In this experiment, we explore the temperature dependence of the resistivity of an NTC (Negative Temperature Coefficient) thermistor, specifically a 10k Ohm NTC-10 k-type thermistor. The system is designed to monitor and log data using an Arduino D1 mini-board, which measures both the thermistor's resistivity and the temperature of the water as it cools down over time. Additionally, a DS18B20 digital temperature sensor is used to measure the water temperature accurately, and the collected data is transmitted to ThingSpeak via Wi-Fi for real-time recording and analysis.

Where:

• R(T) is the thermistor’s resistance at temperature T (in Kelvin),

• R0​ is the resistance at a reference temperature T0​ (usually 25°C),

• β is the thermistor’s material constant (typically provided by the manufacturer).

The thermistor used in this experiment is rated at 10k Ohms at 25°C, meaning at room temperature (298K), the resistance is 10k Ohms. As the water cools down, the thermistor’s resistance increases in response to the decreasing temperature.

2. DS18B20 Digital Temperature Sensor: The DS18B20 is a digital thermometer that provides precise temperature measurements and can be directly interfaced with the Arduino. It outputs temperature values with high accuracy (±0.5°C from -10°C to +85°C). This sensor serves as a reference for the actual water temperature, enabling a comparison with the resistivity data from the thermistor.

3. Resistance-Temperature Relationship in NTC Thermistors: As temperature decreases, the resistance of the NTC thermistor increases. We can determine its resistance at various temperatures by continuously measuring the voltage across the thermistor in a voltage divider circuit. The resistance R can be derived from the voltage across the thermistor using Ohm’s Law in the context of the voltage divider:

Where:

• Vin​ is the input voltage,

• Vout is the measured voltage across the thermistor,

• Rfixed​ is a known resistor value in the voltage divider.

4. Data Logging with ThingSpeak: The Arduino D1 mini board has a Wi-Fi module, allowing it to send real-time data to ThingSpeak, an IoT analytics platform. ThingSpeak provides a way to visualize the temperature and resistivity data over time, creating graphs displaying how the resistance changes as the water cools. This enables further analysis, such as fitting the experimental data to theoretical models and extracting parameters like the thermistor’s β-value.

5. Experimental Setup:

• The thermistor is submerged in hot water, and the DS18B20 monitors the cooling process.

• The Arduino reads the thermistor’s resistance by measuring the voltage drop across it and sends this data and the temperature readings from the DS18B20 to ThingSpeak over Wi-Fi.

• Over time, the thermistor's resistivity increases as the water temperature decays, and both sets of data (temperature and resistivity) are recorded for analysis.

 Detailed Description:

• NTC Thermistor and Manufacturer Data: The table on the right provides the relationship between the resistance of the NTC-10 k thermistor and temperature, as defined by the manufacturer. These values allow us to estimate the thermistor’s behavior across different temperatures.

• β Calculation with Two Points: A common method to calculate the thermistor’s β value involves using two specific temperature points from the available data. While this approach gives a rough approximation of the β value, it doesn’t fully capture the non-linear behavior of the thermistor over a wider temperature range.

• Limitations of the Two-Point Method: The resistance of an NTC thermistor does not follow a simple linear relationship with temperature, making the two-point calculation less accurate. The resulting β value only approximates the thermistor’s characteristics over the selected range, leading to deviations from the actual resistance-temperature curve.

• Steinhart-Hart Equation: The Steinhart-Hart equation can be used to improve accuracy. This method involves three known temperature-resistance points and provides a more accurate NTC thermistor behavior model. The Steinhart-Hart equation is:

• Where:

  • T is the temperature in Kelvin,

  • R is the thermistor’s resistance at that temperature,

  • A, B, and C are constants determined by using three reference temperature-resistance pairs.

• This approach allows for more precise modeling of the thermistor’s temperature response across a broader range, leading to a more accurate β value.

Thus, while the two-point method provides a quick and approximate solution, the Steinhart-Hart equation is recommended for more precise calculations, especially in applications where accuracy across a broader temperature range is critical.

The temperature coefficient of resistance (α) refers to the rate of change in the thermistor's zero-load resistance for every 1°C change in temperature at any given temperature. The relationship between the temperature coefficient of resistance (α) and the β value of the thermistor can be expressed using the following formula:

Detailed Description:

• Temperature Coefficient of Resistance (α): This coefficient quantifies how much the resistance of a thermistor changes in response to a 1°C shift in temperature. It is a critical parameter for understanding the sensitivity of the thermistor to temperature variations. The larger the absolute value of α, the more sensitive the thermistor's resistance is to temperature changes.

• Zero-Load Resistance: Zero-load resistance refers to the thermistor's resistance when no external electrical load is applied. In this context, α describes how this resistance shifts with temperature changes, directly measuring the thermistor’s temperature sensitivity.

• Relationship to the β Value: The β value characterizes the overall temperature behavior of an NTC thermistor. The relationship between α and β shows that the temperature coefficient α is inversely proportional to the square of the absolute temperature (T), and it scales with the β value. This means that for higher β values, the thermistor's resistance becomes more sensitive to temperature changes, as reflected by a higher absolute value of α.

• Application of the Formula: The α value at a specific temperature can be calculated using the β value and the absolute temperature T (in Kelvin). This formula highlights the connection between the long-term temperature behavior (represented by β) and the immediate sensitivity of the thermistor (represented by α) at a given temperature.

Understanding the temperature coefficient of resistance and its relationship to the β value allows for more accurate predictions of how the thermistor will respond to temperature changes in various applications, such as temperature sensing and control systems.

 To enhance the understanding of thermistor behavior, let’s add some information on PTC (Positive Temperature Coefficient) thermistors for comparison with the NTC (Negative Temperature Coefficient) thermistor used in this experiment.

PTC Thermistor Characteristics

1. Definition: A PTC thermistor is a type of thermistor in which the resistance increases as the temperature rises. This behavior contrasts with NTC thermistors, where the resistance decreases with increased temperature.

2. Behavior: PTC thermistors exhibit a non-linear increase in resistance with temperature, particularly beyond a critical threshold known as the Curie temperature. Below this temperature, the PTC thermistor behaves similarly to a typical resistor with a slight increase in resistance. However, once the Curie temperature is reached, the resistance rises sharply.
   The temperature-resistance relationship can be expressed as:

1. Where:

   • R(T) is the resistance at temperature T,

   • R0​ is the resistance at the reference temperature T0,

   • α is the temperature coefficient of resistance.

2. After passing the Curie point, α\alphaα becomes significantly larger, causing a sharp increase in resistance.

3. Applications:

   • Over-current protection: PTC thermistors are widely used in circuits to protect against overheating. When the current rises and the temperature increases, the thermistor’s resistance increases sharply, limiting the current flow.

   • Temperature control: PTC thermistors are used to control heating elements. As the temperature increases, the PTC thermistor reduces current, preventing overheating.

   • Self-regulating heaters: PTC thermistors can be used in heaters that regulate their temperature, as the increase in temperature reduces current flow, preventing excessive heating.

4. Comparison with NTC Thermistors:

   • Response to temperature: In NTC thermistors, resistance decreases with increasing temperature, while in PTC thermistors, resistance increases with increasing temperature, especially past the Curie temperature.

   • Applications: NTC thermistors are used in temperature sensing and precision measurements where a decrease in resistance is desired with temperature rise (e.g., temperature control systems, thermometers). PTC thermistors are used in self-regulating circuits, over-current protection, and heating elements where a sharp increase in resistance with temperature is beneficial.

   • Resistance range: NTC thermistors generally provide a wider range of resistance changes over temperature, making them more suitable for precise temperature measurements over a broad range. PTC thermistors have a more abrupt resistance change, making them ideal for switching or control applications.

PTC and NTC Comparison in Practice:

In this experiment, we focus on the NTC thermistor to measure how its resistivity changes with temperature as the water cools. By contrast, a PTC thermistor would show the opposite behavior, with increasing resistivity as the water temperature drops. Both types of thermistors are used in practical applications, but their differing behaviors make them suited for different types of temperature-related functions.

This comparison highlights the complementary nature of NTC and PTC thermistors in various applications, particularly in thermal management and temperature sensing technologies.