ECE 1270 Introduction to Electric Circuits Suketu Naik

0EE 1270: Introduction to Electric Circuits

Lecture 7:

Mesh Analysis

Chapter 4

Techniques of Circuit

Analysis: Sections 4.5-4.7

ECE 1270 Introduction to Electric Circuits Suketu Naik

1Node, Branch, Loop, MeshNode

(current

sum) Mesh

(voltage

sum)

Branch

Node: A point where two or more circuit elements join

Mesh: A loop that does not enclose any other loops

Branch: A circuit path that contains two nodes

Loop: A path with starting node=last node; can contain many meshes

ECE 1270 Introduction to Electric Circuits Suketu Naik

2Mesh: More Examples

Remember that mesh current represents shared current

within a mesh as you go around the loop

ECE 1270 Introduction to Electric Circuits Suketu Naik

3Mesh in an Actual Circuit

Can you identify meshes in the above circuit?

ECE 1270 Introduction to Electric Circuits Suketu Naik

4Mesh-Current Method

Find unknown currents by summing the voltages in a mesh

Step1: Draw Mesh

Currents

Example 4.4: a) Find the power for each voltage source

b) Find vo

ECE 1270 Introduction to Electric Circuits Suketu Naik

5Mesh-Current Method

Step2: Write

Mesh-Current

Equations by

Summing

Voltages

around the

Meshes

0204)(6

0)(66)(8

0)(8240

cbc

cbbab

baa

iii

iiiii

iii

Step3: Solve

Simultaneous

Equations in

Standard Form

Passive Sign

Convention

201060

06208

400810

cba

cba

cba

iii

iii

iii

ECE 1270 Introduction to Electric Circuits Suketu Naik

6Mesh-Current Method

Passive Sign

Convention

ia= 5.6 A

ib= 2 A

ic= -0.8 A

p40V= (40 V)(-5.6 A)=-224 W

p20V= (20 V)(-0.8 A)=-16 W

Both vol. sources are delivering (generating)

power to the circuit

v0= 8(ia-ib)=8(5.6-2)=28.8 V

ECE 1270 Introduction to Electric Circuits Suketu Naik

7AP4.7

Simultaneous Equations: Passive Sign

Convention

Solution

p80 V =

p8 Ω =Positive Power means it is consumed (dissipated)

Negtive Power means it is generated (delievered)

Find the power associated with the voltage source and the power dissipated in the

8 Ω resistor

ECE 1270 Introduction to Electric Circuits Suketu Naik

8Positive and Negative Power

Positive Power means it is consumed by a circuit element,

i.e. vol. source, cur. source, resistor, capacitor, inductor etc

Negtive Power means it is generated (delievered) by a cur. source

or a vol. source

The positive or negative sign depends on the polarity of the voltage

and direction of the current

Q: Where happens to the dissipated or consumed power in a

resistor?

A:

ECE 1270 Introduction to Electric Circuits Suketu Naik

9AP4.8b

Simultaneous Equations:

Passive Sign

Convention

Solution

p-3vϕ =

Find the power associated

with the dependent source

ECE 1270 Introduction to Electric Circuits Suketu Naik

10

Super Mesh

ECE 1270 Introduction to Electric Circuits Suketu Naik

11Supermesh

Circuit with current

source between two

meshes

Combine meshes to

create supermesh

and ignore the

current source

ECE 1270 Introduction to Electric Circuits Suketu Naik

12AP4.12

Simultaneous Equations:

Passive Sign

Convention

Solution

p1Ω =

Find the power dissipated in the 1 Ω resistor

ECE 1270 Introduction to Electric Circuits Suketu Naik

13Example: Transistor Circuit

An NPN transistor can be used as an amplifier

ECE 1270 Introduction to Electric Circuits Suketu Naik

14Example Fig. 4.27-4.28: Transistor CircuitThe transistor circuit can be analyzed using the supermesh

Find iB, iE, and iC if Vcc=15 V, R1=100 kΩ, R2=50 kΩ, Vo=0.65 V,

Rc=10 kΩ, RE=4.25 kΩ, β=300