1. EE 1270 Introduction to Electric Circuits Suketu Naik 0 EE 1270: Introduction to Electric Circuits Lecture 7: Mesh Analysis Chapter 4 Techniques of Circuit Analysis: Sections 4.5-4.7

2. EE 1270 Introduction to Electric Circuits Suketu Naik 1 Node, Branch, Loop, Mesh Node (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

3. EE 1270 Introduction to Electric Circuits Suketu Naik 2 Mesh: More Examples Remember that mesh current represents shared current within a mesh as you go around the loop

4. EE 1270 Introduction to Electric Circuits Suketu Naik 3 Mesh in an Actual Circuit Can you identify meshes in the above circuit?

5. EE 1270 Introduction to Electric Circuits Suketu Naik 4 Mesh-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 v o

6. EE 1270 Introduction to Electric Circuits Suketu Naik 5 Mesh-Current Method Step2: Write Mesh-Current Equations by Summing Voltages around the Meshes Step3: Solve Simultaneous Equations in Standard Form Passive Sign Convention

7. EE 1270 Introduction to Electric Circuits Suketu Naik 6 Mesh-Current Method Passive Sign Convention i a = 5.6 A i b = 2 A i c = -0.8 A p 40V = (40 V)(-5.6 A)=224 W p 20V = (20 V)(-0.8 A)=-16 W Both vol. sources are delivering (generating) power to the circuit v 0 = 8(i a -i b )=8(5.6-2)=28.8 V

8. EE 1270 Introduction to Electric Circuits Suketu Naik 7 AP4.7 Simultaneous Equations: Passive Sign Convention Solution p 80 V = p 8 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

9. EE 1270 Introduction to Electric Circuits Suketu Naik 8 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. EE 1270 Introduction to Electric Circuits Suketu Naik 9 AP4.8b Simultaneous Equations: Passive Sign Convention Solution p -3v ϕ = Find the power associated with the dependent source

11. EE 1270 Introduction to Electric Circuits Suketu Naik 10 Supermesh Circuit with current source between two meshes Combine meshes to create supermesh and ignore the current source

12. EE 1270 Introduction to Electric Circuits Suketu Naik 11 AP4.12 Simultaneous Equations: Passive Sign Convention Solution p 1Ω = Find the power dissipated in the 1 Ω resistor

13. EE 1270 Introduction to Electric Circuits Suketu Naik 12 Example: Transistor Circuit An NPN transistor can be used as an amplifier

14. EE 1270 Introduction to Electric Circuits Suketu Naik 13 Example Fig. 4.27-4.28: Transistor Circuit The transistor circuit can be analyzed using the supermesh Find i B, i E, and i C if Vcc=15 V, R 1 =100 kΩ, R 2 =50 kΩ, Vo=0.65 V, R c =10 kΩ, R E =4.25 kΩ, β=300