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.


This will be lost on many but may sponsor the odd useful thought in those
wanting to use resistors usefully.
(Not a hard subject but as with all simple things, not without its slightly
brain bending aspects).

> >eg if you use an LM317 to provide 5.0V for your processor you

> ... I haven't gone that far with LM317s, but have
> found that using a 270 ohm resistor instead of the recommended 240 ohm
> output to feedback resistor, with an 820 ohm from reference to ground has
> given me a reliable 5V supply using E12 values.

> To use these devices I have an Excel spreadsheet with E48 values on it for
> R1 and R2 on the two axis, and then read off the resultant voltage (it
makes
> allowance for the nominal reference current, but not the tolerances), with
> the E12 values on both axis highlighted in one colour, and the e24 values
> highlighted in another colour.

Another approach to resistor selection for a divider is to use the obvious
once you think of it property which I mentioned, that the ratio between any
two resistors N apart in a series is constant. Set 1 resistor to 1 or 100 or
1000 or ... to start with. This can be changed later.
THEN if you want a ratio of eg 3.4:1 then on an E12 scale, you can use 3.3
or 3.9. The 3.3 is about 3% low and the 3.9 about 15% high. If this isn't
good enough you can consider the E24 330 or 360 or the E48 332 or 348 or the
E96 340 (which is perfect).
Imagine that you decided to use the E96 340. If you wanted a 3.4:1 ratio but
wanted the lower resistor to be say 1k5 then you KNOW there will be another
E96 value that is 3.4 x as high as 1k5 within the tolerance of the series*.
1k5 x 3.4 = 5k1. E96 values straddling this are 4k87 & 5k11. Closer of these
is 5k11. 511/150 = 3.407.

* Note that "the tolerance of the series" here is NOT the tolerance due to
the manufacturing process BUT the tolerance with which the Exx series fits a
3 digit numbering range. eg for an E96 series the first few resistors
starting at 1 k are 1000. 1024.275, 1049.14, 1074.608, 1100.694. ...

The actual E96 values are 1000, 1020, 1050, 1070, 1100 ... as would be
expected.
The errors between these values and the 'ideal" E96 series are 0, -0.42%,
+0.08%, -0.43%, 0.006%, +0.23%, ...
That is, the error in fitting 3 digit resistor values to an E96 series is up
to about 0.5% (as it must be when trying to fit a smooth line to a stepped
approximation of ~1% steps) ). As E96 will usually be 1% resistors this
accuracy is more or less "within the noise" but will add slightly to overall
errors.

If one wants to be VERY hobbyist friendly and use only E12 values, it is
possible to get quite good results using 2 resistors on parallel to produce
and eg E96 value. In a circuit that requires only a few precision resistor
ratios this trick may be useful. Note that using 2 E12's in parallel to
simulate an E96 is pointless if the e12 resistors are not themselves 1%
parts. However, modern metal film 5% resistors are usually far better than
the claimed 5% (especially if you use Philips parts :-) ) and a reasonable
result can be expected. If essential 'select on test" may be used assuming
that one's ohmmeter is calibrated to the accuracy required. Cheaper DMMs may
well not be.

I have long ago seen parallel resistor charts which give best combinations
of E12s for synthesising an E96 range. This could be derived
'programmatically' or a simple doubles chart produced using a spreadsheet.
(A program that blindly paralleled ALL sensibly possible E12 R values for
each E96 value and took the closest match could be written in short order
with about zero thinking power.

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




        RM

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