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CHAPTER 6: INTRODUCTION TO PASSIVE FILTERS

CHAPTER 6: INTRODUCTION TO PASSIVE FILTERS. Series & Parallel Resonance Passive Filter. Resonance. Resonance is a condition in an RLC circuit in which the capacitive and inductive reactances are equal in magnitude, thereby resulting in a purely resistive impedance.

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CHAPTER 6: INTRODUCTION TO PASSIVE FILTERS

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  1. CHAPTER 6: INTRODUCTION TO PASSIVE FILTERS Series & Parallel Resonance Passive Filter DEE2113 : Chap 6 - Introduction to Passive Filters

  2. Resonance Resonance is a condition in an RLC circuit in which the capacitive and inductive reactances are equal in magnitude, thereby resulting in a purely resistive impedance. The series resonant circuit DEE2113 : Chap 6 - Introduction to Passive Filters

  3. Series Resonance Input impedance: Resonance occurs when imaginary part is 0 Resonant/center frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  4. Series Resonance • At resonance: • The impedance is purely resistive, Z = R • The voltage and the current are in phase, pf=1 • The magnitude of transfer function H(w) = Z(w) is minimum • The inductor voltage and capacitor voltage can be much more than the source voltage DEE2113 : Chap 6 - Introduction to Passive Filters

  5. Series Resonance Average power dissipated by the RLC circuit: Where: DEE2113 : Chap 6 - Introduction to Passive Filters

  6. Series Resonance The current amplitude vs. frequency for the series resonant circuit Maximum power: Power at certain frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  7. Series Resonance Half power frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  8. Series Resonance The “sharpness” of the resonance in a resonant circuit is measured quantitatively by the quality factor Q The quality factor of a resonant circuits is the ratio of its resonant frequency to its bandwidth DEE2113 : Chap 6 - Introduction to Passive Filters

  9. Series Resonance Relation between Q and bandwidth B: The higher the circuit Q, the smaller the bandwidth DEE2113 : Chap 6 - Introduction to Passive Filters

  10. Series Resonance High Q circuit if, and half power frequency can be approximated as: DEE2113 : Chap 6 - Introduction to Passive Filters

  11. Example 1 • R=2Ω, L=1mH, C=0.4μF. Determine : • The resonant frequency and the half-power frequency • The quality factor and bandwidth • The amplitude of the current at ω0, ω1 and ω2 DEE2113 : Chap 6 - Introduction to Passive Filters

  12. Parallel Resonance The parallel-resonant circuit DEE2113 : Chap 6 - Introduction to Passive Filters

  13. Parallel Resonance Input admittance: Resonance occurs when imaginary part is 0 Resonant frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  14. Parallel Resonance Half power frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  15. Parallel Resonance DEE2113 : Chap 6 - Introduction to Passive Filters

  16. Parallel Resonance High Q circuit if, and half power frequency can be approximated as: DEE2113 : Chap 6 - Introduction to Passive Filters

  17. Example 2 • R=8 kΩ, L=0.2 mH, C=8 μF. Determine : • The resonant frequency, quality factor and bandwidth • The half-power frequencies • The power dissipated at ω0, ω1 and ω2 DEE2113 : Chap 6 - Introduction to Passive Filters

  18. DEE2113 : Chap 6 - Introduction to Passive Filters

  19. Filters A filter is a circuit that is designed to pass signals with desired frequencies and reject or attenuate others. • 4 types of filters: • Lowpass filter: passes low frequencies and stops high frequencies • Highpass filter: passes high frequencies and rejects low frequencies • Bandpass filter: passes frequencies within a frequency band and blocks or attenuates frequencies outside the band • Bandstop filter: passes frequencies outside a frequency band and blocks or attenuates frequencies within the band DEE2113 : Chap 6 - Introduction to Passive Filters

  20. Filters Ideal frequency response of four types of filters: a) lowpass b) highpass d) bandstop c) bandpass DEE2113 : Chap 6 - Introduction to Passive Filters

  21. Lowpass Filters A lowpass filter is designed to pass only frequencies from dc up to the cutoff frequency ωc DEE2113 : Chap 6 - Introduction to Passive Filters

  22. Lowpass Filters Transfer function: Cutoff frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  23. Highpass Filter A highpass filter is designed to pass all frequencies above its cutoff frequency ωc DEE2113 : Chap 6 - Introduction to Passive Filters

  24. Highpass Filters Transfer function: Cutoff frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  25. Bandpass Filter A bandpass filter is designed to pass all frequencies within a band of frequencies, ω1 < ω0 < ω2 DEE2113 : Chap 6 - Introduction to Passive Filters

  26. Bandpass Filters Transfer function: Center frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  27. Bandstop Filter A bandstop filter is designed to stop or eliminate all frequencies within a band of frequencies, ω1 < ω0 < ω2 DEE2113 : Chap 6 - Introduction to Passive Filters

  28. Bandstop Filters Transfer function: Center frequency: DEE2113 : Chap 6 - Introduction to Passive Filters

  29. Example 3 • Bandstop filter rejects 200 Hz while passing other • frequencies. For R=150 Ω and bandwidth 100 Hz, • determine: • L • C DEE2113 : Chap 6 - Introduction to Passive Filters

  30. Exercise 1 • For a series RLC bandstop filter, R=2 kΩ, L=0.1 mH, • C=40 pF. Determine : • The center frequency • The bandwidth • The half-power frequencies • The quality factor DEE2113 : Chap 6 - Introduction to Passive Filters

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