1 / 18

Sallen and Key Two Pole Filter

Buffer amplifier. Sallen and Key Two Pole Filter. But. Apply Kirchoff’s current law to v 1 node:. Substituting,. Two-Pole Low-Pass Filter. Two-Pole High-Pass Filter. So,. Eg. Two-Pole Example. Design a second order normalised Butterworth low pass filter. Higher Order Filters.

betty_james
Télécharger la présentation

Sallen and Key Two Pole Filter

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. Buffer amplifier Sallen and Key Two Pole Filter

  2. But Apply Kirchoff’s current law to v1 node:

  3. Substituting,

  4. Two-Pole Low-Pass Filter

  5. Two-Pole High-Pass Filter

  6. So, Eg. Two-Pole Example Design a second order normalised Butterworth low pass filter.

  7. Higher Order Filters • Using a single op-amp the highest order practical filter design is two. • For higher order filters, more than one op-amp is needed. • Simplest design technique is cascade synthesis or synthesis by sections.

  8. Synthesis by Sections • When two (or more) filters are cascaded in series, the total transfer function is the product of the individual transfer functions. • HTOT(s) = H1(s) H2(s) • The required transfer function must be factorised into second order sections. H1(s) H2(s) VIN(s) VIN(s)H1(s) VIN(s)H1(s) H2(s)

  9. Factorising the Transfer Function • Filter design techniques usually generate the positions of the poles (and zeros) of the transfer function. • Grouping complex conjugate pairs together is essential for physically realisable sections. • If the required filter order is odd, a single pole will be left over. This is realised by a first order section.

  10. Transfer function is, therefore: Fourth Order Example The poles of a normalised fourth order low pass Butterworth filter are:

  11. Fourth Order Realisation

  12. Third Order Example The poles of a normalised third order low pass Bessel filter are: Transfer function is, therefore:

  13. Ordering the Sections • In theory, using ideal op-amps, it doesn’t matter which section is first or second. • In practice, the decision is based on considerations of: • Saturation Levels • Noise Figure From fourth order example:

  14. Second Order Frequency Response • If the damping ratio, z, is less than 1/Ö2, the peak gain is greater than one. • This means that the maximum input level is reduced, to avoid op-amp saturation. 10 z=0.2 0.707 1 0.5 1 Gain z=2 0.1 0.01 1 0.1 10 Frequency [rad/s]

  15. Butterworth Filter Example

  16. H1(s) H2(s) H2(s) H1(s) At w = 1 rad/s,

  17. Section Ordering • To get the highest maximum input signal range. • Sections with the largest damping ratio (lowest Q) should come first. • Resonant sections with low damping ratios come last, possibly susceptible to noise. • To get the lowest output noise. • Highest gain sections (i.e. most resonant) should come first. • Subsequent sections attenuate noise. • What’s the best order ? • It depends.

  18. Summary • The Sallen and Key configuration realises a two-pole filter section using a single op-amp. • Synthesis by sections creates higher order filters by cascading first and second order sections. • Under ideal assumptions, the order of the sections is irrelevant. • Practically, dynamic range considerations decide the order of the sections.

More Related