1995 Mar 31 2
Philips Components
NTC Thermistors Introduction to NTCs
GENERAL
Definition and composition
Negative Temperature Coefficient thermistors (NTCs) are
resistive components, of which the resistance decreases
as temperature increases. They are made from
polycrystalline semiconductors, the composition of which
is a mixture of chromium (Cr), manganese (Mn), iron (Fe),
cobalt (Co) and nickel (Ni).
Manufacture
The manufacturing process is comparable to that of
ceramics. After intensive mixing and the addition of a
plastic binder, the mass is shaped into the required form,
e.g. pressing (discs), and fired at a temperature high
enough to sinter the constituent oxide. New technologies
have led to the sawing of isostatic pressed wafers, the
compositions of which are very stable, with as a result,
high accuracy and high reproducibility.
Electrical contacts are then added by burning them in with
silver paste or by other methods, such as evaporation.
Finally, leads (isolated or not) are fitted. Different
encapsulations are possible, depending on the size of the
ceramic and the application of the component.
Miniature NTC thermistors are made by placing a bead of
oxide paste between two parallel platinum alloy wires and
then drying and sintering. The platinum alloy wires are
60 µm in diameter and spaced 0.25 mm apart. During
sintering, the bead shrinks onto the wires to make a solid
and reliable contact. Miniature NTC thermistors are
usually mounted in glass to protect them against
aggressive gases and fluids.
Relationship of resistance with temperature
The conductivity (σ) of the material is its capacity to drive
a current when a voltage is applied to it. As the current is
driven by carriers that are free to move (i.e. which are not
bound to atoms), then it follows that the conductivity will be
proportional to the number of carriers (n) that are free and
also to the mobility (µ) that those carriers can acquire
under the influence of electrical fields.
Thus:
where e is the unit of electrical charge stored by each
carrier.
Both n and µ are functions of temperature. For µ, the
dependency on temperature is related to the interactions
of a carrier with other carriers and with the total net amount
of vibrating atoms, the vibration varying with temperature.
σne×µ×=
It can be shown that:
For n, the dependency on temperature can be explained
as follows: electrons are bound to atoms by certain
energies. As one gives the electron an energy equal to, or
greater than, the binding energy (e.g. by raising its
temperature), there is a probability that the electron will
become free to move. As for many semiconductors, this
probability has the form of the well-known
Maxwell-Boltzmann distribution. Thus:
The total temperature dependency of the conductivity is:
In practice, the exponential factor is the most important.
Remembering that resistivity is the inverse of conductivity,
the following can be derived:
where
or
where A and B are parameters depending on each
component (resistivity and shape).
Shape of an NTC curve and determination of B-value
In Fig.1, the resistance is plotted as a function of the
inverse of the temperature. Even in semi-logarithmic
scale, it can be seen that this curve is not a straight line.
This is due to the fact that A and B are not perfectly
constant with temperature. However, over a wide range of
temperatures, it may be assumed that these parameters
are constant. If this range is defined between T1 and T2,
and it is assumed that the curve for this range could be
approximated with a straight line, the slope of which will be
B, this last value between T1 and T2 can be found as
follows:
The resistance value is measured at T1 and T2:
and
µTc–e×÷ q2kT⁄–
ne÷q
1kT⁄–
σTc–e×÷ q1q2
+()kT⁄–
RAe
BT⁄
×=
Bq
1q
2
+=
log R A B
T
----
+=
R1Ae
BT
1
⁄
×=
R
2Ae
BT
2
⁄
×=