Engineering Guide
Resistive Temperature Sensing with NTC Thermistors and RTDs
Turn resistance into defensible temperature data by choosing the right sensor model, limiting measurement power, controlling wiring error, and budgeting the complete analog signal chain.
Temperature Measurement Is a System Problem
An NTC thermistor or platinum RTD does not directly output temperature. The element produces a temperature-dependent resistance, while excitation, wiring, conversion model, ADC, reference, mounting, and self-heating determine the reported value. A correct nominal curve is therefore necessary but not sufficient.
The NTC Thermistor Calculator and RTD PT100 / PT1000 Calculator solve the nominal resistance-temperature relationships and first-order self-heating. This guide connects those equations to a practical measurement workflow.
NTC and Platinum RTD Comparison
| Characteristic | NTC thermistor | PT100 / PT1000 RTD |
|---|---|---|
| Response | Resistance decreases strongly with temperature | Resistance increases predictably with temperature |
| Sensitivity | High but nonlinear | Lower and comparatively linear |
| Typical model | Beta, Steinhart-Hart, or table | Callendar-Van Dusen / standard curve |
| Range | Part- and model-dependent | Broad standardized platinum range |
| Wiring sensitivity | Often modest at high resistance | Important for PT100; lower relative error for PT1000 |
| Strength | Cost, sensitivity, compact size | Repeatability, stability, interchangeability |
| Key risk | Curve tolerance and self-heating | Lead resistance and excitation error |
Formula reference
NTC Resistance–Temperature Models
Never substitute Celsius directly into reciprocal-temperature equations, and do not mix coefficients from another part or resistance-unit convention.
Beta: R = R0 × exp[B(1/T - 1/T0)]Inverse Beta: 1/T = 1/T0 + ln(R/R0)/BSteinhart-Hart: 1/T = A + B ln(R) + C[ln(R)]³Variable definitions
- T and T0 are absolute temperatures in kelvin.
- R and R0 must follow the resistance-unit convention used by the coefficients.
- A Beta value is interval-dependent; Steinhart-Hart coefficients are valid only over their characterized range.
Using the NTC Model in a Circuit
A common interface is an NTC and fixed resistor forming a divider. The fixed resistor affects voltage span, local sensitivity, source impedance, and measurement power. Choosing it equal to the thermistor resistance near the center of the desired range often gives a useful starting point, but it is not a universal optimum.
Calculate divider voltage at the cold, midpoint, and hot resistance limits. Then check ADC headroom, quantization, acquisition settling, leakage, and thermistor power at every corner. If the ADC reference and divider supply share the same source, a ratiometric calculation can cancel much of the supply tolerance.
Formula reference
Platinum RTD Model
Use coefficients and tolerance classes from the applicable sensor specification; nominal equations do not include class tolerance.
T ≥ 0°C: R(T) = R0(1 + AT + BT²)T < 0°C: R(T) = R0[1 + AT + BT² + C(T - 100)T³]PT100: R0 = 100 Ω at 0°CPT1000: R0 = 1000 Ω at 0°CVariable definitions
- The adopted coefficient convention uses temperature in degrees Celsius.
- The negative-temperature branch includes the C term.
- Inverse resistance-to-temperature conversion is normally solved numerically below 0°C.
Two-, Three-, and Four-Wire RTD Measurement
| Method | Lead-resistance behavior | Use boundary |
|---|---|---|
| 2-wire | Both leads add directly to measured resistance | Accept only when lead error is small or characterized |
| 3-wire | Instrument can cancel matched lead resistance | Lead mismatch and topology create residual error |
| 4-wire | Separate force and sense paths largely remove lead drop | Best precision; still subject to sensor and electronics errors |
A PT100 changes by roughly 0.385 Ω/°C near 0°C. Two 1 Ω leads can therefore resemble several degrees of error. A PT1000 has about ten times the resistance slope, so the same lead resistance is a smaller fraction of the signal, though it is not automatically negligible.
Excitation and Self-Heating
Every resistance measurement injects energy. With current excitation, P = I²R; with voltage across the element, P = V²/R. A first-order temperature-rise estimate is ΔT ≈ P/D, where D is the installed dissipation constant in W/K. The installed value may differ sharply between still air, moving air, liquid, a probe sheath, and a PCB footprint.
| Case | Power | First-order implication |
|---|---|---|
| PT100, 1 mA, 100 Ω | 0.1 mW | At D = 1 mW/K, approximately 0.1 K rise |
| PT100, 2 mA, 100 Ω | 0.4 mW | Doubling current quadruples self-heating power |
| 10 kΩ NTC, 100 µA | 0.1 mW | Check how resistance and current change over the divider range |
| Pulsed excitation | Depends on duty and thermal dynamics | Reduces average power only when acquisition and settling remain valid |
ADC and Analog Front-End Design
- 1. Define the temperature and resistance range.
- 2. Choose the sensor model and coefficient source.
- 3. Set excitation from signal and self-heating limits.
- 4. Choose 2-, 3-, or 4-wire measurement as needed.
- 5. Map the full signal range into ADC headroom.
- 6. Check source impedance and acquisition settling.
- 7. Budget ADC noise, offset, gain, INL, and reference drift.
- 8. Calibrate and verify at representative installed temperatures.
Oversampling can reduce uncorrelated noise but does not remove systematic errors. Likewise, a high-resolution ADC does not guarantee accurate temperature when the reference, excitation resistor, lead compensation, or sensor model dominates the error budget.
Worked Design Examples
| Scenario | Calculation | Engineering result |
|---|---|---|
| 10 kΩ B3950 NTC at 25°C | R = R0 | 10 kΩ nominal |
| 10 kΩ B3950 NTC near 100°C | Beta equation | Approximately 697.5 Ω nominal |
| PT100 at 100°C | R0(1 + AT + BT²) | Approximately 138.5055 Ω nominal |
| PT1000 at 100°C | Same normalized curve | Approximately 1385.055 Ω nominal |
| PT100 with two 1 Ω leads | Rmeas = Rsensor + 2 Ω | Lead error is large relative to ~0.385 Ω/°C sensitivity |
| PT100 at 1 mA | I²R at 100 Ω | 0.1 mW element power |
| PT100 at 2 mA | I²R at 100 Ω | 0.4 mW, four times the heating |
| 10 kΩ NTC at 100 µA | I²R | 0.1 mW at that operating point |
| 12-bit ADC over 3.3 V | 3.3/4096 | About 0.806 mV per code before analog errors |
| Ratiometric divider | ADC code depends on resistance ratio | Supply variation can largely cancel |
Building the Error Budget
| Source | Mechanism | Mitigation |
|---|---|---|
| Sensor tolerance | Nominal curve differs from actual element | Select class/tolerance and calibrate if needed |
| Model error | Beta or polynomial fit has limited validity | Use correct interval or coefficient set |
| Lead resistance | Adds series resistance | 3/4-wire topology or characterized compensation |
| Self-heating | Measurement power raises element temperature | Reduce excitation and verify installed D |
| ADC/reference | Offset, gain, noise, INL, drift | Ratiometric design, filtering, calibration |
| Mounting | Thermal gradients and response lag | Place and attach sensor for the measured quantity |
| Aging | Resistance and insulation change over time | Use stability specifications and maintenance calibration |
Common Design Mistakes
- Using Celsius in an NTC reciprocal-temperature equation.
- Treating every 10 kΩ NTC as the same curve.
- Using one Beta value outside its characterized interval.
- Omitting the RTD C term below 0°C.
- Assuming PT100 is 100 Ω at 25°C rather than 0°C.
- Ignoring two-wire lead resistance.
- Assuming three-wire leads are perfectly matched.
- Increasing excitation current without recalculating I²R.
- Using an air dissipation constant for an installed probe.
- Rounding resistance before inverse conversion.
- Equating ADC resolution with system accuracy.
- Ignoring thermal gradients and response time.
Reference Data and Verification
Use the NTC Thermistor and Temperature-Coefficient Reference and PT100/PT1000 Resistance Reference for terminology and derived nominal values. Then verify the selected part's coefficients, tolerance, current limits, dissipation constant, response time, wiring, and environmental ratings from its datasheet.
Support reference
FAQ
Should I use an NTC thermistor or an RTD?
Use an NTC when high sensitivity, low cost, and a limited calibrated range fit the application. Use a platinum RTD when repeatability, standardized behavior, broad range, and long-term stability justify the added interface complexity.
Why must NTC equations use kelvin?
The Beta and Steinhart-Hart relationships contain reciprocal absolute temperature. Celsius or Fahrenheit cannot be substituted directly into those terms.
What is the difference between PT100 and PT1000?
They have nominal resistances of 100 ohms and 1000 ohms at 0°C. Under the same normalized platinum curve, PT1000 produces ten times the resistance change and reduces the relative effect of a given lead resistance.
What causes sensor self-heating?
Excitation current dissipates I²R in the sensing element. The resulting temperature rise depends on power and the installed dissipation constant, which changes with mounting, airflow, and medium.
How much RTD excitation current should I use?
Use enough current for signal-to-noise performance but low enough to meet the self-heating error budget. Verify the selected sensor's datasheet and calculate I²R at the highest relevant resistance.
Why is a four-wire RTD more accurate?
Separate force and sense conductors keep most lead voltage drop out of the resistance measurement. It does not remove sensor tolerance, self-heating, ADC, reference, or installation errors.
Can I use a voltage divider for an NTC thermistor?
Yes. Choose the fixed resistor to balance sensitivity, ADC span, source impedance, and self-heating across the intended temperature range. A midpoint match is not automatically optimal for every range.
What is ratiometric measurement?
A ratiometric design derives sensor excitation and ADC reference from the same source so common source variation largely cancels. Resistor tolerance, reference routing, settling, and noise still matter.
Does nominal resistance tolerance equal temperature accuracy?
No. Temperature error also includes curve or coefficient tolerance, readout error, leads, self-heating, drift, and installation gradients.
When should I calibrate the complete measurement chain?
Calibrate when the required system accuracy is tighter than the combined sensor, excitation, wiring, ADC, reference, and mounting uncertainty or when installation effects are significant.
Can a single linear coefficient model an NTC over a wide range?
Usually not. NTC response is strongly nonlinear. Use a valid Beta interval, Steinhart-Hart coefficients, or manufacturer table with suitable interpolation.
Do these equations model thermal response time?
No. Resistance-temperature conversion describes an operating point. Dynamic response also depends on sensor thermal mass, packaging, mounting, fluid flow, and surrounding thermal impedance.
Summary
Accurate resistive temperature sensing comes from matching the sensor and mathematical model to the range, controlling excitation and lead error, designing the ADC interface as a complete chain, and verifying the installed thermal behavior. Nominal conversion is the starting point; the error budget determines whether the measurement is trustworthy.