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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