1 / 29

Second order Low-pass Frequency Response

Second order Low-pass Frequency Response. For Q =0.707,magnitude response is maximally flat (Butterworth Filter: Maximum bandwidth without peaking) For Q >0.707, response shows undesired peaking. For Q <0.707: Filter’s bandwidth capability is wasted. At w << w o , filter has unity gain.

curran-marquez
Download Presentation

Second order Low-pass Frequency Response

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Second order Low-pass Frequency Response For Q=0.707,magnitude response is maximally flat (Butterworth Filter: Maximum bandwidth without peaking) For Q>0.707, response shows undesired peaking. For Q<0.707: Filter’s bandwidth capability is wasted. At w<<wo, filter has unity gain. At w>>woresponse exhibits two-pole roll-off at -40dB/decade. At w=wo, gain of filter =Q.

  2. Second order Low-pass Frequency Response

  3. Second order High-pass Frequency Response • For Q=0.707,magnitude response is maximally flat (Butterworth Filter response). • Amplifier gain is constant at w>wo, the lower cutoff frequency of the filter.

  4. Second-order Band-pass Frequency Response • Response peaks approximately at wo. • At w<<wo or w>>wo, filter response corresponds to single-pole high-pass or low-pass filter changing at a rate of 20dB/decade.

  5. Single amplifier Biquad (SAB) Enhanced Positive Feedback (EPF) Enhanced Negative Feedback (ENF)

  6. Sallen-Key Low-pass Filter (1955)

  7. Sallen-Key using voltage follower The transfer function is: • Op amp is voltage follower with unity gain over a wide range of frequencies. • Uses positive feedback through C1 at frequencies above dc to realize complex poles without inductors. • V1 and V2 are parasitic sensitive nodes with a large voltage swing • Large capacitor spread for large Q In standard form, For equal R design

  8. Equal-R & Equal-C design (K≠1) Can get high Q without high Capacitor spread Condition: K < 3 Rarely used design due to high sensitivity !!

  9. Accuracy of integrated capacitors

  10. Frequency denormalization

  11. Impedance denormalization

  12. Example: Equal-R & k=1 Sallen-Key LPF for Q=√2 Frequency Denormalization 1MHz Impedance Denormalization 10kΩ

  13. Sallen-Key High-pass Filter

  14. Enhanced positive feedback general structure

  15. Multiple Feedback SAB • One virtual ground node with no voltage swing

  16. BP Multiple Feedback SAB

  17. Enhanced negative feedback ENF Equal-C & a=1 Deliyannis SAB (1968) Q enhancement

  18. Friend SAB (1970) Need to have Feedforward paths to implement notch filters

More Related