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Thermistors Explained With Circuits, Calculations and Testing

FREE-SKY (HK) ELECTRONICS CO.,LIMITED / 11-04 14:56

A thermistor is a resistor whose resistance changes significantly with temperature. It is used to measure temperature, compensate for thermal drift, limit startup current, and respond to overheating. Thermistors fall into two main categories: negative temperature coefficient (NTC) and positive temperature coefficient (PTC). Although both rely on temperature-sensitive resistance, they behave differently and serve different purposes. This guide explains their operating principles, specifications, differences from other temperature sensors, and practical applications.


Catalog

1. What Is a Thermistor
2. Types of Thermistors
3. How Do Thermistors Work
4. Key Characteristics and Specifications of Thermistors
5. Thermistors vs. Other Temperature Sensors
6. Applications of Thermistors
7. How to Test a Thermistor
8. Thermistor Compatibility and Replacement
9. Conclusion

What Is a Thermistor

Thermistor combines “thermal” and “resistor”. Unlike fixed resistors, thermistors deliberately exhibit a characterized resistance change with element temperature. Metal-oxide ceramics are common in NTC sensors; doped barium titanate in switching ceramic PTCs. Silicon and conductive polymers support other behaviors.

Packages include SMD chips, beads, leaded discs and protected probes. Thermal contact, airflow, insulation and mounting affect response time and the temperature actually sensed. Appearance does not identify NTC versus PTC.

Representative Thermistor Packages (Generic Illustrations)

Figure 1. Representative Thermistor Packages (Generic Illustrations)

Types of Thermistors

Negative Temperature Coefficient (NTC) Thermistors

NTC resistance decreases as temperature rises. Sensing NTCs use a specified R–T curve under low excitation. Inrush NTCs instead self-heat under load: high cold resistance limits startup current, then falls. Matching R25 does not make these parts interchangeable.

Positive Temperature Coefficient (PTC) Thermistors

PTC resistance rises within its specified positive-coefficient region. Switching ceramic PTCs (often barium titanate) show a sharp rise near a transition and serve protection, threshold sensing and heating. Silicon PTCs, including TI TMP61, provide a more nearly linear sensing curve. Polymer PPTC resettable protectors, such as Littelfuse 1206L, heat under overcurrent and have distinct hold/trip characteristics. These three classes are not interchangeable.

 NTC/PTC Electrical Symbols (−t°/ +t° Identify Coefficient Direction)

Figure 2. NTC/PTC Electrical Symbols (−t°/ +t° Identify Coefficient Direction)

NTC vs. PTC Thermistors: Application and Specification Checkpoints

Function / device
Operating behavior
Ratings and data to verify
NTC temperature sensor
Low-power sensing; R decreases with T
R25; R–T table; Beta interval/tolerance; response; temperature; insulation
NTC inrush limiter
Cold resistance limits startup surge; self-heating lowers R
Cold R; continuous current; pulse tests; derating; hot restart
Switching ceramic PTC protector
Resistance rises around switching temperature
Switching curve; voltage/current; trip; residual current; reset
Silicon sensing PTC
Nearly linear positive temperature coefficient
Reference R; TCR; tolerance; bias; temperature range
Polymer resettable PPTC
Fault current heats polymer; resistance rises
Ihold/Itrip; Vmax/Imax; trip time; derating; reset
PTC heater
Fixed-voltage heating decreases near transition
Voltage; thermal balance; power; mounting; insulation


These categories describe temperature response, not complete application specifications. The manufacturer’s product family and datasheet determine what each device is designed to do.

How Do Thermistors Work

Temperature-Dependent Resistance

Heating increases charge transport and lowers resistance in typical metal-oxide NTCs. Switching ceramic PTCs rise sharply near a transition; silicon sensing PTCs respond more nearly linearly. Figure 3 shows qualitative shapes, not measured device curves.

Qualitative NTC and Switching Ceramic PTC R–T Curves

Figure 3. Qualitative NTC and Switching Ceramic PTC R–T Curves

Self-Heating Effect

A current-carrying thermistor dissipates power:

P=I2R=V2R


Excess heating biases a sensing device above its target temperature; inrush and protective devices exploit heating. The steady-state estimate ΔT≈Pδ requires a dissipation constant δ measured for the relevant mounting and environment.

Worked example: Figure 5 uses 3.3 V across a 10 kΩ fixed resistor and a hypothetical 10 kΩ NTC at 25°C. Both resistors carry I = 3.3 V / 20 kΩ = 0.165 mA. The NTC therefore dissipates (0.165 mA)² × 10 kΩ = 0.27225 mW. If, solely as an illustration, the installation-specific δ were 1.0 mW/K, the estimated steady-state rise would be 0.272°C; at δ = 5.0 mW/K it would be °C. These are assumed dissipation constants, not claims about the Vishay sensor.

Intermittent excitation can lower average heating if the sensing and sampling sequence allows stabilization. With an ADC, the source impedance of the divider and the ADC sample-and-hold capacitance also matter: acquisition time must allow the input to settle after channel switching or power gating. Where the ADC reference tracks the same stable divider supply, a ratiometric conversion (ADC code divided by full scale) suppresses much of the supply-amplitude dependence. This does not remove resistor, ADC nonlinearity, or thermal errors.

Key Characteristics and Specifications of Thermistors

Nominal Resistance and Tolerance

R25 is an NTC’s specified resistance at 25°C, not a constant over temperature. Its tolerance applies near the reference point. Two 10 kΩ parts can differ substantially elsewhere on their R–T curves.

Beta Value and Relative Sensitivity

Beta (K) approximates an NTC’s R–T slope over a stated interval, such as B25/50 or B25/85. Under the constant-Beta model, relative sensitivity is:

α(T)=1RdRdT≈−BT2


At 25°C (298.15 K), B = 3950 K yields α≈−0.04444K−1, or −4.44%/°C. This local slope does not apply uniformly across temperature. Higher Beta raises relative sensitivity at a fixed temperature, not necessarily measurement accuracy.

Resistance–Temperature Relationships

For an NTC, the Beta equation uses absolute temperatures T and T₀ (K):

R(T)=R0·exp[B(1T−1T0)]


A hypothetical sensor with R25 = 10 kΩ and B = 3950 K gives:

Temperature
Calculated R (hypothetical model)
−10°C58.25 kΩ
0°C
33.62 kΩ
25°C
10.00 kΩ
50°C
3.588 kΩ
85°C
1.087 kΩ


Resistance–Temperature Curve of a 10 kΩ NTC Thermistor

Figure 4. Resistance–Temperature Curve of a 10 kΩ NTC Thermistor

Use the manufacturer’s full R–T table or validated Steinhart–Hart coefficients for greater accuracy:

1T=A+BSH·ln(R)+CSH·[ln(R)]3


A, BSH and CSH depend on the product and resistance units; BSH is not the Beta value. Follow the manufacturer’s fitting range and equation convention.

Datasheet Example: Vishay NTCLE100E3103JB0

The Vishay NTCLE100E3103JB0 is an actual radial-leaded NTC sensor, distinct from the hypothetical 3950 K example. Its ordering code identifies a 10 kΩ R25 with ±5% resistance tolerance; the published series table lists B25/85 = 3977 K with ±0.75% B tolerance. The manufacturer’s nominal R–T table is therefore the correct source for its readings—not Figure 4.

Characteristic
Vishay NTCLE100E3103JB0
R25
10 kΩ nominal
R25 tolerance
±5% (“J” ordering code)
B25/85
3977 K
B25/85 tolerance
±0.75%
Nominal R at 0 / 25 / 50 / 85°C
32,554 / 10,000 / 3,605 / 1,070 Ω
Operating range at zero power
−40 to +125°C continuously (series datasheet)
Mechanical form
Radial-leaded, solder-mounted; do not infer insulation from coating


To read Vishay’s table, locate the column headed NTCLE100E3103 (the 10 kΩ series entry), then select a temperature row. At 50°C it reports 3,605 Ω nominal; at 25°C it reports 10,000 Ω. The adjacent TCR and B-tolerance-deviation columns explain temperature-dependent behavior and uncertainty. A listed nominal R does not include the full ±5% part tolerance or assembly error; see Vishay’s tolerance-combination guidance.

Mounting restrictions matter. The coating has no specified insulation properties, and the family datasheet says the parts are not intended for potted applications. Vishay’s dedicated handling sheet limits soldering heat/time and minimum distance from the body according to lead material, advises against pin-in-paste reflow, and prohibits bending the leads closer than 4 mm to the coated body. Do not substitute these generic material rules for a verified drawing when configuring the production footprint.

Other Electrical and Thermal Specifications

Specification
Why it Matters
Thermal time constant
63.2% response to a temperature step under test conditions
Dissipation constant δ
Steady power for a 1°C rise; depends on installation
Operating temperature limits
Rated temperature limits and applicable derating
Insulation and isolation
Explicitly rated coating, housing and voltage isolation
Surge/current ratings
Product-specific continuous current and pulse ratings
PTC switching/reset
PTC trip and reset behavior under stated conditions


Thermistors vs. Other Temperature Sensors

For temperature measurement, NTC sensors compete with RTDs, thermocouples and IC sensors. These differ in sensed quantity and interface requirements:

Feature
NTC Thermistor
RTD
Thermocouple
IC sensor
Sensed quantity
Resistance
Metal resistance
Small thermal voltage
Analog or digital signal
Curve
Nonlinear
Relatively linear
Nonlinear
Often calibrated internally
Typical strength
High local sensitivity
Repeatability, stability
High-temperature capability
Integrated signal conditioning with analog or digital output
Key design issue
Bias self-heating; R–T data
Lead/excitation errors
Cold-junction compensation
Supply/interface and location
Typical use
Battery / PCB monitoring
Industrial process
Furnace / high-temperature
Board / system monitoring


Accuracy, response and cost depend on the specific part and installation. This comparison excludes inrush NTCs, protection PPTCs and PTC heaters.

Applications of Thermistors

Temperature Sensing and Monitoring: Voltage-to-Temperature Example

Figure 5 uses a hypothetical 10 kΩ, B = 3950 K NTC from Vout to ground and a 10 kΩ resistor from Vout to 3.3 V. Assume a high-impedance, settled ADC input. This is not the Vishay datasheet example.

Low-side 3.3 V NTC Divider, Vout Falls as Temperature Rises

Figure 5. Low-side 3.3 V NTC Divider, Vout Falls as Temperature Rises

Step 1: At 50°C, the Beta model gives

RNTC=10,000e3950(1323.15−1298.15)=3,588.18Ω


Step 2: Vout=3.3×3,588.1810,000+3,588.18=0.87142V≈0.871V

Step 3: Recover resistance from the measured voltage:

RNTC=RfixedVoutVCC−Vout


Using the unrounded voltage gives 3,588.18 Ω, or approximately 3.59 kΩ. If the ADC reference equals VCC, the same expression can be applied using the measured ADC fraction instead of absolute voltage.

Step 4: Apply the inverse Beta equation:

T=[1T0+ln(RNTCR0)B]−1


With T₀ = 298.15 K, R₀ = 10,000 Ω and B = 3950 K, this gives T = 323.15 K = 50.00°C. This ideal calculation is not a system-accuracy claim.

Temperature-Measurement Error Budget

A practical accuracy claim requires a component-level and system-level error budget. Estimate each source in its own units and operating conditions before combining independent errors. In particular, ±5% R25 tolerance, fixed-resistor error, ADC gain/offset/INL and reference mismatch, model-fitting error, self-heating, and thermal contact are not the same quantity.

Error source
What to check / effect
Sensor R25 and B tolerances
R25/B tolerances change resistance and curve shape
Fixed resistor
Tolerance in divider resistor skews resistance inversion
ADC / reference
Gain, offset, INL, reference mismatch and settling
Curve conversion
Beta fit or lookup-table residual error
Self-heating
Dissipation raises thermistor above target temperature
Thermal contact / placement
Sensor placement and imperfect thermal coupling


For the hypothetical 3950 K sensor at 25°C, α≈−4.44%/°C. A small 1% relative resistance error corresponds to |ΔT|≈0.010.04444=0.225°C, or about 0.23°C locally. This is only one sensitivity conversion—not a total system accuracy specification. The sign depends on whether measured resistance is high or low. For reliable reporting, test the assembled circuit over temperature and document any calibration.

Temperature Compensation

Electronic components change behavior with temperature. A thermistor placed in an appropriate resistor network can counter part of that variation. For example, a temperature-dependent bias or reference circuit can use the thermistor’s changing resistance to offset an unwanted drift elsewhere in the circuit.

Successful compensation depends on matching the required correction curve rather than merely matching a resistance at room temperature. If the thermistor and the affected component change at different rates, the correction will be accurate only over a limited span. Circuit designers therefore evaluate the full operating-temperature range and the tolerances of all relevant components.

Inrush Current Limiting

A cold NTC in series with an input supply limits the capacitor-charging current at startup. As load current heats it, resistance decreases and the normal-operation voltage drop becomes lower than its cold-start value. Figure 6 depicts an AC-input arrangement with the NTC ahead of a bridge rectifier and the polarized bulk capacitor on the rectified DC bus. The arrangement is illustrative; actual mains input design requires appropriate fusing, isolation, grounding, and approvals.

Series NTC Before AC Bridge Rectifier

Figure 6. Series NTC Before AC Bridge Rectifier

A separate illustrative 24 V DC source charging a discharged 4,700 μF capacitor stores E=12CV2=12×0.0047F×(24V)2=1.3536J at full voltage. This is capacitor stored energy, NOT proof that a specific NTC will dissipate exactly 1.35 J. Energy is shared among source resistance, wiring, charging path, the NTC and other components, and depends on waveform and switching conditions.

Suitability requires cold resistance and peak-current evaluation, manufacturer pulse-test waveform and repeated-pulse limits, continuous current and ambient-temperature derating, steady-state temperature, and the shortest expected off/on restart interval. A still-hot NTC may not limit a second surge adequately. Never select a current limiter solely because its nominal energy rating exceeds 1.35 J.

Overcurrent and Overtemperature Protection

A protection PTC changes to a high-resistance state when self-heating under a fault exceeds its thermal balance. The datasheet must be read as a protection characteristic: Ihold is the maximum current that does not trip under a specified ambient condition, while Itrip is the minimum current that trips under the specified test condition. Between these limits, the response depends on temperature and time; trip-time curves, maximum voltage/fault current, ambient derating, and residual current after tripping all matter.

For a documented polymer example, Littelfuse’s 1206L020/30 PPTC lists Ihold = 0.20 A, Itrip = 0.42 A at 20°C still air, Vmax = 30 V DC, and a maximum time to trip of 0.10 s at a specified 8 A test current. The manufacturer’s temperature-rerating table lowers the hold current to approximately 0.14 A at 60°C. These figures belong only to that particular PPTC product and its stated conditions, not to silicon sensing PTCs, ceramic PTC sensors, or heater elements.

Residual current flows while a tripped PPTC remains powered. Remove the fault and let it cool to reset. It is not automatically a substitute for a safety fuse; sensing ceramic PTCs instead signal a controller.

Self-Regulating Heating

A ceramic PTC heater self-limits power at near-constant voltage as resistance rises (P=V2R). Mounting and airflow determine its thermal balance; use heater-specific insulation and voltage ratings.

Thermistor Testing and Troubleshooting

Troubleshooting should separate an actual sensor fault from the connector, wiring, ADC, or conversion setting. Work on a de-energized isolated circuit. Disconnect power, discharge all relevant capacitors safely, and verify the voltage is zero before resistance or continuity testing. For any mains-connected appliance, use an appropriate service procedure and qualified personnel. Do not use the ohmmeter on a powered circuit.

First identify the exact sensor and datasheet. Disconnect at least one lead or isolate the sensor from parallel circuitry, allow the element to stabilize at a known temperature, and measure resistance with a suitably low test current. Repeat at a second stabilized temperature using a calibrated temperature reference and the correct R–T curve. Do not judge a sensor from a single room-temperature reading alone; compare expected values with tolerance, and do not heat a live assembly without adequate safeguards.

After the sensor checks, reconnect and inspect connector contact resistance, lead continuity, solder joints, cable pinout, the fixed resistor, ADC reference, code scaling, and the selected curve or coefficients. Recheck the input voltage under normal operation using proper electrical precautions. In Figure 5 only, a low-side NTC that opens pulls Vout toward 3.3 V through Rfixed; a shorted NTC pulls Vout toward 0 V. Other divider topologies reverse or change these symptoms.

Observation (Figure 5 circuit)
Likely cause and discriminating test
Vout near 3.3 V
Open lower NTC path: test sensor, connector and return wire
Vout near 0 V
Short NTC/lower wire, or missing upper supply; test both
R correct off board; wrong Vout
Check fixed resistor, wiring, reference and ADC settling
R correct at two temperatures; wrong displayed °C
Check Beta/R–T data, orientation, software and units
Intermittent reading
Check contacts, moisture, leads and solder joints
Persistent offset or sluggish response
Check self-heating, thermal contact and placement


Confirm open/short symptoms with safe low-voltage measurements or a simulated resistor; do not swap parts on an energized circuit. Passing two-point resistance checks does not exclude ADC or firmware errors.

Thermistor Replacement and Compatibility

A thermistor replacement is not determined by package shape or a shared “10 kΩ” marking. Compare R25, resistance tolerance, the complete R–T table, Beta value AND its reference interval, conversion model, operating temperature, thermal time constant, dissipation constant, lead arrangement, package size, chemical exposure, electrical insulation/isolation rating, and attachment method. For inrush and protection products, current, voltage, surge, and reset ratings are additional hard requirements.

Mismatch example: assume a genuine hypothetical NTC has R25 = 10 kΩ and B = 3950 K. At an actual 50°C its resistance is about 3.588 kΩ. If unchanged software incorrectly decodes that resistance with B = 3435 K, the inverse Beta equation reports approximately 54.11°C—about + 4.11°C error. The two devices may have the same nominal 10 kΩ value at 25°C, yet are not equivalent throughout the range. This calculated example is separate from Vishay’s NTCLE100E3103JB0, which has B25/85 = 3977 K and its own datasheet curve.

Confirm any factory calibration, lookup table and firmware thresholds before substitution. A matching package does not guarantee electrical compatibility; an unrated coating is not verified insulation.

Conclusion

Thermistors turn temperature changes into useful resistance changes. NTC devices are widely used for sensing, compensation, and startup-current limiting, while suitable PTC devices support temperature detection, circuit protection, and controlled heating. Their behavior is defined by material properties, R–T characteristics, and thermal conditions. Understanding these factors—and checking the relevant manufacturer specifications—makes it easier to apply thermistors correctly in electronic equipment.


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