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# PTC Thermistor

Positive temperature coefficient (PTC) thermistor

Libraries:
Simscape / Electrical / Sensors & Transducers

## Description

The PTC thermistor block models a positive temperature coefficient (PTC) thermistor. To model a switching PTC thermistor or a resistance temperature detector (RTD), use this block. To model a non-switching linear PTC thermistor, use the Thermal Resistor block.

The thermal behavior of the block uses the equation

`$Q={K}_{d}{t}_{c}\frac{dT}{dt}-{I}^{2}R,$`

where:

• Q is the net heat flow into the A port.

• Kd is the Dissipation factor parameter value.

• tc is the Thermal time constant parameter value.

• dT/dt is the rate of change of temperature with respect to time.

• I is the current.

• R is the resistance.

Note

You must not connect the PTC Thermistor block to an ideal current source. This arrangement creates a positive feedback loop that results in thermal runaway because:

• Increasing the temperature increases the resistance

• Increasing the resistance with an ideal current source increases the voltage

• Increasing the voltage increases the dissipated power

• Increasing the dissipated power increases the temperature, which closes the loop

### Temperature Operating Limits

Since R2024a

If you set the Thermistor parameterization type parameter to `Switching Thermistor`, you can choose whether to specify the range of operating temperatures by using the Enable temperature operating limits parameter. If you set the Thermistor parameterization type parameter to `RTD (Callendar - Van Dusen coefficients)`, you must specify the range of operating temperatures.

Specify the lower and upper temperature operating limits by setting the Minimum operating temperature and Maximum operating temperature parameters, respectively. Find these values on a datasheet. If the temperature falls outside of the operating limits:

• If you set Reporting if operating limits exceeded to `Warn`, Simulink® displays a warning and the simulation continues.

• If you set Reporting if operating limits exceeded to `Error`, Simulink displays an error and terminates the simulation.

### Switching Thermistor

To model a switching PTC thermistor, set the Thermistor parameterization type parameter to `Switching Thermistor`. This type of thermistor has a decreasing resistance with increasing temperature up to the Curie temperature Tc. Above the Curie temperature, the resistance increases rapidly with increasing temperature. The region to the right of Tc in this figure is called the PTC regime.

This equation defines the resistance R at temperature T,

`$R=\left\{\begin{array}{r}{R}_{0}{e}^{{\alpha }_{0}\left(T-{T}_{0}\right)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}T\le {T}_{c}\\ {R}_{1}{e}^{{\alpha }_{1}\left(T-{T}_{1}\right)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{​}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}T\ge {T}_{c}\end{array}$`
`${T}_{c}=\frac{\mathrm{log}\left({R}_{1}\right)-\mathrm{log}\left({R}_{0}\right)+{\alpha }_{0}{T}_{0}-{\alpha }_{1}{T}_{1}}{{\alpha }_{0}-{\alpha }_{1}}$`

where:

• R0 is the resistance at the nominal temperature.

• R1 is the resistance at the reference temperature.

• α0 is the temperature coefficient at the nominal temperature.

• α1 is the temperature coefficient at the reference temperature.

• T0 is the nominal temperature at which you quote the nominal resistance, usually room temperature. T0 must be less than the Curie temperature.

• T1 is the reference temperature at which you quote the reference resistance. T1 must be in the PTC regime.

### Resistance Temperature Detector

Since R2024a

To model an RTD, set the Thermistor parameterization type to `RTD (Callendar - Van Dusen coefficients)`. The Callendar–Van Dusen equation defines the resistance R at temperature T. This equation uses T measured in degC,

`$R=\left\{\begin{array}{r}{R}_{0}\left(1+AT+B{T}^{2}+C\left(T-100\right){T}^{3}\text{​}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{​}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}T\le 0\\ {R}_{0}\left(1+AT+B{T}^{2}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}T\ge 0\end{array}$`

where:

• R0 is the resistance at the nominal temperature of 0 degC.

• A, B, and C are the Callendar–Van Dusen coefficients.

You can find these coefficients on a datasheet. The default parameter values that the block uses are typical for platinum RTDs. The R-T characteristic is approximately linear within the range of operating temperatures so choose values of B and C that are several orders of magnitude smaller than A.

Simulink displays a warning if the resistance does not increase monotonically over the range of operating temperatures. If you set the Reporting if operating limits exceeded parameter to `Warn` and the temperature falls outside of the operating range, the block uses linear extrapolation to calculate the resistance with respect to temperature.

### Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Use nominal values to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources. One of these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

## Ports

### Conserving

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Thermal conserving port associated with the thermal mass.

Electrical conserving port associated with the positive terminal.

Electrical conserving port associated with the negative terminal.

## Parameters

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### Electrical

Since R2024a

Thermistor type. This parameter determines the equations that the block uses to calculate the resistance as a function of temperature. Choose one of these options:

• `Switching Thermistor` — Model a switching thermistor. Specify the temperature coefficient and electrical resistance at a nominal temperature and a reference temperature.

• ```RTD (Callendar - Van Dusen coefficients)``` — Model a resistance temperature detector. Specify the Callendar–Van Dusen coefficients and the nominal resistance at 0 degC.

Resistance at the nominal temperature. Datasheets often list the nominal resistance at 25 degrees Celsius as R25.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```Switching Thermistor```.

Temperature coefficient at the nominal temperature.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```Switching Thermistor```.

Temperature at which you quote the nominal resistance.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```Switching Thermistor```.

Resistance at the reference temperature.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```Switching Thermistor```.

Temperature coefficient at the reference temperature.

Temperature at which you quote the reference resistance. This temperature must be in the PTC regime.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```Switching Thermistor```.

Since R2024a

Resistance at the nominal temperature of 0 degrees Celsius.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

Since R2024a

`A` coefficient in the Callendar–Van Dusen equation. The default value is typical for platinum RTDs.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

Since R2024a

`B` coefficient in the Callendar–Van Dusen equation. The default value is typical for platinum RTDs.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

Since R2024a

`C` coefficient in the Callendar–Van Dusen equation. The default value is typical for platinum RTDs.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

### Temperature Operating Limits

Since R2024a

Option to specify the operating limits for the temperature.

#### Dependencies

To enable this parameter, set Thermistor parameterization type to ```Switching Thermistor```.

Since R2024a

Reporting if the temperature falls outside of the operating limits. Choose one of these options:

• `Warn` — Simulink displays a warning and the simulation continues.

• `Error` — Simulink displays an error and terminates the simulation.

#### Dependencies

To enable this parameter, choose one of these options:

• Set Thermistor parameterization type to ```Switching Thermistor``` and Enable temperature operating limits to `Yes`.

• Set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

Since R2024a

Lower limit of the operating temperature range.

#### Dependencies

To enable this parameter, choose one of these options:

• Set Thermistor parameterization type to ```Switching Thermistor``` and Enable temperature operating limits to `Yes`.

• Set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

Since R2024a

Upper limit of the operating temperature range.

#### Dependencies

To enable this parameter, choose one of these options:

• Set Thermistor parameterization type to ```Switching Thermistor``` and Enable temperature operating limits to `Yes`.

• Set Thermistor parameterization type to ```RTD (Callendar - Van Dusen coefficients)```.

### Thermal

Time it takes for the thermistor temperature to change by 63% of the final temperature change when there is a step change in the ambient temperature.

Thermal power needed to raise the thermistor temperature by 1 K.

## Version History

Introduced in R2012b

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