Visualize the NTC thermistor resistance-temperature characteristic with the beta-parameter model. Vary R0, B constant and temperature to learn how resistance, divider voltage and sensitivity behave in real time.
Parameters
Reference resistance R0
kΩ
B constant
K
Temperature T
°C
Reference temperature T0
°C
Output of a voltage divider with supply Vs = 3.3 V and series resistor Rs = R0.
Results
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Resistance R(T)
—
Output voltage Vout
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Sensitivity dR/dT
—
R/R0
Resistance-Temperature Curve R(T)
Horizontal axis = temperature T (°C) / Vertical axis = resistance R (kΩ, log) / yellow = current (T, R), blue = reference (T0, R0)
Voltage Divider Circuit
3.3 V supply -> series resistor Rs = R0 -> thermistor R(T) -> GND. Midpoint voltage is Vout
Theory & Key Formulas
The resistance-temperature characteristic of an NTC thermistor is described by the beta-parameter model. T and T0 are absolute temperatures (K).
Temperature sensitivity (negative because resistance decreases as T rises):
$$\frac{dR}{dT} = -\frac{R(T)\,B}{T^2}$$
B is typically 3000-4500 K. Around 25°C, a 1°C change in temperature gives roughly a 4-5% change in resistance.
What is the NTC Thermistor Simulator
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Air conditioners have a tiny temperature sensor at the outlet. How does it actually measure temperature?
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That little black grain is an NTC thermistor — a semiconductor whose resistance drops as temperature rises, following an exponential curve $R(T) = R_0\,\exp[B(1/T - 1/T_0)]$. The microcontroller reads a voltage from a divider circuit, infers the resistance, and from there back-calculates the temperature. Try moving the temperature slider in the simulator: you can see R drop sharply with T.
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The B constant shows 3950 — what does that number mean? I see it in datasheets a lot.
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B is the material constant that expresses how "responsive" that thermistor is, in units of kelvin. The larger B, the steeper the resistance change with temperature. Around 25°C, a 1°C change gives a 4-5% resistance change, which is roughly ten times the sensitivity of a Pt100. Compare B = 3000 vs 5000 in the simulator and you will see the slope of the curve clearly differs — that is the sensitivity difference.
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There is a voltage divider diagram. Why use Rs equal to R0? Anything would work, right?
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Good question. With Rs = R0, at the reference temperature (25°C) Vout becomes Vs/2 = 1.65 V. You sit in the middle of the ADC range, so swings either way map cleanly into voltage you can read. Make Rs too small and the low-temperature side saturates; too large and the high-temperature side saturates. Watch the "Vout = " value in the schematic as you sweep T from -40 to 150°C.
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So a microcontroller reads Vout and back-calculates T, right?
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Exactly. Read Vout via ADC, then R = Rs · Vout/(Vs - Vout) gives the resistance, and inverting the B equation gives $T = 1/(1/T_0 + \ln(R/R_0)/B)$ for the temperature. Embedded systems often replace the inversion with a lookup table for speed, or use the Steinhart-Hart equation $1/T = A + B\ln R + C(\ln R)^3$ when ±0.1°C accuracy is needed across a wide range.
Physical Model and Key Equations
The resistance-temperature characteristic of an NTC thermistor comes from the activation-energy behavior of conduction electrons crossing the semiconductor band gap. The simplest model is the beta-parameter equation $R(T) = R_0\,\exp[B(1/T - 1/T_0)]$, where T and T0 are absolute temperatures (K) and R0 is the resistance at the reference T0. The B constant corresponds to a material-specific activation energy and typically falls in the range 3000-4500 K.
Differentiating gives the temperature sensitivity $\frac{dR}{dT} = -\frac{R\,B}{T^2}$. Sensitivity is largest at low temperature (small T) and where R is large, which is why NTC thermistors give excellent resolution from room temperature up to about 100°C. At high temperatures R drops exponentially, so the absolute sensitivity in Ω/K shrinks rapidly.
In a real circuit a voltage divider $V_\text{out} = V_s\,R(T)/(R(T)+R_s)$ converts resistance into a voltage that an ADC can read. Choosing Rs equal to R0 puts the reference temperature at Vout = Vs/2, which uses the ADC dynamic range most efficiently.
Real-world Applications
Appliances and HVAC: Air conditioners, refrigerators, water heaters, coffee makers and most household thermal appliances use NTC thermistors. They are inexpensive, fast to respond and accurate enough across -30°C to +150°C, making them the de facto standard for white goods.
Automotive electronics: Coolant temperature sensors (CTS), intake-air temperature, cabin temperature and exhaust temperature are commonly NTC-based. The engine ECU compensates fuel injection and ignition timing using coolant temperature, so thermistor accuracy translates directly into fuel economy and emissions.
Lithium-ion battery monitoring: Battery management systems (BMS) place an NTC thermistor near each cell group to monitor temperature during charge and discharge. Detecting overheating to halt charging is the safety backbone of EVs, laptops and smartphones.
Medical devices: Electronic thermometers, infant incubators, ventilators and IV warmers all use NTC thermistors to measure body or fluid temperature. Their small size and low thermal mass give sub-second response, making rapid measurement possible.
Common Misconceptions and Pitfalls
The biggest mistake is assuming the B-parameter model is accurate over the full temperature range. Within ±20°C of T0 the error is below 1°C, but at -40°C or +150°C the model deviates by several °C because B itself depends on temperature. For wide-range, high-accuracy work the Steinhart-Hart equation, calibrated from at least three reference points, is required.
Next, connecting the thermistor directly to a power rail with no current limit causes self-heating. A 10 kΩ thermistor carrying 1 mA dissipates 10 mW, which can warm the bead by about 1°C in still air and bias the reading. With Vs = 3.3 V and Rs = 10 kΩ the maximum current is around 0.165 mA, keeping dissipation below 0.5 mW. Lower current reduces self-heating but makes the signal noisier — a real trade-off.
Finally, treating the datasheet response time as universal. Datasheet times are quoted under specific media, flow and packaging conditions. A bare bead in still air may take hundreds of milliseconds; a sheathed probe in a thick stem can take seconds. Account for medium, flow velocity, contact pressure and thermal resistance, and apply a first-order lag compensation filter where needed.
Frequently Asked Questions
NTC (Negative Temperature Coefficient) thermistors decrease in resistance as temperature rises and are used for temperature measurement. PTC (Positive Temperature Coefficient) thermistors increase in resistance with temperature, often with a sharp transition at the Curie point, and are used for over-current protection or self-regulating heaters. The two have very different uses: NTC for measuring temperature, PTC for protecting against it.
Measure resistance R1 and R2 at two known temperatures T1 and T2 (in kelvin), then $B = \ln(R_1/R_2) / (1/T_1 - 1/T_2)$. Datasheets typically quote B25/50 or B25/85, derived from 25°C with 50°C or 85°C as the second point. For wide-range accuracy use multiple piecewise B values, or move to the three-coefficient Steinhart-Hart model.
Read Vout from the divider with the ADC. Compute R = Rs · Vout/(Vs - Vout), then solve the B equation for T: T_K = 1/(1/T0_K + ln(R/R0)/B), and subtract 273.15 for °C. On microcontrollers like Arduino or ESP32, a precomputed lookup table is common to avoid runtime exp/log. The Steinhart-Hart equation gives ±0.1°C accuracy across wide ranges if you can spare the cycles.
Reduce the current through the thermistor: increase the divider resistor Rs, drive the bias only briefly (pulsed measurement), and use a high-impedance ADC. As a rule of thumb, dissipation below 0.1 mW gives negligible self-heating. Note that the thermal dissipation constant differs by medium — water cools the bead far better than still air, so the same current may be safe in liquid but not in gas.