# Sallen Key Filter with Resonance

**URL:** <https://lookmumnocomputer.discourse.group/t/sallen-key-filter-with-resonance/1562>\
**Category:** DIY STUFF\
**Created:** [August 6, 2020, 9:34am UTC](https://lookmumnocomputer.discourse.group/t/sallen-key-filter-with-resonance/1562 "2020-08-06T09:34:05Z")\
**Posts on this page:** 1\
**Showing post:** 6

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**Author:** ![telec16](https://yyz2.discourse-cdn.com/free1/user_avatar/lookmumnocomputer.discourse.group/telec16/32/4510_2.png) [@telec16](https://lookmumnocomputer.discourse.group/u/telec16)\
**Post date:** [August 6, 2020, 2:38pm UTC](https://lookmumnocomputer.discourse.group/t/sallen-key-filter-with-resonance/1562/6 "2020-08-06T14:38:48Z")

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I’m not sure that you need to have the components matches.

To go a little deeper into the theory, it’s important to differentiate the filter topology from the “filter approximation function”.  
Examples of functions:

- 1st/2nd order
- Butterworth
- Chebychev
- …

And the topologies can be:

- Simple RC/LC circuits
- Sallen-Key
- Rausch (Multi-FeedBack)
- …

If you want a resonance, you probably want to select the 2nd order approximation function: ![image](https://global.discourse-cdn.com/free1/uploads/lookmumnocomputer/original/2X/6/65659c22b5ec13d7bfdebb03966ec594531509ce.png)  
Where `d` is the damping, the inverse of `Q`, the resonance.  
You want Q to be higher than `sqrt(2)`:  
 ![image](https://global.discourse-cdn.com/free1/uploads/lookmumnocomputer/original/2X/8/8af416c3b39c77d146be786ece8109fd1bd761fb.png)

Ok, so now you need to choose the topology that suits you. If you go for Sallen-Key, you have something like that:

 ![image](https://global.discourse-cdn.com/free1/uploads/lookmumnocomputer/original/2X/7/7f229b5f3ee9e26a7be96305e11ad2943cd043c7.png)  
Where the Zx are the complexes impedances (can be either R, C, or L).  
By choosing Z1,Z3 as resistors and Z2,Z4 as capacitors, you get a low-pass filter, and you can rearrange the Sallen-Key transfer function to match the 2nd order one. This way you can tell the component’s values you need, depending of the resonance and cutting frequency (maths are here: [https://en.wikipedia.org/wiki/Sallen–Key\_topology#Application:\_low-pass\_filter](https://en.wikipedia.org/wiki/Sallen%E2%80%93Key_topology#Application:_low-pass_filter))

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