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Understanding First Order Circuits: Thevenin and Norton Techniques

In this lecture, we delve into the essential concepts of first-order circuits, focusing on the complete response which combines transient and steady-state responses. Students will learn about the significance of Thevenin and Norton equivalents in simplifying circuit analysis. The session covers the natural and forced responses to both constant and sinusoidal inputs. Key objectives include grasping the dynamics of first-order circuits with capacitors and inductors, calculating initial conditions, and applying differential equations to solve for voltage and current over time.

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Understanding First Order Circuits: Thevenin and Norton Techniques

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  1. CHAPTER 8 NETWORKS 1: 0909201-01 11 December 2002 – Lecture 8b ROWAN UNIVERSITY College of Engineering Professor Peter Mark Jansson, PP PE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Autumn Semester 2002

  2. admin • hw 7 due today, hw 8 due at final • hw 8 posted end of today • last lab 6 due by end of day monday • final exam: Next Wed 18 Dec 10:15am • take – home portion • Pick up at end of day from office window • Yellow and Blue folders (by Lab Section)

  3. networks I • Today’s learning objectives – • understand first order circuits • build your knowledge of the concept of complete response • learn how Thevenin and Norton equivalents help simplify analysis of first order circuits • learn how to calculate the natural (transient) response and forced (steady-state) response

  4. new concepts from ch. 8 • response of first-order circuits • to a constant input • the complete response • stability of first order circuits • response of first-order circuits • to a nonconstant (sinusoidal) source

  5. What does First Order mean? • circuits that contain capacitors and inductors can be defined by differential equations • circuits with ONLY ONE capacitor OR ONLY ONE inductor can be defined by a first order differential equation • such circuits are called First Order Circuits

  6. complete response? Complete response = transient response + steady state response For circuits we will review today: both – constant source p.315 and sinusoidal source p. 304… Complete response = natural response + forced response

  7. finding the CR of 1st Ord. Cir • Find the forced response before the disturbance. Evaluate at t = t(0-) to determine initial conditions • Find forced response (steady state) after the disturbance t= t(0+) • Add the natural response (Ke-t/) to the new forced response. Use initial conditions to calculate K

  8. simplifying for analysis • Using Thevenin and Norton Equivalent circuits can greatly simplify the analysis of first order circuits • We use a Thevenin with a Capacitor • and a Norton with an Inductor

  9. Rt + v(t) - C Voc + – Thevenin Equivalent at t=0+ i(t) + -

  10. + v(t) - Isc Rt i(t) L Norton equivalent at t=0+

  11. t = 0 R1 R2 + v(t) - R3 vs C + – 1st ORDER CIRCUITS WITH CONSTANT INPUT

  12. Example (before switch closes) • If vs = 4V, R1 = 20kohms, • R2 = 20 kohms • R3 = 40 kohms • What is v(0-) ?

  13. as the switch closes… • THREE PERIODS emerge….. • 1. system change (switch closure) • 2. (immediately after) capacitor or inductor in system will store / release energy (adjust and/or oscillate) as system moves its new level of steady state (a.k.a. transient or natural response) …. WHY??? • 3. new steady state is then achieved (a.k.a. the forced response)

  14. Rt + v(t) - C Voc + – Thevenin Equivalent at t=0+ i(t) + - KVL

  15. SOLUTION OF 1st ORDER EQUATION

  16. SOLUTION CONTINUED

  17. SOLUTION CONTINUED

  18. so complete response is… complete response = v(t) = forced response (steady state) = Voc + natural response (transient) = (v(0-) –Voc) * e -t/RC)

  19. Example • 8.3-1, p. 315

  20. + – WITH AN INDUCTOR t = 0 R1 R2 R3 i(t) vs L Why ?

  21. + v(t) - Isc Rt i(t) L Norton equivalent at t=0+ Why ? KCL

  22. SOLUTION

  23. so complete response is… complete response = i(t) = forced response (steady state) = Isc + natural response (transient) = (i(0-) –isc) * e -tR/L)

  24. Example • 8.3-2, p. 316

  25. for more practice: Exercises • 8.3-1, p. 321 • 8.3-2, p. 321

  26. forced response summary

  27. Example • 8.7-2, p. 336

  28. HANDY CHART ELEMENTCURRENT VOLTAGE

  29. IMPORTANT CONCEPTS FROM CHAPTER 8 • determining Initial Conditions • determining T or N equivalent to simplify • setting up differential equations • solving for v(t) or i(t)

  30. Don’t forget HW 8 (test review) • Course Evals……

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