### Author Topic: Filter topology Sallen-Key and MFB: resistor order matter based on their values?  (Read 603 times)

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##### Filter topology Sallen-Key and MFB: resistor order matter based on their values?
« on: January 05, 2021, 05:47:02 pm »
I was designing a needed low pass filter in Sallen-Key configuration and everything goes as normal. Casually look at the Chapter 8 - Analogue Filters by AD, a few reports from TI and follow the procedures. But suddenly, I've got a QUESTION: does the order of resistors matter in Sallen-Key or MFB filters based on their values? From a calculation point of view, there is no difference, but fundamentally there might be some effects?

Added a simple buffered sallen-key circuit bellow. Should R1 always be smaller than R2 whatever values they are?

It would be glad if you guys could share your ideas. [attachimg=1]

#### Benta

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##### Re: Filter topology Sallen-Key and MFB: resistor order matter based on their values?
« Reply #1 on: January 05, 2021, 06:14:45 pm »
There are indeed ramifications, the main one called "component sensitivity".

Component sensitivity refers to how component tolerances influence key filter parameters.
As an example: if a resistor value is off by 2%, how much does this influence cut-off frequency, gain or Q.

The Sallen-Key filter is pretty bad in this respect, the MFB filter is quite good.
With proper component selection, it is possible to keep the sensitivities below 1 for the MFB filter, Sallen-Key is always 1 or greater.

The figure indicates tolerance influences. With 1, a 2% resistor or capacitor tolerance will influence key filter parameters by 2%.

The maths are not simple, but online filters calculators like the one from TI handles this quite well.

« Last Edit: January 05, 2021, 06:39:28 pm by Benta »

#### mawyatt

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##### Re: Filter topology Sallen-Key and MFB: resistor order matter based on their values?
« Reply #2 on: January 06, 2021, 03:41:22 pm »
30~40 years ago we struggled with finding the various R and C values for active filters, especially the C values. This led to the development of an active Butterworth 3rd Order filter with equal value resistors and equal value capacitors. Simply interchanging the Rs and Cs configures from a low pass to a high pass filter and the values are the same for the same corner frequency.

Anyway, might be an interesting topology active filter to consider.

BTW this was published in EDN long ago, but I can't remember the actual date or issue. No need for a filter calculator as the -3dB Butterworth corner radian frequency is simply 1/(RC), or the corner in Hertz is 1/(2*pi*RC).

Best,
« Last Edit: January 06, 2021, 03:58:19 pm by mawyatt »
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