Move Beyond Active Filter Design Mythology To Improve Your Discrete Op-Amp-Based Designs

This suggests that the noise added by the two filter resistors should not add significantly to the noise produced by the op amp and that the “noise gain” inside the SKF should not peak more than it already does due to the target filter poles. These two ideas lead to lower noise and distortion solutions and show up physically with R’s that are relatively low and in a ratio of 0.15 to 0.7 (where this is the ratio of the input resistor to the second resistor feeding the op-amp input).²

Constraining the resistor sum to reduce their noise impact and their ratio to reduce noise gain peaking leaves only the two C’s to be resolved to hit the desired filter shape. This target resistor ratio also moves in the direction of better sensitivity and gain margin as reported by more recent authors.³ 

This same issue of noise gain peaking inside the SKF loop gain also leads to a different gain sequencing in multi-stage filters than typically reported. It is quite common to see most of the gain in the first stage. This is the right thing to do if low-frequency spot noise were the dominant contributor to total output integrated noise.

The noise gain peaking hiding inside the SKF can outweigh this issue and suggests the highest Q stage first at a low amplifier gain for a multi-stage filter. This physically provides a large noise peak at the output of that first stage. Note that asking for a lot of dc gain in this stage is going in the wrong direction. The subsequent lower-Q, higher-gain stages then will “filter” this noise peak. Comparative simulations of output spot and integrated noise have validated this approach.⁴

While there has been a vast amount written on the SKF, most of it seems to have been produced for IC implementation (low and matched C values) and/or well before the easy availability of wideband op amps and low-cost precision surface-mount device (SMD) capacitors. Take advantage of the fabulous SKF design elements that are available today, and move beyond the myths to improved dynamic range designs.

References
1. Sallen, R.P., Key, E.L., (1955-03), “A Practical Method of Designing RC Active Filters,” IRE Transactions on Circuit Theory 2 (1), 74-85 
2. Intersil’s iSim Active Filter Designer, www.intersil.com/iSim
3. “A new set of Sallen-Key filter equations,” Martin Cano, EDN, Oct. 1, 2009
4. Intersil Application Note AN1580, “Testing Intersil’s ‘Active Filter Designer’ gain and Q Sequencing Impact on Output Noise,” Michael Steffes and Oscar Mansilla, July 2010.