Contents
1. What is TCR?
Temperature Coefficient of Resistance (TCR) quantifies how much a resistor's value changes with temperature. It is expressed in parts per million per degree Celsius (ppm/°C) and is defined as:
Where R₁ is the resistance at the reference temperature T₁ (typically 25°C) and R₂ is the resistance at the test temperature T₂.
A resistor with a TCR of 50 ppm/°C will change its resistance by 0.005% for every 1°C of temperature change. Over an 80°C range (e.g. –40°C to +40°C from 25°C), this amounts to a 0.4% shift — which may be acceptable for some applications but can dominate the error budget in precision designs.
Positive and Negative TCR
Most metal film and thick film resistors have a positive TCR — resistance increases with temperature. Wirewound resistors using certain alloys can have near-zero or slightly negative TCR. The datasheet specification typically gives a magnitude, with the sign noted separately. For current sense applications, the sign matters less than the magnitude, since both directions shift the measured current reading.
2. Calculating the TCR Error
The resistance shift due to temperature is:
The percentage error in a current measurement (assuming voltage-mode sensing with a fixed reference voltage) is equal to ΔR/R₀:
Worked Example
Example: Battery current monitor in an EV charger
| Sense resistor | 5 mΩ, 50 ppm/°C |
| Calibration temperature | 25°C |
| Operating temperature range | –20°C to +85°C |
| Maximum ΔT from calibration | 60°C (at +85°C) |
| TCR error at worst case | 50 × 60 × 10⁻⁴ = 0.30% |
| Initial tolerance | ±1% |
| Worst-case resistance error | ±1.30% |
If the system target is ±2% current accuracy, this budget is achievable. If ±0.5% is required, a lower TCR (≤15 ppm/°C) and tighter tolerance (≤0.5%) part is needed.
3. Self-Heating: The Hidden TCR Multiplier
When current flows through a sense resistor, it dissipates power as heat: P = I² × R. This self-heating raises the component's temperature above ambient, causing additional TCR-driven resistance shift that is not accounted for by the ambient temperature range alone.
Estimating Self-Heating Temperature Rise
Where θJA is the thermal resistance from component to ambient (see the datasheet; typical values are 50–200 °C/W for chip resistors depending on PCB copper area).
The effective temperature at which to evaluate TCR error is:
Reducing Self-Heating
- Use a larger package — a 2512 typically has 3–5× lower θJA than a 0402
- Extend the copper land patterns to spread heat into the PCB
- Use a lower resistance value (accepting a lower sense voltage) to reduce P = I²R
- Derate the resistor — operate it at 50% of rated power rather than 100%
4. Moisture and Long-Term Stability
Standard thick film and thin film resistors are susceptible to moisture absorption, which shifts the resistance over time. In humid environments or outdoor equipment, this drift can exceed the TCR-induced shift over the product lifetime.
The RNCS series from Stackpole addresses this with a moisture-resistant coating applied during manufacture. The coating prevents moisture ingress into the resistive element, maintaining long-term resistance stability even in high-humidity environments (such as automotive underhood or industrial outdoor applications).
5. Building an Error Budget
A complete accuracy analysis for a precision resistor in a measurement circuit should include:
| Error Source | Typical Range | Notes |
|---|---|---|
| Initial tolerance | ±0.1% to ±5% | Fixed at manufacture; can be reduced by purchasing tighter-spec parts |
| TCR (ambient temperature) | 0.05% to 1%+ | Depends on TCR and operating range; see formula above |
| Self-heating TCR | 0.05% to 0.5% | Power dissipation × θJA × TCR |
| Moisture drift | 0.01% to 0.5% | Use moisture-resistant parts (RNCS) to minimise |
| Ageing / long-term drift | 0.1% to 0.5% | Over product lifetime; worst for thick film |
| Mechanical stress (PCB flexure) | 0.01% to 0.1% | Thick film more susceptible than metal alloy |
Add these contributions in quadrature (RSS) for a statistical worst-case, or simply sum them for a worst-case absolute bound.
6. Selecting the Right TCR
| Application | Accuracy Target | Max TCR (ppm/°C) | Recommended Series |
|---|---|---|---|
| General purpose / consumer | ±5% | <200 | RMCF |
| Industrial measurement | ±1% | <75 | CSR, CSRT |
| Automotive (body/chassis) | ±0.5% | <50 | CSS, RNCS |
| EV/HEV current sense | ±0.3% | <25 | CSS, CSSH |
| High-precision instrumentation | ±0.1% | <15 | CSRF (foil), CSS (15 ppm) |