本章教学重点
1
A B Q
2 KCL KVL
3
15-1
(1) Q
(2) Q G
4 3
21
5
6
1
34
2
5
6
Q1,{ 2,5,4,6 }
Q G
4 3
21
5
6
4 3
21
5
6
4 3
21
5
6
Q4,{ 1,5,2 }Q3,{ 1,4 6}Q2,{ 2,3,6 }
KCL
KCL
KCL
4 3
21
5
6
4 3
21
5
6
Q3,{ 1,5,3,6 }Q2,{ 3,5,4}
4 3
21
5
6
Q1,{ 2,3,6 }
n
b n-1
n-1
2
,A
aij
aij = 1 j i i
aij= -1 j i i
aij =0 j i
Aa={aij}n? b
6
4
5
3
21
Aa=
1
2
3
4
1 2 3 4 5 6
1 0 0 -1 0 1
-1 -1 0 0 1 0
0 1 1 0 0 -1
0 0 -1 1 -1 0
Aa=
1
2
3
4
1 2 3 4 5 6
1
-1
0
0
0
-1
1
0
0
0
1
-1
-1
0
0
1
0
1
0
-1
1
0
-1
0
-1 -1 0 0 1 0A=
1
2
3
1 2 3 4 5 6
1 0 0 -1 0 1
0 1 1 0 0 -1
A (n-1)?b
:
6
4
5
3
21
-1 -1 0 0 1 0A=
1
2
3
1 2 3 4 5 6
1 0 0 -1 0 1
0 1 1 0 0 -1

6
5
4
3
2
1
u
u
u
u
u
u
u
6
5
4
3
2
1
i
i
i
i
i
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i

3
2
1
n
n
n
n
u
u
u
u
KCL
Ai =



632
521
641
iii
iii
iii
-1 -1 0 0 1 0
1 0 0 -1 0 1
0 1 1 0 0 -1
6
5
4
3
2
1
i
i
i
i
i
i
6
4
5
3
21
A i = 0
0?
i
i
i
3
2
1
KVL

31
2
1
3
32
21
nn
n
n
n
nn
nn
uu
u
u
u
uu
uu
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u
u
u
u
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1
101
010
001
100
110
011
n
n
n
u
u
u
uu n?TA
6
4
5
3
21
-1 -1 0 0 1 0A=
1
2
3
1 2 3 4 5 6
1 0 0 -1 0 1
0 1 1 0 0 -1
KVL
,B
2,
1 j i i
-1 j i i
0 j i
bij=
1,
B = { b i j } l? b
4 5 6 1 2 3
1
2
3
B =
4 5 6 1 2 3
1 -1 0 1 0 0
1 -1 1 0 1 0
= [ Bt 1 ]
Tiiiiiii ] [][ 321654?
KVL
T
lt uu
uuuuuuu ] [][ 321654
0 1 -1 0 0 1
Bt Bl
B u = 0
1
2 3

3
2
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
i
i
i

3
2
1
6
5
4
3
2
1
32
321
21
i
i
i
i
i
i
i
i
i
ii
iii
ii
B=[ Bt 1 ]



1
BB TT t?


l
t
l
t
i
ii
1
B T
ltt ii
TB?
BT il = iKCL
KCL
1
2 3
,Q
(1)
(2) ( ),( )
qij=
1 j i i
-1 j i i
0 j i
Q = { q i j } n-1? b
Q=
4 5 6 1 2 3
C1
C2
C3
1 0 0 -1 -1 0
0 1 0 1 1 -1
C1:{1,2,4} C2:{1,2,3,5} C3:{2,3,6}
T321654 ] [][ iiiiiii? ut=[ u4 u5 u6 ]
T
KCL
0 0 1 0 -1 1
QlQt
Qi =0
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l
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l i
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llt ii Q
lTtt ii B?
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tll uu TQ?
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Q
Qi=0
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lTtt ii B?
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llt ii Q
tll uu TQ?
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A B
Ai=0 BTil=iKCL
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B =
3 4 5 1 2 6
1
2
6
1 -1 0 1 0 0
-1 0 1 0 1 0
0 - 1 1 0 0 1
Bt Bl
Q=
3 4 5 1 2 6
3
4
5
1 0 0 -1 1 0
0 1 0 1 0 1
0 0 1 0 -1 -1
QlQt