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Electric Circuits Mesh Analysis Techniques

Learn about node, branch, loop, and mesh in circuit analysis, apply mesh current method, solve simultaneous equations, and analyze transistor circuits. Identify mesh currents and calculate power in various circuit elements.

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Electric Circuits Mesh Analysis Techniques

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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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