, .. . , , . , .
f(t) , ,
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(1) |
p = a + jb - , F(p).
f(t) , F(p) - .
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(2) |
p, F(p).
(1) (2) . 1.
1.
C |
C/p |
t |
1/p2 |
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.
F(p) ( )
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(3) |
,
n < m ,
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(4) |
pk - F2(p) = 0.
Ak. (4) (p - p1)
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(5) |
p = p1 (5) A1, , .. F2(p1) = 0. ,
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(6) |
, (4)
F2(p) = 0.
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(7) |
F(p) (7). F1(pk)/F2'(pk), 1/( p - pk), (. 1) epkt.
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(8) |
(8) . .
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(9) |
.
2
Af(t) |
AF(p) |
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-
, , ,
p, - .L C. .
. 2,
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(10) |
i(0) - . pL L. Li(0) . , Li(0).
2
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(11) |
uC(0) - . 1/(pC) (11) C. .
R. R.
(10) (11) .
, . 3.3.
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u = Ri |
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U(p) = RI(p) |
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U(p) = pLI(p)- Li(0) |
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, , 3, , .
, . 1 ). , .
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, , , ( 2),
a bZ(p)=R+pL+1/(pC) . , , p jw .
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(12) |
(12) . , , .. . (12)
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(13) |
. , , ,
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(14) |
, . , ,
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(15) |
q w - . , . , , , .
, , . . :
. 2 ) , E = 100 , R1 = 20 , R2 = 5 , L = 100 , C = 10 .
S , , , , . 2 ).
,
b2 = R1LC; b1 = L+R1R2C; b0 = R1+R2; a2 = LC; a1 = R2C.
I1(p)
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p1 = - 261 p2 = - 4789. , 3t 1 = 3/261 = 11.5 .
(9). i1
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Z2(p) = R2+pL Z3(p) = 1/(pC) . I1(p), I3(p)
, ,
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, i3 5.0 , . i2 , 4.0 . 5.0 4.0 .
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