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

11.1 Non-ideal Circuit Operation: Sallen-Key

At frequencies well above the cutoff, simplified high-frequency models help show the expected behavior of the circuits. Figure 11-1 is used to show the expected circuit operation for a second-order low-pass Sallen-Key circuit at high frequency. The assumption made here is that C1 and C2 are effective shorts when compared to the impedance of R1 and R2, so the input of the amplifier is at AC ground. In response, the amplifier generates an AC ground at the output, limited only by the closed-loop output impedance ZOUT. Different amplifiers have different closed-loop output impedances ZOUT and can impact the high frequency filter response based on ZOUT.

Figure 11-1 Second-Order Low-Pass Sallen-Key High-Frequency Model

Placing a low-pass RC filter at the output of the amplifier can help nullify the feedthrough of high-frequency signals. Figure 11-2 shows a comparison between the original Sallen-Key Butterworth filter and one using an RC filter on the output. A 100-Ω resistor is placed in series with the output and a 47-nF capacitor is connected from the output to ground. This places a passive pole in the transfer function at about 40 kHz that improves the high-frequency response.

Figure 11-2 Sallen-Key Butterworth Filter With RC Added in Series With the Output