[sdiy] Best 2-pole Sallen Key LPF calculator

[Richie Burnett]

I normally set the two resistor values equal, and the two capacitor values 
equal to start with.  Then choose an R and C value to get the cutoff 
frequency where I want it to be.  That uses that long equation for fc with 
everything on the bottom of the square-root, but since R1 and R2 values are 
the same, and C1 and C2 values are the same, it simplifies to be just fc = 1 
/ (2 pi RC).  This takes care of the cutoff frequency.  Then I will alter 
the ratio of C1 and C2 in order to get the Q factor that I want.  For 
instance if you double C1 and halve C2, the cutoff frequency stays the same 
but the Q increases.  It is the ratio of the capacitances that determines 
the Q factor.

Once you have a prototype filter with some cutoff frequency and some Q 
factor, you can easily modify the cutoff frequency by scaling the resistors. 
Or by scaling the two capacitor values by the same amount, so keeping them 
in the same ratio to each other so that the Q doesn't change.  Or 
alternatively you can change the Q factor by multiplying and dividing the 
capacitor values by some figure to keep the overall product C1C2 the same 
and not affecting the cutoff frequency.

That's how I do Sallen Key filter design.  Once i've got values that result 
in the response that I want, I can try plugging in preferred values and see 
what affect it has on the response.  You can either do this mathematically 
or using a simulator.  Spice Monte Carlo analysis etc.  Usually either Q 
factor or cutoff frequency will be more important, so you can choose values 
to optimise the thing that is most important to you.  If you really must 
have a specific Q-factor, and capacitor choices are quite limited, you can 
always use series or parallel combinations.

Hope this helps,

-Richie,

-----Original Message----- 
From: Tom Wiltshire
Sent: Tuesday, February 24, 2015 1:34 PM
To: synthdiy diy
Subject: [sdiy] Best 2-pole Sallen Key LPF calculator

Hi All,

What's your favourite 2-pole Sallen Key LPF calculator?

I'm looking for one that gives actual component values rather than 
2.31573452nF, like many of the javascript ones do.

I read a very interesting article on the Electronic Design site, which gives 
many useful simplifications for the equations.

http://electronicdesign.com/analog/learn-limitations-low-pass-sallen-key-filters

It occurred to me seeing "Simplification 2: Set filter components as ratios 
and gain as 1" that the obvious ratio n for the capacitors would be the E 
series (either E6 or E12). So then I started playing with the maths for 
that, assuming a Butterworth filter (e.g. Q = 2^-0.5 = 0.707). A decent 
calculator would help me check I'm not going wildly wrong.

Thanks,
Tom

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