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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