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

7 Low-Pass Multiple Feedback (MFB) Architecture

Figure 7-1 shows the low-pass MFB filter architecture and the transfer function.



Figure 7-1 Low-Pass MFB Architecture
Equation 22. H f = - R 2 R 1 j 2 π f 2 ( R 2 R 3 C 1 C 2 ) + j 2 π f R 3 C 1 + R 2 C 1 + R 2 R 3 C 1 R 1 + 1

Again, the transfer function looks different from standard form in Equation 17. By substituting K = - R 2 R 1 , F S F × f c = 1 2 π R 2 R 3 C 1 C 2 , and Q = R 2 R 3 C 1 C 2 R 3 C 1 + R 2 C 1 + R 3 C 1 - K , the functions become the same.

Depending on how you use the previous equations, the design process can be simple or tedious. Appendix A shows simplifications that help to ease this process.

The Sallen-Key and MFB circuits shown are second-order low-pass stages that can be used to realize one complex pole pair in the transfer function of a low-pass filter. To make a Butterworth, Bessel, or Chebyshev filter, use the previous substitutions with the standard form equations that come from filter coefficients to find circuit component values.