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Chapter 9 (A)

Chapter 9 (A). Band-Pass Filters (BPF ) Basics. Transfer Functions. A(f). v out. v in. A(f) = v out / v in. Review: LPF. f = 0 Hz (dc) A = A 0. LPF. f < f 0 / 10 A  A 0. f = f 0 A  A 0 - 3 dB. f = 10 N f 0 A  A 0 - 20 dB  N . Review: HPF. f =  Hz A = A 0.

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Chapter 9 (A)

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  1. Chapter 9 (A) Band-Pass Filters (BPF) Basics

  2. Transfer Functions A(f) vout vin A(f) = vout / vin

  3. Review: LPF f = 0 Hz (dc) A = A0 LPF f < f0 / 10 A  A0 f = f0 A  A0- 3 dB f = 10N f0 A  A0-20 dB  N

  4. Review: HPF f =  Hz A = A0 HPF f = f0/10N A  A0-20 dB  N f > 10 f0 A  A0 f = f0 A  A0- 3 dB

  5. Review: dB

  6. Preview: BPF LPF HPF vout vout vin vin vout vin The order of the filters are not important

  7. f = fcenter A = A0 f = fhigh A  A0- 3 dB BPF f = flow A  A0- 3 dB f < flow (= flow /10N) A  A0-20 dB  N f > fhigh (= fhigh10N) A  A0-20 dB  N flow < f < fhigh A  A0 (midband gain)

  8. Narrow Band BPF For narrow band BPF it is usually easier to describe the filter’s characteristics in terms of center frequency and bandwidth. flow fhigh fcenter = Bandwidth = f = fhigh-flow

  9. Basic definitions • Passbandgain A0: Maximum gain • Center frequency fcenter: The frequency at which the gain is maximum. • Lower cutoff frequency flow: The frequency belowfcenter at which the gain is 3 dB below A0. • Higher cutoff frequency fHigh: The frequency above fcenterat which the gain is 3 dB below A0. • Quality factor Q (Selectivity): A measure of the filter’s sharpness. • Bandwidth (BW) f: The difference between the upper cutoff and lower cutoff frequencies.

  10. Formulas

  11. Summary of BPF Basics • LPF + HPF = BPF • Q-factor = Selectivity (Bandwidth) • High-Q BPFs are narrow-band filters • Low-Q BPFs are broadband filters • Q, BW, fcenter, fhigh, and floware all related. • In general, given two parameters you can find the other three.

  12. Analysis: A BPF Circuit is Given Next week • Q and fcenterare calculated from component values. • fhighand floware then calculated from Q and fcenter • Finally, BW is calculated from fhigh, and flow . Qand fcenter BW CKT fhigh and flow Next week

  13. Example: The selectivity of a BPF

  14. Design: fcenterand BW are specified Next week • Determinecircuit type (practical concerns). • Q is calculated from fcenterand BW. • From Q and fcentercircuit component values can be determined. Next week CKT Type Component Values BWand fcenter Q

  15. Design: fhighand floware specified Next week • Determinecircuit type (practical concerns). • fcenterand BWare calculated fromfhighand flow. • Q is calculated from fcenterand BW. • From Q and fcentercircuit component values can be determined. Next week CKT Type fhigh and flow Component Values BWand fcenter Q Next week

  16. Example: Q and fcenter of a BPF What is the significance of Q?

  17. Summary • Analysis: Circuit  Behavior (fcenter, BW, Q, fhigh, and flow) • Design: Specifications (fcenter, BW, Q, fhigh, and flow) Circuit

  18. Problems A narrow-band BPF has a Q of 15 and center frequency of 75 kHz. Determine the bandwidth and cutoff frequencies of the BPF. A broadband BPF has a lower cutoff frequency of 30 kHz and a upper cutoff frequency of 55 kHz. Determine the bandwidth and Q of the BPF. A narrow-band BPF has a Q of 40 and bandwidth of 20 kHz. Determine cutoff frequencies of the BPF. A narrow-band BPF has a Q of 20 and a upper cutoff frequency of 5 kHz. Determine the bandwidth of the BPF.

  19. Problems A narrow-band BPF has a Q of 15 and center frequency of 75 kHz. Determine the bandwidth and cutoff frequencies of the BPF.

  20. Problems A broadband BPF has a lower cutoff frequency of 30 kHz and a upper cutoff frequency of 55 kHz. Determine the bandwidth and Q of the BPF.

  21. Problems A narrow-band BPF has a Q of 40 and bandwidth of 20 kHz. Determine cutoff frequencies of the BPF.

  22. Problems A narrow-band BPF has a Q of 20 and a upper cutoff frequency of 5 kHz. Determine the bandwidth of the BPF.

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