e e 1205
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E E 1205. Lecture 08 -Mesh Current Analysis. Introduction to Mesh Current Method. More direct than branch equations Fewer equations to solve Express all variables in terms of mesh currents Solution is set of mesh currents Solution completely defines the circuit - PowerPoint PPT PresentationTRANSCRIPT
E E 1205
Lecture 08 -Mesh Current Analysis
Introduction to Mesh Current Method
• More direct than branch equations• Fewer equations to solve• Express all variables in terms of mesh
currents• Solution is set of mesh currents• Solution completely defines the circuit• Most Convenient Method to Model
Magnetic Coupling (E E 2446 Topic)
Mesh Current Example 1 (1/2)
KVL at Mesh 1:
KVL at Mesh 2:
Using Ohm’s Law:
Vs1 Vs2
Ra Rb
RcI1 I2
+ va - + vb -+vc-
10 s a cV v v
20 c b sv v V
1 1 1 2s a cV R I R I I
2 1 2 2s c bV R I I R I
Mesh Current Example 1 (2/2)
Above linear equations can be solved for mesh currents I1 and I2.
Vs1 Vs2
Ra Rb
RcI1 I2
+ va - + vb -+vc-
1 1
2 2
s a c c
s c b c
V R R R IV R R R I
Mesh Current Example 1a (1/2)
120 V 64 V
8
24 I1 I2
6
KVL at Mesh 1:
KVL at Mesh 2: 1 1 20 120 6 24I I I
2 1 20 64 24 8I I I
1
2
120 30 2464 24 32
II
Solve: 1
2
62.5
I AI A
Forced Mesh (1/2)
• No KVL equation possible for mesh 2• But I2 is known: I2 = Is
Vs Is
Ra Rb
RcI1 I2
Forced Mesh (2/2)
KVL for mesh 1:
Substitute and Solve:
Vs Is
Ra Rb
RcI1 I2
1 1 20 s a cV R I R I I
1s c s
a c
V R IIR R
Forced Mesh Example 3a
108 V 5 A
6 8
20 I1 I2
KVL for mesh 1:
Substitute and Solve:
1 10 108 6 20 5I I
1108 1006 20
I
1 8I A
Supermesh Example (1/5)
• No KVL possible for meshes 1 or 2• Use Supermesh (dotted loop) for KVL
Vs1 Vs2
Is
Ra Rb
Rc Rd
Re
I1 I2
I3
Supermesh Example (2/5)
Supermesh KVL:
Mesh 3 KVL:
Vs1 Vs2
Is
Ra Rb
Rc Rd
Re
I1 I2
I31 1 2
2 2 3
1 3
0( )
( )
s a b
s d
c
V R I R IV R I IR I I
3 1 3 2 30 ( ) ( )c d eR I I R I I R I
Supermesh Example (3/5)
Also:
Vs1 Vs2
Is
Ra Rb
Rc Rd
Re
I1 I2
I3
2 1 2 1s sI I I I I I
1 2 1 1
1 3 1 3
( )( ) ( )
s s a b s
d s c
V V R I R I IR I I I R I I
Subst for I2:
Supermesh Example (4/5)
And:
Rearranging the equations:
Vs1 Vs2
Is
Ra Rb
Rc Rd
Re
I1 I2
I3
3 1 3 1 30 ( ) ( )c d s eR I I R I I I R I
Supermesh Example (5/5)
Vs1 Vs2
Is
Ra Rb
Rc Rd
Re
I1 I2
I3
1 2 1
3
s s b d s a b c d
c d
V V R R I R R R R I
R R I
1 3d s c d c d eR I R R I R R R I
Supermesh with Numbers (1/3)
200 V 120 V20 A
4 6
12 8
20
I1 I2
I3
Supermesh with Numbers (2/3)
1
3
40 30 20160 20 40
IVIV
1
3
67
I AI A
2 20 6 26I A A A
Supermesh with Numbers (3/3)
200 V 120 V20 A
4 6
12 8
20
6A 26A
7A
+24V- +156V-
-152V++12V-
-140V+