On Mon, 2 Aug 2004, Russell McMahon wrote:
> SUMMARY:
> 1. Discussion re using standard resistors to make N:1 voltage dividers
> for eg LM317 voltage setting.
> 2. Discussion of accuracy with which resistor values match ideal E series
> values.
> 3. Paralleling E12 resistors to get E96 values.
<snip>
{Quote hidden}> Rtarget = Rmin to Rmax step Exx K factor ' (multiplied)
> Rbest = something_stupid
> X = Rmin to Rmax step Exx K factor
> Y = Rmin to Rmax step Exx K factor
> Rbest fn(X,Y) = min((|Rtarget - Rbest|, |Rtarget - X//Y|) '
> save best X, Y
> Next
> Next
> Output Rtarget, Rbest fn(X,Y)
> Next
This can be solved in closed form (to within the precision of the
resistance tolerances) using this formula:
Ri = Ro * 10 ^ (i/N)
Where i is the i'th resistor in the decade, N is the number of resistors
in the decade and Ro is the first one. For example, in E96, the first few
resistance values using this formula are:
1.000, 1.024, 1.049, 1.0746, 1.1007
compared with the standard values:
1.00, 1.02, 1.05, 1.07, 1.10
If you want to find the closest ratio of any two resistors, then you can
use a variation of this formula.
Ra = Ro * 10^(a/N)
Rb = Ro * 10^(b/N)
Ra/Rb = 10^((a-b)/N)
Ra = Rb * 10 ^ ((a-b)/N)
I'd be wary of trying to use resistors in one family to create the more
precise resistors of another family. The specifications are such that you
can't guarantee the tolerances are good enough. For example, if you're
using the 5% family (E12) to create 1% resistors (E96) then you're
assuming that the 5% resistors have a 1% accuracy. It may turn out that
this is true in certain circumstances for practical manufacturing reasons
but designs shouldn't count on it. (For example, the 10k resistor across
all families may all be same.)
Scott
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