§ 2-4 Thevenin's and Norton's theorems
One of the main uses of Thevenin's and Norton's theorems is
the replacement of a large part of network very simple equivalent.
)(a
?
?
V12
3
LR6
7
)(b
3 LR6
7
A4
)c(
?
?
V8
2
LR
7
)d(
?
?
V8
9
LR
Thevenin's theorem:
Given any linear circuit,rearrange it in the form of
two networks A and B that are connected together by two
resistance-less conductors,If either network contains a
dependent source,its control variable must be in that
same network,Define a voltage voc as the open-circuit
voltage,which would appear across the terminals of A,if
B were disconnected so that no current is drawn from A.
Then all currents and voltages in B will remain uncharged
if A is killed (all independent voltage sources and
independent current sources in A replaced by short circuits
and open circuits,respectively) and an independent voltage
source is connected,with proper polarity,in series with
t h e d e a d ( i n a c t i v e ) A n e t w o r k,
A B
voc---open-voltage,Rth---equivalent-resistance.
Proving:
A
c ir c u it
e q u iv a le n t
T h e v e n in
?
oc?
thR
?
?
B
?
?
oc?
thR
i
B
oc?
thRA
oc?
thR
i
B
A
A
oc? oc?
?? ??
B
oc?
thRA
0'?i
??
oc?
B
oc?
thRA
''i
??
oc?
?
?
oc?
thR
c i r c u i te q u i v a l e n tT h e v e n i n ??
B
''ii?
R1
2k
7,9 9 8 V4,0 0 0 V
0V
2 m A
R2
3k
4V
7,9 9 6 V
R3
1 0 0 0 0 k
0
R3
0,000 001
1,600 m A
R1
2k
40 0,0 uA
2m A
2,000 m A
R2
3k
1,600 m A
0
4V
40 0,0 uA
Solution:
1.Find voc.
(A),Method of short-circuit current(电源保留 ).
Vxocxx 8,4 0 0 02 0 0 04 ?????? ????
.8.05 4,04000,0 mAki scxx ??????? ??? ????? ? kiR
sc
octh 10
108.0
8
3
?
Example 2,Find and,
OC? thR
2,Find Rth.
?
sci
4000x
?
?
?
x?
k2 k3
?
?
V4
4000x
?
?
?
x?
k2 k3
?
?
V4
oc?
thR
sci
?
?
?
?
?
sc
oc
th iR
??
（ B),We apply a 1A source externally,measure the
resultant voltage,and then set,Rth=v/1(独立源为零 )
kV
kkk
10
252)4 0 0 01(13
?
??????
?
???
??? kR th 101?
（ C）,We could also apply a 1V source externally,
determine i=1/Rth,and then set Rth=1/i.(独立源为零 )
ki
kikiki
x
xx
10/11
2
52)
4 0 0 0
(31
???
?????
?
??
??? kiR th 101
TheThevenin-equivalent circuit:
4000x
?
?
?
x?
k2 k3
A1
??
4000x
?
?
?
x?
k2 k3
V1
i
?
?
V8??
k10
R2
3k
8 0 0, 0 u A
+
-
G1
G
R3
0,0 0 0 0 0 0 0 1
8 0 0, 0 u A
4V
8 0 0, 0 u A
0
R1
2k
8 0 0, 0 u A
7,9 9 9 V 7,9 9 9 V
0
R1
2k
4V
R2
3k
+
-
G1
G
0V
R3
1 0 0 0 0 0 k
4,0 0 0 V
Norton's theorem:
Given any linear circuit,rearrange it in the form of two
networks A and B that are connected together by two resistance-
less conductors,If either network contains a dependent
source,its control variable must be in that same network.
Define a current isc as the short-circuit current,which would
appear at the terminals of A,if B were short-circuited so that no
voltage is provide by A,Then all voltages and currents in B will
remain uncharged if A is killed (all independent voltage sources
and independent current sources in A replaced by short circuits
and open circuits,respectively) and an independent current source
isc is connected,with proper polarity,in parallel with the dead
(inactive) A network.