Mesh analysis is applicable only to those networks,which
are planar.
§ 2-2 Mesh(网孔 ) analysis
If it is possible to draw the diagram of a circuit on a plane
surface in such a way that no branch passes over or under any
other branch,then that circuit is said to be a planar circuit.
(Non -planar-circuit) (Planar -circuit)
Mesh analysis:
42)ii(3i6:L 2111 ???
10i4)ii(3:L 2212 ????
??
?
?
?
Ai
Ai
4
6
2
1
We define a mesh current as a current,which flows only
around the perimeter of a mesh.
42)ii(3i6:L )2()1()1(1 ???
10i4)ii(3:L )2()2()1(2 ????
?
?
?
??
??
Aii
Aii
4
6
)2(2
)1(1
A mesh current may often be identified as a branch
current,— (支路中只有一个网孔电流通过时，有 i1=i(1) and
i2=i(2))
?
?
V42
61i 4
3
2i
213 iii ??
?
?
V10
1L 2L
?
?
V42
61i 4
3
2i
213 iii ??
?
?
V101L 2L
)(i1 )(i2
0)(26)(17 3121 ??????? iiii
0)(32)(1 32212 ????? iiiii
01)(36)(2 32313 ?????? iiiii
??
?
?
?
????
????
???
6632
036
123
321
321
321
iii
iii
iii
or
.3
39
117
632
361
213
636
360
211
1
Ai ??
??
??
??
?
?
??
?
Ai 22 ? Ai 33 ?
4
?
?
V7
3
1
1 2
?
?
V6
2
2i
1i
3i
When a current source is present in the network,We should
assign an unknown voltage across the current source,apply
KVL around each mesh,and then relate the source current to
the assigned mesh currents.
)5(01)(3)(17:)3()1( 32321 ???????? iiiii
)2(0)(32)(1 32212 ????? iiiii
)3(01)(3)(2 32313 ?????? iiivii
)4(731 ?? ii
)1(0)(2)(17 3121 ??????? iivii
?
?
?
?
?
???
??
????
744
7
036
321
31
321
iii
ii
iii
or We have:i
1=9A,i2=2.5A,i3=2A.
?
?
?
?
?
V7
3
1
1 2
2
2i
1i
3i
A7
Let us summarize the method by which we obtain a set
of mesh equations for a resistive circuit:
1.Make certain that the network is a planar network,
If it is non-planar,mesh analysis is not applicable.
2.Make a neat,simple,circuit diagram,Indicate all
element and source values,Resistance values are
preferable to conductance values,Each source should
have its reference symbol.
3,Assuming that the circuit has M meshes,assign a
clockwise current in each mesh,i1,i2,…,iM.
4,If the circuit contains only voltage sources,apply
Kirchhoff 's voltage law around each mesh,To obtain
the resistance matrix if a circuit has only independent
voltage sources,equate the clockwise sum of all the
resistor voltages to the counter-clockwise sum of all
the source voltages,and order the terms,from i1 to iM,
For each dependent voltage source present,relate the
source voltage and the controlling quantity to the
variables i1,i2,…,iM,if they are not already in that
form.
5,If the circuit contains current sources,temporarily
modify the given circuit by replacing each source by
a open circuit,thus reducing the number of meshes
by one for each current source that is present,The
assigned mesh currents should not be changed.
Using these assigned mesh currents,apply Kirchhoff 's
voltage law around each of the meshes or super-meshes
in this modified circuit,Relate each source current to
the variables i1,i2,…,iM,if it is not already in that form.
are planar.
§ 2-2 Mesh(网孔 ) analysis
If it is possible to draw the diagram of a circuit on a plane
surface in such a way that no branch passes over or under any
other branch,then that circuit is said to be a planar circuit.
(Non -planar-circuit) (Planar -circuit)
Mesh analysis:
42)ii(3i6:L 2111 ???
10i4)ii(3:L 2212 ????
??
?
?
?
Ai
Ai
4
6
2
1
We define a mesh current as a current,which flows only
around the perimeter of a mesh.
42)ii(3i6:L )2()1()1(1 ???
10i4)ii(3:L )2()2()1(2 ????
?
?
?
??
??
Aii
Aii
4
6
)2(2
)1(1
A mesh current may often be identified as a branch
current,— (支路中只有一个网孔电流通过时，有 i1=i(1) and
i2=i(2))
?
?
V42
61i 4
3
2i
213 iii ??
?
?
V10
1L 2L
?
?
V42
61i 4
3
2i
213 iii ??
?
?
V101L 2L
)(i1 )(i2
0)(26)(17 3121 ??????? iiii
0)(32)(1 32212 ????? iiiii
01)(36)(2 32313 ?????? iiiii
??
?
?
?
????
????
???
6632
036
123
321
321
321
iii
iii
iii
or
.3
39
117
632
361
213
636
360
211
1
Ai ??
??
??
??
?
?
??
?
Ai 22 ? Ai 33 ?
4
?
?
V7
3
1
1 2
?
?
V6
2
2i
1i
3i
When a current source is present in the network,We should
assign an unknown voltage across the current source,apply
KVL around each mesh,and then relate the source current to
the assigned mesh currents.
)5(01)(3)(17:)3()1( 32321 ???????? iiiii
)2(0)(32)(1 32212 ????? iiiii
)3(01)(3)(2 32313 ?????? iiivii
)4(731 ?? ii
)1(0)(2)(17 3121 ??????? iivii
?
?
?
?
?
???
??
????
744
7
036
321
31
321
iii
ii
iii
or We have:i
1=9A,i2=2.5A,i3=2A.
?
?
?
?
?
V7
3
1
1 2
2
2i
1i
3i
A7
Let us summarize the method by which we obtain a set
of mesh equations for a resistive circuit:
1.Make certain that the network is a planar network,
If it is non-planar,mesh analysis is not applicable.
2.Make a neat,simple,circuit diagram,Indicate all
element and source values,Resistance values are
preferable to conductance values,Each source should
have its reference symbol.
3,Assuming that the circuit has M meshes,assign a
clockwise current in each mesh,i1,i2,…,iM.
4,If the circuit contains only voltage sources,apply
Kirchhoff 's voltage law around each mesh,To obtain
the resistance matrix if a circuit has only independent
voltage sources,equate the clockwise sum of all the
resistor voltages to the counter-clockwise sum of all
the source voltages,and order the terms,from i1 to iM,
For each dependent voltage source present,relate the
source voltage and the controlling quantity to the
variables i1,i2,…,iM,if they are not already in that
form.
5,If the circuit contains current sources,temporarily
modify the given circuit by replacing each source by
a open circuit,thus reducing the number of meshes
by one for each current source that is present,The
assigned mesh currents should not be changed.
Using these assigned mesh currents,apply Kirchhoff 's
voltage law around each of the meshes or super-meshes
in this modified circuit,Relate each source current to
the variables i1,i2,…,iM,if it is not already in that form.
