# The E-Series system of preferred numbers

#### subatomic particle

Joined May 8, 2018
71
Hello guys,
I am new here, and i am also new to the world of electrical engineering.
Currently i am learning how to read resistors value using resistor color code chart.
The term "E-Series" has been mentioned several times in my lectures, but i really don't know what is the use of it.

Can someone explain to me please? What is this E-Series system and why do we need it?

#### OBW0549

Joined Mar 2, 2015
3,566
It's pretty well explained here.

#### WBahn

Joined Mar 31, 2012
27,409
Hello guys,
I am new here, and i am also new to the world of electrical engineering.
Currently i am learning how to read resistors value using resistor color code chart.
The term "E-Series" has been mentioned several times in my lectures, but i really don't know what is the use of it.

Can someone explain to me please? What is this E-Series system and why do we need it?

In addition (or more properly in clarification) to the Wikipedia article, the notion and concept of the series is pretty easy to explain.

First, let's step back nearly a century to when manufacturing processes weren't nearly as well under control as they are today.

Let's say that your manufacturing processes are such that any component you make ends up being with 20% of the value it was supposed to be. There might be all kinds of reasons for this -- perhaps the humidity and temperature when the part is made has an effect on the final value and your ability to control them is such that the best you can do is ±20%. Perhaps it changes some with age or varies depending on the temperature, humidity, current, or whatever at the time it is being used. Whatever.

That means that if you make (let's say they're resistors) a 1000 Ω resistor, it's actual value when used might be anywhere between 800 Ω and 1200 Ω. But you mark it as a 1000 Ω resistor (its "nominal" value) with a 20% tolerance and the person that buys it understands that its actual value can be anywhere in this range, so they only use it in places where any resistance within that range is "good enough". Or, if they need something tighter (say they need something that is between 1100 Ω and 1150 Ω), then they buy a bunch of 1000 Ω resistors and "bin" them, meaning that they measure them individually and use only the ones in the range they need. If they have no use for the rest of the resistors, they can sell them to someone that deals in surplus electronics.

But 1000 Ω resistors are not the only resistors you make. What should the next larger resistor value that you make be?

Let's say that you consider making 1200 Ω resistors. This means that their actual value falls anywhere between 960 Ω and 1440 Ω. This causes a number of problems. First, it becomes quite likely that your 1200 Ω resistor is actually lower in resistance than you 1000 Ω resistor, and this can cause all kinds of problems in circuits. It also means that someone that wants an 1100 Ω resistor can bin two (or more) different nominal valued resistors, and this is a logistical headache and asking for confusion.

Let's say that, to avoid this, you consider making the next larger size 2000 Ω. These can have values that fall anywhere between 1600 Ω and 2400 Ω. But now someone needing 1400 Ω can't get one, even if they are willing to buy a bunch and bin them.

The obvious solution is to make the upper edge of the tolerance for one resistor, R1, coincide with the lower edge of the tolerance for the next larger size, R2.

(1+20%)R1 = (1-20%)R2

R2 = [(1+20%)/(1-20%)]·R1

So our ideal value for the next size up would be

R2 = (1.2/0.8) 1000 Ω = 1500 Ω.

The next sizes up would be 1.5x the size before, giving us the following sequence.

1000 Ω, 1500 Ω, 2250 Ω, 3375 Ω, 5062.5 Ω, 7593.75 Ω, 11390.625 Ω

If you consider two values in this sequence, R(n) and R(k), then they are related by

R(k) = R(n) * [(1+tol)/(1-tol)]^(k-n)

If we use a multiplicative factor, α, that gets us from one step to the next, it is currently

α = [(1+tol)/(1-tol)]

So that

R(k) = R(n) * α^(k-n)

While this gives us nice, exact breaks so that any possible resistance value (in this range) is within 20% of one of the nominal values, it's insane to label a part with eight significant figures when the tolerance is such that it barely rates two.

Also, from a logistical standpoint, it would be nice to have as nominal values resistors like 100 Ω, 1000 Ω, 10,000 Ω, 100,000 Ω and so forth -- known as "decade tiers", or factors of ten.

Looking at our sequence, we see that it takes 6 steps to go from 1000 Ω to the first value that is greater than 10,000 Ω. So we adjust our multiplicative factor to be such that it moves us by a factor of 10 in exactly six steps, meaning instead of

α = [(1+tol)/(1-tol)] = 1.5 (for 20%)

we need

10 = α^6

requiring

α = 1.4678

Using that, our sequence is now (rounding to the nearest ohm)

1000 Ω, 1468 Ω, 2154 Ω, 3162 Ω, 4642 Ω, 6813 Ω, 10,000 Ω

But we still are only justified in marking the resistors with two sig figs (and we want to use the minimum because we don't want to waste time and materials putting marks on them that don't mean anything). So we round things to two sig figs, although for reasons partly lost to history, some of the rounding is what you might expect. What we ended up with is

10, 15, 22, 33, 47, 68

These six values are the E6 series.

#### WBahn

Joined Mar 31, 2012
27,409
Something else that might be of interest to you.

You might want to sell, at a premium, resistors that are within 5% or 10% of their nominal value in addition to your 20% normal line. Does this mean that you have to have different production lines, two which have considerably higher production tolerances?

Not necessarily. If the main source of variation is the production itself (as opposed to factors that cause the value to change in the field after it's been bought), then you simply make lots of resistors on your normal line (it might only be able to hit with 50% of the value you are actually trying to make, that's fine) and then you measure each individual resistor you make. If a resistor measures 1020 Ω, then you mark it as a 1000 Ω 5% resistor. Any given resistor can be marked in most, if not all, of the series and so you get to choose which based on what your distributors need.

Today this isn't done too much, at least not on commodity parts, because the production tolerances are good enough that the added expense doesn't justify it. But this used to be very common. And, yes, the manufacturers truly would measure each and every single component coming of the line. Of course, they developed high-speed, automated ways of doing it.

But you used to be able to take a bunch of 1000 Ω 10% resistors and measure all of them and one thing you often quickly discovered was that very few of them were within about 3% of 1000 Ω. Why? Because those had been separated out and marked as 5% tolerance parts.