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indicated or that other measures may not be required. Specifications are typical and may not apply to all applications.
1
NTC Thermistors
General Characteristics
1 – INTRODUCTION
NTC thermistors are thermally sensitive resistors made from
a mixture of Mn, Ni, Co, Cu, Fe oxides. Sintered ceramic
bodies of various sizes can be obtained. Strict conditions
of mixing, pressing, sintering and metallization ensure an
excellent batch-to-batch product characteristics.
This semi-conducting material reacts as an NTC resistor,
whose resistance decreases with increasing temperature.
This Negative Temperature Coefficient effect can result from
an external change of the ambient temperature or an inter-
nal heating due to the Joule effect of a current flowing
through the thermistor.
By varying the composition and the size of the thermistors,
a wide range of resistance values (0.1Ω to 1MΩ) and tem-
perature coefficients (-2 to -6% per °C) can be achieved.
RoHS (Restriction of Hazardous Substances - European
Union directive 2002/95/EC).
ELV (End of Life-Vehicle - European Union directive
2000/53/EC).
All Thermistor Products have been fully RoHS/ELV since
before 2006.
Chip Thermistor NB RoHS/ELV Status: external Plating
100% smooth semi-bright Sn as standard SnPb Termination
available on request.
2.1.2. Temperature -
Resistance characteristics R (T)
This is the relation between the zero power resistance and
the temperature. It can be determined by experimental mea-
surements and may be described by the ratios R (T) /R
(25°C) where:
R (T)
is the resistance at any temperature T
R (25°C) is the resistance at 25°C.
These ratios are displayed on pages 29 to 33.
2.1.3. Temperature coefficient (α)
The temperature coefficient ( ) which is the slope of the
curve at a given point is defined by:
=
100
dR
•
R
dT
and expressed in % per °C.
2.1.4. Sensitivity index (B)
The equation R = A exp (B/T) may be used as a rough
approximation of the characteristic R (T).
B is called the sensitivity index or constant of the material
used.
To calculate the B value, it is necessary to know the resis-
tances R
1
and R
2
of the thermistor at the temperatures
T
1
and T
2
.
1 1
The equation: R
1
= R
2
exp B T - T
1
2
R
1
1
leads to:
B (K) =
• n
1-1
R
2
T T
2
1
Conventionally, B will be most often calculated for tempe-
ratures T
1
= 25°C and T
2
= 85°C (298.16 K and 358.16 K).
In fact, as the equation R = A exp (B/T) is an approximation,
the value of B depends on the temperatures T
1
and T
2
by
which it is calculated.
For example, from the R (T) characteristic of material M
(values given on page 29), it can be calculated:
B (25 – 85) = 3950
B (0 – 60) = 3901
B (50 – 110) = 3983
When using the equation R = A exp (B/T) for this material,
the error can vary by as much as 9% at 25°C, 0.6% at 55°C
and 1.6% at 125°C.
Using the same equation, it is possible to relate the values of
the index B and the coefficient
α:
(
)
2 – MAIN CHARACTERISTICS
2.1 CHARACTERISTICS WITH NO DISSIPATION
2.1.1. Nominal Resistance (Rn)
The nominal resistance of an NTC thermistor is generally
given at 25°C. It has to be measured at near zero power
so that the resultant heating only produces a negligible
measurement error.
The following table gives the maximum advised measure-
ment voltage as a function of resistance values and thermal
dissipation factors.
This voltage is such that the heating effect generated by the
measurement current only causes a resistance change of
1%
ΔRn/Rn.
Ranges of
values
(Ω)
R 10
10 < R 100
100 < R 1,000
1,000 < R 10,000
10,000 < R 100,000
R < 100,000
(
)
( )
Maximum measuring voltage
(V)
δ
= 2 mW/°C
δ
= 5 mW/°C
δ
= 10 mW/°C
δ
= 20 mW/°C
0.13
0.38
1.1
3.2
9.7
0.18
0.53
1.5
4.6
14.5
0.10
0.24
0.24
2.0
=
1
-B
1
dR =
•
• A exp (B/T) • T
2
A exp (B/T)
R
dT
B
= – T
2
expressed in %/°C
0.25
0.73
2.1
6.4
thus
2
NTC Thermistors
General Characteristics
2.1.5. Further approximation of R (T) curve
The description of the characteristic R (T) can be improved
by using a greater number of experimental points, and by
using the equation:
1 = A + B ( n R) + C ( n R)
3
T
The parameters A, B and C are determined by solving the
set of equations obtained by using the measured resis-
tances at three temperatures.
The solution of the above equation gives the resistance at
any temperature:
2
n R (T) = 1 3 - 27 A- 1/T + 3 3 27 A- 1/T + 4 B
3
C
C
C
2
2
Thus, the tolerance on the resistance ( R
2
/R
2
) at a temper-
ature T
2
is the sum of two contributions as illustrated on
Figure 1:
– the tolerance R
1
/R
1
at a temperature T
1
used as a
reference.
– an additional contribution due to the dispersion on
the characteristic R (T) which may be called
“Manufacturing tolerance” (Tf).
Graph with B
RΩ
Graph with B
±
ΔB
[
(
)
( (
2
) ())
R
25
3
- 3 + 27 A- 1/T + 3
C
2
2
(
)
3
B
1/T
(
27
(
A-C
)
+ 4
(
C
) )
]
3
}
(ΔR)
25°C
The precision of this description is typically 0.2°C for the
range –50 to +150°C (A, B, C being determined with exper-
imental values at –20, +50 and 120°C) or even better if this
temperature range is reduced. The ratios R(T)/R(25°C) for
each of the different materials shown on pages 29 to 33
have been calculated using the above method.
}
(ΔR)
+
}
T
F
25°C
}
= (ΔR)
T
25°C
T
Temperature (°C)
2.1.6. Resistance tolerance and temperature
precision
An important characteristic of a thermistor is the tolerance
on the resistance value at a given temperature.
This uncertainty on the resistance (DR/R) may be related to
the corresponding uncertainty on the temperature (DT),
using the relationship:
R 1
T = 100 • R •
Example: consider the thermistor ND06M00152J —
• R (25°C) = 1500 ohms
• Made from M material
• R (T) characteristic shown on page 23 gives:
= - 4.4%/°C at 25°C
• Tolerance R/R = ±5% is equivalent to:
T = 5%/4.4%/°C = ±1.14°C
Figure 1
Differentiating the equation R = A exp (B/T), the two contri-
butions on the tolerance at T can also be written:
R
2
= R
1
+
⎪
1 - 1
⎪
• B
T T
2
1
R
1
R
2
The T(f) values given with the resistance – temperature
characteristics on pages 29 to 33 are based on a computer
simulation using this equation and experimental values.
2.1.8. Designing the resistance tolerances
Using the fact that the coefficient decreases with temper-
ature (α = –B/T
2
), it is generally useful to define the closest
tolerance of the thermistor at the maximum value of the
temperature range where an accuracy in °C is required.
For example, let us compare the two designs 1 and 2
hereafter:
T
(°C)
0
25
55
85
100
2.1.7. Resistance tolerance at any temperature
Any material used for NTC manufacturing always displays a
dispersion for the R (T) characteristic.
This dispersion depends on the type of material used
and has been especially reduced for our accuracy series
thermistors.
R
(Ω)
3275
1000
300
109
69.4
α
(%/°C)
-5.2
-4.4
-3.7
-3.1
-2.9
Design 1
R/R(%)
3.5
3.0
3.5
4.1
4.5
Design 2
R/R(%)
5.0
4.5
4.0
3.4
3.0
T(°C)
0.7
0.7
1.0
1.3
1.6
T(°C)
1.0
1.1
1.1
1.1
1.0
Only the Design 2 is able to meet the requirement
ΔT
from 25°C to 100°C.
1°C
3
NTC Thermistors
General Characteristics
2.1.9. Shaping of the R (T) characteristic
By the use of a resistor network, it is possible to modify the
R (T) characteristic of a thermistor so that it matches the
required form, for example a linear response over a restrict-
ed temperature range.
A single fixed resistor Rp placed in parallel with a thermistor
gives a S–shape resistance–temperature curve (see Figure 2)
which is substantially more linear at the temperature range
around the inflexion point (Ro, To).
R
(kΩ)
R
TO
R
p
2.2 CHARACTERISTICS WITH ENERGY
DISSIPATION
When a current is flowing through an NTC thermistor, the
power due to the Joule effect raises the temperature of the
NTC above ambient.
The thermistor reaches a state of equilibrium when the
power supplied becomes equal to the power dissipated in
the environment.
The thermal behavior of the thermistor is mainly dependent
on the size, shape and mounting conditions.
Several parameters have been defined to characterize these
properties:
R
p
2.2.1. Heat capacity (H)
The heat capacity is the amount of heat required to change
the temperature of the thermistor by 1°C and is expressed in
J/°C.
2.2.2. Dissipation factor ( )
R
O
This is the ratio between the variation in dissipated power
and the variation of temperature of the NTC. It is expressed
in mW/°C and may be measured as:
U.I
=
85 – 25
T
O
T (°C)
Figure 2 – Linearization of a thermistor
where U.I is the power necessary to raise to 85°C the tem-
perature of a thermistor maintained in still air at 25°C.
2.2.3. Maximum permissible temperature (T max)
It can be calculated that better linearization is obtained when
the fixed resistor value and the mid-range temperature are
related by the formula:
B – To
Rp = R x
To
B+ 2To
For example, with a thermistor ND03N00103J —
R
25°C
= 10kΩ, B = 4080 K
good linearization is obtained with a resistor in parallel where
the value is:
4080 - 298
Rp = 10,000 Ω x
= 8088 Ω
4080 + (2 x 298)
This is the maximum ambient temperature at which the ther-
mistor may be operated with zero dissipation. Above this
temperature, the stability of the resistance and the leads
attachment can no longer be guaranteed.
2.2.4. Maximum permissible power at 25°C (Pmax)
This is the power required by a thermistor maintained in still
air at 25°C to reach the maximum temperature for which it is
specified.
For higher ambient temperatures, the maximum permissible
power is generally derated according to the Figure 3 here-
after and TL = Tmax – 10°C.
2.1.10. Demonstration of the R (T) parameters
calculation
To help our customers when designing thermistors for
temperature measurement or temperature compensation,
software developed by our engineering department is avail-
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