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March 3, 2019 / consort3

More 3rd order filters

More on the third order low pass Sallen and Key filter. Dale Eagar in Linear Tech AN67 came up with the E3 capacitor, E24 resistor Sallen and Key filter. Dale had noted that capacitors were typically only available in E3 values i.e. 1nF 2.2nF 4.7nF. So he produced tables that allowed for that. I found it easier to make my own table for audio based on Dales generic table, so here is my table for Butterworth filters.

Freq kHz R1 R2 R3 C1 C2 C3
1.0 3.6K 33K 33K 47N 10N 2.2N
1.1 4.7K 4.7K 62K 47N 47N 1N
1.2 3.6K 6.2K 10K 47N 47N 4.7N
1.3 2.7K 20K 3.3K 47N 47N 4.7N
1.5 2.4K 16K 3K 47N 47N 4.7N
1.6 2.7K 4.3K 8.2K 47N 47N 4.7N
1.8 4.3K 12K 1.3K 22N 100N 4.7N
2.0 3.6K 75K 1.8K 22N 47N 10N
2.2 2.4K 2.4K 30K 47N 47N 10N
2.4 3.3K 9.1K 430 22N 220N 4.7N
2.7 2.7K 56K 620 22N 100N 10N
3.0 2.4K 51K 560 22N 100N 10N
3.3 2.2K 16K 300 22N 22N 2.2N
3.6 2.2K 5.6K 680 22N 100N 4.7N
3.9 2.4K 3.9K 6.8K 22N 22N 2.2N
4.3 1.8K 5.1K 240 22N 220N 4.7N
4.7 1.6K 13K 390 22N 100N 2.2N
5.1 1.6K 3.6K 510 22N 100N 4.7N
5.6 1.3K 11K 330 22N 100N 2.2N
6.2 1.3K 36K 160 22N 220N 4.7N
6.8 2.4K 1.6K 3.3K 10N 10N 1N
7.5 1.2K 3K 12K 22N 10N 1N
8.2 1.2K 1.1K 240 22N 220N 4.7N
9.1 1.8K 15K 910 10N 22N 1N


My tracking idea was used in the 3rd order low pass filter table page on this blog where I used E12 capacitors and equal value E24 resistors. Tayda do a range of 5% E12 capacitors from 1nF to 820nF. Surprisingly, there is not much evidence of tracking on the Eagar table, the obvious one being the transition from 2.7 to 3.0. To combine the Eagar idea (E3 capacitors) with my tracking idea I have created the following table Caps  C1 22nF C2 47nF and C3 4.7nF

Freq kHz R1 R2 R3
1.0 8.2K 13K 7.5K
1.1 7.5K 12K 6.8K
1.2 6.8K 11K 6.2K
1.3 6.2K 10K 5.6K
1.5 5.6K 9.1K 4.7K
1.6 5.1K 8.2K 4.3K
1.8 4.7K 7.5K 3.9K
2.0 4.3K 6.8K 3.6K
2.2 3.9K 6.2K 3.3K
2.4 3.6K 5.6K 3k
2.7 3K 5.1K 2.7k
3.0 2.7K 4.7K 2.4k
3.3 2.7K 4.3K 2.2k
3.6 2.4K 3.9K 2k
3.9 2.2K 3.6K 1.8K
4.3 2K 3.3K 1.6k
4.7 1.8K 3K 1.5k
5.1 1.6K 2.7K 1.5k
5.6 1.5K 2.4K 1.3k
6.2 1.3K 2.2K 1.2K
6.8 1.2K 2K 1.1K
7.5 1.1K 1.8K 910
8.2 1K 1.6K 910
9.1 910 1.5K 820

I used the Filter tool here:

Note that the values do not always track. Also I do not like too low value resistors, so personally for filters above 6.8kHz, I would make the resistors 10X higher and the capacitors 10X lower to compensate


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