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    Tab  Yahoo  - , , Hits: 993



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1.1. .

, , ., . , f(t) t, ,

F(p)= (1.1)

F(p) p=δ+iω . f(t) F(p) (1.1) , F(p)=[f(t)] f(t) F(p), - .



, t≥0. , δ(t) . .

:

) 111b15cb

σ(t)═{ [σ(t)]==. (1.2)

)

f(t)={ = e F(p)= =. (1.3)

)

F(p)=[δ(t)== e-p0 = 1. (1.4)

. , -, , , . F(p) , .

  1. :

[] = . (1.5)

  1. :

[] = pn. (1.6)

  1. :

[]=. (1.7)

  1. :

[f(t-θ)] = e-pF(p) (1.8)

  1. :

[dτ]=F1(p)F2(p). (1.9)

6. :

[f(t)eat]=F(p-a). (1.10)

7. :

[f(t)]=F(). (1.11)

  1. tn:

[tn f(t)]=(-1)n F(n)(p). (1.12)

  1. :

[f(t)]=. (1.13)

  1. :

[f1(t)f(t)]= (1.14)

, .

: ) :

Acosω0tσ(t)=½A(eiωt + e-iωt) ½A()=. (1.15)

) :

(t)=A[σ(t) - σ(t-θ)] (1 - e-p θ). (1.16)

) :

A(t)cosωt σ(t) =½A(t)(eiωt + e-iωt)σ(t)½[A(p-iω) + A(p+iω)]. (1.17)

, , :

f(t)= [F(p)]= (1.18)

- F(p)=. , ( , )

F(p)= (t≥0). (1.19)

 

1.2. .

. (t) : u(t) , i(t) , S(t) .

, .. - , , .

, , , .. , , , , , .

, . - .

, . U(p)=[u(t)], I(p)=[i(t)]. . , , (. 1). : E(p)=[e(t)]; I(p)=[i(t)]; Z(p) Y(p) . (. 1). :

- ⠠ (1.20)

- (1.21)

, ( ), ( ). , .

, , : , , , . . .

1

i(t)= j(t)

j(t) i(t)

I(p)=J(p)

I(p) J(p)

U(t)=Ri(t)

I(t)=Gu(t)

u(t)

R i(t)

U(p)=RI(p); I(p)=GU(p);

ZR(p)=R; YR(p)=G;

ZR(p)=R I(p)

U(p)

U(t)=L

i(t)=+i(0)

L i(t)

U(p)

U(p)=pLI(p); I(p)=U(p);

Zp(p)=pL; Yp(p)=;

Zp(p)=pL I(p)

U(p)

U(p)=pLI(p)-Li(0);

Zp(p)=pL E(p) = Li(0)

I(p)

U(p)

I(p)=U(p)+

J0 (p)=

I(p)


U(p)

1

2

3

1

2

3

i(t)=C;

u(t)=;

C i(t)

U(t)

I(p)=pCU(p); U(p)=

Zc(p)=; Yc(p)=pC;

ZC(p)=; I(p)

U(p)

I(p)=pCU(p)-Cu(0);

J(p)=Cu(0)

I(p)

YC(p)=pC

U(p)

U(p)=;

Z(p)= E(p) =

I(p)

U(p)

1.3 .

, t=0 . , t=0 uC(0) , iL(0). uC(0) iL(0) , . , .

S(t), , , k- . ,

S(p)= (1.22)

∆(p) ∆k(p) , ; A(p) , , , . S(p) -

, (1.23)

m≤n, bk ak .

V(p) . . M(p) , , .

S(p) , .

, V(p) , , . a1, a2 an, V(p) , pk - . ; ; . ,

(t≥0), (1.24)

s(ωlt+φl), (t≥0) (1.25)

pk= - δk . , - , . (1.25) , ψl=arg. , .

, . V(p) , S(t)

S(t)= , (t ≥ 0), (1.26)

mk k- ,

Akr = . (1.27)

m - , ,

, (1.28)

m -

(1.29)

, V(p) pl=iωl.

, (1.30)

.

- V(p) : pl =ll, Sleδltcos(ωlt+ψl). , , . . (). , , , , .

, , . , , V(p) . V(p) .

, , , . - .

V(p)=0 ,

Δ1=a1; Δ2=; Δ3=; ; Δn=; (1.31)

,

        t=0, uc(0) iL(0).

        . .

        ( ) .

        .

        . -.

        , V(p), .

        . .

        .

.

1.

.1.1 t=0 , , . I0. Cp (.. CpC) U(t) t0. E

1)     

Oval:

S 󠠠 iL(0)= I0; uc(0)= 0

I0 Cp

L C R U(t)

.1.1. .

2)  

pL R U(p) = U(p)

.1.2. , .

3)  

(pC + G + 1pL ) U(p) = I0 ⁄ p.

4)  

U(p) =, 0; >0.

5)                  V(p)= p2 + 2δp + . p1,2 = -δ ( ) - p1,2 = - , = . , - .

6)                 

U(t) = U1e δt cos (ω1t + ψ1 ) , (t 0).

7)      U1 ψ1

U1 = 2 = ; ψ1 = arg = - .

8)          

U = , (t 0 ).

9)           . U(t) (.1.3) , I0, ω0; , R ( ) ..

U(t)

t

.1.3. U(t) .

 

 

2 .

(.1.4). , , .


.1.4..

.1.4. ( , ).

. 1.4..

1. , , t = 0 () , , . J0(t).

2. .

3.

( pC + Gi + ) U(p) = nSU(p) + J0(p) .

( pC + Gi ─ nS + ) U(p) = J0(p) .

4.

U(p) = , 0; 0.

5. V(p) = p2 + 2δp + .

p1,2 = - ( ) , . GnS , , . G nS , ,

U(p) = U1, (t 0).

6.    . GnS, . GnS , , , , (.1.5). , S n, , ω0.





.1.5. U(t).( f= )

3 .

.1.6. , .1.7. ( 1) ( 2). g = , g,0. R, L, C E , . , , .

 

 

 

 


φ(U)

 

 

 

.1.6.. .1.6..

.5. (.1.6. , .5. ).


I=φ(U)

 

 

 

 

 

 

 

 

 

 

 

.1.7. .

1.    , , . E0(p).

2.    , , .

 

 

 

 

 

 

.1.8. .

3.

4.

, =.

5. . ; , .

- ,

=a1a20, a10 a20. .. G,0, G0 ( ).

1: , a20, . , . .

V(p): p1=+δ, ,

i(t)= , (t0).

, . , .

2: a10; a20 , -

p1,2 = -

i(t)= , (t≥0).

.

3: a10; a20 - ,

p1,2 =

, p1,2 = +δ iω. 젠 i(t)= . , =.

, V(p) , p1 = -δ1, - p2 = δ2.

i(t)= ,

, . . .. .

, R, GA, C L , , .

1.4 .

t=0 S(t), . Ƞ S(t) - , S(t) . . .

, .

(1.32)

, :

(1.33)

- Δ() - ; Δkl() - , k , , l - , ; () - , , , ; () - , . k=l ( , ), () Z(), Y().

() . , . T() , . () (=jω) ()|p==(ω), () Z-1[T()]=g(t) - S(t)=δ(t)

S() .

S(p)=()S(p) 5 :

(1.34)

() .

, T(p) - , T(p)=M(p)/V(p), V(p) - , S() , S()=N(p)/W(p). - , , , S(p) :

(t≥0), (1.35)

pk - W() V (). , V(p), , W(p), , . , . . S(t) , , . W(p) , , .

S(p)

(t≥0) (1.36)

p > 0 p < 0 V(p) W(p), - - 頠 lll, Sk, Sl Ψl :

(1.37)

Sk, Sl Ψl.

. . : , , . , - . S(t)=S0σ(t) S(t)=S0cos(ωt+Ψ)σ(t), , , .

, :

;

;

;

;

;

;

;

;

;

.

4.

(.1.9) E

-

θ U0. R R

-

-

, p>>. -

. R u(t)

u(t)

I)                   蠠

(.1.10).

.1.9. ࠠ , p

.1.10. , p

: Gi+Gk=G1; Cp=C1; C=Cz2; GH=Gz2.

2) :

3) :

4) 4 :

5) :

.

6) :

 V(p)

ࠠ :

7) 5:

8) :

9)

U(t), , b< 0 (.1.11).

10) . , . α01<<α2) .

α2 Cp.

.1.11 .

5.

(.1.12) Uo ω, ω0. U(t), (Q>>I),

1) (.1.13).

.1.12

.1.13 .

2) 젠 젠

3) 젠 :

4) :

5) 젠 :

6)

p1,2=-δiω1, 堠 p1,2=iω0

7)

U(t)=U1e-δtcos(ω1t+Ψ1)+ U2cos(ω0t+Ψ2), t≥0.

8) ωC0; δ<<ω0, .. ω1≈ω0.

9) :

U(t) U (t) (..1.14).

.1.14 .

10) 젠 .

- , .

. Q, δ, ..

 

 

1.5.

, , , , l>λ, (, , .).

, , , . , t.

: I) ; 2) ; 3) , .

, , , . , , , , ( ) . () : R0, L0 , 0 Go . . , , .

, , :

(1.38)

, , . .

1.5.1.

R, L, G , .

R, L, G , .

R, L, G U

i , .

1.5.2. ( ) .

, . , , U(x,t) i (x,t ).

, , . :

(1.39)

U (x,t) i (x,t) , , , .

(1.40)

, :

(1.41)

Z=pL + R; Y=C+G. , :

(1.42)

- ; - . U(x, p) U0:

U(p, x)= 1() e-γx+ A2() eγx +U0. (1.43)

ࠠ :

(1.44)

- ; 1() A2() .

U(,x) I(,x) . 堠 , U( x, t) I(,t ). . .

R=G= 0 .

(1.45)

, :

(1.46)

, . .

. ,

(1.47)

(1.48)

, :

(1.49)

, , . , , , , .

 

1.5.3.

1. .

2. .

3. .

4. U(x,) I(,).

5. 1() 2() .

6. .

7. .

8. .

. (R=G=0), .

(.1.15).

.1.15. .

I. :

U(x,0)=E0; i(x,0)=0.

E0. .

2. :

3. . ( ), U0=const . , :

-p2LCU0=-pLCE0; ࠠ

4. :

U0 i(0,), :

5. A1, 2. :

x=0, U(0)=-RI(0),

, x=l I(l)=0.

, x=0


x=l

6. :

- , .. , .

7. :

8. .

) x=0, l/2 l x=0,

. , , 1/2 . , . 2τ , 2τ ½E0.

.1.16 =0.

) x=l/2 (.1.17);

=l/2 τ/2 ½, t=τ , , (.1.17).

.1.17 x=l/2.

x=l/2 3/2 τ (.1.17).

) x= l (.1.18);

x=l

E0 τ, , τ.

.1.18 x = l

) (.1.19). , , t=τ/2,

E, - E/2, , - E/2, . 0<x<l .

.1.19 .