§ 17-3 Loop analysis
§ 17-4 Analysis of networks containing dependent sources
A typical branch with dependent current source.
skekdkbk iiiiK C L ???:
)()()()( sIsIsIsIor sedb
????
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)()()( sIsVsY see
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)()]()()[( sIsVsVsY ssbe
????
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)()( sIsI db
??
? )()]()()[( sIsVsVsY ssbe
????
???
bki eki
ski
?? ek?
?? bk?
sk?
ekZ
?
dki
)()( sIsI db
??
? )()]()()[( sIsVsVsY ssbe
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)]()()[(][ sVsVsY sbejk
???
?? ?
][ jk? represent the strengths of current sources in branch j as a function of the element current in branch k,For one such source
the matrix is zero except for the element j,k,(the j,k-and the
general branch have the same orientation,)??
jk?
)]([)(][)( sysYsYL e t kkjkejk ?? ??
??
?
It is a matrix of zeros except the jk-th element,whose value
is ).( sy
kkjk?
)]()()[()( sVsVsYsI sbd
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?
?
???
)()]()() ] [()([)( sIsVsVsYsYsI ssbeb
????
?
??
????
1,If
)(][)( sIsI ejkd
??
? ?
)()]()() ] [()([)( sIsVsVsYsYsI ssbeb
????
?
??
????
)()(0)( sVAsVa n dsIA nTbb
??????
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)]()]()([)( sVsYsYAsIA ses
??
?
????
??? )()]()([ sVAsYsYA nTe
???
?
??
?
)]()()([ sVsYsIA sbs
????
?? )()( sVAsYAor nTb
????
m a t r i xcet a na d m i tb r a n c h)s(Y)s(Y)s(Y eb ????
?
?
??
???? ?
Tbn AsYAsYL et )()( )()()()( sIAsVsYAsJ ssbn
??????
???
The node voltage equations are
)()()( sJsVsY nnn
???
?
2,If
)(][)( sVgsI ejkd
??
? )]()()[()()( sVsVsGsVsG sbe ????? ???
)(sG?
is matrix of zeros except
jkg,0?
)()]()() ] [()([)( sIsVsVsGsYsI ssbeb
??????
?????
)()(0)( sVAsVa n dsIA nTbb
??????
???
)]()]()([)( sVsGsYAsIA ses
??????
??? )()]()([ sVAsGsYA nTe
?????
?
)]()()([ sVsYsIA sbs
????
?? )()( sVAsYAor nTb
????
)]()()([ sVsYsIA sbs
????
?? )s(VA)s(YA nTb
????
???? ?
Tbn AsYAsYL et )()(
)()()()( sIAsVsYAsJ ssbn
??????
???
The node voltage equations are
)()()( sJsVsY nnn
???
?
m a t r i xcet a na d m i tb r a n c h)]s(G)s(Y)s(Y[)s(Y eb ?????
??
?
??