I need the formula for calculating EIA standard decade values (RS-276) and don't want to use a list. I've tried what I could find on the web and they all fizzle out the same way for E24 and less.
Example, calculating E12 (10%) values gives:
10, 12, 15, 18, 22, 26, 32, 38, 46, 56, 68, 82, 100 <- using formula
10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, 100 <- EIA series
It's not a rounding or truncation problem - the 27 value is actually 26.10, the 47 value is actually 46.42
Anyone know why the middle values are off? 😕
Formula:
R = 10* 10 ^ (n / b) ; where ^ is exponentiation, and b is the series number (12 for 10%, 24 for 5%, 96 for 1%), and n is the step progression 0-b.
Some links I found useful:
MightyOhm Blog Archive EIA Resistor Values Explained
Excel Formula Calculates Standard 1%-Resistor Values
standard resistor value table - Ekswai
Example, calculating E12 (10%) values gives:
10, 12, 15, 18, 22, 26, 32, 38, 46, 56, 68, 82, 100 <- using formula
10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, 100 <- EIA series
It's not a rounding or truncation problem - the 27 value is actually 26.10, the 47 value is actually 46.42
Anyone know why the middle values are off? 😕
Formula:
R = 10* 10 ^ (n / b) ; where ^ is exponentiation, and b is the series number (12 for 10%, 24 for 5%, 96 for 1%), and n is the step progression 0-b.
Some links I found useful:
MightyOhm Blog Archive EIA Resistor Values Explained
Excel Formula Calculates Standard 1%-Resistor Values
standard resistor value table - Ekswai
I don't think they actually follow a mathematical series. they are a convenient approximation to a mathematical series, which is why it slightly differs..
After a bit more research, it's a geometric series of "preferred numbers" derived from Renard numbers, dating back to the 1870's.
A guess is the E6 to E24 values are quirky and adjusted to keep some backward compatiblity with old E4 values. Source Otherwise I could find no reason for inconsistencies.
The math works for E48 (2%), E96 (1%) and E192 (0.5%, 0.25%, 0.1%) tolerances. i.e. using MS Excel with resistor value in cell A1:
E192 value=ROUND((10^(ROUND(192*LOG(A1),0)/192))/10^INT(LOG((10^(ROUND(192*LOG(A1),0)/192)))),2)*10^INT(LOG((10^(ROUND(192*LOG(A1),0)/192))))
E96 value =ROUND((10^(ROUND(96*LOG(A1),0)/96))/10^INT(LOG((10^(ROUND(96*LOG(A1),0)/96)))),2)*10^INT(LOG((10^(ROUND(96*LOG(A1),0)/96))))
E48 value =ROUND((10^(ROUND(48*LOG(A1),0)/48))/10^INT(LOG((10^(ROUND(48*LOG(A1),0)/48)))),2)*10^INT(LOG((10^(ROUND(48*LOG(A1),0)/48))))
It's in EIA standard RS-385 and IEC 60063, but I don't have them. If you do these calcs in S/W watch there are many different ways to round off numbers i.e. "banker's rounding"
A guess is the E6 to E24 values are quirky and adjusted to keep some backward compatiblity with old E4 values. Source Otherwise I could find no reason for inconsistencies.
The math works for E48 (2%), E96 (1%) and E192 (0.5%, 0.25%, 0.1%) tolerances. i.e. using MS Excel with resistor value in cell A1:
E192 value=ROUND((10^(ROUND(192*LOG(A1),0)/192))/10^INT(LOG((10^(ROUND(192*LOG(A1),0)/192)))),2)*10^INT(LOG((10^(ROUND(192*LOG(A1),0)/192))))
E96 value =ROUND((10^(ROUND(96*LOG(A1),0)/96))/10^INT(LOG((10^(ROUND(96*LOG(A1),0)/96)))),2)*10^INT(LOG((10^(ROUND(96*LOG(A1),0)/96))))
E48 value =ROUND((10^(ROUND(48*LOG(A1),0)/48))/10^INT(LOG((10^(ROUND(48*LOG(A1),0)/48)))),2)*10^INT(LOG((10^(ROUND(48*LOG(A1),0)/48))))
It's in EIA standard RS-385 and IEC 60063, but I don't have them. If you do these calcs in S/W watch there are many different ways to round off numbers i.e. "banker's rounding"
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