This filter is composed of two sections labeled “a” and “b”. The schematic for each section is shown in the rectangular frame. The output of the first (a) section is connected to the input of the second (b) section. Although the schematic of each section is the same, the component values aren’t. The resistors and capacitors in the first section are referred to as Ra, Rga, and Ca. The components in the section section are designated Rb, Rgb, and Cb.

Entering a value for the cutoff frequency (-3db or 0.707 point) will find the optimum resistor and capacitor values for both sections. You can optionally enter a value for Ra & Rb or Ca &r Cb along with the cutoff frequency to find the missing values. Note that if you enter a value for one R, Ra for instance, you must enter a value for the other R, which is Rb in this case. The same is true for the capacitor values. Also note that you cannot enter a value for both R and C. This is because the sections of this filter interact with each other and entering both R & C for one section may result in a nonsensical result in the other section.

By default the solver finds values for a Bessel implementation. For general information about filters and specific details about filter implementations, see the Filter Types article. You can change the implementation by entering a value for Type. The following table lists the acceptable values for Type and the filter implementation for each Type value.

Unless otherwise specified, the capacitor’s tolerance is assumed to be 5%. If you wish to specify a different tolerance, enter it as a percentage (10% = 10).

Even though solutions are provided for a number tolerance bands, this filter design (Sallen-Key or VCVS) performs best when the component values are more closely matched. The use of 1% tolerance resistors and reasonably high grade film capacitors are recommended. In addition, it is best to use resistor values that are greater than 10K (other than Rg) to minimize frequency errors.

If you are interested in the details, an excellent downloadable resource is available an Application Report from Texas Instruments. Search for SLOA049B, “Active Low-Pass Filter Design” by Jim Karki. Excellent, and concise, coverage of the subject matter is also given in the Art of Electronics by Horowitz and Hill.