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EE 1105 : Introduction to EE Freshman Seminar

EE 1105 : Introduction to EE Freshman Seminar. Lecture 4: Circuit Analysis Node Analysis, Mesh Currents Superposition, Thevenin and Norton Equivalents. Circuits. Abstraction describing how (the topology) electrical or electronic modules are interconnected. Closely related to a GRAPH.

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EE 1105 : Introduction to EE Freshman Seminar

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  1. EE 1105: Introduction to EEFreshman Seminar Lecture 4: Circuit Analysis Node Analysis, Mesh Currents Superposition, Thevenin and Norton Equivalents

  2. Circuits • Abstraction describing how (the topology) electrical or electronic modules are interconnected. • Closely related to a GRAPH. • Nomenclature: • Nodes, Extraordinary nodes, Supernodes (adjacent nodes sharing a voltage source) • Edges(Branches) • Paths (collection of edges with no node appearing twice), • Loops (closed paths) • Meshes (loop containing no other loop), Supermeshes (adjacent meshes sharing a current source)

  3. Kirchhoff’s Voltage Law • The sum of the voltage drops around a closed path is zero. • Example: -120 + V1 + V2 + V3 + V4 = 0

  4. Kirchhoff’s Current Law • A node is a point where two or more circuit elements are connected together. • The sum of the currents leaving a node is zero.

  5. Nodal Analysis • Identify all extraordinary nodes. Select one as ground reference and assign node voltages to the other ones. • Write KCL at the non-zero voltage nodes in conjunction with Ohm’s law. • Solve a system of simultaneous equations • In the case of a supernode, apply KVL along the connection, and ignore any resistors in parallel to a voltage source.

  6. Example

  7. Superposition Principle • Fundamental Property of Linear Circuits • Replace all but one source in the circuit with a short (voltage source) or an open (current sources). • Apply analysis to find nodal voltages. • Repeat for all sources • Add all nodal voltages to find the total result.

  8. More complex example

  9. Example • Replace EG1 with a short (zero). Solve resulting circuit for Va1. • Replace EG2 with a short. Solve resulting circuit for Va2. • Total Va=Va1+Va2 • Exercise in Lab – you should obtain the same result as in the previous case.

  10. Mesh Analysis • Identify all meshes and assign them an unknown current, clockwise. • Write KVL on each mesh • Solve a system of simultaneous equations • In the case of a supermesh, add an extra equation with the dependence between the currents

  11. Example • Two meshes with currents I1 and I2. • KVL: • Resulting current through R3 is I1-I2.

  12. More complex example

  13. Mesh Analysis by Inspection • Applies only if all sources be independent voltage sources • Same procedure to assign mesh currents. • Define Rij – resistances as follows: • Rii – sum of all resistances connected to mesh I • Rij=Rji – minus sum of all resistances shared between mesh I and J • Define total voltages from voltage sources along mesh I as Vi. • Write and solve matrix equation RI=V, in which R=(Rij), V=(Vi), I=(Ii).

  14. Nodal Analysis By Inspection • Applies only if all sources be independent current sources • Same procedure to assign node voltages. • Define Gij– conductances as follows: • Gii – sum of all conductances connected to node I • Gij=Gji– minus sum of all conductances connected between node I and J • Define currents from current sources entering node I as Ii. • Write and solve matrix equation GV=I, in which G=(Gij), V=(Vi), I=(Ii).

  15. Solving Linear Systems of Equations AX=B a11x1 + a12x2 + · · · + a1nxn = b1 a21x1 + a22x2 + · · · + a2nxn= b2 am1x1 + am2x2 + · · · + amnxn = bm Methods to solve: • Elimination • Substitution • Cramer’s rule • Matrix inverse

  16. Thévenin’s Theorem • A linear circuit can be represented at its output terminals as an equivalent circuit consisting of a voltage source Vth in series with a resistor Rth. • Vth is determined when no load is applied on the output. • Rth is determined by deactivating all independent sources in circuit. A • Network 1 Network 2 B • Application: Coupled networks.

  17. Example – Note, this does not work with dependent sources Place a voltmeter across terminals A-B and read the voltage. We call this the open-circuit voltage. No matter how complicated Network 1 is, we read one voltage. We call this voltage VAB =VTHEVENIN = VTH Deactivate independent sources Place an ohmmeter across A-B and read the resistance. We call this the Thevenin equivalent Resistance RTH

  18. Alternate Method: Shortcircuit

  19. Example: Voltage Divider

  20. Combining Voltage Sources Voltage sources are added algebraically

  21. Combining Voltage Sources Voltage sources are added algebraically

  22. Combining Voltage Sources Don’t do this. Why is this illogical? Whose fundamental circuit law is violated by this?

  23. Combining Current Sources Current sources are added algebraically

  24. Combining Current Sources Current sources are added algebraically

  25. Combining Current Sources Don’t do this. Why is this illogical? Whose fundamental circuit law is violated by this?

  26. Norton Equivalent

  27. Homework 4 due next class!!Available online at course website Acknowledgements: Dr. Bill Dillon http://tuttle.merc.iastate.edu/ee201/topics/equivalent_circuits/thevenin.pdf http://web.eecs.utk.edu/~green/notes/Lesson%2010%20Thevenin%20and%20Norton.ppt Questions?

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