§ 17-2 Nodal analysis
The node-to-datum voltage vector:
T
nNnnn ][ 21 ???? ??
?The branch voltage vector:
T
bBbbb ][ 21 ???? ??
?
???
?? seb ??????? ? nTb A ??
????
??? nTse A ???
???
? 0biA?
???
?? seb iii
???????
???? 0seb iAiAiA
????
? se iAiA
bki eki
ski
?? ek?
?? bk?
sk?
ekZ
????
? se iAiA
d o m a i nf r e q u e n c ec o m p l e xsVsYsI eee ???
???
)()()(
)()()()( sIAsIAsVsYA seee
???????
???
)()()()()( sVsVAsVsVsV snTsbe
??????
?????
)()()()()( sIAsVsYAsVAsYA ssenTe
?????????
??
)()()()()( sIAsVsYAsVAsYAor ssenTe
?????????
???
bki eki
ski
?? ek?
?? bk?
sk?
ekZ
)s(IA)s(V)s(YA)s(VA)s(YA ssenTe
?????????
???
)()()()( sIAsVsYAsJ ssen
??????
???
The node voltage equation,)()()( sJsVsY
nnn ??? ?
)()()( 1 sJsYsVor nnn
??
?
?
?
----node admittance matrix
----equivalent current source vector
????
? Ten AsYAsYL et )()(
2,Find the element admittance matrix from the branch VCR.
)(sYe
?
1,Choose an arbitrary node as the datum and write down the
incidence matrix from the network graph.
?A
4,Obtain the voltage and current source vectors and
from the network,)(sVs? )(sIs?
5,Use and to compute from
)(sYn
?
)(sVn?
)()()( sJsVsY nnn
???
?
)()()()( sIAsVsYAsJ ssen ?????? ???
6,Use to compute branch voltage,
)()( sVAsV nTb
???
? )(sVb
?
Let us now summarize the steps required for a
complete nodal analysis of given network.
3,Use,obtained in step 1,to calculate from:
???? ?
Ten AsYAsY )()()(sYn
??
A
DP,Write node voltage equations.
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en AYAY
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T
s
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0
0
1
1
)( sesn VYIAJ
???
? nnn JVY
S1
A2
S1 S1
S1
S1S1
S1
S1
A1
V4
?
?
1n
2n 3n
4n
1n
2n 3n
4n
0?
1
2
3
4 5
6 7 8