NTC
Thermistor Theory
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Resistance:
Thermistors
are devices that
obey Ohms Law,
which relates the
current through
a resistor to the
voltage across
it. Ohms law
is usually stated
as: V=IR,
where:
V is the
voltage across
the resistor
in units of Volts,
I is
the current
through
the resistor
in units
of Amps,
R is
the resistance
of the
resistor
in units
of Ohms.
The
word Thermistor
is derived from
the term Thermally
sensitive resistor.
The resistance
of the thermistor
depends on the
temperature of
the thermistor,
and at temperature
points in it’s
useful range, the
thermistor obeys
Ohms Law.
Thermistors exhibit a relatively
large negative change in
resistance with a change
in body temperature, typically
-3% to -6% per °C.
This sensitivity is a major
advantage of thermistors
over other electrical temperature
sensing devices.
The concept of electrical
resistivity and the material
resistivity constants that
are described in the notes
on volume
resistivity can be
used to calculate the resistance
of thermistor components.
The physical dimensions
of the thermistor and the
material resistivity at
the relevant temperature
are required. The reference
temperature is usually
taken to be 25°C. Referring
to Equation #1 and the
definition of resistivity,
the resistance (R) of the
thermistor at the reference
temperature of 25°C
is calculated from Equation
# 1 which is repeated below:
Equation #1: (Resistance
formula repeated)
Where:
R is the resistance
of the component in ohms.
 is
the material resistivity
in ohm-cm
T is the thickness
of the component (cm).
(This dimension represents
the current path through
the thermistor.).
L is
the length
of the
metalized
surface
of the
thermistor
(cm).
W is
the width
of the
metalized
surface
of the
thermistor
(cm).
While the equation represents
a common calculation in
general electronic applications,
it is a very important
one in the Thermistor industry,
in particular where the
dimensions of the component
are critical. It can be
used to determine the dimensional
options available to produce
the required thermistor.
It is very important in
the use of equation 1 to
maintain consistency of
measurement units.
Example: Calculate
the resistance
at 25°C of
a thermistor chip
made from BetaTHERM’s
Curve 3 Material.
The resistivity
of the material
is 3300 ohm-cm
(at 25°C) and
the chip dimensions
are 0.04" x
0.04" x 0.01" thick.
The required resistance
and resistivity for a given
material dictate the realistic
size of the finished product.
For instance, a thermistor
made from BetaTHERM’s
material curve # 3 can
have a practical resistance
range, at 25°C, from
2000 ohms to 100000 ohms.
Values outside this resistance
range are not practical
to produce because of the
calculated size of the
thermistor element.
The 2000 ohm thermistor
has a calculated size of
approximately (0.070" x
0.050" x 0.006" thick)
and the 100000 ohm thermistor
has a calculated size of
approximately (0.014" x
0.014" x 0.015" thick).
The sizes are feasible
to manufacture, but are
at the limits where chip
handling becomes difficult.
The discussion so far has
effectively considered
the resistance of thermistors
at a single temperature
point. The next stage in
understanding thermistor
operation is to consider
the electrical behaviour
over an extensive temperature
range.
The Resistance-Temperature
Characteristics for a common
thermistor (30K5) are displayed
in Graph 1 below over a
range from 0°C to 70°C.
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