TUTORIAL

Summary of one point: Design where possible to use E12 series or less unless
your design demands higher precision.

> >> I've never heard of "E12" and "E24"...
> >Is not that numbering system used everywhere ?
> That's the first place that I've ever seen that "E" series of numbers
> used to indicate different precisions of resistors. I've been working
> in electronics so long that I've been accused of having worked as an
> intern for Volta. :=)

This ramble may be worth following for people wanting to design things with
resistors.
It starts off talking about WHY a series eg E12 exists, and ends up talking
about what resistors you should probably spec for your project.

FIRST - here's an excellent table showing all values in E6/12/24/48/96 & 192
ranges and their relationships
Recommended that people have a look if not familiar with the ranges.

    http://www.logwell.com/tech/components/resistor_values.html  <- ***
EXCELLENT ***

An Exx  series is  one whose xx members are distributed geometrically
symmetrically across a decade.

ie for resistors Rn+1 = Rn x K
        where K = 10^(1/xx)
For E12 series K = 1.21 (see below) so if R1 = 1k
then R2 = 1.2K
R3 = 1.21 x 1.21 = 1.468k = 1.5k
R4 = 1.21^3 = 1.778k = 1.8K etc

Far easier to use than conceptualise :-)

The point is that the relationship between the resistance of members M steps
apart is always the same to within the precision of the series.

So E12 = 1.0 1.2 1.5 1.8 2.2 2.7 3.3 3.9 4.7 5.6 6.8 8.2 (10 ...)

10^/(1/12) ~= 1.211528 ~=  1.2

Example. Take any 2 values 4 steps apart
eg  1.2 and 2.7
2.7/1.2 = 2.25
Now try again
eg 2.2 and 4.7
4.7/2.2 = 2.136 = 2.2

Slight difference in ratios due to rounding of values in standard series.
________

So you'd expect each value to increase by a factor of about 1.2 times.
And it does
For this series to be useful the variation in a given value caused by
manufacturing and operating variations shouldn't allow it to assume a value
which may reasonably be assumed by an adjacent member. This means that if
each member is 1.2 x the prior one then a step of about sqrt(1.2) will bring
you to the boundary between the neighbours. sqrt(1.2) = 1.095. Each value
could be about +/-10% before impinging on the others space.
In the good old days where resistors were quite imprecise unless especial
care was taken to make them otherwise, E12 series were indeed usually +/-
10% values. The resistors of a given value spread across this error range
and by selecting you could get almost any resistor value at all. How stable
it was with voltage, temperature time etc was another matter.

With time the standard accepted E12 resistor tolerance came to be 5%.
Even with 5% accuracy E12 values cluster as "islands" around the nominal
value. If you want a 1.1k resistor you may have to test a lot of 5% 1K0 or
1K2 resistors. Ongoing process improvements make such resistors increasingly
well defined unless you buy double flying horse brand or equivalent. Using
resistors of unknown parentage is asking for other unexpected problems. They
may only cost a cent or so each in bulk, but there is still a lot of
technology in there.

With increasing accuracy you can fit more resistor values in a decade
without overlapping.
The E96 series can fit in 96 resistors between eg 1K and 10K. The stepping
ratio K is  10^(1/96) or 1.024 so you'd expect that E96 resistors would
usually be 1% tolerance or better so that values don't overlap.

Note, you can still specify E12 values and use 1% components.
You may want 1k or 1.0k or 1.00k or even 1.000k
The precisions implied by the above figures are +/- 500r !!!! (1k)
+/- 50r (1.0k), +/15r and +/- 0.5 r
or 50%, 5%, 0.5% and 0.05%
These would be About E2, E24, E240 and E2400 ranges, *should such exist.*
Buying and using E2400 resistors would be extremely hard ! ;-)

The standard "off the shelf' resistor ranges available everywhere are E12.

    The much loved 1.0   1.2   1.5   1.8   2.2   2.7   3.3   3.9   4.7   5.6
6.8   8.2

Even if you NEED 1% values you can still specify eg 1k8 1%.
In most circuits involving microprocessors you don't NEED such accuracy.
The exceptions usually occur when you are sitting or measuring analog
levels.
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.
In this case use of a resistor from a higher  series would help.
Using the chart at
    http://www.logwell.com/tech/components/resistor_values.html

we see that the E24 series contains a 3.00 k value.
E24 is notionally at least 100/24/2 = 2% accuracy.
In practice 1 1K 1% and a 3K 1% would be just fine.

Importantly - not that on the E24 range the 100 value and 300 value are 11
steps apart.
ANY two values on the E24 range which are 11 steps apart will have a 3:1
resistance ratio.

Now lets look at transistor base driving from a PIC.
A BC337 has a beta of 300 say at 100 mA.
So we need about 100/300 = 0.333 mA base drive
PIC output is 5v nominal so we need about a (5-0.6)/0.333 MA = 13.2K drive
resistor.

An E92 13k2 would work just fine .
**** STOP *********** Don't you dare !!!!!

An E12 10K would work just fine too.
Or an 8k2 or a 6k8 even.
A bit much current won't hurt unless things are really tight. (In which case
the above "design: was way too rough and should have been done using worst
case values - but that's another story).

TRY to design using E1 values wherever possible !!!!!!!!!!!!!!!!
ie E1 = 1k, 10k, 100k, 1m etc.
90% + of simple digital design can be done with E1 ! ;-)

Next use E2 = 1 3.3 10 33 100

E4 =  1 1.8 3.3 5.6 10 18 ....

This is perhaps quite intuitive and we MAY feel more comfortable with eg 1
3.3 6.8 10 etc
Whatever. Try to minimise values used unless essential.
Use percentage accuracy that suits.
Spec E96 or whatever as essential
Even when you need 1% tolerance, try to stick to E12 values where possible.
It often is.

Sometimes the "precision" of a desired voltage level etc may attract you to
E96 values. Always ask - is this precision necessary?. If you are doing it
for yourself and have the parts then maybe it's an OK choice. If it's for
production then the precision may allow you wider tolerances elsewhere and
it may be justified. If it's going to be used by others who have limited
access to more exotic parts then try really hard to avoid such choices.



        Russell McMahon

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