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Simplifying Circuits: Thevenin and Norton Equivalents in Electrical Engineering

This lecture, part of the Electrical and Computer Engineering course at Rowan University, focuses on advanced circuit analysis techniques, specifically Thevenin's and Norton's theorems. Students will learn to reduce complex circuits to simpler forms using these methods, gaining insights into maximum power transfer principles and operational amplifiers. The session covers essential concepts such as equivalent circuits, superposition, and practical applications like electric power distribution, ensuring a solid foundation for real-world engineering challenges. Homework and lab problems are included to reinforce understanding.

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Simplifying Circuits: Thevenin and Norton Equivalents in Electrical Engineering

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  1. CHAPTERS 5 & 6 NETWORKS 1: 0909201-01 8 October 2002 – Lecture 5b ROWAN UNIVERSITY College of Engineering Professor Peter Mark Jansson, PP PE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Autumn Semester 2002

  2. networks I • Today’s learning objectives – • apply new methods for reducing complex circuits to a simpler form • equivalent circuits • superposition • Thévenin’s equivalent • Norton’s equivalent • build understanding of maximum power • introduce the operational amplifier

  3. new concepts from ch. 5 • electric power for cities - done • source transformations - done • superposition principle - done • Thévenin’s theorem - continue • Norton’s theorem • maximum power transfer

  4. homework 5 • Problems 5.3-1, 5.3-4, 5.3-5, 5.3-6, 5.4-1 review(ed) in lab, 5.4-2, 5.4-6,5.5-1, 5.5-3, 5.5-9, 5.6-2, 5.6-4, 5.7-1, 5.7-6 • Chapter 6 Pages 244-245Problems 6.4-1, 6.4-2, 6.4-6

  5. next monday’s - test two • covers Chapters 3.4-6.4 • current division • node voltage circuit analysis • mesh current circuit analysis • when to use n-v vs. m-c • source transformations • superposition principle • Thevenin’s equivalent - Norton’s equivalent • maximum power transfer • operational amplifiers

  6. Thévenin’s theorem • GOAL: reduce some complex part of a circuit to an equivalent source and a single element (for analysis) • THEOREM: for any circuit of resistive elements and energy sources with a terminal pair, the circuit is replaceable by a series combination of vtand Rt

  7. Thévenin equivalent circuit Rt a О + _ vt orvoc b О

  8. Thévenin method • If circuit contains resistors and ind. sources • Connect open circuit between a and b. Find voc • Deactivate source(s), calc. Rt by circuit reduction • If circuit has resistors and ind. & dep. sources • Connect open circuit between a and b. Find voc • Connect short circuit across a and b. Find isc • Connect 1-A current source from b to a. Find vab • NOTE: Rt = vab / 1 or Rt = voc / isc • If circuit has resistors and only dep. sources • Note that voc = 0 • Connect 1-A current source from b to a. Find vab • NOTE: Rt = vab / 1

  9. HW example • see HW problem 5.5-1

  10. Norton’s theorem • GOAL: reduce some complex part of a circuit to an equivalent source and a single element (for analysis) • THEOREM: for any circuit of resistive elements and energy sources with a terminal pair, the circuit is replaceable by a parallel combination of iscand Rn (this is a source transformation of the Thevenin)

  11. Norton equivalent circuit • a О isc Rn = Rt • b О

  12. Norton method • If circuit contains resistors and ind. sources • Connect short circuit between a and b. Find isc • Deactivate ind. source(s), calc. Rn =Rt by circuit reduction • If circuit has resistors and ind. & dep. sources • Connect open circuit between a and b. Find voc = vab • Connect short circuit across a and b. Find isc • Connect 1-A current source from b to a. Find vab • NOTE: Rn =Rt = vab / 1 or Rn =Rt = voc / isc • If circuit has resistors and only dep. sources • Note that isc = 0 • Connect 1-A current source from b to a. Find vab • NOTE: Rn =Rt = vab / 1

  13. HW example • see HW problem 5.6-2

  14. maximum power transfer • what is it? • often it is desired to gain maximum power transfer for an energy source to a load • examples include: • electric utility grid • signal transmission (FM radio receiver) • source  load

  15. maximum power transfer • how do we achieve it? a О Rt + _ vt orvsc RLOAD b О

  16. maximum power transfer • how do we calculate it?

  17. maximum power transfer theorem • So… • maximum power delivered by a source represented by its Thevenin equivalent circuit is attained when the load RL is equal to the Thevenin resistance Rt

  18. efficiency of power transfer • how do we calculate it for a circuit?

  19. Norton equivalent circuits • using the calculus on p=i2R in a Norton equivalent circuit we find that it, too, has a maximum when the load RL is equal to the Norton resistance Rn =Rt

  20. HW example • see HW problem 5.7-6

  21. new concepts from ch. 6 • electronics • operational amplifier • the ideal operational amplifier • nodal analysis of circuits containing ideal op amps • design using op amps • characteristics of practical op amps

  22. definition of an OP-AMP • The Op-Amp is an “active” element with a high gain that is designed to be used with other circuit elements to perform a signal processing operation. • It requires power supplies, sometimes a single supply, sometimes positive and negative supplies. • It has two inputs and a single output.

  23. _ + + – + – OP-AMP symbol and connections INVERTING INPUT NODE v1 OUTPUT NODE i1 vo io i2 v2 POSITIVE POWER SUPPLY NON-INVERTING INPUT NODE NEGATIVE POWER SUPPLY

  24. THE OP-AMPFUNDAMENTAL CHARACTERISTICS INVERTING INPUT NODE _ + Ri v1 OUTPUT NODE i1 vo io Ro i2 v2 NON-INVERTING INPUT NODE

  25. INVERTING INPUT NODE v1 OUTPUT NODE i1 _ + vo io i2 v2 NON-INVERTING INPUT NODE THE IDEAL OP-AMPFUNDAMENTAL CHARACTERISTICS

  26. _ + + – THE INVERTING OP-AMP Rf Ri Node a v1 i1 vo io vs i2 v2 1. Write Ideal OpAmp equations. 2. Write KCL at Node a. 3. Solve for vo/vs

  27. _ + + – THE INVERTING OP-AMP Rf Ri Node a v1 i1 vo io vs i2 v2 At node a:

  28. _ + THE NON-INVERTING OP-AMP Rf Ri Node a v1 i1 vo io i2 v2 + – vs At node a:

  29. HW example • see HW problem 6.4-1

  30. Test Two • next Monday • review needed? • if so… select 5-6 problems that you would like presented discussed

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