> 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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