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EE 1270: Introduction to Electric Circuits

EE 1270: Introduction to Electric Circuits. Lecture 7: Mesh Analysis Chapter 4 Techniques of Circuit Analysis: Sections 4.5-4.7. Node, Branch, Loop, Mesh. Node (current sum). Mesh (voltage sum). Branch. Node: A point where two or more circuit elements join

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EE 1270: Introduction to Electric Circuits

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

  2. 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. 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. 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. AP4.7 Find the power associated with the voltage source and the power dissipated in the 8 Ω resistor Simultaneous Equations: Passive Sign Convention 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. 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. AP4.12 Find the power dissipated in the 1 Ω resistor Simultaneous Equations: Passive Sign Convention 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

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