Tolerance
of Thermistors
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Alpha
( )
(Temperature
Coefficient):
Alpha,
a material characteristic,
is defined as the
percentage resistance
change per degree
Centigrade. Alpha
is also referred
to as the temperature
coefficient. For
Negative Temperature
Coefficient (NTC)
Thermistors, typical
values of alpha
are in the range -3%/°C
to -6%/°C. The
temperature coefficient
is a basic concept
in thermistor calculations.
Because the resistance
of NTC thermistors is a
nonlinear function of temperature,
the alpha value of a particular
thermistor material is
also nonlinear across the
relevant temperature range,
as illustrated in graph
# 2 below.
Curve
for 30K5 Thermistor
0°C to 70°C Range
with Slope and Alpha details.
Graph
# 2
For
example, BetaTHERM’s
Standard Curve
5 thermistor
material has
an alpha of
-4.30%/°C
at 25°C,
and an alpha
of -3.42%/°C
at 70°C.
The alpha value
is a material
constant and
is independent
of the resistance
of the component
at that temperature.
Calculation
of alpha values:
The relevance of alpha
values to the Resistance
vs Temperature curve of
particular material is
illustrated in Graph
# 3. In this graph,
a tangent line is drawn
along the R-T curve at
25°C. This line represents
the gradient or "steepness" of
the curve at 25°C.
From the definition of
Alpha given above, it may
be calculated as follows
:
(Equation
# 3) Definition
of Alpha:
Where RT is the resistance
of the component at the
relevant temperature T
(°C), dR/dt is the
gradient of the Resistance
vs Temperature curve at
that temperature point,
and alpha is expressed
in units of "percentage
change per degree Centigrade".
(Note: In some texts the "100" term
is omitted from the equation,
but it is understood or
implied in the units in
which alpha values are
specified.)
Detail
from Graph #
2 showing Alpha
Slope Line of
the
30K5 Thermistor @ 25°C.
Graph
# 3
The
purpose of the
concepts that have
been introduced
and discussed so
far is to enable
some basic calculations
to be performed.
The most important
calculations required
in the thermistor
industry are those
that relate the
resistance of thermistor
components to their
temperature. An
example illustrating
typical use of
alpha value to
do this is given
next:
Example:
A thermistor made from
BetaTHERM material 3 has
a resistance of 10000 ohms
at 25°C. The alpha
value for this material
at 25°C is listed in
the catalog to be –4.39
%/°C. If the resistance
of the device in a stable
environment at ideal measurement
conditions (discussed later)
is measured as 10200 ohms,
what temperature is the
device at ?
By re-writing Equation
3 in the form:
where  R/T
is used as an approximation
for the true derivative
dR/dt , the reference
temperature is
25°C, on re-arranging,
the equation becomes:
Inserting
the numerical values
given above, the
value for T,
the temperature
difference from
25°C, is given
by:
so
that the temperature
of the thermistor
is:
(25°C - 0.456°C)
= 24.554°C
The example is applicable
for certain thermistor
resistance and temperature
calculations. In particular,
because of the approximation
used for the differential
of the R / T curve, it
is of relevance for small
percentage changes in resistance
around the temperature
value for which the particular
alpha value is quoted.
The alpha value is a very
useful parameter provided
it is used in a logical
way and that it is applied
with the constraints in
mind.
Limitations
in the use of temperature
coefficients:
The approach of using temperature
coefficient values is adequate
provided that accurate
alpha values and resistance
values are available for
a range of temperature
points for the thermistor
materials. Data is included
for Betatherm products
in the products
section of this website.
The use of such look-up
tables and substitution
in equation 3 are useful
for initial selection of
thermistors for applications.
The method is somewhat
slow and highlights the
need for a mathematical
model that can be used
to relate the resistance
and temperature of thermistors
by a single equation. The
need for such a model is
especially relevant to
allow computation of R/T
values using modern calculators,
computers or microcontrollers.
To discuss the issue further
it is instructive to look
at a typical NTC thermistor
R/T curve, as shown in
graph #1. The curve is
non-linear, and that presents
certain difficulties in
developing a useful model.
Modelling of the R/T curve
is discussed in the notes
on mathematical
modelling of thermistors
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