§ 17-1 Direct analysis methods
??? ? 0,biAK C L ??? ? 0,bfBKVL ?
00 )( ?? ?tCC)(ti
?? )(t?
Let the initial voltages on the capacitors be represented
as voltage sources in series with the capacitors and the
initial currents through the inductors be represented as
current sources in parallel with the inductors.
C)(ti
?? )( t?
?? 0?
0)( 0 ?tC?
)(ti
?? )( t?
L 00 )( itiL ?
)(ti
?? )( t?
0i
0)( 0 ?tiLL
General branch of a linear time-invariant network
c u r r e n tb r a n c hi bk ??
v o l t a g eb r a n c hbk ???
cu r r en tel e m en ti ek ??
v o l t a g ee l e m e n tek ???
s o u r c ev o l t a g esk ???
s o u r c ec u r r e n ti sk ??
i m p e d a n c ee l e m e n tZ ek ??
B,,,kiii:KCL skekbk ?21??? BkK V L skekbk,,,,?21??? ???
BkiRV C R ekkek,,2,1)1(,????
)(1)()(1)2(
0
sIsCsVordiC ek
k
ek
t
t ekkek
?? ? ???
)()()3( sIsLsVordtdiL ekkekekkek ???
bki eki
ski
?? ek?
?? bk?
sk?
ekZ
skekbk iiiK C L ??:
skekbkK V L ??? ??:
TbBbbb ][ 21 ???? ??
?
TbBbbb iiiiL et ][,21 ??
?
TsBsss iiii ][ 21 ??
?
TeBeee iiii ][ 21 ??
?
)( K C Liii seb
???
??
TeBeee ][ 21 ???? ??
?
TsBsss ][ 21 ???? ??
?
)( K V Lseb
???
?? ???
bki eki
ski
?? ek?
?? bk?
sk?
ekZ
Source transformation
We remove this voltage source and add a voltage
source to all the other branches that are incident to
one of the terminal of
sk?
.kb
The voltage source transformation
sk?
?
?
kb
sk?sk
?
? ?
? ?
kb
We remove the branch altogether and a current
source parallel to each branch of any one loop of
which is a branch.ski
kb
kb
The current source transformation
ski
ski
ski
ski
kb