SLOA049D July   2000  – February 2023

 

  1.   Abstract
  2.   Trademarks
  3. 1 Introduction
  4. 2 Filter Characteristics
  5. 3 Second-Order Low-Pass Filter Standard Form
  6. 4 Math Review
  7. 5 Examples
    1. 5.1 Second-Order Low-Pass Butterworth Filter
    2. 5.2 Second-Order Low-Pass Bessel Filter
    3. 5.3 Second-Order Low-Pass Chebyshev Filter with 3-dB Ripple
  8. 6 Low-Pass Sallen-Key Architecture
  9. 7 Low-Pass Multiple Feedback (MFB) Architecture
  10. 8 Cascading Filter Stages
  11. 9 Filter Tables
  12. 10Example Circuit Simulated Results
  13. 11Non-ideal Circuit Operation
    1. 11.1 Non-ideal Circuit Operation: Sallen-Key
    2. 11.2 Non-ideal Circuit Operation: MFB
  14. 12Comments About Component Selection
  15. 13Conclusion
  16.   A Filter Design Specifications
    1.     A.1 Sallen-Key Design Simplifications
      1.      A.1.1 Sallen-Key Simplification 1: Set Filter Components as Ratios
      2.      A.1.2 Sallen-Key Simplification 2: Set Filter Components as Ratios and Gain = 1
      3.      A.1.3 Sallen-Key Simplification 3: Set Resistors as Ratios and Capacitors Equal
      4.      A.1.4 Sallen-Key Simplification 4: Set Filter Components Equal
    2.     A.2 MFB Design Simplifications
      1.      A.2.1 MFB Simplification 1: Set Filter Components as Ratios
      2.      A.2.2 MFB Simplification 2: Set Filter Components as Ratios and Gain = –1
  17.   B Higher-Order Filters
    1.     B.1 Fifth-Order Low-Pass Butterworth Filter
    2.     B.2 Sixth-Order Low-Pass Bessel Filter
  18.   C Revision History

13 Conclusion

This document has explored building second-order low-pass Butterworth, Bessel, and 3-dB Chebyshev filters using the Sallen-Key and MFB architectures. The same techniques are extended to higher-order filters by cascading second-order stages for even order and adding a first-order stage for odd order.

The advantages of each filter type come at the expense of other characteristics. The Butterworth can be considered to offer the best all-around filter response. The filter has maximum flatness in the pass band with moderate rolloff past cutoff and shows only slight overshoot in response to a pulse input.

The Bessel is important when signal-conditioning square wave signals. The constant group delay means that the square wave signal is passed with minimum distortion (overshoot). This comes at the expense of a slower rate of attenuation above cutoff.

The 3-dB Chebyshev sacrifices pass-band flatness for a high rate of attenuation near cutoff. This filter also exhibits the largest overshoot and ringing in response to a pulse input of the three filter types discussed.

The Sallen-Key and MFB architectures also have some trade-offs. The simplifications that can be used when designing the Sallen-Key provide for easier selection of circuit components, and at unity gain, Sallen-Key has no gain sensitivity to component variations. The MFB shows less overall sensitivity to component variations and has better high-frequency performance.