I. Definition and importance of temperature coefficient

Temperature Coefficient of Resistance (TCR) is an important parameter that measures the degree of change in resistor resistance value with temperature, and is measured in ppm/°C (parts per million per degree Celsius). For a precision measurement element such as a shunt, the TCR directly determines the stability of the measurement accuracy in different temperature environments.

The TCR is calculated by the formula:

TCR = (R₂ - R₁) / R₁ / (T₂ - T₁) × 10⁶ ppm/°C

Where R₁, R₂ are the resistance values at temperature T₁, T₂ respectively.

For example, a shunt with a TCR of 50 ppm/°C will have a resistance change of 50 × 50 = 2500 ppm = 0.251 TP3T when the temperature is increased from 25°C to 75°C. This change is unacceptable for applications requiring 0.11 TP3T accuracy.

II. Factors affecting the TCR

2.1 Resistance Alloy Materials

Different alloy materials have different TCR properties:

2.2 Material ratios

The TCR can be adjusted by precisely controlling the proportions of the elements in the alloy. e.g. Changes in manganese content in manganese-copper alloys can significantly affect the TCR.

2.3 Manufacturing processes

• hot treatment (e.g. of metal): Proper annealing treatment can reduce the internal stress of the material and improve the TCR.
• cold processing: Excessive cold working increases internal stresses and worsens TCR
• Welding quality: The solder interface between the terminals and the resistive material affects the overall TCR

2.4 Structural design

The structural design of the shunt also affects the temperature distribution and TCR performance during actual operation:

• Resistive element to terminal length ratio
• Thermal Path Design
• Heat distribution uniformity

III. Measurement Methods of TCR

3.1 Two-point method

In two temperature points (such as 25 ℃ and 85 ℃) were measured resistance value, according to the formula to calculate the TCR. method is simple but can not reflect the change rule of TCR with temperature.

3.2 Multi-point approach

Resistance values are measured at multiple temperature points and R-T curves are plotted for a more complete understanding of TCR characteristics. Differences in the TCR of certain materials can be found in different temperature intervals.

3.3 Standardized test conditions

In accordance with national standards, TCR tests are usually performed under the following conditions:

• Reference temperature: 20°C or 25°C
• Test temperature range: -40°C to +85°C or wider
• Constant temperature time: long enough to reach thermal equilibrium
• Measuring current: small enough to avoid self-heating effects

IV. Analysis of the impact of TCR on system accuracy

4.1 Example of error calculation

Assume an energy storage BMS system:

• Shunt nominal resistance value: 100μΩ @25℃
• TCR: 50ppm/°C
• Operating temperature range: -20°C to +60°C

Maximum temperature change: 60°C - (-20°C) = 80°C
Maximum resistance change: 50 × 80 = 4000ppm = 0.4%

If the system requires a total accuracy of 0.51 TP3T, the TCR alone takes up an error budget of 0.41 TP3T, leaving little room for other error sources.

4.2 Temperature gradient effects

In practice, the shunt itself heats up as a result of the current passing through it, causing the resistive element to be warmer than the ambient temperature. This self-heating effect exacerbates the effects of the TCR.

4.3 Dynamic temperature changes

Under operating conditions such as charge/discharge switching, the temperature of the shunt changes rapidly, which can lead to dynamic errors in the measured value if the TCR is large.

V. Low TCR shunt selection strategy

5.1 Define accuracy requirements

Inverse TCR requirements based on system accuracy requirements and temperature range:

TCR (max) = allowable error / temperature range × 10⁶.

Example: Allow 0.1% error, temperature range 50°C
TCR (max) = 0.1% / 50 × 10⁶ = 20ppm/°C

5.2 Material selection

• General Applications (TCR)<100ppm>
• Medium Precision (TCR)<50ppm>
• High Precision (TCR)<20ppm>
• Measurement level (TCR)<5ppm>

5.3 Cost considerations

Low TCR means higher material costs and manufacturing process requirements. A balance needs to be struck between performance and cost to avoid over-design.

5.4 Alternative: software temperature compensation

For cost-sensitive applications, a shunt with a slightly higher TCR can be selected and temperature compensated by a software algorithm:

1. Installation of a temperature sensor (e.g. NTC) near the shunt
2. Create a TCR correction table or formula
3. Real-time correction of measured values

This approach effectively reduces the impact of TCR, but increases system complexity.

VI. Practical application cases

6.1 Electric Vehicle BMS

BMS current detection requirements for an OEM:

• Accuracy: ±0.5%
• Temperature range: -40°C to +85°C
• Solution: Select TCR<30ppm>

6.2 Metering of energy storage plants

Energy metering requirements for an energy storage plant:

• Accuracy: ±0.2%
• Temperature range: 0°C to +55°C
• Solution: Select TCR<15ppm>

VII. Summary

Temperature coefficient is one of the most important performance indicators of shunt, which directly affects the accuracy and stability of current measurement. When selecting a product, it is necessary to consider the temperature range of the application scenario, the accuracy requirements and the cost budget, and choose a product with the appropriate TCR rating. For demanding applications, hardware selection and software compensation strategies can be combined to optimize system costs while meeting performance requirements.