[sdiy] Fixed filter bank questions

ASSI Stromeko at nexgo.de
Sat May 11 12:27:34 CEST 2019

On Friday, May 10, 2019 5:06:01 AM CEST rsdio at audiobanshee.com wrote:
> Earlier this year, I got a copy of Douglas Self’s “Small Signal Audio
> Design” book. In that, he seems fond of a technique of using multiple
> capacitors in order to improve the tolerance. I didn’t pay close attention
> to the math, but two 20% capacitors end up giving you a value that is
> within 10% of the combined value.

It doesn't (the resulting tolerance wuld be slightly above 14%), you'd need to 
parallel four capacitors to get to half the tolerance of the individual parts.  
Actually that is only true if the deviation from nominal for all the 
capacitors that you combine are independent (not correlated), which however 
they will be (strongly so) if you pick four capacitors from the same batch.

> His examples even used four or eight of
> the same value capacitor, with further improvements of the accuracy. At
> some point it gets ridiculous, so he didn’t quite recommend eight
> capacitors instead of one, but the one, two, three, four series was
> recommended.

Under the condition of independent and identically distributed (i.i.d.) error 
the tolerance goes down with 1/sqrt(n), so yes, that gets old pretty fast.

> In my experience, highly accurate resistors are cheap. By the time I select
> a quality resistor, I can usually find any 0.1% value for the same cost.
> Capacitors tend to have larger tolerances, and it’s way more expensive to
> get precise. Then there’s the benefit of reduced unit cost when you buy
> larger quantities. I haven’t really looked at whether you can save money
> combining several cheap, large tolerance caps instead of fewer tight
> tolerance caps, but it seems like it could work out in some specific cases.

One of the first programs (in BASIC no less) that I've typed into a computer 
was one that would ask for some value and tolerance specification, what E 
series you were having parts for and then spit out which combination of 
resistors would give you that value, either with the the least number of 
parts, or (if you'd put in a tight tolerance) the closest approach to what you 
were asking.  IIRC, that one could deal with parallel/series combinations of 
up to four units, but these later got extended to somewhere on the order of a 
dozen elements (you could limit that number).

The idea was that you could stock E6 or E12 parts only, but design for E24 or 
E48.  However, if you were actually doing that you quickly learned that in 
particular the E6 parts more often than not didn't have the wide distribution 
around the nimonal the program assumed based on the tolerance spec, but 
clustered more tightly around values that were either on E12 (but a different 
value the E6 was) or E24 values (meaning that this particular batch was 
downgraded to E6 from an E12 or E24 production run).  Sometimes you'd see a 
double distribution around a supicious hole where the nominal should have 
been, meaning that the center of the distribution was selected out for better 
tolerance parts.

You can of course keep a reduced selection of 1% or better parts and still use 
the combination technique to obtain inbetween values that you don't stock, 
you'll just need to do the calculation with the correct distribution width for 
the batch(es) you have.

As to the original question:
> > Yves did it a different way.  He used the same three resistor values in
> > every filter (R2 = 47k, R1A = 22k, and R1B = 1.8k), and used capacitors
> > in parallel to find two capacitors which add up to the correct capacitor
> > value for each frequency.  This means that his resistor choices are very
> > convenient, but each dual filter requires 8 capacitors at two different
> > sizes, rather than just 4 capacitors of a single size.  He has restricted
> > himself to the six most common standard capacitor mantissas (10, 15, 22,
> > 33, 47, 68) in selecting these sizes.  The frequency errors he gets
> > (ignoring capacitor tolerances) are as high as 3.7%, with an average of
> > 1.4%.

I think that this decision was done by recognizing that resistors are usually 
much tighter speced than capacitors, so combining two capacitors of different 
values gives you a simple way of reducing the effective tolerance of the RC.    
Unless you plan on producing in volume (where indeed you'd need to consider 
the extra cost of having to have two dozen more feeders on the pick and place 
machine and inventory of oddball values you might not be using up soon in 
other projects), I don't really see much of a difference between your idea and 
the way Yves is doing it.  If you actually measure the capacitors before you 
order the resistors to match those values, your's might even be preferrable.

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