Definition and Basic Principles

A thermistor (thermal resistor) is a temperature-sensitive semiconductor device whose electrical resistance varies significantly with temperature. Unlike metallic resistors, which exhibit a nearly linear resistance-temperature relationship, thermistors display highly nonlinear behavior, making them ideal for precision temperature sensing, compensation, and control applications.

Fundamental Operating Principle

The resistance R of a thermistor is governed by its material composition and follows an exponential relationship with temperature T. For Negative Temperature Coefficient (NTC) thermistors, resistance decreases with increasing temperature, while Positive Temperature Coefficient (PTC) thermistors exhibit the opposite behavior.

where:

• R₀ = Resistance at reference temperature T₀ (typically 25°C)
• B = Material constant (typically 2000–5000 K)
• T, T₀ = Absolute temperatures in Kelvin

NTC vs. PTC Thermistors

NTC thermistors are commonly made from transition metal oxides (e.g., Mn, Ni, Co) sintered into a polycrystalline ceramic. Their resistance follows the Arrhenius equation:

PTC thermistors, often based on barium titanate (BaTiO₃), exhibit a sharp resistance increase above a critical temperature due to ferroelectric phase transitions. Their behavior is modeled using:

Steinhart-Hart Equation

For higher precision, the Steinhart-Hart equation provides a third-order approximation of the NTC thermistor's resistance-temperature relationship:

where A, B, and C are curve-fitting coefficients derived from calibration data.

Practical Applications

• Temperature sensing in medical devices, automotive systems, and industrial equipment.
• Inrush current limiting using PTC thermistors as self-resetting fuses.
• Thermal compensation in oscillators and analog circuits.

1.2 Types of Thermistors: NTC and PTC

Negative Temperature Coefficient (NTC) Thermistors

NTC thermistors exhibit a decrease in resistance with increasing temperature, following an approximately exponential relationship. The resistance-temperature behavior is governed by the Steinhart-Hart equation:

where T is the absolute temperature (in Kelvin), R is the resistance, and A, B, C are device-specific coefficients. For many practical applications, a simplified beta parameter equation suffices:

Here, R₀ is the reference resistance at temperature T₀ (typically 25°C), and β is the material constant (typically 2000–5000 K). NTC thermistors are commonly fabricated from transition metal oxides such as manganese, nickel, or cobalt oxides sintered into ceramic structures.

Applications of NTC Thermistors

• Temperature sensing in automotive, medical, and industrial systems due to high sensitivity (~3–5%/°C).
• Inrush current limiting in power supplies, where the thermistor's initial high resistance suppresses surge currents.
• Thermal compensation for circuits affected by temperature drift (e.g., crystal oscillators).

Positive Temperature Coefficient (PTC) Thermistors

PTC thermistors demonstrate a sharp increase in resistance beyond a critical temperature (T_c), often modeled as:

where k is the positive temperature coefficient. This behavior arises from the polycrystalline barium titanate (BaTiO₃) ceramic structure, which undergoes a ferroelectric-to-paraelectric phase transition at T_c. Below T_c, the material behaves as a semiconductor; above it, grain boundary effects dominate, causing resistance to rise abruptly.

Applications of PTC Thermistors

• Self-regulating heaters, where the resistance rise at T_c limits current and stabilizes temperature.
• Overcurrent protection in transformers and motors, acting as resettable fuses.
• Liquid level detection by exploiting thermal coupling differences between air and liquid environments.

Comparative Analysis

The choice between NTC and PTC thermistors depends on the application requirements:

1.3 Material Composition and Structure

Ceramic Semiconductor Materials

Thermistors are primarily composed of polycrystalline ceramic semiconductor materials, which exhibit a strong temperature-dependent resistivity. The most common base materials include:

• Metal oxides (e.g., manganese, nickel, cobalt, copper, iron, titanium).
• Doped transition metal oxides (e.g., Mn₃O₄, NiO, Co₂O₃).
• Perovskite-type oxides (e.g., BaTiO₃ for PTC thermistors).

These materials are sintered at high temperatures (1200–1500°C) to form a dense polycrystalline structure with controlled grain boundaries, which significantly influence the electrical conduction mechanism.

NTC Thermistor Composition

Negative Temperature Coefficient (NTC) thermistors are typically made from transition metal oxides mixed in precise stoichiometric ratios. A common formulation is:

where x and y are doping concentrations that tune the resistivity and thermal sensitivity (β-value). The conduction mechanism is governed by hopping conductivity between mixed-valence metal ions (e.g., Mn³⁺/Mn⁴⁺).

PTC Thermistor Composition

Positive Temperature Coefficient (PTC) thermistors are often based on barium titanate (BaTiO₃) doped with rare-earth elements (e.g., Y, Nb, La) to create donor states. The abrupt resistivity increase near the Curie temperature (T_c) is due to:

• Ferroelectric phase transition causing domain boundary scattering.
• Grain boundary potential barriers that become highly resistive above T_c.

Microstructural Characteristics

The electrical properties are heavily influenced by microstructure:

• Grain size (typically 1–10 µm): Smaller grains increase boundary scattering, raising resistivity.
• Porosity: Higher porosity reduces effective conduction paths, increasing resistivity.
• Secondary phases: Impurities or segregation at grain boundaries can modify conduction.

Manufacturing Process

The synthesis involves:

1. Powder preparation: Mixing raw oxides via solid-state reaction or sol-gel methods.
2. Pressing: Uniaxial or isostatic pressing into pellets or discs.
3. Sintering: High-temperature firing to densify the material and establish grain boundaries.
4. Electrode application: Firing silver, platinum, or other conductive pastes onto the surface.

Doping and Property Tuning

Key parameters can be adjusted via doping:

where E_a is the activation energy and k_B is Boltzmann’s constant. For example:

• Adding CuO lowers resistivity but reduces β.
• Adding Fe₂O₃ increases stability at high temperatures.

2.1 Resistance-Temperature Relationship

Fundamental Behavior of Thermistors

Thermistors exhibit a highly nonlinear resistance-temperature dependence, governed by the Arrhenius equation. Unlike RTDs (Resistance Temperature Detectors), which follow a nearly linear trend, thermistors are categorized into two types based on their thermal response:

• Negative Temperature Coefficient (NTC): Resistance decreases exponentially with increasing temperature.
• Positive Temperature Coefficient (PTC): Resistance increases sharply beyond a critical temperature threshold.

Mathematical Model for NTC Thermistors

The resistance-temperature relationship for NTC thermistors is described by the Steinhart-Hart equation, an empirical third-order approximation:

Where:

• T is the absolute temperature in Kelvin (K)
• R is the resistance in ohms (Ω)
• A, B, and C are device-specific coefficients determined through calibration

For many practical applications, a simplified two-parameter version suffices:

Where:

• R₀ is the reference resistance at temperature T₀ (typically 25°C)
• β (beta) is the material constant, typically ranging from 3000K to 5000K for NTC thermistors

Derivation of the Beta Parameter Equation

Starting from the simplified Steinhart-Hart model, we can derive the β parameter equation:

1. Take the natural logarithm of both sides of the resistance equation:
   $$ \ln R = \ln R_0 + \beta \left( \frac{1}{T} - \frac{1}{T_0} \right) $$
2. Rearrange to solve for β:
   $$ \beta = \frac{\ln(R/R_0)}{\frac{1}{T} - \frac{1}{T_0}} $$

PTC Thermistor Behavior

PTC thermistors exhibit a radically different response characterized by:

• A gradual positive temperature coefficient below the Curie temperature
• A sharp, nonlinear increase in resistance above the transition temperature
• Often modeled using polynomial approximations or piecewise functions

Practical Considerations in Measurement

The extreme nonlinearity of thermistors presents both challenges and opportunities:

• Sensitivity: NTC thermistors typically offer 10× greater sensitivity than RTDs in their operating range.
• Linearization: Common techniques include:
  • Analog circuitry with logarithmic amplifiers
  • Lookup tables in digital systems
  • Piecewise polynomial approximations
• Self-heating effects: Must be carefully managed through current limiting and thermal design.

Material Science Perspective

The resistance-temperature relationship stems from fundamental semiconductor physics:

• NTC behavior arises from thermally activated charge carriers in transition metal oxides (e.g., Mn₃O₄, NiO).
• PTC effects in barium titanate ceramics result from grain boundary potential barriers.
• Doping strategies allow precise tuning of the β parameter and operating range.

Measurement Accuracy and Calibration

High-precision applications require:

• Three or four-point calibration to determine Steinhart-Hart coefficients
• Thermal stabilization techniques to minimize measurement drift
• Consideration of the thermistor's thermal time constant (Ï„) in dynamic measurements

2.2 Temperature Coefficient

The temperature coefficient of a thermistor defines the rate at which its resistance changes with temperature. For thermistors, this coefficient is highly nonlinear and is typically expressed as a percentage change per degree Celsius (%/°C). Unlike metals, which exhibit a positive temperature coefficient (PTC), thermistors are predominantly negative temperature coefficient (NTC) devices, meaning their resistance decreases as temperature rises.

Mathematical Definition

The temperature coefficient of resistance (α) for a thermistor is derived from the first derivative of its resistance-temperature relationship. For an NTC thermistor, the resistance R(T) is modeled by the Steinhart-Hart equation:

where T is the temperature in Kelvin, R is the resistance, and A, B, C are device-specific coefficients. The temperature coefficient α is then calculated as:

Substituting the Steinhart-Hart equation and differentiating yields:

Practical Implications

The temperature coefficient is not constant but varies with temperature, making thermistors highly sensitive in specific ranges. For example, a typical NTC thermistor may have α ≈ -4%/°C at 25°C, significantly higher than platinum RTDs (α ≈ +0.39%/°C). This high sensitivity enables precise temperature detection in applications like medical thermometry and battery thermal management.

Comparison with PTC Thermistors

While NTC thermistors dominate, PTC thermistors exhibit a positive α, often with a sharp resistance increase above a critical temperature. This behavior is exploited in self-regulating heaters and overcurrent protection devices. The coefficient for PTC thermistors follows:

where T_c is the Curie temperature and k is a material constant.

Measurement and Calibration

Accurate determination of α requires calibration at multiple temperatures. Industrial standards (e.g., IEC 60751) specify testing protocols, ensuring consistency across devices. Modern calibration employs polynomial regression to minimize error in the coefficient’s temperature-dependent profile.

2.3 Steinhart-Hart Equation and Calibration

The Steinhart-Hart equation provides a highly accurate empirical model for describing the resistance-temperature relationship of thermistors, particularly useful for precision temperature measurement applications. Unlike simpler approximations, it accounts for nonlinearities across a wide temperature range.

Mathematical Formulation

The general form of the Steinhart-Hart equation is:

where:

• T is the absolute temperature in Kelvin (K),
• R is the thermistor resistance in ohms (Ω),
• A, B, and C are Steinhart-Hart coefficients specific to the thermistor.

The logarithmic terms capture the nonlinear behavior of the thermistor's resistance-temperature curve. The cubic term (C(ln R)³) significantly improves accuracy compared to simpler two-parameter models.

Derivation from First Principles

The equation can be derived by considering the thermistor's resistance as an exponential function of reciprocal temperature. Expanding this relationship as a Taylor series in ln(R) and truncating after the cubic term yields the Steinhart-Hart form:

Rearranging and keeping terms up to third order in ln(R) produces the inverse relationship used in the Steinhart-Hart equation.

Determining the Coefficients

The coefficients A, B, and C must be determined empirically through calibration. This requires measuring the thermistor's resistance at three or more known temperatures and solving the resulting system of equations.

For three calibration points (T₁, R₁), (T₂, R₂), (T₃, R₃), the coefficients can be found by solving:

This system of equations is linear in A, B, and C and can be solved using matrix methods or numerical techniques.

Practical Calibration Procedure

For high-accuracy applications:

1. Measure the thermistor's resistance at three precisely known temperatures spanning the intended operating range (e.g., 0°C, 25°C, and 50°C).
2. Use a high-precision resistance measurement bridge or calibrated ohmmeter.
3. Solve for the coefficients using the measured data points.
4. Validate the model by checking additional temperature points.

For even better accuracy, more than three calibration points can be used, with the coefficients determined via least-squares fitting.

Applications and Limitations

The Steinhart-Hart equation is widely used in:

• Precision temperature measurement systems
• Medical equipment
• Aerospace and automotive sensors
• Industrial process control

Its main limitation is the need for calibration data specific to each thermistor batch. However, manufacturers often provide pre-calibrated coefficients for their devices.

3.1 Temperature Sensing and Control

Fundamentals of Thermistor-Based Sensing

Thermistors operate on the principle of thermally sensitive resistance, where their electrical resistance varies predictably with temperature. Negative Temperature Coefficient (NTC) thermistors exhibit a decrease in resistance with increasing temperature, while Positive Temperature Coefficient (PTC) thermistors show the opposite behavior. The resistance-temperature relationship for NTC thermistors is governed by the Steinhart-Hart equation:

where T is the temperature in Kelvin, R is the resistance, and A, B, and C are device-specific coefficients derived from calibration. For most practical applications, a simplified beta parameter equation suffices:

Here, R₀ is the reference resistance at temperature T₀ (typically 25°C), and β is the material constant, typically ranging from 3000 to 5000 K for NTC thermistors.

Linearization Techniques

Due to the exponential nature of the resistance-temperature relationship, linearization is often required for accurate measurements. A common approach involves using a voltage divider circuit with a fixed reference resistor R_ref:

Optimal linearity is achieved when R_ref is chosen to match the thermistor's resistance at the midpoint of the desired temperature range. Alternatively, digital linearization can be performed using polynomial approximations or lookup tables stored in microcontrollers.

Precision Measurement Circuits

For high-precision applications, a Wheatstone bridge configuration minimizes errors due to lead resistance and power dissipation effects:

The bridge output voltage V_out is given by:

When balanced (V_out = 0), the thermistor resistance R₂ can be determined from the other resistors, eliminating supply voltage dependence.

Closed-Loop Temperature Control

Thermistors are widely used in feedback control systems, where their fast response time and high sensitivity make them ideal for precision regulation. A proportional-integral-derivative (PID) controller processes the thermistor signal to adjust heating or cooling elements:

where u(t) is the control output, e(t) is the temperature error (setpoint - measured), and K_p, K_i, and K_d are tuning parameters. Modern implementations often use digital PID algorithms running on microcontrollers with pulse-width modulation (PWM) outputs for actuator control.

Practical Considerations

• Self-heating effects: Power dissipation in the thermistor must be minimized to avoid measurement errors. Operating currents should typically be kept below 100 µA.
• Thermal time constant: The response speed depends on the thermistor's mass and thermal coupling to the environment, typically ranging from 1 to 10 seconds for bead-type thermistors.
• Long-term stability: High-quality glass-encapsulated NTC thermistors exhibit drift rates below 0.1°C/year in controlled environments.

Applications in Industry and Research

Thermistor-based systems achieve temperature control with millikelvin stability in precision applications such as:

• Thermal cyclers for polymerase chain reaction (PCR) machines
• Cryogenic temperature monitoring in superconducting magnets
• Battery temperature management in electric vehicles
• Medical diagnostic equipment requiring ±0.01°C accuracy

3.2 Inrush Current Limiting

Inrush current, the transient surge of current occurring when an electrical device is first powered on, poses a significant risk to power supply circuits, capacitors, and semiconductor components. Thermistors, particularly Negative Temperature Coefficient (NTC) types, are widely employed as inrush current limiters due to their nonlinear resistance-temperature characteristics.

Mechanism of NTC Thermistors in Current Limiting

At room temperature, an NTC thermistor exhibits a high resistance, which restricts the initial current flow when power is applied. As current passes through the thermistor, Joule heating causes its temperature to rise, decreasing its resistance exponentially. This behavior is governed by the Steinhart-Hart equation:

where T is the temperature in Kelvin, R is the resistance, and A, B, C are device-specific coefficients. The time-dependent resistance R(t) during inrush can be approximated by solving the thermal differential equation:

where C_th is the thermal capacitance, k is the thermal dissipation constant, and I is the current.

Design Considerations for Inrush Limiting Circuits

Selecting an appropriate NTC thermistor requires balancing:

• Initial resistance (R₂₅): Must be high enough to limit peak inrush current to safe levels.
• Thermal time constant: Should allow the device to heat sufficiently during normal operation to minimize power loss.
• Current rating: Must exceed the steady-state operating current after stabilization.

The peak inrush current I_peak when charging a capacitor C through an NTC thermistor is:

where Ï„ = R₂₅C is the time constant. For repetitive power cycling, PTC thermistors or relay bypass circuits may be preferable to avoid cooling delays.

Practical Implementation and Trade-offs

In switch-mode power supplies, NTC thermistors are typically placed in series with the AC input or DC bus. Key challenges include:

• Energy dissipation: Thermistors in high-power applications may require heatsinking or active cooling.
• Recovery time: After power-off, the thermistor must cool before providing full inrush protection again.
• Failure modes: Cracked thermistors due to thermal cycling can fail short-circuit, eliminating protection.

Advanced designs often combine NTC thermistors with MOSFET-based active limiting circuits for improved reliability in mission-critical systems.

3.3 Overcurrent Protection

Thermistors play a critical role in overcurrent protection by leveraging their nonlinear resistance-temperature characteristics. When subjected to excessive current, a thermistor's self-heating effect causes its resistance to change dramatically, either limiting the current (in the case of PTC thermistors) or triggering a protective circuit (for NTC thermistors).

PTC Thermistors as Resettable Fuses

Positive Temperature Coefficient (PTC) thermistors exhibit a sharp increase in resistance beyond a critical temperature threshold, known as the switching temperature (T_sw). This behavior makes them ideal for resettable fuse applications. The power dissipation in a PTC thermistor under overcurrent conditions can be modeled as:

where R(T) is the temperature-dependent resistance. As the current exceeds the rated value, Joule heating raises the temperature beyond T_sw, causing R(T) to increase exponentially and effectively limiting the current. The time-to-trip depends on the thermal time constant (Ï„) of the device:

where C_th is the heat capacity and R_th is the thermal resistance to the environment.

NTC Thermistors in Inrush Current Limiting

Negative Temperature Coefficient (NTC) thermistors are often used to mitigate inrush currents in power supplies. Initially, their high resistance at ambient temperature limits the surge current. As they self-heat, their resistance drops, allowing normal operation. The energy absorption capability (E_max) is a critical parameter:

where T₀ is ambient temperature and T_max is the maximum allowable temperature. Exceeding E_max can lead to irreversible degradation.

Design Considerations

• Hold current vs. trip current: For PTCs, the hold current is the maximum steady-state current before tripping, while the trip current is the threshold for rapid resistance increase.
• Derating: Ambient temperature and heat dissipation conditions must be accounted for to avoid premature triggering or failure.
• Failure modes: PTCs may fail short-circuit if overheated beyond thermal runaway, while NTCs can crack under thermal shock.

Practical Implementation

In circuit design, PTC thermistors are often placed in series with the load, while NTCs are used in parallel with a bypass relay or MOSFET. For example, a telecom power supply might use a 10Ω NTC thermistor to limit inrush current to 12A (from a potential 100A surge), with a relay closing after 500ms to shunt the thermistor once steady-state is reached.

4.1 Thermistor Selection Criteria

Key Parameters for Thermistor Selection

Selecting an appropriate thermistor requires careful consideration of several critical parameters, each influencing performance in specific operating conditions. The primary factors include:

• Resistance-Temperature Characteristics (R-T Curve) – Defines the thermistor's response to temperature changes, typically following the Steinhart-Hart equation for NTC thermistors.
• Beta (β) Value or B-Parameter – A material constant describing the thermistor's sensitivity over a defined temperature range.
• Tolerance and Accuracy – Specifies permissible deviation from nominal resistance values at reference temperatures.
• Dissipation Constant (δ) – Measures self-heating effects due to power dissipation, critical for precision applications.
• Time Constant (Ï„) – Characterizes thermal response speed, crucial for dynamic temperature sensing.
• Operating Temperature Range – Determines the thermistor's functional limits.

Mathematical Modeling of Thermistor Behavior

The Steinhart-Hart equation provides a highly accurate model for NTC thermistor resistance as a function of temperature:

where T is temperature in Kelvin, R is resistance, and A, B, C are device-specific coefficients. For most applications, a simplified two-parameter version suffices:

Here, R₀ is the reference resistance at temperature T₀ (typically 25°C), and β is the material constant derived from:

Dissipation and Self-Heating Effects

Power dissipation in thermistors generates internal heat, introducing measurement errors. The dissipation constant δ (mW/°C) quantifies this effect:

where ΔT is the temperature rise and P is the applied power. For example, a bead-type thermistor with δ = 2 mW/°C dissipating 1 mW will self-heat by 0.5°C. Minimizing excitation current mitigates this error.

Stability and Aging Considerations

Thermistor stability degrades over time due to material oxidation or mechanical stress. Key aging mechanisms include:

• Resistance Drift – Gradual change in nominal resistance, typically <0.1°C/year for glass-encapsulated NTCs.
• Thermal Hysteresis – Discrepancy between heating/cooling cycles, particularly in PTC thermistors.

Epoxy-coated thermistors exhibit higher drift (up to 0.5°C/year) compared to hermetically sealed units.

Package Selection and Environmental Factors

Thermistor packaging directly impacts performance in harsh environments:

• Bead-Type – Fast response but fragile; suited for air/gas measurements.
• Surface-Mount (SMD) – Compact size with moderate thermal inertia, ideal for PCB temperature monitoring.
• Probe Assemblies – Metal-sheathed designs for liquid immersion or high-pressure applications.

Conformal coatings or hermetic sealing is essential for operation in corrosive or high-humidity environments.

Application-Specific Selection Guidelines

Precision Temperature Measurement: Use glass-encapsulated NTCs with tight tolerances (±0.1°C) and low self-heating. For example, medical thermometry requires MIL-STD-202 Method 108 testing for stability.

Inrush Current Limiting: Select PTC thermistors with:

Thermal Compensation: Match β values to the compensated component's temperature coefficient (e.g., crystal oscillators typically need β ≈ 4000K).

4.2 Signal Conditioning and Interfacing

Voltage Divider Configuration

Thermistors are commonly interfaced with microcontrollers or data acquisition systems using a voltage divider circuit. The thermistor (R_T) is placed in series with a fixed reference resistor (R_ref), and the output voltage (V_out) is measured across the thermistor. The relationship between resistance and voltage is given by:

Selecting R_ref requires careful consideration of the thermistor's resistance range. For NTC thermistors, R_ref is often chosen near the midpoint of the thermistor's operational range to maximize sensitivity. Nonlinearity can be mitigated by using a parallel resistor or applying software linearization techniques.

Analog-to-Digital Conversion

Since most microcontrollers accept analog voltage inputs, the voltage divider output is fed into an ADC. The ADC resolution and reference voltage (V_ref) determine the temperature measurement precision. For a 10-bit ADC with V_ref = 5V, the voltage quantization step is:

Higher-resolution ADCs (e.g., 16-bit) improve accuracy, particularly when measuring small resistance changes in high-precision applications.

Linearization Techniques

Thermistor response is inherently nonlinear, following the Steinhart-Hart equation:

Linearization can be achieved through:

• Hardware Linearization: A parallel resistor (R_p) can approximate linearity over a limited range. The optimal value is given by:

• Software Linearization: Polynomial fitting or lookup tables convert ADC readings to temperature values. The Steinhart-Hart coefficients (A, B, C) are derived from calibration data.

Noise Reduction and Filtering

Thermistor signals are susceptible to noise, particularly in long cable runs or high-EMI environments. Techniques include:

• Low-Pass Filtering: An RC filter with cutoff frequency f_c = 1/(2\pi RC) attenuates high-frequency noise.
• Averaging: Sampling the ADC multiple times and computing the mean reduces random noise.
• Shielding: Twisted-pair or shielded cables minimize electromagnetic interference.

Current Excitation Methods

For precision applications, constant-current excitation avoids self-heating errors. A current source (I) biases the thermistor, producing a voltage:

Self-heating must be minimized by limiting I to a few milliamps. For example, a 100 µA current through a 10 kΩ thermistor dissipates only 100 µW, reducing temperature drift.

Wheatstone Bridge Configuration

In high-precision applications, a Wheatstone bridge improves sensitivity. The bridge output voltage is:

When balanced (R_TR₄ = R₂R₃), V_out = 0. Small resistance changes unbalance the bridge, producing a measurable voltage proportional to temperature.

Digital Interface Solutions

Modern systems often use digital temperature sensors with I²C or SPI interfaces. However, thermistors remain advantageous in high-temperature or low-cost applications. Integrating a thermistor with a microcontroller requires:

• Calibration: Two-point calibration at known temperatures improves accuracy.
• Lookup Tables: Precomputed resistance-temperature pairs reduce real-time computation.
• Linear Approximation: For small ranges, a first-order Taylor expansion simplifies calculations.

4.3 Common Pitfalls and Troubleshooting

Self-Heating Errors

Thermistors dissipate power when current flows through them, leading to self-heating. This effect introduces measurement errors, particularly in high-resolution applications. The power dissipation \( P \) is given by:

where \( I \) is the bias current and \( R \) is the thermistor resistance. To minimize self-heating:

• Use the lowest feasible excitation current (typically µA to mA range).
• Employ pulsed measurements to reduce continuous power dissipation.
• Verify thermal time constants to ensure equilibrium before sampling.

Nonlinearity Compensation

The Steinhart-Hart equation models thermistor resistance-temperature relationships with high accuracy:

5.1 Key Research Papers and Datasheets

• PDF Ntc Disc Thermistors - Kyocera Avx — NTC DISC THERMISTORS Packaging for Automatic Insertion PACKAGING AND KINK SUFFIXES Tables below indicate the suffixes to specify when ordering to get the ... Paper 42 (1.66) Inside 48(1.99) Outside 31 (1.22) 360 (14.2) L I H 330 (13.0) 46 (1.81) 290 (11.4) h h H1 H1 H P1 P0 P d W E t A B W2 W1 H0 E I2 D0 p p W0 A - B Cross section
• PDF NTC thermistors for temperature measurement - TDK Electronics AG — SMD NTC thermistors, case size 1206 (3216) Standard series Please read Cautions and warnings and Page 6 of 25 Important notes at the end of this document. 4 Taping of radial leaded NTC thermistors Dimensions and tolerances Lead spacing F = 2.5 mm and 5.0 mm (taping to IEC 60286-2) Dimensions (mm) Lead spacing 2.5 mm Lead spacing
• PDF NTC thermistors for temperature measurement - TDK — Not applicable for SMD thermistors (component has no marking, color coding or coating) Mechanical shock MIL-STD-202, method 213 Peak value: 1500 g Half sine Condition F < 5% Temperature measurement and compensation B573**V5 SMD NTC thermistors, case size 0603 (1608) Automotive series Please read Cautions and warnings and Page 4 of 29
• PDF PTC thermistors, general technical information - TDK Electronics AG — vidual types of PTC thermistors it is defined as the temperature at which the zero-power resis-tance is equal to the value Rref = 2 · Rmin. In the data sheet section we specify typical values of Tref. 5.1.5 Temperature coefficient α The temperature coefficient of resistance αis defined as the relative change in resistance re-
• PDF PTC thermistors, general technical information - TDK Electronics AG — 5.1.2 RatedresistanceRR TheratedresistanceRRistheresistancevalueattemperatureTR.PTCthermistorsareclassified accordingtothisresistancevalue.ThetemperatureTRis25°C ...
• PDF Temperature Sensing with Thermistors (Rev. A) - Texas Instruments — integrated circuit temperature sensors, thermistors, thermocouples and resistance temperature detectors; all have their pros and cons. In this white paper, I'll focus on one of the most common temperature sensors, the thermistor; highlight some important considerations when using thermistors for temperature-sensing applications; and compare two
• Thermistors,Their Theory,Manufacture and Application — Thermistors are components of comparatively recent development, although the phenomenon of conduction in metallic salts was recorded by Faraday over a century ago. The paper, in a broad survey of the subject, describes the theory of their operation, explains why they, in common with other semiconductor devices, possess a negative temperature coefficient of resistance and develops the ...
• (PDF) Semiconductor Thermistors - ResearchGate — Semiconductor thermistors operating in the variable range hopping conduction regime have been used in thermal detectors of all kinds for more than fifty years.
• (PDF) Thermistor - ResearchGate — A thermistor is defined in conjunction with its application as a two-terminal circuit element. The three major thermistor characteristics, by which all applications are classified, are defined and ...
• Evaluation of Thermistors Used for Temperature Measurement in ... — In this paper, both the design and hardware of Fault Detection (FD) in Wireless Sensor Network (WSN) was implemented using FPGA NI myRIO kit, wireless temperature sensors network with small size ...

5.2 Recommended Books and Articles

• PDF PTC thermistors, general technical information - TDK Electronics AG — 5.1.2 Rated resistance RR The rated resistance RR is the resistance value at temperature TR.PTC thermistors are classified according to this resistance value. The temperature TR is 25 °C, unless otherwise specified. 5.1.3 Minimum resistance Rmin The beginning of the temperature range with a positive temperature coefficient is specified by the
• PDF PTC thermistors, general technical information - TDK Electronics AG — 5.1.2 RatedresistanceRR TheratedresistanceRRistheresistancevalueattemperatureTR.PTCthermistorsareclassified accordingtothisresistancevalue.ThetemperatureTRis25°C ...
• Fundamentals of Thermal Sensors - SpringerLink — But thermistors have the advantages of being small in size, inexpensive to buy and very sensitive to temperature changes, so they can be ideal to use in many electronics applications (Janata 2009). 2.1.2.4 Silicon Sensors. These sensors are made of silicon, a semiconductor that is used as the base material for most electronic microprocessors.
• (PDF) Hand Book of Electronics - ResearchGate — PDF | On Jan 1, 2010, D.K. Kaushik published Hand Book of Electronics | Find, read and cite all the research you need on ResearchGate
• Recent Advances in Flexible Temperature Sensors: Materials, Mechanism ... — Her research interests focus on the functional thermistor membranes. Aimin Chang is a full professor at Xinjiang Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, and director of Xinjiang Key Laboratory of Electronic Information Materials and Devices. He received his Ph.D. from University of Electronic Science and ...
• Strategies for thermal management of electronics: Design, development ... — Download: Download full-size image Fig. 2. Examples of air-cooling systems for electronic devices, (A) a typical passive air-cooling battery thermal management system (BTMS) in which air passes from the battery inlets on one side of the battery pack between cells, and finally exits through outlets under the relative movement of the vehicle [50], (B) an additively manufactured air jet ...
• Thermistor - an overview | ScienceDirect Topics — The metre M, which measures the output voltage across terminals, instantly follows the variations of the sensor, and with an appropriate choice of R 1, R 2, and R 3, the output voltage directly equals the value of the thermistor temperature.Output accuracy and departure from linearity can be better than 0.1°C. Main sources of errors are instability of the bridge excitation; condensation or ...
• Smart temperature sensors and temperature sensor systems — Thermistors are very sensitive but not as stable as Pt resistors. They are widely applied for the temperature range of about −80°C to 180°C. In addition to their high sensitivity, thermistors offer the advantages of being small in size and inexpensive. However, their strong nonlinearity complicates the processing of the thermistor signal.
• NTC PCB Thermistors as Temperature Sensors | Projects - Altium — In the introduction to this series, we started work on testing all the different types of temperature available by building a set of project templates: one for analog sensors and one for digital sensors. You can find those templates and the sensor implementations for these NTC thermistors on GitHub.As always, these projects are open source, released under the MIT license allowing you to use ...
• Silicon diode temperature sensors—A review of applications — Silicon diodes provide the best possible solution for temperature measurement and compensation of pressure sensors, because of the simplicity of circuit design and ease of on-chip integration. One such example is a resonant beam pressure sensor [37] , where temperature measurement and compensation was done by an on-chip silicon diode ...

5.3 Online Resources and Tutorials

• 5.3 Transistor 2021 - Flip eBook Pages 1-50 | AnyFlip — Transistor ialah alat electronic yang berfungsi sebagai ... TUTORIAL 5.3 Amplifier / suis automatik Amplifier / automatic switch Bila ada cahaya, rintangan LDR ... Thermistor / heat dependent resistor and siren / bell. V = IR = (40000) 6 = 4.8 V 50000 I = V/R = 6/[10000 + 40000]
• Module 5 new - Hand written notes use properly - Studocu — The resistance thermometer has a potentially -higher sensitivity and higher resolution, almost throughout the range. One such type, recommended for precision measurements is the platinum resistance thermometer which is ideally suited in the temperature range 93 to 873 K. The semiconductor-type resistance thermometers, such as thermistors and ...
• What Is Thermistor and How Does It Works？ - JAK Electronics — â…ª Thermistor Application Circuits. Thermistor Application Circuit (1) The figure is a temperature compensation circuit using a thermistor. It is a temperature compensation circuit of infrared light-emitting diode VD1. VD1 is used as a photoelectric detector for modulating light. The maximum current is 5OmA and the temperature range is 10-55 °C.
• PDF PTC thermistors, general technical information - TDK Electronics AG — 5.1.2 RatedresistanceRR TheratedresistanceRRistheresistancevalueattemperatureTR.PTCthermistorsareclassified accordingtothisresistancevalue.ThetemperatureTRis25°C ...
• 5.10 Thermometer — SunFounder ESP32 Starter Kit documentation — RT =RN expB(1/TK - 1/TN) RT is the resistance of the NTC thermistor when the temperature is TK.. RN is the resistance of the NTC thermistor under the rated temperature TN. Here, the numerical value of RN is 10k. TK is a Kelvin temperature and the unit is K. Here, the numerical value of TK is 273.15 + degree Celsius.. TN is a rated Kelvin temperature; the unit is K too.
• PDF S2014, BME 101L: Applied Circuits Lab 1 Temperature measurement|Thermistor — material used in the thermistor, and R T 0 is the resistance at some calibration temperature T 0. We can also write this as R = R T 0 e B(1=T 1=T 0) or R = R 1eB=T; where R 1is the projected \resistance at in nity", R T 0 e B=T 0. For example, the thermistor we will use in this lab (NTCLE413E2103F520L) has a data sheet at
• Make an Arduino Temperature Sensor using Thermistor - Circuit Geeks — A thermistor would be ideal for your remote weather stations project, home automation systems, temperature control, protection circuit, etc. In this tutorial, I will explain how a thermistor works and how you can build a small circuit with Arduino and a thermistor that displays the temperature on the serial monitor or on an LCD display.
• PDF PTC thermistors, application notes - TDK Electronics AG — 1.1.4 Selectioncriteria Incircuitdesign,thefollowingconsiderationsshouldbeborneinmindwhenselectingaPTCther-mistorasovercurrentprotector. Maximumvoltage
• PDF Experiment 5 Thermocouples 3 - Michigan Technological University — Objective: To implement a thermocouple circuit, including thermistor-based cold-junction compensation, for temperature sensing. I. Introduction to Thermocouples A. Fundamental laws 1. Seebeck Voltage When two dissimilar metals are joined at one end, an electrical potential called the "Seebeck voltage" is generated, which changes ...