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+