Chapter 16

2. Chapter 16 Tuned Circuits and RCL Networks

3. Objectives • Explain resonant frequency and how it affects various RCL circuits. • Calculate a resonant frequency. • Discuss the characteristics of a series RCL circuit at its resonant frequency. • Discuss the characteristics of a parallel RCL circuit at its resonant frequency. Permission granted to reproduce for educational use only.

4. Objectives • Calculate circuit Q and bandwidth. • Describe filtering action. • List four types of filters and explain their action. Permission granted to reproduce for educational use only.

5. RCL Networks • Also called RCL circuits • Resonance • Acceptor circuits • Tank circuits • Reject circuits Permission granted to reproduce for educational use only.

6. Review of Electronics Principles • ac circuit with resistance only • Applied voltage and current in phase • No reactive power • Power consumed equals product of volts and amperes Permission granted to reproduce for educational use only.

7. Review of Electronics Principles (Cont.) • ac circuit with inductance only • Current lags voltage by 90° • Power consumed by circuit is zero • ac circuit containing resistance and inductance • Current lags voltage by less than 90° • Total resistive force is vector sum of resistance and inductive reactance Permission granted to reproduce for educational use only.

8. Review of Electronics Principles (Cont.) • ac circuit with capacitance only • Current leads voltage by 90° • Power consumed is zero • ac circuit with resistance and capacitance • Current leads voltage by less than 90° • Impedance is vector sum of resistance and capacitive reactance Permission granted to reproduce for educational use only.

9. Resonance • Exists when XL= XC • Resonant frequency (fO) • Tuned circuits Permission granted to reproduce for educational use only.

10. Resonance • fO= resonant frequency in hertz • L = inductance in henrys • C = capacitance in farads Permission granted to reproduce for educational use only.

11. Resonance Example • Find resonant frequency with 200 µH inductance and 200 pF capacitance Permission granted to reproduce for educational use only.

12. Acceptor Circuits • Increase in impedance as frequency varies around resonance • Maximum current flows at resonance Permission granted to reproduce for educational use only.

13. Acceptor Circuit Example I = 50 µA • XL = 2 × 800 × 103 Hz × 200 × 10-6 H XL= 1000 Ω Permission granted to reproduce for educational use only.

14. Acceptor Circuit Example (Cont.) XC = 1000 Ω Esource= 500 µV Permission granted to reproduce for educational use only.

15. Tank Circuits Permission granted to reproduce for educational use only.

16. Tank Circuits (Cont.) • Behave differently than series tuned acceptor circuits • Charge and discharge of capacitance are similar to flywheel action • Current is oscillating in different directions Permission granted to reproduce for educational use only.

17. Reject Circuits • Parallel tuned circuit connected across a variable frequency generator • Current in circuit at resonance is at minimum • Maximum line impedance • Parallel tuned circuit rejects signals at or near its resonant frequency and allows signals of other frequencies to pass Permission granted to reproduce for educational use only.

18. Reject Circuits (Cont.) Permission granted to reproduce for educational use only.

19. Reject Circuits (Cont.) • Current flowing in XL branch lags applied voltage by 90° • Current flowing in XC branch leads applied voltage by 90° • Currents are 180° out of phase and cancel each other out Permission granted to reproduce for educational use only.

20. Reject Circuit Example XL = 2fL = 1000 Ω Permission granted to reproduce for educational use only.

21. Quality Factor (Q) of Tuned Circuits • Figure of merit • Has no units Permission granted to reproduce for educational use only.

22. Q Example • Find Q in a series circuit with an inductive reactance of 1000 Ω at resonance and with a resistance of 10 Ω in the wire of the coil Permission granted to reproduce for educational use only.

23. Acceptor Circuit Q • Sharpness of reject or accept characteristics of the RCL circuit • Quality factor • Increase in resistance reduces the maximum current at resonance Permission granted to reproduce for educational use only.

24. Acceptor Circuit Q (Cont.) • High Q circuits useful for electronic circuits • Selectivity set by bandwidth (BW) • Half-power points Permission granted to reproduce for educational use only.

25. Reject Circuit Q • Can be used to learn maximum impedance of circuit at resonance • Z = Q× XL • Example Z = 100 × 1000 Ω Z = 100,000 Ω Permission granted to reproduce for educational use only.

26. Damping Resistors • RS broadens circuit response • Carries part of current that cannot be canceled at resonance • Shunt damping lowers Q of a circuit Permission granted to reproduce for educational use only.

27. Loading the Tank Circuit • Parallel tuned circuit used when coupling energy from one circuit to another • Feeds energy into other systems • Example: radio receiver • Attenuation • Alignment Permission granted to reproduce for educational use only.

28. Review What is resonant frequency? Frequency at which inductive reactance equals capacitive reactance Permission granted to reproduce for educational use only.

29. Review What type of circuit provides maximum response to currents at its resonant frequency? An acceptor circuit Permission granted to reproduce for educational use only.

30. Review What is another name for a parallel tuned circuit that has oscillating current? Tank circuit Permission granted to reproduce for educational use only.

31. Review What is a reject circuit? A parallel tuned circuit that rejects signals at or near its resonant frequency, while letting other frequencies pass Permission granted to reproduce for educational use only.

32. Review What are the units of the quality factor of a circuit? There are no units for Q Permission granted to reproduce for educational use only.

33. Filtering Circuits • Four basic types of filters • Low-pass • High-pass • Band-pass • Band-reject Permission granted to reproduce for educational use only.

34. Filtering Action • A capacitor blocks dc, but it passes ac • A conductor carries current that has dc and ac components Permission granted to reproduce for educational use only.

35. Filtering Action (Cont.) • Capacitor C charges up to the average dc level of voltage • Current flowing through R charges capacitor C • Voltage drops, C discharges through R • R’s value is 10 times or more value of the reactance of C at input voltage frequency Permission granted to reproduce for educational use only.

36. Bypassing • Creating a voltage drop across a resistor resulting from the dc’s signal voltage • Connect a capacitor that has low reactance to ac voltage in parallel with the resistor • Choose a capacitor that will form a low-reactance path around a resistor for currents of chosen frequencies Permission granted to reproduce for educational use only.

37. Bypassing (Cont.) I = 3.3 mA Permission granted to reproduce for educational use only.

38. Low-Pass Filters • Resistance or inductance in series with incoming signal voltage • Capacitor in shunt or across the line • Frequency increases, XL increases for larger voltage across L • Low frequencies are passed, higher are rejected Permission granted to reproduce for educational use only.

39. High-Pass Filters • Capacitor in series with incoming signal voltage • Inductance shunt across the line • XL increases with frequency • XC decreases, providing low-reactance path for high-frequency signals Permission granted to reproduce for educational use only.

40. Low- and High-Pass Filters • Two or more sections are often joined for better filtering action • Named according to type of circuit Permission granted to reproduce for educational use only.

41. Tuned Circuit Filters • Band-pass filters • Band-reject filters Permission granted to reproduce for educational use only.

42. Tuned Circuit Filter Examples • Parallel tuned circuit • Provides maximum impedance • Rejects frequencies around resonant frequency • Can be used to provide greater attenuation Permission granted to reproduce for educational use only.

43. A Nomograph Permission granted to reproduce for educational use only.

44. Magnetic Resonance Imaging (MRI) • Technique based on principles of magnetism and radio wave transmission  • Instead of exposing patients to radiation, MRI transmits radio waves through the patient, causing atoms to emit energy in the form of weak radio signals  • Typically used to examine head and spine, as well as heart, lungs, and joints Permission granted to reproduce for educational use only.

45. Review What does a filter do? Separates specific frequencies Permission granted to reproduce for educational use only.

46. Review What component is used to create a bypass? Capacitor Permission granted to reproduce for educational use only.

47. Review What filter passes high-frequency current and rejects low frequencies? High-pass filter Permission granted to reproduce for educational use only.

48. Review What are two types of tuned circuit filters? Band-pass and band-reject Permission granted to reproduce for educational use only.

49. Review Which tuned circuit filter accepts only currents near its resonant frequency? Band-pass filter Permission granted to reproduce for educational use only.