In the transistor amplifier lesson I introduced a new concept without talking about it too much. I kind of just shoved it in there and assumed that you'd get to know what I was talking about.
If you found it confusing or didn't have the foggiest what I was talking about, then read on.
Standardising the values allows manufacturers to make a handful of components, in bulk quantities, therefore keeping costs down.
Can you imagine the size of the hobby section in electronics shops if every component value imaginable was actually made? 1oh, 2 ohm, 3 ohm, etc or 1 and 1.1 and 1.2 and 1.3 and 1.4ohms all the way up to millions of ohms?
Instead of making every size imaginable, the manufacturers use standard values instead.
This values are spaced in the same kind of range of values as notes on a piano, (white and black).
in an Octave, there are 7 white keys and 5 black keys.
C, C#, D, D#, E, F, F#, G, G#, A, A#, B then we get back to C
Those notes are all equally spaced apart and the gap between then is called a semitone.
Standard resistor values have the same sort of spacing, the spacing between them is 10^(1/12)
(or ~1.212). (there are, just like on a piano, 12 values in a range, and the ratio of the spacing of these is equal.)
This is why it's called the E12 series (there are 12 values in the series)
This makes values that start a 1,
then (multiply by 1.2 = 1.2), x1.2 = ~1.5
Therefore the actual values are
1, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2 and 10 (the ten is the start of the next range, kinda like how that C was the start of the next scale on the piano.)
Of course this is a bit of a trouble, when we're designing circuits we often come up with values where there just isn't a standard value.
In the amplifier lab none of the values were standard! all had to have a closest fit.
However, when you look at the range of values, it's not all that bad...
Margins of error/Tolerance
If you look at the values, they are all equally spaced, with not more than 20% between the values.
The gap between 5.6 and 6.8 is 1.2Ohms, so lets hit exactly in the middle, and say that you need a 6.2Ohm resistor.
If you go for a 6.8Ohm, resistor you're 0.6Ohms over,
If you go for a 5.6Ohm resistor you're 0.6Ohms under.
In short, whichever way (up or down) you go, you're only ever going to be 10% or less out of what you want the value to actually be.
I suppose you could say that 10% is a large percentage and does makes a difference.
You would of course be right to say that.
But consider two things, firstly, your designs, are mathematical models, not measured values,
And that even the values on the data sheet, though they are measured values, they are measured from a sample, not the component that you have in front of you, -hence data sheets provide minimum, typical and maximum values, measured from a range of samples.
Whether you chose a higher or lower value depends what you're working with, if you're getting close to the absolute maximum values of current, then choosing a lower value, and possibly exceeding that absolute maximum would not be a good idea. However, if you're well within the absolute maximum, then choosing a slightly lower value of resistor isn't going to cause too much current to flow, nothing is going to fail or melt!
Also, you should remember that if you desperately need an exact non standard value, you can add resistances together.
if you need exactly 45Ohms, no more no less then instead of settling for 47 ohms, use a 12 ohm and 33 ohm resistor in series!
Also remember that on resistors there is a tolerance band.
If you're using a silver tolerance band then your components may be as much as 10% out of their marked values anyway!