> I think I did a version of this that used 6 =A0switches or so. IIRC I
> found the best solution was to feed the the power via a constant
> current source. That way the voltage across the resistors was directly
> proportional to the resistance & I had a larger working voltage range
> and well defined voltages.

After a quick skim through the posts so far Richards suggestion sounds
most useful, albeit taking slightly more electronics than a simple
divider.

Off the top of my head - lets see how we go:
E&OE.

Assume resistors are scaled in steps of 2:1. Lower than this will
cause negative steps in the output for monotonically increasing binary
values of the switches (000000 000001 000010 000011 ...)
Higher ratios between switches produce "interesting" results.
It's not obvious that this is useful.

With a constant current source and series string the voltage is
"exactly" proportional to the sum  of resistances. The worst case
error has to be less than 1/2 of the change from excluding/including
the smallest resistor =3D < 0.5 LSB effectively. Worst worst case you
can assume that all the errors sum. So for 6 resistors you want 6 x
delta R < Rmin/2 or delta R =3D Rmin/12 or more generally delta-R =3D
Rmin/2N for N resistors. The required resistor tolerance is worst for
the largest resistor. Rmax =3D Rminx 2^(N-1)
So required accuracy of largest resistor =3D 1:(Rmin/2N)/ (Rmin x 2^(N-1))

             Accuracy of largest resistor =3D 1:N x 2^N

or for a 6 stage network  =3D 1: 6 x 2^6 =3D 1:384 =3D 0.26% !

This is assuming that all resistors add equal delta R in the same
direction and that all resistors are at worst case error limit and
that all resistors are in circuit. This is extremely unlikely to be
true.

Less completely:

Error allowed in largest R is less than 1/2 value of lowest R =3D 1:
2^(N-1) x 2 =3D   1:2^N
For 6 resistors =3D 1/64 =3D 1.6% so 1% resistors would be OK.

BUT this assumes that this is the sole error source.
BUT for resistors in 2:1 ratios a 1% resistor at R/2 will look like
0.5%, at R/4 will look like 0.25% etc.
SO worst case 6x 1%  resistors with all worst case delta R in one
direction will look like
1% + 0.5% + 0.25% + ... -> asymptotes to 2% for N large (and 98%+
there at 6 steps)

As "allowed" error =3D 1.6%, using 1% resistors will "almost always work OK=
" [tm].

ie trimming the Rmax value may be wise.

Note that the above is for a perfect conversion accuracy and perfectly
controlled current source.
One workaround is to note observed values and calculate likely true
value of current source wrt nominal.
Not necessary in most cases but could be useful.

One reason that this accuracy is about 1/2 as good as may be intuitive
or desireable is the swamping effect of Rmax - as it is 2 x the sum of
all lower values it dominates the error result and the error doubles
for every stage added. By scaling at some lesser ratio you get overlap
between values. By scaling at higher values you place more demands on
the higher stages. This would allow eg very precise values of the top
few resistors to be used with the others requiring much less accuracy.
Temperature effects alone are liable to make this unattractive.

E&OE, again


            Russell McMahon

--=20
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