1. EE 1270: Introduction to Electric Circuits
Lecture 7:
Mesh Analysis
Chapter 4
Techniques of Circuit Analysis: Sections

2. Node, Branch, Loop, Mesh Branch Node (current sum) Mesh (voltage sum)
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

3. Mesh: More Examples
Remember that mesh current represents shared current within a mesh as you go around the loop

4. Mesh in an Actual Circuit
Can you identify meshes in the above circuit?

5. Mesh-Current Method
Find unknown currents by summing the voltages in a mesh
Example 4.4: a) Find the power for each voltage source
b) Find vo
Step1: Draw Mesh
Currents

6. Mesh-Current Method
Step2: Write Mesh-Current Equations by Summing Voltages around the Meshes
Passive Sign Convention
Step3: Solve Simultaneous Equations in Standard Form

7. Passive Sign Convention
Mesh-Current Method
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
Passive Sign Convention
Both vol. sources are delivering (generating)
power to the circuit
v0= 8(ia-ib)=8(5.6-2)=28.8 V

8. Passive Sign Convention
AP4.7
Find the power associated with the voltage source and the power dissipated in the 8 Ω resistor
Simultaneous Equations:
Passive Sign Convention
Students work on this example
Solution
p80 V =
p8 Ω =
Positive Power means it is consumed (dissipated)
Negtive Power means it is generated (delievered)

9. Positive 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:

10. Passive Sign Convention
AP4.8b
Find the power associated
with the dependent source
Simultaneous Equations:
Passive Sign Convention
Solution
p-3vϕ =

11. Super Mesh

12. Supermesh Circuit with current source between two meshes
Combine meshes to create supermesh and ignore the current source

13. Passive Sign Convention
AP4.12
Find the power dissipated in the 1 Ω resistor
Simultaneous Equations:
Passive Sign Convention
Students do this example
Solution
p1Ω =

14. Example: Transistor Circuit
An NPN transistor can be used as an amplifier

15. Example Fig. 4.27-4.28: Transistor Circuit
The 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