[sdiy] Best 2-pole Sallen Key LPF calculator

[Tom Wiltshire]

Yeah, this sounds pretty close to what I've been doing.

I started out by assuming the capacitors would be adjacent-but-one values from the E6 series (so 470p and 1n, for example). That gives them a ratio of 10^1/3 = 2.1544.
Setting the resistors equal with those capacitors gives you Q=0.734. Close enough to Butterworth for the likes of me, if marginally more peaky.

Tom

On 24 Feb 2015, at 14:51, "Richie Burnett" <rburnett at richieburnett.co.uk> wrote:

> 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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