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Lecture 19 High Pass Filters, 2 nd Order Filters, Active Filters, Resonances

Lecture 19 High Pass Filters, 2 nd Order Filters, Active Filters, Resonances. Series Resonance. For resonance the reactance of the inductor and the capacitor cancel:. Series Resonance. Quality factor Q S. Series Resonance. Series Resonance. Series Resonant Band-Pass Filter.

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Lecture 19 High Pass Filters, 2 nd Order Filters, Active Filters, Resonances

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  1. Lecture 19High Pass Filters, 2nd Order Filters, Active Filters, Resonances

  2. Series Resonance For resonance the reactance of the inductor and the capacitor cancel:

  3. Series Resonance Quality factor QS

  4. Series Resonance

  5. Series Resonance

  6. Series Resonant Band-Pass Filter

  7. Series Resonant Band-Pass Filter

  8. Series Resonant Band-Pass Filter

  9. Series Resonant Band-Pass Filter For QS>>1

  10. Parallel Resonance At resonance ZP is purely resistive:

  11. Parallel Resonance Quality factor QP

  12. Parallel Resonance

  13. Parallel Resonance Vout for constant current, varying the frequency

  14. Ideal Filters

  15. Second Order Low-Pass Filter

  16. Second-Order Low-Pass Filter

  17. Second Order Low-Pass Filter

  18. Second Order High-Pass Filter At low frequency the capacitor is an open circuit At high frequency the capacitor is a short and the inductor is open

  19. Second Order Band-Pass Filter At low frequency the capacitor is an open circuit At high frequency the inductor is an open circuit

  20. Second Order Band-Reject Filter At low frequency the capacitor is an open circuit At high frequency the inductor is an open circuit

  21. Exercise 6.20 Design a filter with QS=1 that passes frequency components lower than 5 kHz and rejects components higher than 5 kHz. Chose L=5 mH

  22. Exercise 6.20

  23. Exercise 6.21 Design a filter that passes frequency components between fL=45 kHz and fH=55 kHz. Chose L=1 mH

  24. Exercise 6.21

  25. Active Filters • Ideally, an active filter circuit should: • Contain few components • 2. Have a transfer function that is insensitive to component tolerances

  26. 3. Place modest demands on the op amp’s gain–bandwidth product, output impedance, slew rate, and other specifications 4. Be easily adjusted 5. Require a small spread of component values 6. Allow a wide range of useful transfer functions to be realized

  27. First-Order Low-Pass Filter A low-pass filter with a dc gain of -Rf/Ri

  28. First-Order High-Pass Filter A high-pass filter with a high frequency gain of -Rf/Ri

  29. Differentiator Circuit

  30. Higher Order Filters

  31. Butterworth Transfer Function Butterworth filters are characterized by having a particularly flat pass-band.

  32. Sallen–Key Circuits

  33. Sallen–Key Circuits Non-inverting amplifier with a gain of K

  34. K Values for Low-Pass and High-Pass Butterworth Filters of Various Orders

  35. Low-Pass Active Filter Design Design a fourth-order low-pass Butterworth filter having a frequency cut-off of 100 Hz

  36. Low-Pass Active Filter Design From the table a fourth order filter requires K values of 1.152 and 2.235. The DC gain is (1.152)(2.235) = 2.575

  37. Low-Pass Active Filter Design

  38. Low-pass Active Filter Design

  39. Low-pass Active Filter Design

  40. Magnetic fields (B flux density, H magnetic field intensity, magnetic permeability ) Right hand rule Forces on charges and current carrying wires moving in a magnetic field Faraday’s Law Lenz’s Law Ampere’s Law Review for Next Lecture!

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