chapter 4 part2 1hour
TRANSCRIPT
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Part 2
Modelling of Electrical System Elements
(1 Hour)
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able to:Derive the dif ferent ial equat ion of Elect rical
Circuit
Implement the Laplace Transform andnverse o ap ace rans orm
Determine the Transfer Function of Electrical
Draw the block diagram Electrical Circuit
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A mathemat ical model of an electrical circuit can beobtained by Kirchhoffs laws.
- - -
3
, , ,relat ionships for capacit ors, resistors, and inductors
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Exam le 1 :
Obtain the transfer function of the RCnetwork shown below.
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Solution:
Network equationV1(t ) = i(t )R + V2(t )
)(
)()( 2
td
tdVCtI =
y us ng ap ace trans orm, trans er unct on o ta ne s,
( )/111)(2 ====sV
sG /111)(1 +++ ssRCssV
where =RC, the time constant of the network
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Example 2 :
Const ruct the block diagram of the system and obtain the t ransfer
funct ion of the RLCnetwork shown below.
Figure: Series RLC network
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Solution I
The network equations are (let all initial cond. Are zero):
tdvt
dt=
tdi
Lsss
C=
tvdt
ttvC
++=
)()()( tvRtitvdt
L C= )()()()( sVRsIsVsLsI C=L
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Block dia ram of the series RLC network
+ 1Ls
1Cs
V(s)VC(s)+ LsI(s) I(s)
-
R
-
I(s)RVC(s)
Reduced block diagram
1Cs
-
V(s) VC(s)+ 1
R+Ls
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The t ransfer funct ion of the s stem is
CsLsRsVC )(1
)( +=
CsLsR
s
1
)(1
=
++
Block dia ramLsRCs
1
1)(
2=
++ of series RLC electricalnetwork
LC
1
=
9
LCs
Ls ++
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Solution II
Using mesh analysis and t ransform method in s-domain Mesh equat ion 1 sVsIRLs =
++
TF
Cs
)(sI
=sI 1)(
++Cs
RLs
)()(
)(
sCsVsIor
CssV
C
C
=
=
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The transfer function of the system is
CsLsR
sV
sVC
1
)(
1
)(
)( +=
CsLsR
1
)(
=
+
Block diagram
RCsLCs 1
12 ++
=
o ser es e ectr canetwork
R
LC
1
1
2
=
11
LCL
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Example 3:
Const ruct a block diagram of this system in the Figure below andobtain t he t ransfer function.
Answer:
)()(
)(2
RLsRLCs
R
sV
sV
i
o
++=
12
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Electrical System Elements representation inLaplace Transform
Transfer funct ion of Elect rical SystemElements
rcu
KCL, KVL and Electrical Circuit Theory