# Differences between 2nd order low pass filters

I don’t know how to design filters, but I need a second order low pass filter. I searched them on the internet and found two schemes. One is Sallen-Key, and the other I don’t know what is called. Question: what is the difference and which is better to use? How is the filter calculated in Figure 42?

• You made me laugh by using "Salena Kay" filters and then selecting the correct "Sallen-Key" tag. :D Jan 19, 2020 at 12:07
• The name of the second filter is literally typed out beneath the picture -> Butterworth Jan 19, 2020 at 12:07
• So, we do expect you to do a bit of research: Both filter types have wikipedia pages, and we can't tell you what is "better" if you don't tell us anything about what your metric for "good" is. Filters have different properties, like stopband suppression, passband flatness, phase linearity, steepness of transition, and you design them to fit your application. Without any info on the application, there's no "better" filter. Jan 19, 2020 at 12:09
• There are filter shapes, and filter implementations, don't confuse the two. Butterworth, Chebyshev, Bessel are shapes. Sallen-Key is an implementation (2nd order non-inverting using an opamp). A Sallen-Key can be many shapes. Jan 19, 2020 at 12:22
• @Swedgin the name typed out is the filter characteristic and not the filter type. That name defines that it is low-pass having a cut-off of 500 kHz that is maximally flat in the pass band (aka Butterworth). Jan 19, 2020 at 13:44

One is Salena Kay, and the other I don’t know what is called.

Sallen Key with unity low pass gain: -

Pictures taken from this useful web calculator.

Sallen Key with gain setting resistors: -

Pictures taken from same calculator page as above - scroll down

MFB or multiple feedback: -

Note that the low frequency gain of the above MFB circuit is $$\-\frac{R3}{R1}\$$

Pictures taken from this useful web calculator.

Question: what is the difference and which is better to use?

The MFB uses one more component but can operate at higher gains. I suggest you use this information (and knowledge of your application) to google for further information.

• Just a note. The Sallen Key image you borrowed doesn't match the OP's image, which is a Sallen Key where gain or damping can be chosen, but not both at once, with gain that must be less than three.
– jonk
Jan 19, 2020 at 12:20
• @jonk - thank you and fixed! Jan 19, 2020 at 12:27
• +1. Anyway, I wish the US Air Force would free up TR-50 by Sallen & Key. It is infinitely better than their published paper a year later. Everyone should master that paper. It is really good and I don't know of anything better, since, for self-learning. Lots of very hard to read, highly mathematical books are around now. But nothing I've seen that provides such good insights for so many types of common filter types in so few pages. Stupid US Air Force insists on receiving justification and approved release only on individual basis. It is insane we are still in that situation.
– jonk
Jan 19, 2020 at 13:01
• @jonk I've not come across TR-50 by Sallen & Key!!! Jan 19, 2020 at 13:05
• another point to add w.r.t. Sallen-Key vs MFB is: Sallen-Key provide for easier selection of circuit components, and at unity gain, it has no gain sensitivity to component variations. The MFB shows less overall sensitivity to component variations and has superior high-frequency performance
– user16222
Feb 1, 2020 at 13:11

first question is what do you want? if you want to make an active filter you should know where you want to use it! which op-amp do you want to use? they always mention about making filter with them in the datasheet.

• There is no mention of what part is being use. Henceforth, you can assume that the op-amp is an ideal device.
– user103380
Jan 20, 2020 at 3:22

For the sallen-key Filter...

Q = 1/(3 - k)

For butterworth response which is a maximally flat pass band and roll off of -12dB/octave (-40dB/decade)....

Must have Q of 0.707 which means a gain,k of 1.59. So set RA = 5k6 and RB = 10k

Then cut off frequency, fc = 1/(2 * pi * R * C)

Where R=R1=R2 and C=C1=C2