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EE201 – Circuit Theory I 2019 – 2020 Fall Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK Lesson-IV

Understand fundamental laws of circuit theory - Ohm's law and Kirchhoff's laws- to analyze circuits using Nodal and Mesh analysis. Learn source transformations and Maximum Power Transfer.

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EE201 – Circuit Theory I 2019 – 2020 Fall Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK Lesson-IV

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  1. ADNAN MENDERES UNIVERSITYFACULTY OF ENGINEERINGDepartment of ElectricalandElectronicsEngineering EE201 – Circuit Theory I 2019 – 2020 Fall Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK Lesson-IV Simple Resistive Circuits

  2. Ch4: Techniques of Circuit Analysis • Having understand the fundamental laws of circuit theory, • Ohm’s law • Kirchhoffs’s laws(KVL&KCL) • Apply these laws to develop two powerful techniques for circuit analysis. • Nodal analysis, which is based on systematic application of Kirchoff’s voltage law(KVL) • Mesh analysis, which is based on a systematic application of Kirchhoff’s voltage law(KVL) EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  3. Ch4: Techniques of Circuit Analysis • Source Transformations • Maximum Power Transfer EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  4. Ch4: Terminology EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  5. Ch4: Terminology EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  6. Ch4: Modal Analysis (Node-Voltage Method) • Nodal analysis provides a general procedure for analyzing circuits using node voltages as the circuit variables. Choosing node voltages instead of element voltages as circuit variables is convenient and reduces the number of equations one must solve simultaneously. • To simplify matters, we shall assume in this section that circuits do not contain voltage sources. Circuits that contain voltage sources will be analyzed later. • In nodal analysis, we are interested in finding the node voltages.Given a circuit with N nodes without voltage sources, the nodal analysis of the circuit involves taking the following three steps. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  7. Ch4: Nodal Analysis (Node-Voltage Method) • Step to determine Node Voltages: • Select a node as the reference node. Assign voltage to the remaining N-1 nodes. The voltages are referenced with respect to the reference node. • Apply KCL to each of the N-1 nonreference node. Use Ohms law to express the branch currents in terms of node voltages. • Solve the resulting simultaneously to obtain the unknown node voltages. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  8. Ch4: Nodal Analysis (Node-Voltage Method) • Steps to Determine (Node-Voltage Method) • Select a node as the reference node. Assign voltage to the remaining N-1 nodes. The voltages are referenced with respect to the reference node. • The reference node is commonly called the ground since it is assumed to have zero potential. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  9. Ch4: Nodal Analysis (Node-Voltage Method) 2. Apply KCL to each of N-1 nonreference nodes. Use Ohms law to express the branch currents in terms of node voltages. • Current flows from a higher potential to a lower potential in a resistor. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  10. Ch4: Nodal Analysis (Node-Voltage Method) Remember that; Cramer’s rule EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  11. Ch4: Nodal Analysis (Node-Voltage Method) 3. Solve the resulting simultaneous equations to obtain the unknown node voltages • Number of nonreference nodes is equal to the number of independent equations that we will derive. • Steps: • Choose a reference node, assign voltages to other nodes w.r.t. reference one. • Apply KCL to each node. (Arbitrary but Consistent). Apply Ohm’s law to find node voltages. • Solve all obtained equations together. • Substitution method • Elimination method • Cramer’s rule • Matrix inversion • ….. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  12. Ch4: Example • Use the node-voltage method to find vin the circuit shown? (Assesment problem 4.2 from textbook) Answer : 15 V EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  13. Ch4: Example EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  14. Nodal Analysis (Node-Voltage Method) with dependent source EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  15. Modified Nodal Analysis (Modified –Voltage Method) • When a voltage source is directly connected in between a reference node and a non-reference node. • The voltage of that non-reference node = voltage of that source. • Hence, the number of required equations is decreased by one. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  16. When a voltage source is the only element between two essential nodes (or non-reference nodes), the node-voltage method is simplified. • For this case, those nodes can be combined to form a SUPERNODE. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  17. Ch4: Modified Nodal Analysis (Modified –Voltage Method) • Note the following properties of a supernode: • The voltage source inside the supernode provides a constraint equation needed to solve for the node voltages. • A supernode has no voltage of its own. • A supernode requires the application of both KCL and KVL. Steps for Supernode case: Assign a current for that branches. Use these currents as the additional variables. For supernode, use KCL to obtain supernode equation. To obtain Node-voltage equations, nodes can be used separately or used as a supernode (if available). Both gives the same result but using supernode is decreased the number of equations EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  18. Ch4: Example • Find the power of 100V source. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  19. Ch4: Example • Use the node-voltage method to find v1in the circuit shown? (Assesment Problem 4.6 from textbook) EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  20. Ch4: Mesh Analysis(Mesh-Current Method) • Mesh: A loop does not enclose any other loops. • Nodal analysis applies KCL to find unknown voltages in a given circuit, while, mesh analysis applies KVL to find unknown currents. • Nodal analysis can be applied all circuits in general. On the other hand, Mesh analysis is not quite as general as nodal analysis because it is only applicable to a circuit that is planar. • A planar circuit is one that can be drawn in a plane with no branches crossing one another; otherwise it is nonplanar. • A circuit may have crossing branches and still be planar if it can be redrawn such that it has no crossing branches. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  21. Ch4: Mesh Analysis(Mesh-Current Method) EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  22. Ch4:Mesh Analysis (Mesh-Current Method) • The current through a mesh is known as mesh current. In mesh analysis, we are interested in applying KVL to find the mesh currents in a given circuit. Steps to Determine Mesh Currents: 1. Assign mesh currents to the N meshes. 2. Apply KVL to each of the N meshes. Use Ohm’s law to express the voltages in terms of the mesh currents. 3. Solve the resulting N simultaneous equations to get the unknown mesh currents. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  23. Ch4: Mesh Analysis (Mesh-Current Method) • Steps to Determine Mesh Currents: 1. Assign mesh currents to the N meshes. Although a mesh current may be assigned to each mesh in an arbitrary direction, it is conventional to assume that each mesh current flows clockwise. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  24. Ch4:Mesh Analysis (Mesh-Current Method) • Steps to Determine Mesh Currents: 2. Apply KVL to each of the N meshes. Use Ohm’s law to express the voltages in terms of the mesh currents. Ohm’sLaw EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  25. Ch4: Mesh Analysis (Mesh-Current Method) • Steps to Determine Mesh Currents: • 3. Solve the resulting N simultaneous equations to get the unknown mesh currents. EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  26. Ch4: Example For the circuit given below, find the branch currents using mesh analysis. Answer: EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  27. Ch4: Example Calculate the mesh currents in the circuitbelow.? Answer: EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  28. Ch4:Mesh Analysis (Mesh-Current Method) with dependent sources • Only difference is that we have an extra constraint equation. • Example: Use mesh analysis to find the current in the circuit below? Answer: EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

  29. Ch4: Example • Calculate the node voltages in the circuit given EE201-Circuit Theory I, Assoc. Prof. Dr. Olcay ÜZENGİ AKTÜRK,2018-2019 Fall

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