methods analysis_nodal & mesh

8/3/2019 Methods Analysis_NODAL & MESH

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METHODS OF ANALYSIS

Mesh Analysis

Nodal analysis



Nodal Analysis 2

Supernode

Determine v 1 , v 2

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A



Nodal Analysis 2

Supernode

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

Step 1

Determine the reference node

Step 2

Assign the rest of the nodes with node voltages

v 1 v 2



Nodal Analysis 2

Supernode

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

v 1 v 2

Step 3

Write down equations using KCL for every non-reference node in terms of nodevoltages

We cannot write equation for current with branch containing 2V voltage source !

To avoid this, we will combine nodes 1 and 2 to form a SUPERNODE



Nodal Analysis 2

Supernode

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

v 1 v 2

To avoid this, we will combine nodes 1 and 2 to form a SUPERNODE

supernode

We will use KCL to sum all current going out of supernode:

074

v

2

v2

21!



Nodal Analysis 2

Supernode

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

v 1 v 2

supernode

074

v

2

v2

21!

We need another equation in order to solve v 1 and v 2

Applying KVL for the loop, 2

vv12!



Nodal Analysis 2

Supernode

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

v 1 v 2

074

v

2

v2

21! 2vv

12!

Step 4

Obtain the node voltages by solving the simultaneous equations in step 3

and

V333.7v1

! V333.5v2

!



Nodal Analysis 2

Supernode

To summarize «.We form a su pernode when there is a voltage source in

between 2 non-reference nodes

For example: Supernode needed since V s in

between non-reference node

+

+

V s



+

+

v b

v a

Nodal Analysis 2

Supernode

To summarize «.

For example:

v 1 v 2 v 3

Supernode needed since v a in between

non-reference node

We don¶t need to formsupernode.

Also note that v 1 = V b

We form a su pernode when there is a voltage source in




Nodal Analysis 2

Supernode

To summarize «.

For example:

We form a su pernode when there is a voltage source in


+

3i o +



Nodal Analysis 2

Supernode

To summarize «.We form a su pernode when there is a voltage source in


Since we have combined two nodes, we lost 1 equation to

solve the circuit. @ we need one more equation to solve thecircuit

We write an equation (using KVL) that defines the voltage

relationship between the two non-reference nodes that forms

the supernodes



Nodal Analysis 2

Verification with Pspice

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

v 1 v 2



Nodal Analysis 2

+

v 1

+

v 2 2; 4;

10;

+

2V

2A 7A

Mark reference node with 0.

Mark the rest of the nodes

with other than 0

0

1 2

Write the NETLIST for the

circuit ans save it with .cir

extension, e.g. example1.cir

EXAMPLE 1

I1 0 1 DC 2

I2 2 0 DC 7

V1 2 1 DC 2R1 1 0 2

R2 1 2 10

R3 2 0 4

.END




Nodal Analysis 2

O pen ³ P s pice AD St u dent´

and simulate the circuit

+

v 1

+

v 2 2

;4;

10;

+

2V

2A 7A

0

1 2 Display the ³ O u tpu t file´


methods analysis_nodal & mesh

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