# Tempco calcs

Fri Nov 26 19:40:59 CET 1999

```Hi All --

More musings on tempcos.

I had a chance the other day to review the theory for electrical
resistivity of metals. For pure elemental metals (Cu, Pt, W, Na, Pb,
etc.) theory shows -- and experiments confirm -- that the resistivity of
every element is described by a single universal function that has just
one parameter, which is different for each metal. It's really a
beautiful sight to see the data from 17 different metals falling exactly
on the same single theoretical curve!

At very low temperatures the resistivity follows a T^5 law. At higher
temperatures the resistivity is linear with temperature, with accurate
linearity being seen over hundreds of degrees. Ordinary room
temperatures are in the linear region of the curve for almost all
metals.

As discussed before, the ideal tempco resistor for compensating
exponential converters has an R(T) characteristic that is linear near
room temperature with this linear region extrapolating through the
origin: R_extrap(0K) = 0. For a pure metal, the linear resistance region
extrapolates to a negative resistance, R_extrap(0K)<0, because of the
T^5 regime at low temperatures. Therefore, an ideal tempco can be made
from a composite of a pure metal in series with a
temperature-independent resistance equal in magnitude to the
extrapolated resistance: R_series = -R_extrap(0K). This correction
resistor can be fairly small. As an example, for Pt the series
resistance is 8% of the resistance at T=273K (0C).

It's interesting to realize that a good tempco could be made from
copper. (The series resistance needs to be about 20% of the 273K
resistance in this case.) Unfortunately, the resistivity of copper is so
low that a large amount of very fine wire would be required. This may
not be practical: but does anyone know of a source of very fine copper
wire? What's the smallest diameter you can get?

Ian

```