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CHAPTERS 7 & 8

CHAPTERS 7 & 8. NETWORKS 1: 0909201-01 4 December 2002 – Lecture 7b ROWAN UNIVERSITY College of Engineering Professor Peter Mark Jansson, PP PE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Autumn Semester 2002. networks I. Today’s learning objectives – review op-amps

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CHAPTERS 7 & 8

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  1. CHAPTERS 7 & 8 NETWORKS 1: 0909201-01 4 December 2002 – Lecture 7b 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 – • review op-amps • introduce capacitance and inductance • introduce first order circuits • introduce concept of complete response

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

  4. Op-Amp Fundamentals • for KCL to apply to Op-Amps we must include all currents: • i1 + i2 + io + i+ + i- = 0 • When power supply leads are omitted from diagrams (which they most often are) KCL will not apply to the remaining 3 nodes

  5. are Op-Amps linear elements?

  6. yes .. and no… • three conditions must be satisfied for an op-amp to be a linear element: • |Vo | <= Vsat • | io | <= isat Slew rate >= | dVo/dt |

  7. Example from Text • the A741 when biased +/- 15 V has the following characteristics: • vsat = 14 V • isat = 2 mA • SR = 500,000 V/S • So is it linear? • When RL = 20 kOhm or 2 kOhm?

  8. Using Op-Amps • Resistors in Op-Amp circuits > 5kohm • Op-Amps display both linear and non-linear behavior

  9. Remember: for Ideal Op-Amp • node voltages of inputs are equal • currents of input leads are zero • output current is not zero

  10. One more important Amp • difference amplifier • See Figure 6.5-1, page 213

  11. Practical Op-Amps

  12. What you need to know • Parameters of an Ideal Op Amp • Types of Amplification Gain (K) vs. Which nodes and Amps circuits are needed to achieve same • How to identify which type of circuit is in use (effect) • How to solve Op Amp problems

  13. new concepts from ch. 7 • energy storage in a circuit • capacitors • series and parallel • inductors • series and parallel • using op amps in RC circuits

  14. _ + _ + i + – DEFINITION OF CAPACITANCE Measure of the ability of a device to store energy in the form of an electric field. CAPACITOR: IMPORTANT RELATIONSHIPS:

  15. CALCULATING ic FOR A GIVEN v(t) Let v(t) across a capacitor be a ramp function. v v t t As Moral: You can’t change the voltage across a capacitor instantaneously.

  16. VOLTAGE ACROSS A CAPACITOR

  17. ENERGY STORED IN A CAPACITOR

  18. + – CAPACITORS IN SERIES + v1 - + v2 - + v3 - C2 C1 C3 i v KVL

  19. CAPACITORS IN SERIES Capacitors in series combine like resistors in parallel.

  20. i2 i3 i1 i C2 C1 C3 CAPACITORS IN PARALLEL KCL Capacitors in parallel combine like resistors in series.

  21. HANDY CHART ELEMENTCURRENT VOLTAGE

  22. DEFINITION OF INDUCTANCE Measure of the ability of a device to store energy in the form of a magnetic field. INDUCTOR: IMPORTANT RELATIONSHIPS: v _ + i

  23. CALCULATING vL FOR A GIVEN i(t) Let i(t) through an inductor be a ramp function. i i t t As Moral: You can’t change the current through an inductor instantaneously.

  24. CURRENT THROUGH AN INDUCTOR

  25. ENERGY STORED IN AN INDUCTOR

  26. INDUCTORS IN SERIES + v1 - + v2 - + v3 - L2 L1 L3 i KVL Inductors in series combine like resistors in series.

  27. + – INDUCTORS IN PARALLEL i3 i1 i2 L1 L2 L3 v KCL

  28. INDUCTORS IN PARALLEL Inductors in parallel combine like resistors in parallel.

  29. HANDY CHART ELEMENTCURRENT VOLTAGE

  30. Cf Ri Node a _ + v1 i1 vo io vs i2 v2 + – OP-AMP CIRCUITS WITH C & L

  31. Rf _ + Node a v1 i1 vo Li io vs i2 v2 + – QUIZ: Find vo= f(vs)

  32. ANSWER TO QUIZ

  33. IMPORTANT CONCEPTS FROM CH. 7 • I/V Characteristics of C & L. • Energy storage in C & L. • Writing KCL & KVL for circuits with C & L. • Solving op-amp circuits with C or L in feedback loop. • Solving op-amp circuits with C or L at the input.

  34. new concepts from ch. 8 • response of first-order circuits • the complete response • stability of first order circuits

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

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

  37. SOLUTION OF 1st ORDER EQUATION

  38. SOLUTION CONTINUED

  39. SOLUTION CONTINUED

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

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

  42. SOLUTION

  43. HANDY CHART ELEMENTCURRENT VOLTAGE

  44. IMPORTANT CONCEPTS FROM CHAPTER 8 • determining Initial Conditions • setting up differential equations • solving for v(t) or i(t)

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