Odp: [sdiy] really basic question .. tolerance

[Neil Johnson]

Tim,

> Tc = (Tc1*R2 + Tc2*R1 + (R1+R2)*Tc1*Tc2*temp)/(R1 + R1*Tc1*temp + R2 +
> R2*Tc2*temp)

Agreed.  I've been working through it as well, and arrived at the same
conclusion, if in a slightly different format:

Tc = R1.Tc2.(1 + Tc1.t) + R2.Tc1.(1 + Tc2.t)
     ---------------------------------------
         R1.(1 + Tc1.t) + R2.(1 + Tc2.t)

where t = temperature

Real nasty that the temperature coefficient depends on the temperature
itself :-(  Folding this into the equation to get the actual resistance:

	Rp(t) = Rp(0).(1 + Tcp.t)

shows that we have a nasty quadratic in t...yeuch!!!

 Rp(t) = actual parallel resistance at temperature 't'
 Rp(0) = ideal parallel resistance at 0 deg.C
 Tcp   = temp. coeff of parallel network, from above
 t     = temperature

I won't expand it out, but I think its obvious we're going to get terms in
t^2.

Nasty.

I think I'll stick with series combinations!!

BTW, interesting discussion on resistor tolerances earlier.  Did we come
to the (correct) conclusion that tolerance is not some statistical 95% or
whatever sampling, but the allowed range that a resistor can be advertised
as?

When they come out of the oven, the resistors are not marked---they pass
through a fast sorting machine that measures each one and puts them into
appropriate bins for subsequent painting and bandoliering.  If you look at
the standard resistor ranges (E12, E24, etc) you can see that they nicely
fit together, with minimal range overlap (accounting for easy values).

E.g. the E6 range (+/- 20%):

	Value	Range

		80
	100 ----|
		120

		120
	150 ----|
		180

		176
	220 ----|
		264

		264
	330 ----|
		396

		376
	470 ----|
		564

		564
	680 ----|
		816

As you can see, the ranges do overlap in some places (e.g. 330 overlaps a
bit with 470) but in most cases they don't.  Same for the other series:
	E12 (10%)
	E24 (5%)
	E48 (2%)
	E96 (1%)

Which is why it is not that expensive to have custom valued resistors
made---all they do at the factory is program one of the sorting machines
to select the value you've asked for at the tolerance you've asked for
(of course, they charge you for the privilege :-)

Cheers,
Neil

--
Neil Johnson :: Computer Laboratory :: University of Cambridge ::
http://www.njohnson.co.uk          http://www.cl.cam.ac.uk/~nej22
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