[sdiy] Fixed filter bank questions

Dave dlmanley at sonic.net
Fri May 10 20:44:08 CEST 2019

Many years ago a professor or colleague told me this technique was commonly used in analog telephone circuits back in the golden days of Bell Labs for high quality, high volume, cost sensitive production.  

Note you can't hand test and bin/select components for high volume manufacturing so paralleling is a good alternative. 

Spice allows you to specify component tolerance and run monte-carlo analysis.  It's instructive to run this type of analysis and see the impact on the corner freq or the Q.

There's also the classical technique known as 'sensitivity analysis', that you should be able to find in any good textbook of filter analysis/synthesis. It will tell you which components need tight tolerance for a specific design goal.  For complex circuits the arithmetic becomes difficult so spice w/ monte carlo is more effective. 

Note you really need to know the distribution of values the component vendor provides across a large population of parts. Companies that cared used to have component engineers that would sample incoming components and verify what the vendor actually shipped vs what they claimed. If you receive a batch that is all -10% paralleling a bunch of them is not going to get you closer to 1%.  :-)


On May 9, 2019 8:06:01 PM PDT, 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.
>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
>> Dave Dixon aka Doc Sketchy
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>Synth-diy at synth-diy.org
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