SLOA049D July   2000  – February 2023


  1.   Abstract
  2.   Trademarks
  3. Introduction
  4. Filter Characteristics
  5. Second-Order Low-Pass Filter Standard Form
  6. Math Review
  7. 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. Low-Pass Sallen-Key Architecture
  9. Low-Pass Multiple Feedback (MFB) Architecture
  10. Cascading Filter Stages
  11. 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


This report focuses on active low-pass filter design using operational amplifiers. Low-pass filters are commonly used to implement anti-aliasing filters in data acquisition systems. Design of second-order filters is the main topic of consideration.

Filter tables are developed to simplify circuit design based on the idea of cascading lower-order stages to realize higher-order filters. The tables contain scaling factors ( F S F ) for the corner frequency ( f c ) and the required quality factor ( Q ) of each of the stages for the particular filter being designed. The tables enable designers to skip straight to calculating required circuit component values.

To illustrate an actual circuit implementation, six circuits, separated into three types of filters (Bessel, Butterworth, and Chebyshev) and two filter configurations (Sallen-Key and Multiple Feedback), are simulated using a TLV9062 operational amplifier. Limiting factors in the high-frequency performance of the filters are also examined. The tables in this document are used in the Analog Engineer’s Circuit Cookbook: Amplifiers.