

(-

) . -

, -

, . -, -

.

, -

( dV/dt)

, ,

, E = U/d. -

,

.

, . ,

, 10,000 ,

, -

, .

-

, . U/f ,

(PWM)

.

,

.

, . , -

-

, ,

-

. , -

, -

. ,

-

.


101/124

102 2

:

-

.

,

(,

), -

. ,

.

,

-

, -

. -. ,

. , ,

, , -

,

.

2.16.2

,

-. :

,

,

,

-.

- .

,

, ,

. uL=L di/dt iC=C

du/dt,. -


102/124

2.16 103

-

p = ui, -

.

-

, -

. -

(H2 E

2),

.

, .

()

222

mVmHVHFe

Fe BfBfppm

Pp +=+==

-,

.

.

, (-

). B/H-

B/H . 1,2 T, -

. ,

- - .

N-

. .


103/124

104 2

2.16.3

2.41 N()

.

.

(), -

(). , -

.

, -

. ,

u = Ri + d/dt= 0. , d/dt= 0, . -

,

(u d/dt).

2.41.

N(). 1 i

, 2 N-

.

(2.68), u i

.

, , .


104/124

2.16 105

[ ]

[ ].,...,...,,

,,...,...,,

,

121

121

1

NNi

T

NNi

T

TN

j

jje

uuuuuu

iiiiii

uiiuP

=

=

=

==

(2.68)

2.16.4

2.19 - -

-.

, N-

. (2.69), u

, i, =N-

. R.

KEMSeRit

Riu +=+=d

d

(2.69)

2.42. -

.

, -

+ ,

. eEMS= - d/dt.

- d/dt,

(B) 2.42.

, (e = +

d/dt), (A) 2.42. eKEMS= + d/dt

-.

(B)

,

. , , -, e = -

d/dt. + -

, -

, .


105/124

106 2

2.42. -.

(A) -

. -

e = + d/dt,

(u e)/R. , ,

. (A) -

-

, . -

. , -

, . ,

,

(e = +/- d/dt).

2.16.5

(2.69). -

N, k-

tiRu kkkk

d

d+= ,

(2.70)

uk, ik, Rkk , , k-, -

. kk ,

k--


106/124

2.16 107

. ik

k-

Lkk. ijjk-

Lk.

NN-

.

[ ]

[ ],,...,...,,

,...,...,,

121

121

NNk

T

NNk

T

uuuuuu

iiiiii

=

=

(2.71)

,

[ ]NNkT

,...,...,, 121 = ,(2.72)

R

=

N

k

R

R

R

R

R

R

0000

0000

0000

0000

0000

3

2

1

(2.73)

.

(2.74), N

(2.69).

,

tiRu

d

d+= .

(2.74)

-

. k- , -

Lkj,

.

NNkkkkkkk iLiLiLiL +++++= ......2211


107/124

108 2

,

,

(2.75), , (2.76).

=

NNN

kkk

Nk

LL

LL

L

LL

LLLL

L

...

...

....

...

.

1

1

33

2221

111211

(2.75)

iL = (2.76)

-

,

.

Lij=Lji, , L=LT.

.

-

()

(). ,

.-

. -

-

. -

2.6, -

-

.

2.16.6

, . -

, . 2.43 -

, .

. -

.


108/124

2.16 109

-

.

,

,

. -

,

. -

, -

. -

. Lm=LSR= LRS,

. -

,

. -

2.41, 2x2. -

-

LSLR. -

, -

, /2. ,

RS

m

LLLk= .

.

NR, , LS= LR,

Lm= kLS= kLR. k< 1, -

. ,

( ) SmSS LkLLL == 1

,

, .

, ,

.

-

.


109/124

110 2

2.43. .

,

2.43,

.

,

mRR

mSS

+=

+=

(S)

(R

)

R

m

S

mm += .

-

,

.

,

RmRRRmRRRR

SmSSSmSSSS

NNNN

NNNN

+=+==+=+==

S , R -

. -

. -


110/124

2.16 111

, .

2.43,

R

R

R

S

S

Si

Li

L

== , .

S

S

mR

R

R

mSRSSRm

i

N

i

NLLL ==== .

. ,

.

.

,

Rm

S

RRSR

S

R

R

R

R

mR

R

RR

R

mR

R

Sm

R

SSRS

R

S

S

S

S

mS

S

SS

S

mS

S

LLN

NLL

N

N

i

N

i

NNL

LLN

NLL

N

N

i

N

i

NNL

+=+=

=

+

=

+

=

+=+=

=+

=+

=

,

.

.

, (-

) , -

,

.

,

RmR

SmS

LLL

LLL

+=+=


111/124

112 2

2.16.7

. -

,

.

,

. -

= BHwm

d .

, , = B/H =

const, wm= BH= H2.

wm-

. -

. , ,

L1i12+ L2i2

2+ L12 i1 i2.

,

. -

(BH) dV. dV= dSdx,

(BH) dSdx = (BdS)

(Hdx). (BdS) ,

(Hdx) -, . ,

iLi2.

N , -

( ) = =

===N

i

N

j

jiij

VV

m iiLVBHVwW1 1

m2

1ddd

.

, Lii-

. Lij-

.

[ ]

[ ].,...,...,,

,,...,...,,

121

121

NNk

T

NNk

Tiiiiii

=

=


112/124

2.16 113

(2.77), L-

.

iLiWT

m2

1=

(2.77)

(2.11):

L1L2.

(L1L2)0,5?

(2.11):

L12= k(L1L2)0,5

, k

. 1, ,

.

1, (L1L2)0,5

.

(2.12):

=j k

kjjkm iiLW2

? -

.

(2.12):-

. ,

2Wm=L1i12+L2i2

2+2L12i1i2=L1i1

2+L2i2

2+2k(L1L2)

0,5i1i2. a=

(L1)0,5

i1b= (L2)0,5

i2, 2Wm= a2+ b

2+ 2kab.

. -

,

, 2Wm 0 k= 1,k< 1. k= 1, 2Wm

= (a+b)2, .

2.16.8

N

,

.

pk= ukik


113/124

114 2

iuuiiupTT

k

kke === . (2.78)

-

, 2.74,

, .

( )

t

iLii

t

LiiRi

iLt

iRit

iRip

TTT

TT

e

d

d

d

d

d

d

d

d

++=

=

+=

+=

(2.79)

, .

Rk, ik,

Rkik2. N-

iRiiRpT

k

kkCu == 2 (2.80)

RNxN,

, -

.

. (2.77), -

(2.81).

+

+

=

=

==

t

iLii

t

LiiL

t

i

iLitt

Wp

TTT

Tmwm

d

d

2

1

d

d

2

1

d

d

2

1

2

1

d

d

d

d

(2.81)

pwm.

(2.81) , -

..

(, 1x1) s=

sT, (Ljk= Lkj,L=L

T),


114/124

2.16 115

=

=

=

t

iLi

t

iLiiL

t

iiL

t

i TTTT

TT

d

d

d

d

d

d

d

d.

(2.81), (2.82).

+

=t

iLii

t

Lip

TT

wmd

d

d

d

2

1

(2.82)

(2.82) -

. -

. -.

, -

. i-

(2.82) .

,

.

,

.

pwmpe, pCu

, pC-

. (-2.33),

. -

(2.34), .

wmCueC pppp =

(2.79), (2.80) (2.82),

( )

.d

d

d

d

2

1

d

d

d

d

+

++=

t

iLii

t

Li

iRit

iLii

t

LiiRip

TT

TTTT

C


115/124

116 2

it

Lip

T

Cd

d

2

1= .

(2.83)

, -

. -

. , -

m m= dm/dt,

(2.84),

iL

it

iL

iit

Lip

m

Tmm

m

TT

C

d

d

2d

d

d

d

2

1

d

d

2

1 === .

(2.84)

(2.84) -

-

m.

, -

. ,

pC (),

(). -

, -

,

. , 2.34, -

, , .

2.16.9

. -

m

m. N

, . -

, L.

t

mm

d

d= ,


116/124

2.16 117

( ) ( )mftfL 21 == .

-

. . -

Mem, -Mem,

. ,

. Mem-

.

, Mem,

m, pC= Memm.

, Mem-, .

, Mem

, pC= Memm. -

-

. , Mem-

, -

.

.

, (2.84)

mem

m

T

mC MiL

ip =

=

d

d

2

1,

Mem, (2.85) .

iL

iMm

T

emd

d

2

1=

(2.85)

N. -

.

(2.67), -

,

,

memmehm MWW ddd == ,


117/124

118 2

m

mem

WM

d

d= .

(2.77), -

= iLiM T

m

em2

1

d

d

.

, -

. -

m.

iL

iMm

T

emd

d

2

1=

-

m. -

, -

.

.

N ,

(2.86).

= =

=

N

k

N

j m

jk

jkem

LiiM

1 1 d

d

2

1

(2.86)

(2.13):

O

.

(2.13):

, m

. m=0, . -

,

. , -

m=0. ,

/2 /2-m.


118/124

2.16 119

,

cosm, ,LSR=Lmcosm.

(2.14):

-

.

(2.14):

. -

, ,

,

. -

. , -

, . ,

,

m.

2.16.10

-

, - .

(). ,

, -

. ,

.

, ,

. -

,

Mem.

. Mem.

,.

Mm, -

Mem . -

, pm=Mmm-

2.42.


119/124

120 2

2.42

.

2.16.11

-

, , -

, -

.

(2.42). -. , -

, -

-

kF m,

2

mFm kp = (2.87)

-

. , , -

.

, 2.42, -

, .

. -

m. -


120/124

2.16 121

2

mVFe kp = .

, -

mV

m

FeFe k

pM == .

pm= kF m2, -

7.

-

, . -, -

3

mFm kp = .

2.16.12

J. -

, Rm, -

J = mR2/2. -

Jm WmehA= Jm2. -

, d(WmehA)/dt = Jmdm/dt. ,, -

, , (). -

7 pFe

, . , pFeMFe. -MFe. MFe-,

, . , , -pFe. -

. , ,. -.


121/124

122 2

, Mm, ,

Mem-

, pC, Mem =

pC/m.

, 2.42, -

.

- ,

mmm Mp = .

2

21

mmahA JW = ,

t

J

t

Wm

m

mahA

d

d

d

d= .

(2.88)

pC,

(2.87),

(-

(2.88)), (

) (2.89).

2

2

d

d

,d

d

,d

d

mFm

mcm

mmmFm

mc

mm

mahA

emmc

kt

Jpp

Mkt

Jp

ppt

WMp

=

++=

++==

(2.89)

2.16.13

(2.89) ,

(2.90), Mm,

.


122/124

2.16 123

mFm

emm kt

JMM =

d

d

(2.90)

, Mm

. , Mm

. -

2.43.

mFmemm kMM

t

J =

d

d,

(2.91)

. - .

, Mem

Mm. -

, Mem> Mm, . , -

. , Mem

.

mFmemm kMM

t

+== ,0

d

d.

2.43. .

2.43 Mem-

Mm .

. , -

, . ,

Mem, -

Mm. , Mm

. ,

MemMm


123/124

124 2

. ,

2.43, -

Mem>0, Mm>0, Mem


124/124

2.16 125

it

LiP

T

cd

d

2

1=

,

( )2d

d

2

1

d

dm

kwk J

tt

Wp == .

2.44. .

,

2

mFm kp = .

, 8 , -

,

mmm Mp = .

8 , , .

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