Temperature Coefficient of Resistance

Chapter 1 - Resistor Fundamentals

Resistance Changes with Temperature

The temperature coefficient of resistance, or TCR, is one of the most important parameters that characterize a resistor performance. The TCR defines the change in resistance as a function of the ambient temperature. The common way to express the TCR is in either ppm/°C (or ppm/°K), which stands for parts per million per degree Celsius (or Kelvin). The temperature coefficient of resistance is calculated as follows:

$$TCR = (\frac{R_2 - R_1}{R_1(T_2 - T_1)})·10^{-6} $$

Where TCR is in ppm/°C or ppm/°K, R1 is in ohms at room temperature, R2 is resistance at operating temperature in ohms, T1 is the room temperature and T2 is the operating temperature (both in °C or °K). Often, instead of TCR, α is used.

Graph showing average TCR for resistorsAverage TCR ΔR/R in ppm for a temperature range from -55 to 25˚C and from 25 to 125˚C

 

Positive or Negative Temperature Coefficient of Resistance?

Resistors are available with a TCR that is negative, positive, or stable over a certain temperature range. Choosing the right resistor could prevent the need for temperature compensation. In some applications it is desired to have a large TCR, for example to measure temperature. Resistors for these applications are called thermistors, and can have a positive temperature coefficient (PTC) or a negative temperature coefficient (NTC).

Measurement Methods for the TCR

The temperature coefficient of resistance for a resistor is determined by measuring the resistances values over an appropriate temperature range. The TCR is calculated as the average slope of the resistance value over this interval. This is accurate for linear relations, since the TCR is constant at every temperature. However, many materials have a nonlinear coefficient. For example, Nichrome, a popular alloy for resistors, has a nonlinear relation between temperature and TCR. Because the TCR is calculated as average slope, it is therefore very important to specify the TCR as well as the temperature interval. The way to measure TCR is standardized in MIL-STD-202 Method 304. With this method, TCR is calculated for the range between -55°C and 25°C and between 25°C and 125°C. Because the highest measured value is defined as TCR, this method often results in over specifying a resistor for less demanding applications.

In the chart below the temperature coefficient of resistance is given for a wide variety of materials. Note that the exact value depends on the purity of the material as well as the temperature.

 

Material

 

 

TCR /°C

 

 

Silicon

 

 

-0.075

 

 

Germanium

 

 

-0.048

 

 

Carbon (amorphous)

 

 

-0.0005

 

 

Manganin

 

 

0.000002

 

 

Constantan

 

 

0.000008

 

 

Nichrome

 

 

0.0004

 

 

Mercury

 

 

0.0009

 

 

Gold

 

 

0.0034

 

 

Zinc

 

 

0.0037

 

 

Copper

 

 

0.0039

 

 

Aluminum

 

 

0.0039

 

 

Lead

 

 

0.0039

 

 

Platinum

 

 

0.00392

 

 

Calcium

 

 

0.0041

 

 

Tungsten

 

 

0.0045

 

 

Tin

 

 

0.0045

 

 

Iron

 

 

0.005

 

 

Nickel

 

 

0.006

 

 

Lithium

 

 

0.006

 

Values for TCR depend on purity and temperature.