teorijaekola07 slozenoperiodican rezonancija - tek.etf.rstek.etf.rs/teorijaekola07_slozenoperiodican...
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(1)
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(2)
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( )
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(3)
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:
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3g2g1gg uuuu ++=
2gu1gu 3gu
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3g2g1gg iiii ++=
2gi1gi 3gi
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gi 1C 2C
1L 2L
1R 2R
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R2
)cos(2)cos(2 2g2g2g1g1g1g0gg ++++= tItIIi
gi 1C 2C
1L 2L
1R 2R
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()
gi 1C 2C
1L 2L
1R 2R
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()
gi 1R 2R
0gg Ii = )0(uu =
DC Analysis
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()
21
210
)0(
RR
RRIu g +
=
gi 1C 2C
1L 2L
1R 2R
DC Analysis (0)
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gi 1C 2C
1L 2L
1R 2R
)cos(2 1g1g1gg += tIi)1g(= uu
AC Analysis (1)
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
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1gj1g
)1g(g e
= II
)eRe(2 1gj)1g()1g( tUu =
gi 1C 2C
1L 2L
1R 2R
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
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gi 1C 2C
1L 2L
1R 2R
)cos(2 2g2g2gg += tIi)2g(= uu
AC Analysis (2)
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
2gj2g
)2g(g e
= II
)eRe(2 2gj)2g()2g( tUu =
gi 1C 2C
1L 2L
1R 2R
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
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)2g()1g()0( ++= uuuu
( ) .
( ).
( ) .
gi 1C 2C
1L 2L
1R 2R
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
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T
:
,
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=++=
1110 ))sin()cos(()(
nnn tnBtnACtu
T
= 21
=T
ttuT
C0
0 d)(1
=T
n ttntuTA
0
1 d)cos()(2
=T
n ttntuTB
0
1 d)sin()(2
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. , , , , , 2016.
)0(0
)0( UCu == , , , DC
)cos(2
)sin()cos()1(
1)1(
1111)1(
+=
+=
tU
tBtAu , , AC
)cos(2
)sin()cos()(
1)(
11)(
nn
nnn
tnU
tnBtnAu
+=
+=
K,4,3,2=n
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=++=
1
)(1
)()0( )cos(2)(n
nn tnUUtu
=
=+=
++=
1
2)(2)0(
1
2220
0
2 )()(2
d|)(|1
n
n
n
nnT
UUBA
CttuT
0lim,0lim,0lim )( ===
n
nn
nn
nUBA
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==
nn tnCtu )jexp()( 1
T
= 21 0,2j = nBAC nnn
=T
n ttntuTC
01 d)jexp()(
1
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=+==
1
2)(2)0(
0
2eff )()(d|)(|
1
n
nT
UUttuT
U
(RMS, , root-mean-square value)
. .
-
. , , , , , 2016.
T0 T2TT2
a
)(tu
t
=
+
+=
11
12
11 )sin(
)2(sin2)cos(
)sin()(
n
tnn
natn
n
na
T
atu
.
.
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16
-2 -1 1 2
0.2
0.4
0.6
0.8
1
5
2
1
1
=
==
T
a
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32
5
2
1
1
=
==
T
a
-2 -1 1 2
0.2
0.4
0.6
0.8
1
-
. , , , , , 2016.
512
5
2
1
1
=
==
T
a
-2 -1 1 2
0.2
0.4
0.6
0.8
1
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a
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()
,
-
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gu
L
R
i
() .
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1. :
=++=
1
)(g1
)(g
)0(gg )cos(2)(
n
nn tnUUtu
, .
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2. :
)0(g
)0()0( 1 UR
Ii ==
, , () .
DC Analysis
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3. : n-
)cos(2)( )(g1)(
g)(
gnnn tnUtu +=
)(gj)(
g)(
g en
nn UU=
LnRUI nn
1
)(g
)(
j
1
+=
)eRe(2 1j)()( tnnn Ii =1= n
n-
n-
( ) n-
( ) n-
AC Analysis
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
4. :
=+=
1
)()0()(n
niiti
( ) .
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
, ,
*)()()( )( nnn IUS =
)Re( )()( nn SP =
)Im( )()( nn SQ =
n-
n-
n-
=+=
1
)()0(
n
nPPP
()
==
1
)(
n
nQQ
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effeff IUS =
222 QPSD =
(Apparent power)
() (Distortion power)
S
PPFkP == (Power factor)
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?
?
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?
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, , , ,
, ,
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eff
)1(
d U
UK =
() (Distortion factor) , 1
DC
ACeff,r U
UK =
(High-harmonics factor))1(
1ACeff,h
U
UK >=
(DC ).
()..
(Ripple factor)
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. , , , , , 2016.
()
T0 T2TT2
a
)(tu
t
10, 100 500 . ?
-
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()
,
, ,
-
. , , , , , 2016.
Tacoma Narrows Bridge, 7. Nov. 1940.
-
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?
,
a
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
()
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
.
.
-
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)()1
sin()( mg ttCL
Utu =
)()1
sin(2
1)( m tt
CLL
tUti =
m : 1
ug
C
L u
i
CLs
1jj ==
-
. , , , , , 2016.
,
-
. , , , , , 2016.
.
()
-
. , , , , , 2016.
?
-4 p -3 p -2 p -p p 2 p 3 p 4 p
-1
1
-
. , , , , , 2016.
(1)
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
(2)
.
Si Fi (Sinusoidal Fidelity): .
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
(3)
.
. ( )
( . , )
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
(1)
.
? ? ?
? ? ? .
-
. , , , , , 2016.
(2)
? ? ? ?
? ? ? ? ? ? ? ? ?
-
. , , , , , 2016.
(3)
? () ? ? ? ? ? ?
-? ?
-
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(4)
-
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(5)
-
. , , , , , 2016.
(6)
-
. , , , , , 2016.
C , R R5 2= , R R R R1 4 6= = = . (5) ( ,
) )(
)()(
g sU
sUsH = .
(5) .
(5) u u t U U t CR U t CRg ( ) sin( ( )) cos( ( ))= + +3 ?
ug
R1
R4C2
C3u
R5 R6
-
. , , , , , 2016.
(1)
-
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(2)
-
. , , , , , 2016.
(3)
-
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(4)
-
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(5)
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-4 p -3 p -2 p -p p 2 p 3p 4 p
-1
1
-
. , , , , , 2016.
(6)
-
. , , , , , 2016.
Jean Baptiste Joseph Fourier 17681830
. Joseph Lagrange. Gustav Dirichlet. cole Polytechnique. . Auxerre, .
J. Fourier, Thorie analytique de la chaleur, Paris: Firmin Didot Pre et Fils, 1822.
-
. , , , , , 2016.
Josiah Willard Gibbs 18391903
. Yale University. . NewHaven, Connecticut, .