Basic Characteristics | Basic Knowledge of NTC Thermistor

Resistance – Temperature Characteristics (R-T Char.)

The resistance value of NTC thermistor is measured with a current that has a sufficiently small amount of self-heating (heat generation due to applied current). It is recommended to use maximum operating current as a guideline.
Also, resistance of thermistors must always be expressed in pairs with temperature.

The characteristic curve is expressed by the following formula.

R1 = R0 exp (B (1T1 − 1T0) )

R0, R1: Resistance at temperature T0, T1
T0, T1: Absolute Temperature
B: B-Constant

Figure 1 : R-T characteristics of NTC thermistor

B-Constant

B-constant is a unique value that characterizes an NTC thermistor. Two points are always required for the regulation of B-constant. B-constant describes the slope of the two points.
If the two points to be selected are different, B-constant will be different, so please be careful when making comparisons. (See Figure 2)

R1 = R0 exp (B (1T1 − 1T0) )

R1, R0: Resistance at temperature T1, T0
T1, T0: Absolute Temperature
B: B-Constant

Transforming this formula
(Refer to resistance value-temperature characteristics)

B = ln (R1R0) / (1T1 − 1T0) → ⊿R⊿T

It represents the slope between two points.

*Murata defines it at 25°C and 50°C. It is written as B (25/50).

Figure 2 : Different B-constants for two point selections

Expressing this formula accurately, 1/T (T is absolute temperature) and resistance are logarithmically proportional, which is shown in the graph in Figure 3. You can see that it is almost straight.

Figure 3 : Temperature characteristics with horizontal axis as 1/T

Voltage-Current Characteristics (V-I Char.)

The V-I characteristics of NTC thermistors are shown in Figure 4.

As the current value is gradually increased, in the small current area, the voltage also gradually increases as the ohmic contact. Self-heating due to current is dissipated from the surface of the thermistor, and the temperature does not rise. However, when the amount of heat generated increases, the temperature of NTC thermistor body rises and the resistance value decreases. In this area, the proportional relationship between current and voltage no longer holds.

Normally, NTC thermistor is used in an area where this self-heating is suppressed as much as possible. As a guideline, it is recommended that the maximum operating current or less be used.

Use in the area beyond the voltage peak can result in a thermal runaway area where heat generation and resistance decrease occur repeatedly. Thermal runaway causes the thermistor to become red hot and may be damaged, so please do not use it.

Figure 4 : V-I characteristics of NTC thermistor

Resistance Temperature Coefficient (α)

The coefficient that expresses the rate of change of the resistance value of NTC thermistor per 1°C is called the temperature coefficient of thermistor. And it is calculated using the following formula.

α = 1R・dRdT

R = R0 exp (B (1T − 1T0) )

R、R0: Resistance at temperature T, T0
T, T0: Absolute Temperature
B: B-Constant

Ex) Around 50°C with a B constant of 3380K

α = − 3380(273.15 + 50)² × 100 [%/°C] ＝ −3.2 [%/°C]

From the above, the temperature coefficient of resistance is as follows.

α = − BT² × 100 [%/°C]

Table 1 : Temperature coefficient of metal

Metal	Temp. coefficient [%/°C]
Platinum	0.39
Copper	0.43
Nickel	0.67
Cobalt	0.60
Iron (Pure Iron)	0.66

Thermal Dissipation Constant (δ)

When thermistor consumes power P (mw) at ambient temperature T1 and the temperature of thermistor becomes T2, the following formula holds.

P = δ（T2 − T1）

δ is called the thermal dissipation constant (mW/°C). Transforming the above formula:

δ = P (T2 − T1)

The thermal dissipation constant δ is the power required to raise the temperature by 1°C due to self-heating. The thermal dissipation constant δ is determined by the balance between “self-heating due to power consumption” and “heat dissipation”, so it varies greatly depending on the usage environment. Murata specifies the thermal dissipation constant for the element itself.

Figure 5 : State of heat dissipation of chip NTC thermistor

Thermal Time Constant (τ)

Thermal time constant (τ) is the time required for Thermistor held at temperature T0 to reach the target temperature T1 when suddenly changed to ambient temperature T1. Usually, it is the time to reach 63.2% of the temperature difference between T0 and T1.

When Thermistor kept at a certain temperature (T0) is exposed to another temperature (T1), the temperature changes exponentially, and the temperature (T) at the elapsed time (t) is , which can be expressed as

T = (T1 − T0) (1 − exp (−t/τ) ) + T0

if t = τ …

T = (T1 − T0) (1−e^-1) + T0

T − T0T1 − T0 ＝1 − e^-1 ＝ 0.632

Therefore, τ is specified as the time to reach 63.2% of the temperature difference.

Figure 6 : Thermal time constant of NTC thermistors

Table 2 : Thermal time constant and temperature change rate

Time	Temp. Change
τ	63.2%
2τ	86.5%
3τ	95.0%
6τ	99.8%
7τ	99.9%

Maximum Voltage (V max)

This is the maximum voltage that can be applied directly to thermistor. If a voltage higher than the maximum voltage is applied, there is a possibility of destruction or deterioration of characteristics.

In addition, the temperature of the element rises due to self-heating. Be careful that the temperature rise does not exceed the maximum operating temperature.

Figure 7 : Maximum voltage derating of NCU15 type

Maximum Operating Current (Iop), Maximum Operating Voltage (Vop)

Murata defines the maximum operating current / maximum operating voltage as the current and voltage at which self-heating is 0.1°C when applied. This is a proposal for utilizing the performance of thermistor to detect temperature more accurately.

Therefore, using thermistor beyond this current or voltage does not immediately lead to destruction or characteristic deterioration of thermistor. However, please be aware that self-heating increases and causes detection temperature errors.

Figure 8 : Change in maximum operating current / voltage due to heat dissipation difference

How Murata calculate maximum operating current

The thermal dissipation constant (1mW/°C) specified for the element itself is used to calculate the maximum operating current. The thermal dissipation constant indicates the degree of heat dissipation, but the heat dissipation state varies greatly depending on the usage environment. It can be said that the specification for element itself is a specification that excludes fluctuations due to the usage environment.
There are various usage environments, such as Substrate material, Thickness, Structure, Land size, Mounting of heat sink, and Resin coating. Most of them are factors in the direction of increasing heat dissipation.
Based on our experience, it is estimated that the thermal dissipation constant will be about 3 to 4 times higher that of element itself in actual use. If when it is 3.5 times, the maximum operating current becomes the red line at that time. It is 1.9 times (√3.5 times) compared to based 1mW/°C.

Zero load Resistance

It is a resistance value measured with a current (voltage) that can ignore self-heating. It is recommended to use the maximum operating current as a guideline.