1. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Introductory Circuit Analysis, 12/e Boylestad Chapter 20 Resonance

2. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] OBJECTIVES Become familiar with the frequency response of a series resonant circuit and how to calculate the resonant and cutoff frequencies. Be able to calculate a tuned network’s quality factor, bandwidth, and power levels at important frequency levels. Become familiar with the frequency response of a parallel resonant circuit and how to calculate the resonant and cutoff frequencies.

3. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] OBJECTIVES Understand the impact of the quality factor on the frequency response of a series or parallel resonant network. Begin to appreciate the difference between defining parallel resonance at the frequency either where the input impedance is a maximum or where the network has a unity power factor.

4. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION This chapter introduces the very important resonant (or tuned ) circuit, which is fundamental to the operation of a wide variety of electrical and electronic systems in use today. The resonant circuit is a combination of R, L, and C elements having a frequency response characteristic similar to the one appearing in Fig. 20.1.

5. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION FIG. 20.1 Resonance curve.

6. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION The resonant electrical circuit must have both inductance and capacitance. In addition, resistance will always be present due either to the lack of ideal elements or to the control offered on the shape of the resonance curve. When resonance occurs due to the application of the proper frequency ( fr), the energy absorbed by one reactive element is the same as that released by another reactive element within the system.

7. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SERIES RESONANT CIRCUIT A resonant circuit (series or parallel) must have an inductive and a capacitive element. A resistive element is always present due to the internal resistance of the source (Rs), the internal resistance of the inductor (Rl), and any added resistance to control the shape of the response curve (Rdesign).

8. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SERIES RESONANT CIRCUIT FIG. 20.2 Series resonant circuit.

9. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SERIES RESONANT CIRCUIT FIG. 20.3 Phasor diagram for the series resonant circuit at resonance. FIG. 20.4 Power triangle for the series resonant circuit at resonance.

10. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SERIES RESONANT CIRCUIT FIG. 20.5 Power curves at resonance for the series resonant circuit.

11. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] THE QUALITY FACTOR (Q) The quality factor Q of a series resonant circuit is defined as the ratio of the reactive power of either the inductor or the capacitor to the average power of the resistor at resonance; that is,

12. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] THE QUALITY FACTOR (Q) FIG. 20.6 Q l versus frequency for a series of inductors of similar construction.

13. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] THE QUALITY FACTOR (Q) FIG. 20.7 High-Q series resonant circuit.

14. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Z T VERSUS FREQUENCY The total impedance of the series R-L-C circuit in Fig. 20.2 at any frequency is determined by

15. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Z T VERSUS FREQUENCY The total-impedance-versus-frequency curve for the series resonant circuit in Fig. 20.2 can be found by applying the impedance-versus- frequency curve for each element of the equation just derived, written in the following form:

16. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Z T VERSUS FREQUENCY FIG. 20.8 Resistance versus frequency.

17. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Z T VERSUS FREQUENCY FIG. 20.9 Inductive reactance versus frequency. FIG. 20.10 Capacitive reactance versus frequency.

18. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Z T VERSUS FREQUENCY FIG. 20.11 Placing the frequency response of the inductive and capacitive reactance of a series R-L-C circuit on the same set of axes. FIG. 20.12 Z T versus frequency for the series resonant circuit.

19. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Z T VERSUS FREQUENCY FIG. 20.13 Phase plot for the series resonant circuit.

20. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SELECTIVITY If we now plot the magnitude of the current I = E/Z T versus frequency for a fixed applied voltage E, we obtain the curve shown in Fig. 20.14: FIG. 20.14 I versus frequency for the series resonant circuit.

21. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SELECTIVITY FIG. 20.15 Effect of R, L, and C on the selectivity curve for the series resonant circuit.

22. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SELECTIVITY FIG. 20.16 Approximate series resonance curve for Q s ≥ 10.

23. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] V R, V L, AND V C FIG. 20.17 V R, V L, V C, and I versus frequency for a series resonant circuit.

24. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] V R, V L, AND V C FIG. 20.18 V R, V L, V C, and I for a series resonant circuit where Qs ≥10.

25. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (SERIES RESONANCE) FIG. 20.19 Example 20.1. FIG. 20.20 Example 20.4

26. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT The basic format of the series resonant circuit is a series R-L-C combination in series with an applied voltage source. The parallel resonant circuit has the basic configuration in Fig. 20.21, a parallel R-L-C combination in parallel with an applied current source.

27. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT FIG. 20.21 Ideal parallel resonant network.

28. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT FIG. 20.22 Practical parallel L-C network.

29. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT FIG. 20.23 Equivalent parallel network for a series R-L combination.

30. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT FIG. 20.24 Substituting the equivalent parallel network for the series R-L combination in Fig. 20.22.

31. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT FIG. 20.25 Substituting R = R s ║ R p for the network in Fig. 20.24.

32. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT Unity Power Factor, f p Maximum Impedance, f m

33. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PARALLEL RESONANT CIRCUIT FIG. 20.26 Z T versus frequency for the parallel resonant circuit.

34. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SELECTIVITY CURVE FOR PARALLEL RESONANT CIRCUITS FIG. 20.27 Defining the shape of the V p (f) curve.

35. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SELECTIVITY CURVE FOR PARALLEL RESONANT CIRCUITS FIG. 20.28 Effect of Rl, L, and C on the parallel resonance curve.

36. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SELECTIVITY CURVE FOR PARALLEL RESONANT CIRCUITS FIG. 20.29 Phase plot for the parallel resonant circuit.

37. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EFFECT OF Q l ≥ 10 The content of the previous section may suggest that the analysis of parallel resonant circuits is significantly more complex than that encountered for series resonant circuits. Fortunately, however, this is not the case since, for the majority of parallel resonant circuits, the quality factor of the coil Q l is sufficiently large to permit a number of approximations that simplify the required analysis.

38. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EFFECT OF Q l ≥ 10 Inductive Reactance, X L P Resonant Frequency, f p (Unity Power Factor) Resonant Frequency, f m (Maximum V C ) R p Z T p Q p

39. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EFFECT OF Q l ≥ 10 FIG. 20.30 Approximate equivalent circuit for Q l ≥ 10.

40. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EFFECT OF Q l ≥ 10 BW I L and I C Conclusions FIG. 20.31 Establishing the relationship between I C and I L and the current I T.

41. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SUMMARY TABLE

42. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (PARALLEL RESONANCE) FIG. 20.32 Example 20.6.

43. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (PARALLEL RESONANCE) FIG. 20.33 Example 20.7.

44. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (PARALLEL RESONANCE) FIG. 20.34 Example 20.8.

45. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (PARALLEL RESONANCE) FIG. 20.35 Example 20.9. FIG. 20.36 Equivalent network for the transistor configuration in Fig. 20.35.

46. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (PARALLEL RESONANCE) FIG. 20.37 Resonance curve for the network in Fig. 20.36. FIG. 20.38 Example 20.11.

47. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] EXAMPLES (PARALLEL RESONANCE) FIG. 20.39 Network designed to meet the criteria in Fig. 20.38.

48. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS Stray Resonance Graphic and Parametric Equalizers

49. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS FIG. 20.40 (a) Dual-channel 15-band “Constant Q” graphic equalizer (Courtesy of ARX Systems.); (b) setup; (c) frequency response.

50. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] APPLICATIONS FIG. 20.41 Six-channel parametric equalizer. (Courtesy of ARX Systems.)

51. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS PSpice Series Resonance FIG. 20.42 Series resonant circuit to be analyzed using PSpice.

52. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS PSpice Series Resonance FIG. 20.43 Resonance curve for the current of the circuit in Fig. 20.42.

53. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS PSpice Parallel Resonance FIG. 20.44 Parallel resonant network to be analyzed using PSpice.

54. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS PSpice Parallel Resonance FIG. 20.45 Resonance curve for the voltage across the capacitor in Fig. 20.44.

55. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS PSpice Parallel Resonance FIG. 20.46 Phase plot for the voltage v C for the parallel resonant network in Fig. 20.44.

56. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS Multisim FIG. 20.47 Using Multisim to confirm the results of Example 20.9.

57. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] COMPUTER ANALYSIS Multisim FIG. 20.48 Magnitude and phase plots for the voltage v C of the network in Fig. 20.47.