[sdiy] Fixed filter bank questions

Ben Bradley ben.pi.bradley at gmail.com
Fri May 10 06:28:14 CEST 2019

I don't think you'd need to go as far as Self says (though I haven't
read that book), especially if you measure each capacitor.

>From what I interpret of what you described from Self, you get a
"better chance" of the combined capacitor being within 10 percent of
twice the nominal value, just by combining (in parallel) two randomly
picked 20% capacitors. This is true, but it doesn't seem that great an
improvement, especially compared to measuring each cap (out of
substantially more than two of the same nominal value) and then
combining them intelligently.

Number them, say, 1 through 20 (write on the cap with a Sharpie or put
a piece of paper with the number on the cap), measure each one (I have
a BK-878 with its 4999 count gives plenty of resolution, still works
great after 18 years), and put the numbers 1 through 20 and the
corresponding measured value in adjacent columns in a spreadsheet.
Sort both columns by measured value, and you can probably match each
one N rows down with  another at or near 21-N rows down so that they
add up to perhaps 2 percent of twice the nominal value. This presumes
they're somewhat equally distributed from the low to high tolerance,
but it seems it should mostly work even if not. I haven't done this
exact thing before, but I've done similar things to get 0.1% resistors
from a pile of 1% resistors (though I probably would have done as well
just buying 0.1% resistors), and it seems this is The Way to get close
tolerance caps.

Let me know if my description is too terse. Maybe I can do a
spreadsheet to show how this is done.

On Thu, May 9, 2019 at 11:07 PM <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. 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.
> 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.
> I think Doug’s examples were mostly where the circuit needed a series of different capacitances, such that creating different values by combining the same value in different series and parallel combinations made sense. One chapter of his book goes into great deal analyzing as many as eight or ten variations of the same circuit, just by looking at different ways to choose caps. I didn’t look at the Mouser BoM costs for any of those to see which option won.
> I don’t know why Yves would have simply doubled every cap. Maybe it was purely for the improvement to tolerance.
> Bottom line: Tolerance and volume discount advantages can be obtained by using multiple capacitors instead of single caps.
> Brian
> On May 8, 2019, at 2:04 PM, David G Dixon <dixon at mail.ubc.ca> wrote:
> > So, I decided the other day that I wanted to build myself a fixed filter bank.  The first thing I did was to look at the YuSynth design on the internet.  I see that he is using pairs of multiple-feedback filters (exactly as described on pages 150-154 of Don Lancaster’s beautiful little book, “Active-Filter Cookbook” which I have sitting on my lap as I type this).  That was exactly what I was going to do as well.  Yves says that his filter sections have a Q of 3.7, and a gain of 1.14.  Actually, his single sections have a Q of 2.66, and a gain of 1.07.  The overall gain is simply the square of the individual gains, which is indeed 1.14.  The overall Q is something that I haven’t calculated (I’m presuming I need to derive the overall transfer function, and I just haven’t bothered).  Also, his filter center frequencies conform to, I’m guessing, the same ones that Moog used in his 914 or whatever (LP at 88, 125, 175, 250, 350, 500, 750, 1000, 1400, 2000, 2800, 4000, 5600, and HP at 7000 Hz).
> >
> > 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%.
> >
> >
> > SECOND QUESTION:  Is there something fundamentally less desirable about doing it my way than doing it Yves’ way?  Does the minor inconvenience of having to order and use about 30 different 1% resistor values somehow outweigh the financial burden of installing twice as many poly film capacitors as are actually needed in the design?  Also, my PCB will be smaller and the layout will be simpler.  Note that I may still decide to decrease my number of capacitor values from 11 to 5 or 6 – just to decrease the total number of different values I need to buy, plus I will probably hand-select these capacitors to get the values as close as possible to the targets.
> >
> > Them’s my questions.  Thanks for your consideration.  Any comments welcomed!
> >
> > Dave Dixon aka Doc Sketchy
> >
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