ee lecture

8/3/2019 Ee Lecture

http://slidepdf.com/reader/full/ee-lecture 1/22

Circuit Analysis Techniques and

Network Theorems

A. Mesh Analysis

Mesh

It is a loop which does not contain any other

loop within it.

8/3/2019 Ee Lecture


In mesh analysis, Kirchhoff·s Voltage Law (KVL) is

used.

Steps:

1. Draw a current loop for each mesh. All

mesh

currents must be in the same or uniform indirection (clockwise or counterclockwise).

2. Formulate mesh equations following the

pattern. For an n-mesh network, we have n-

mesh equations.3. Solve for the unknown mesh current by

applying techniques involved in evaluating

linear equations.

8/3/2019 Ee Lecture


Equation Pattern:

V1

= R11

I1

- R12

I2

- . . . . . . - R1N

IN

.

V2 = -R21I1 + R22I2 - . . . . . . . - R2NIN .

.

.

VN

= -RN1

I1

- RN2

I2

- . . . . . . + RNN

IN

.

where:

V1 , V2 . . . . Vn = algebraic sum of all voltage

sources in a mesh

R11 , R22 . . .RNN = sum of all resistance in a mesh

R12 , R22 . . .RN = common or mutual resistance

between two meshes

I1 , I2 . . . . . . .IN = mesh currents

8/3/2019 Ee Lecture


V1

V2

V3

R1 R2

R3

1 2

I1 I2

Mesh 1: V1 - V2 = (R1 + R3) I1 - R3 I2

Mesh 2: V2 - V3 = - R3 I1 + (R2 + R3) I2

8/3/2019 Ee Lecture


1 2

I1 I2

10V

2 3

4

6V

3V

;

; ;

4 A 5 ohms

10 V

40 ohms

1 ohm4 ohms

2 ohms

10 A

io

1. Determine mesh currents I1 and I2.

2. Determine io by mesh analysis.

8/3/2019 Ee Lecture


3. Determine the mesh currents.

2

2

3 4

10V

15V

10A 1

;

;

;

;

;

8/3/2019 Ee Lecture


B. Nodal Analysis

I3

I1 I2

R3

R1 R2

Node

A point at which two or more elements have a

common connection.

Nodal analysis is a method that uses Kirchhoff·s Current Law

(KCL) to obtain a solution of simultaneous equations that

when manipulated will provide a means of solving for the

voltages on each node and for every branch.

8/3/2019 Ee Lecture


Steps:

1. Identify the nodes of the given circuit

(including the reference node). All nodeshave corresponding voltages (except the

reference node) and must have the same

voltage sign convention where the given

node is positive and the reference node isnegative.

2. Formulate node equations following the

pattern. For an n - node network, we have

n -1 node equations.3. Solve for the unknown mesh current by

applying techniques involved in evaluating

linear equations

8/3/2019 Ee Lecture


Equation Pattern:

I1 = G11 V1 - G12 V2 - . . . . . . - GN1 VN

I2 = G21 V1 - G22 V2 - . . . . . . - G2N VN

.

.

IN

= -GN1

V1

- GN2

V2

- . . . . . .+ GNN

VN

where:

I1 , I2 , IN = algebraic sum of all current sources

connected to a node.

G11 , G22 , GNN = sum of all conductance connectedto a node.

G12 , G21 , GN = common conductance between two

nodes.

V1 , V2, VN = unknown node voltages

8/3/2019 Ee Lecture


Node 1 :

I1

- I3

= (G1

+ G3) V

1- G

3V

2----1

Node 2 :

I3

+ I2

= - G3

V1

+ (G3

+ G2) V

2---2

2

3

1

31

31

111V

RV

R R I I ¹¹

º

¸©©ª

¨!

1

32

1

3

23

111V

R RV

R I I ¹¹

º

¸©©ª

¨!

I3

I1 I2

R3

R1 R2

8/3/2019 Ee Lecture


Sample Problems:

Determine the node voltages.5A

10A 3A

4S

2S 3S

Determine Vx.

10A

5A0.5Vx1;

2;

3;

- Vx +

8/3/2019 Ee Lecture


Find i using nodal analysis.

8/3/2019 Ee Lecture


B. Superposition theorem

Find v using superposition theorem.

8/3/2019 Ee Lecture


Solution: To get v1, we set the current source to zer o.

Applying KVL,

8/3/2019 Ee Lecture


Find i. Answer: 2A

8/3/2019 Ee Lecture


i3

8/3/2019 Ee Lecture


Thevenin Equivalent Circuit

(TEC)

8/3/2019 Ee Lecture


Obtain the TEC. Determine the current thru R L if R L = 6 ohms, 16 ohms, 36 ohms

8/3/2019 Ee Lecture


Applying mesh analysis;

8/3/2019 Ee Lecture


The TEC is shown below.

The current thru R L is now calculated :

8/3/2019 Ee Lecture


TH N R R !

TH

TH

N

R

V I !

Norton Equivalent Circuit (NEC)

To get INNOTE:

8/3/2019 Ee Lecture


ee lecture

Documents