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'[EE:] Resistors, was Olin's Easyprog'
2004\08\02@042806 by Alan B. Pearce

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>eg if you use an LM317 to provide 5.0V for your processor you
>probably want the 5.0V to be as accurate as the LM317 can provide.
>The LM317 has an internal uncorrected reference accuracy of the
>order of +/- 4%. If you set the voltage divider to scale its
>nominal 1.25v value up to 5v and you use 5% components then you
>will probably degrade the accuracy of the resultant voltage.
>HOWEVER the required ratio of the voltage setting resistors is
>ABOUT 3:1. In practice it's very slightly on the low side of 3:1
>due to technical considerations (see LM317 datasheet).
>With E12 resistors we are locked into ratios which are of the
>form  1.21^N:1 where N is the number of steps apart.
>1.21^6 = 3.16.   1.21^5 = 2.61
>Both are less accurate than we'd like.


Interesting analysis Russell. 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. However it is only in recent
years that I have used this device, so my work has all been done with 1% or
2% surface mount resistors, which hides some of the problem.

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. I highlighted the 270 ohm in a third colour
as my preferred value for the feedback resistor, and select on that line
where possible, unless it makes good sense to use a different value to get
closer to the voltage I want.

Anyone interested in the file, I can send it as a zip, about 232kb, but it
is quite easy to make your own. Once you get the formula in one square then
copy it columns and rows, it doesn't take long.

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2004\08\02@051655 by Russell McMahon

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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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2004\08\02@103743 by Scott Dattalo

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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}

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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2004\08\02@110648 by Russell McMahon

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> This can be solved in closed form (to within the precision of the
> resistance tolerances) using this formula:
>
> Ri = Ro * 10 ^ (i/N)

Yes - that's the formula that I stated a few posts back - it's the Kfactor
that I mention.
To make it useful it's a good idea to round the resistors to appropriate
precision as you go as otherwise you can get values that aren't in the
actual range (ask me how I know).

> 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)

Yes. That's what the above program effectively implements.
It brute force searches the paralle resistor combinations for the lowest
error paralle combination.
I had a quick hack at it tonight and it works OK BUT I need to add rounding
to be sure to get standard values.

> 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.)

Yes. I covered this in my fairly rambling discussions. I noted that modern
"5%" resistors (especially good quality ones) tend to cluster around their
nominal values far more closely than their claimed precision would suggest.
YMMV.

Also, importantly, one reason for this exercise MIGHT be to allow an E12
valued subset of 1%  (ie E96) resistors to be carried and then used to
derive any E96 value using no more than 2 resistors.The point is that 1/8 as
many resistors need to be stocked and in most cases the 1% resolution in
value is not needed. 1% accuracy may be. In many cases such work arounds are
unneeded, but for amateurs, carrying "only" 84 resistor values to get from
1R0 to 8M2 is preferable to having to stock 8 times as many. Few amateurs
would stock 700 odd resistor values. For my design work I use E12 values as
standard at whatever precision is required and supplement them with other
values if needed or in the final design. I seldom need to use resistors
outside the E12 range. I standardise on Philps 5% metal film for
"work-horse" use.








       Russell McMahon
>
> Scott
>
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2004\08\02@112143 by Alan B. Pearce
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>Yes. I covered this in my fairly rambling discussions. I
>noted that modern "5%" resistors (especially good quality
>ones) tend to cluster around their nominal values far more
>closely than their claimed precision would suggest. YMMV.

It is quite likely that resistors manufactured to a 5% tolerance will
cluster around a value within the quoted tolerance, with an extremely small
(quite possibly <1%) tolerance around the central value of the cluster due
to modern manufacturing methods.

>Also, importantly, one reason for this exercise MIGHT be
>to allow an E12 valued subset of 1%  (ie E96) resistors
>to be carried and then used to derive any E96 value using
>no more than 2 resistors.The point is that 1/8 as many
>resistors need to be stocked and in most cases the 1%
>resolution in value is not needed. 1% accuracy may be. In
>many cases such work arounds are unneeded, but for amateurs,
>carrying "only" 84 resistor values to get from 1R0 to 8M2
>is preferable to having to stock 8 times as many.

This would be a typical scenario for someone buying a book of SMD resistors.
For example RS Components stock a Welwyn book of 2% resistors in E12 values.
Even some of the books with 1% tolerance still have only the E12 range, with
some having the E24 range.

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