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### Topic: Resistors Scale (Read 2419 times)previous topic - next topic

#### chiva

##### Jul 01, 2010, 11:20 pm
Seeming that no one in the Spanish forum has the knowledge to answer this question I will post it here

To get the resistor scales (E12, E24, E48...) you use the following formula:

10^(i/n)

Where n is the scale number (12,24,48...) and n is a natural number from 0 to n

The problem is that when getting the E12 resistor values, the first ones come ok, but when arriving to higher values like 4.7 Ohms, the formula gives 4.64 so even with rounding you can't get the 4.7 value

Rounding up isn't valid as for 3.3 it gives 3.16

Anybody knows why?
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#### westfw

#1
##### Jul 02, 2010, 02:34 am
The wikipedia article http://en.wikipedia.org/wiki/E24_series implies that your formula is true for "Renard numbers" (R5, R10), but that the resistor series has numbers that were derived some other way (no formula given, but there's a Standard that has the list of values.)

#### chiva

#2
##### Jul 02, 2010, 08:40 amLast Edit: Jul 02, 2010, 08:42 am by chiva Reason: 1
Yep, I saw it a bit late, seems that the formula gives numbers that should be aproximated to Renard ones or something similar

I will get the E6 and E48 as a base and build the rest

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#### Grumpy_Mike

#3
##### Jul 02, 2010, 11:00 am
It all started with the now very old 20% resistors. The values were chosen so that going from one value to the next one would always result in an increase in resistance even if the first value was 20% up and the second value was 20% down. With such a wide tolerance it makes no sense going for values more precise than two places.

When 10% and then 5% and 1% resistors came in there were opportunities to "fill in the gaps" hence the different series. The formulae is an actual description of the process but doesn't reflect the fact that only two significant places were used. In other words 4.64 is 4.7 when rounded up for two places.

#### chiva

#4
##### Jul 02, 2010, 11:22 am
What do you mean by rounding up two places? Using the 4 and 6 only?
But how do you get the 7?

Thanks
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#### Grumpy_Mike

#5
##### Jul 02, 2010, 12:29 pm
Quote
What do you mean by rounding up two places?

Rounding up so that the precision of the number is expressed by, at the most, two numbers followed by one or more zeros.

In the specific case of 4.64 then the value of 4.6 is too low to prevent the overlap so in order to have a monotonic series the next value has to be rounded up to 4.7. To leave it at 4.6 would be to round it down.

#### chiva

#6
##### Jul 02, 2010, 02:05 pm
I was stuck on thinking round up was rounding down...
If you realize i have written it in the first post, but whatever...

Now i understand it, round up to prevent overlap, ok

In the 3.3 case, where you have 3.16 if you round up to 3.2 it is still overlaping so you keep adding 0.1 until you prevent it, is that correct?
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#### Grumpy_Mike

#7
##### Jul 02, 2010, 03:46 pm
Yes that's right.

#### chiva

#8
##### Jul 02, 2010, 04:55 pm
OK
Thanks Mike
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#### chiva

#9
##### Jul 02, 2010, 11:32 pmLast Edit: Jul 03, 2010, 04:55 pm by chiva Reason: 1
I have redone the calcs and still doesn't work.

If we want to get the E12 it has a 10% tolerance
From the formula we get 1.78 rounded to 1.8 and the previous one was 1.5.
Now we search for overlapping:

1.5*1.1=1.65 <- 1.5 plus the 10%
1.8*0.9=1.62 <- 1.8 less the 10%

They overlap but, theorically, they are valid...

Any ideas?
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#### Grumpy_Mike

#10
##### Jul 05, 2010, 12:25 pm
I think your problem is that you are trying to apply a formula to the values that were not derived for the formula in the first place.
Have a read of this site:-
http://www.logwell.com/tech/components/resistor_values.html

#### chiva

#11
##### Jul 05, 2010, 03:57 pm
I have seen all those sites, but they just say: here you have the values the standard sais, no one tells how they were achieved.

So, I think I should stick to the easy copy all values.

Thanks
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