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CHAPTER 4 RESONANCE CIRCUITS

CHAPTER 4 RESONANCE CIRCUITS. Content. Series Resonance Parallel Resonance Important Parameters Resonance Frequency, ω o Half-power frequencies, ω 1 and ω 2 Bandwidth,  Quality Factor, Q Application. Introduction.

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CHAPTER 4 RESONANCE CIRCUITS

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  1. CHAPTER 4RESONANCE CIRCUITS

  2. Content • Series Resonance • Parallel Resonance • Important Parameters • Resonance Frequency, ωo • Half-power frequencies, ω1and ω2 • Bandwidth,  • Quality Factor, Q • Application

  3. Introduction • Resonance is a condition in an RLC circuit in which the capacitive and reactive reactance are equal in magnitude, thereby resulting in a purely resistive impedance. • Resonance circuits are useful for constructing filters and used in many application.

  4. Series Resonance Circuit

  5. At Resonance • At resonance, the impedance consists only resistive component R. • The value of current will be maximum since the total impedance is minimum. • The voltage and current are in phase. • Maximum power occurs at resonance since the power factor is unity.

  6. Series Resonance Total impedance of series RLC Circuit is At resonance The impedance now reduce to The current at resonance

  7. Resonance Frequency Resonance frequency is the frequency where the condition of resonance occur. Also known as center frequency. Resonance frequency

  8. Half-power Frequency Half-power frequencies is the frequency when the magnitude of the output voltage or current is decrease by the factor of 1 / 2 from its maximum value. Also known as cutoff frequencies.

  9. Bandwidth,  Bandwidth,  is define as the difference between the two half power frequencies. The width of the response curve is determine by the bandwidth.

  10. Current Response Curve

  11. Voltage Response Curve

  12. Quality Factor (Q-Factor) The ratio of resonance frequency to the bandwidth The “sharpness” of response curve could be measured by the quality factor, Q.

  13. Q-Factor Vs Bandwidth • Higher value of Q, smaller the bandwidth. (Higher the selectivity) • Lower value of Q larger the bandwidth. (Lower the selectivity)

  14. High-Q It is to be a high-Q circuit when its quality factor is equal or greater than 10. For a high-Q circuit (Q ≥ 10), the half-power frequencies are, for all practical purposes, symmetrical around the resonant frequency and can be approximated as

  15. Maximum Power Dissipated The average power dissipated by the RLC circuit is The maximum power dissipated at resonance where Thus maximum power dissipated is

  16. Power Dissipated at ω1 and ω2 At certain frequencies, where ω = ω1 and ω2, the dissipated power is half of maximum power Hence, ω1 and ω2 are called half-power frequencies.

  17. Example 14.7If R=2Ω, L=1mH and C=0.4 F, calculate • Resonant frequency, ωo • Half power frequencies, ω1 and ω2 • Bandwidth,  • Amplitude of current at ωo, ω1 and ω2.

  18. Solution Resonant frequency Bandwidth Quality Factor

  19. Solution Since Q ≥10 , we can regard this as high-Q circuit. Hence

  20. Solution Current, I at ω= ωo Current, I at ω = ω1 , ω2

  21. Practice Problem 14.7 • A series connected circuit has R=4Ω and L=25mH. Calculate • Value of C that will produce a quality factor of 50. • Find ω1 , ω2 and . • Determine average power dissipated at ω=ωo , ω1andω2. Take Vm = 100V

  22. Solution Value of C that will produce Q = 50 Bandwidth

  23. Solution Since Q ≥10 , we can regard this as high-Q circuit. Hence

  24. Solution Power dissipated at ω = ωo Power dissipated at ω = ω1 , ω2

  25. Parallel Resonance

  26. Parallel Resonance The total admittance Resonance occur when

  27. At Resonance • At resonance, the impedance consists only conductance G. • The value of current will be minimum since the total admittance is minimum. • The voltage and current are in phase.

  28. Parameters in Parallel Circuit Parallel resonant circuit has same parameters as the series resonant circuit. Resonance frequency Half-power frequencies

  29. Parameters in Parallel Circuit Bandwidth Quality Factor

  30. Example 14.8If R=8kΩ, L=0.2mH and C=8F, calculate • ωo • Q and  • ω1 and ω2 • Power dissipated at ωo, ω1 and ω2.

  31. Solution Resonant frequency Bandwidth Quality Factor

  32. Solution Since Q ≥10 , we can regard this as high-Q circuit. Hence

  33. Solution Power dissipated at ω = ωo Power dissipated at ω = ω1 , ω2

  34. Practice Problem 14.8 • A parallel resonant circuit has R=100kΩ, L=25mH and C=5nF. Calculate • ωo • ω1 and ω2 • Q • 

  35. Solution Resonant frequency Bandwidth Quality Factor

  36. Solution Since Q ≥10 , we can regard this as high-Q circuit. Hence

  37. APPLICATION

  38. PASSIVE FILTERS • A filter is a circuit that is designed to pass signals with desired frequencies and reject or attenuates others • A filter is a Passive Filters if it consists only passive elements which is R, L and C. • Filters that used resonant circuit • Bandpass Filter • Bandstop Filter

  39. BANDPASS FILTER • A bandpass filter is designed to pass all frequencies within ω1ωo ω2

  40. BANDPASS FILTER SERIES RLC CIRCUIT

  41. BANDPASS FILTER PARALLEL RLC CIRCUIT

  42. BANDSTOP FILTER • A bandstop or bandreject filter is designed to stop or reject all frequencies within ω1ωo ω2

  43. BANDSTOP FILTER SERIES RLC CIRCUIT

  44. BANDSTOP FILTER PARALLEL RLC CIRCUIT

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