Temperature Coefficient of Resistance (TCR)
The resistance of most resistors changes slightly as their temperature changes. The Temperature Coefficient of Resistance (TCR) describes how much the resistance changes for every degree Celsius (°C) change in temperature. TCR is especially important in precision electronics, measurement instruments, laboratory equipment and high-quality analogue circuits where stable resistance values are essential.
What Is TCR?
The Temperature Coefficient of Resistance is a specification that indicates how much a resistor's value changes with temperature.
TCR is normally expressed in parts per million per degree Celsius (ppm/°C).
The smaller the TCR value, the more stable the resistor remains as the temperature changes.
Understanding ppm/°C
A value of 100 ppm/°C means the resistor changes by 100 parts per million of its nominal resistance for every 1°C change in temperature.
Lower values such as 5 ppm/°C or 10 ppm/°C indicate much better temperature stability than values of 100 ppm/°C or 300 ppm/°C.
Typical TCR Values
| Resistor Type | Typical TCR |
|---|---|
| Carbon Composition | ±500 to ±1500 ppm/°C |
| Carbon Film | ±200 to ±500 ppm/°C |
| Metal Oxide | ±100 to ±350 ppm/°C |
| Metal Film | ±5 to ±100 ppm/°C |
| Precision Thin Film | ±1 to ±10 ppm/°C |
| Wirewound | ±5 to ±50 ppm/°C |
Calculating Resistance Change
The approximate change in resistance can be calculated using the following relationship:
ΔR = R × (TCR ÷ 1,000,000) × ΔT
| Symbol | Meaning |
|---|---|
| ΔR | Change in resistance (Ω) |
| R | Nominal resistance (Ω) |
| TCR | Temperature coefficient (ppm/°C) |
| ΔT | Temperature change (°C) |
Worked Example 1
A 10 kΩ resistor has a TCR of 100 ppm/°C. The temperature rises by 20°C.
ΔR = 10,000 × (100 ÷ 1,000,000) × 20 ΔR = 20 Ω
The resistance becomes approximately:
10,000 Ω + 20 Ω = 10,020 Ω
Worked Example 2
A 1 kΩ precision resistor has a TCR of 10 ppm/°C. The temperature increases by 50°C.
ΔR = 1,000 × (10 ÷ 1,000,000) × 50 ΔR = 0.5 Ω
The resistance changes to approximately:
1,000.5 Ω
Why TCR Matters
| Application | Recommended TCR |
|---|---|
| LED Circuits | 100–500 ppm/°C |
| Power Supplies | 50–200 ppm/°C |
| Audio Amplifiers | 25–100 ppm/°C |
| Voltage References | 10–25 ppm/°C |
| Precision Instruments | 1–10 ppm/°C |
| Calibration Equipment | 1–5 ppm/°C |
Factors Affecting Resistance
- Ambient temperature.
- Self-heating caused by power dissipation.
- Resistor construction material.
- Ageing.
- Humidity.
- Mechanical stress.
Tolerance vs TCR
| Tolerance | Temperature Coefficient (TCR) |
|---|---|
| Manufacturing accuracy. | Resistance change caused by temperature. |
| Expressed as a percentage. | Expressed in ppm/°C. |
| Measured at manufacture. | Applies throughout the operating temperature range. |
| Does not change with temperature. | Determines how resistance varies as temperature changes. |
Applications Requiring Low TCR
- Digital multimeters.
- Oscilloscopes.
- Precision voltage references.
- Medical equipment.
- Sensor conditioning circuits.
- Laboratory power supplies.
- Audio preamplifiers.
- Industrial instrumentation.
- Calibration standards.
- Aerospace electronics.
Key Points
- TCR describes how resistance changes with temperature.
- It is measured in ppm/°C.
- Lower TCR values provide better temperature stability.
- Precision resistors typically have very low TCR values.
- Both tolerance and TCR should be considered when selecting resistors for precision circuits.