What is the formula for thermistor?
1 Answer
A thermistor is a type of resistor whose resistance changes significantly with temperature. The relationship between the resistance of a thermistor and temperature is typically nonlinear and can be expressed using a few common formulas. The most widely used formulas are the **Steinhart-Hart equation** and the **Beta parameter equation**.
### 1. **Steinhart-Hart Equation**
This is a more accurate and widely used equation for thermistors, especially for a broad range of temperatures. The Steinhart-Hart equation is given by:
\[
\frac{1}{T} = A + B \ln(R) + C (\ln(R))^3
\]
Where:
- \( T \) is the temperature (in Kelvin, K),
- \( R \) is the resistance of the thermistor at temperature \( T \),
- \( A \), \( B \), and \( C \) are constants that are specific to the thermistor.
This equation is typically used for thermistors with high accuracy requirements across a broad range of temperatures. The constants \( A \), \( B \), and \( C \) are determined experimentally for each specific thermistor type.
### 2. **Beta Parameter Equation (simplified version)**
The Beta parameter equation is a simpler form of the relationship between the thermistor's resistance and temperature. It is generally accurate over a smaller range of temperatures and is often used for thermistors with a known Beta value. The equation is given by:
\[
R(T) = R_0 \exp\left( \frac{\beta}{T} \left( \frac{1}{T} - \frac{1}{T_0} \right) \right)
\]
Where:
- \( R(T) \) is the resistance at temperature \( T \) (in ohms),
- \( R_0 \) is the resistance at a reference temperature \( T_0 \),
- \( \beta \) is the Beta constant (in Kelvin),
- \( T \) and \( T_0 \) are the temperatures in Kelvin (the temperature at which \( R_0 \) is measured and the temperature of interest).
In this equation:
- \( T_0 \) is usually a reference temperature (often 25°C or 298 K),
- \( R_0 \) is the resistance at this reference temperature,
- \( \beta \) is a material-specific constant that determines the rate of resistance change with temperature.
### 3. **Simplified Linear Approximation (for small temperature ranges)**
For small temperature ranges, the resistance of a thermistor can be approximated linearly. This is useful when high accuracy is not needed but a simple calculation is sufficient:
\[
R(T) = R_0 \left( 1 + \alpha (T - T_0) \right)
\]
Where:
- \( \alpha \) is the temperature coefficient of resistance (in per degree Celsius),
- \( T \) is the temperature (in °C or K),
- \( T_0 \) is the reference temperature (usually 25°C).
This approximation is generally used when the temperature change is relatively small and the resistance change is roughly linear.
### Key Considerations
- **Thermistor Type**: There are two main types of thermistors: **NTC (Negative Temperature Coefficient)** and **PTC (Positive Temperature Coefficient)**. In NTC thermistors, resistance decreases as temperature increases, whereas in PTC thermistors, resistance increases as temperature increases.
- **Beta Value**: The Beta value describes how sensitive a thermistor is to temperature changes. It is a key factor in determining the accuracy of the thermistor's resistance-temperature relationship.
### Summary of Key Equations:
1. **Steinhart-Hart Equation**: For high accuracy over a wide temperature range.
2. **Beta Parameter Equation**: For simpler applications with known Beta values.
3. **Linear Approximation**: For small temperature ranges or when only an approximation is needed.
Each formula is suitable for different applications depending on the level of accuracy required and the temperature range in question.
### 1. **Steinhart-Hart Equation**
This is a more accurate and widely used equation for thermistors, especially for a broad range of temperatures. The Steinhart-Hart equation is given by:
\[
\frac{1}{T} = A + B \ln(R) + C (\ln(R))^3
\]
Where:
- \( T \) is the temperature (in Kelvin, K),
- \( R \) is the resistance of the thermistor at temperature \( T \),
- \( A \), \( B \), and \( C \) are constants that are specific to the thermistor.
This equation is typically used for thermistors with high accuracy requirements across a broad range of temperatures. The constants \( A \), \( B \), and \( C \) are determined experimentally for each specific thermistor type.
### 2. **Beta Parameter Equation (simplified version)**
The Beta parameter equation is a simpler form of the relationship between the thermistor's resistance and temperature. It is generally accurate over a smaller range of temperatures and is often used for thermistors with a known Beta value. The equation is given by:
\[
R(T) = R_0 \exp\left( \frac{\beta}{T} \left( \frac{1}{T} - \frac{1}{T_0} \right) \right)
\]
Where:
- \( R(T) \) is the resistance at temperature \( T \) (in ohms),
- \( R_0 \) is the resistance at a reference temperature \( T_0 \),
- \( \beta \) is the Beta constant (in Kelvin),
- \( T \) and \( T_0 \) are the temperatures in Kelvin (the temperature at which \( R_0 \) is measured and the temperature of interest).
In this equation:
- \( T_0 \) is usually a reference temperature (often 25°C or 298 K),
- \( R_0 \) is the resistance at this reference temperature,
- \( \beta \) is a material-specific constant that determines the rate of resistance change with temperature.
### 3. **Simplified Linear Approximation (for small temperature ranges)**
For small temperature ranges, the resistance of a thermistor can be approximated linearly. This is useful when high accuracy is not needed but a simple calculation is sufficient:
\[
R(T) = R_0 \left( 1 + \alpha (T - T_0) \right)
\]
Where:
- \( \alpha \) is the temperature coefficient of resistance (in per degree Celsius),
- \( T \) is the temperature (in °C or K),
- \( T_0 \) is the reference temperature (usually 25°C).
This approximation is generally used when the temperature change is relatively small and the resistance change is roughly linear.
### Key Considerations
- **Thermistor Type**: There are two main types of thermistors: **NTC (Negative Temperature Coefficient)** and **PTC (Positive Temperature Coefficient)**. In NTC thermistors, resistance decreases as temperature increases, whereas in PTC thermistors, resistance increases as temperature increases.
- **Beta Value**: The Beta value describes how sensitive a thermistor is to temperature changes. It is a key factor in determining the accuracy of the thermistor's resistance-temperature relationship.
### Summary of Key Equations:
1. **Steinhart-Hart Equation**: For high accuracy over a wide temperature range.
2. **Beta Parameter Equation**: For simpler applications with known Beta values.
3. **Linear Approximation**: For small temperature ranges or when only an approximation is needed.
Each formula is suitable for different applications depending on the level of accuracy required and the temperature range in question.