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Learning Outcome

ECA1212 Introduction to Electrical & Electronics Engineering Chapter 2: Circuit Analysis Techniques by Muhazam Mustapha, September 2011. Learning Outcome. Understand and perform calculation on circuits with mesh and nodal analysis techniques

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Learning Outcome

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  1. ECA1212Introduction to Electrical &Electronics EngineeringChapter 2: Circuit Analysis Techniquesby Muhazam Mustapha, September 2011

  2. Learning Outcome • Understand and perform calculation on circuits with mesh and nodal analysis techniques • Be able to transform circuits based on Thevenin’s or Norton’s Theorem as necessary By the end of this chapter students are expected to:

  3. Chapter Content • Mesh Analysis • Nodal Analysis • Source Conversion • Thevenin’s Theorem • Norton’s Theorem

  4. Mash Analysis Mesh CO2

  5. Mesh Analysis • Assign a distinct current in clockwise direction to each independent closed loop of network. • Indicate the polarities of the resistors depending on individual loop. • [*] If there is any current source in the loop path, replace it with open circuit – apply KVL in the next step to the resulting bigger loop. Use back the current source when solving for current. Steps: CO2

  6. Mesh Analysis • Apply KVL on each loop: • Current will be the total of all directions • Polarity of the sources is maintained • Solve the simultaneous equations. Steps: (cont) CO2

  7. Mesh Analysis Example: [Boylestad 10th Ed. E.g. 8.11 - modified] R2 R1 4Ω R3 1Ω 2Ω a b I1 I2 I3 Ia Ib 6V 2V CO2

  8. Mesh Analysis Example: (cont) Loop a: 2 = 2Ia+4(Ia−Ib) = 6Ia−4Ib Loop b: −6 = 4(Ib−Ia)+Ib = −4Ia+5Ib After solving: Ia = −1A, Ib = −2A Hence: I1 = 1A, I2 = −2A, I3 = 1A CO2

  9. Noodle Analysis Nodal CO2

  10. Nodal Analysis • Determine the number of nodes. • Pick a reference node then label the rest with subscripts. • [*] If there is any voltage source in the branch, replace it with short circuit – apply KCL in the next step to the resulting bigger node. • Apply KCL on each node except the reference. • Solve the simultaneous equations. CO2

  11. Nodal Analysis Example: [Boylestad 10th Ed. E.g. 8.21 - modified] a R2 b I2 12Ω I3 I1 R1 2A 6Ω 4A 2Ω R3 CO2

  12. Nodal Analysis Example: (cont) Node a: Node b: After solving: Va = 6V, Vb = − 6A Hence: I1 = 3A, I2 = 1A, I3 = −1A CO2

  13. Mesh vs Nodal Analysis • Mesh: Start with KVL, get a system of simultaneous equations in term of current. • Nodal: Start with KCL, get a system of simultaneous equations on term of voltage. • Mesh: KVL is applied based on a fixed loop current. • Nodal: KCL is applied based on a fixed node voltage. CO2

  14. Mesh vs Nodal Analysis • Mesh: Current source is an open circuit and it merges loops. • Nodal: Voltage source is a short circuit and it merges nodes. • Mesh: More popular as voltage sources do exist physically. • Nodal: Less popular as current sources do not exist physically except in models of electronics circuits. CO2

  15. Thevenin’s Theorem CO2

  16. Thevenin’s Theorem Statement: Network behind any two terminals of linear DC circuit can be replaced by an equivalent voltage source and an equivalent series resistor • Can be used to reduce a complicated network to a combination of voltage source and a series resistor CO2

  17. Thevenin’s Theorem • Calculate the Thevenin’s resistance, RTh, by switching off all power sources and finding the resulting resistance through the two terminals: • Voltage source: remove it and replace with short circuit • Current source: remove it and replace with open circuit • Calculate the Thevenin’s voltage, VTh, by switching back on all powers and calculate the open circuit voltage between the terminals. CO2

  18. Thevenin’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] Convert the following network into its Thevenin’s equivalent: 3Ω 6Ω 9V CO2

  19. Thevenin’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] RTh calculation: 3Ω 6Ω CO2

  20. Thevenin’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] VTh calculation: 3Ω 6Ω 9V CO2

  21. Thevenin’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] Thevenin’s equivalence: 2Ω 6V CO2

  22. Norton’s Theorem CO2

  23. Norton’s Theorem Statement: Network behind any two terminals of linear DC circuit can be replaced by an equivalent current source and an equivalent parallel resistor • Can be used to reduce a complicated network to a combination of current source and a parallel resistor CO2

  24. Norton’s Theorem • Calculate the Norton’s resistance, RN, by switching off all power sources and finding the resulting resistance through the two terminals: • Voltage source: remove it and replace with short circuit • Current source: remove it and replace with open circuit • Calculate the Norton’s voltage, IN, by switching back on all powers and calculate the short circuit current between the terminals. CO2

  25. Norton’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] Convert the following network into its Norton’s equivalent: 3Ω 6Ω 9V CO2

  26. Norton’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] RN calculation: 3Ω 6Ω CO2

  27. Norton’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] IN calculation: 3Ω 6Ω 9V CO2

  28. Norton’s Theorem Example: [Boylestad 10th Ed. E.g. 9.6 - modified] Norton’s equivalence: OR, We can just take the Thevenin’s equivalent and calculate the short circuit current. 2Ω 3A CO2

  29. Maximum Power Consumption An element is consuming the maximum power out of a network if its resistance is equal to the Thevenin’s or Norton’s resistance. CO2

  30. Source Conversion Use the relationship between Thevenin’s and Norton’s source to convert between voltage and current sources. 2Ω 2Ω 3A 6V V = IR CO2

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