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Introduction to Op-Amps, Capacitance, and Inductance in Electrical Circuits

In this lecture from Rowan University's College of Engineering, Professor Peter Mark Jansson discusses key concepts in electrical engineering including operational amplifiers (op-amps), capacitance, and inductance. Students will explore fundamental characteristics of op-amps, their linear and non-linear behaviors, and how to analyze first-order circuits. Importance is placed on energy storage components like capacitors and inductors, along with practical applications in RC circuits. Key learning objectives include understanding node voltage relations and solving circuit problems using Kirchhoff's laws.

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Introduction to Op-Amps, Capacitance, and Inductance in Electrical Circuits

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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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