Model switching type positive temperature coefficient (PTC) thermistor

Sensors

The PTC Thermistor block represents a switching type PTC thermistor. This type of thermistor has a decreasing resistance with temperature increasing up to the Curie temperature. Above the Curie temperature the resistance increases very rapidly with increasing temperature, as shown in the following plot. The region to the right of the Curie temperature is called the Positive Temperature Coefficient (PTC) regime. To represent a non-switching linear PTC thermistor, use the Thermal Resistor block.

For a switching type PTC thermistor, the resistance *R* at
temperature *T* is given by

$$R=\{\begin{array}{ll}{R}_{0}{e}^{{\alpha}_{0}\left(T-{T}_{0}\right)}\hfill & \text{for}T\text{}{T}_{\text{c}}\hfill \\ {R}_{1}{e}^{{\alpha}_{1}\left(T-{T}_{1}\right)}\hfill & \text{for}T\text{}\ge \text{}{T}_{\text{c}}\text{}\hfill \end{array}$$

$${T}_{c}=\frac{\mathrm{log}\left({R}_{1}\right)-\mathrm{log}\left({R}_{0}\right)+{\alpha}_{0}{T}_{0}-{\alpha}_{1}{T}_{1}}{{\alpha}_{0}-{\alpha}_{1}}$$

where:

*T*_{c}is the Curie temperature.*R*_{0}is the resistance at nominal temperature*T*_{0}.*R*_{1}is the resistance at reference temperature*T*_{1}.*T*_{0}is the nominal temperature at which the resistance is quoted, usually room temperature.*T*_{0}is less than the Curie temperature*T*_{c}.*T*_{1}is the reference temperature, equal or greater than the Curie temperature*T*_{c}, which means that at this temperature the PTC regime is in force.*α*_{0}is the temperature coefficient at nominal temperature*T*_{0}.*α*_{1}is the temperature coefficient at reference temperature*T*_{1}.

The following equation describes the thermal behavior of the block:

$$Q={K}_{d}{t}_{c}\frac{dT}{dt}$$

where:

*Q*is the net heat flow into port A.*K*_{d}is the**Dissipation factor**parameter value.*t*_{c}is the**Thermal time constant**parameter value.*dT/dt*is the rate of change of the temperature.

**Nominal resistance R0 at T0**The nominal resistance of the thermistor at the nominal temperature. Many datasheets quote the nominal resistance at 25°C and list it as R25. The default value is

`1000`

Ω.**Temperature coefficient alpha0 at T0**The temperature coefficient at the nominal temperature. The value must be less than zero. The default value is

`-0.01`

1/K.**Nominal temperature T0**The temperature at which the nominal resistance is measured. The default value is

`298.15`

K.**Reference resistance R1 at T1**The reference resistance of the thermistor at the reference temperature. The default value is

`10000`

Ω.**Temperature coefficient alpha1 at T1**The temperature coefficient at the reference temperature. The value must be greater than zero. The default value is

`1`

1/K.**Reference temperature T1**The temperature at which the reference resistance is measured. This temperature must be in the PTC regime. The default value is

`398.15`

K.

**Thermal time constant**The time it takes the sensor temperature to reach 63% of the final temperature change when a step change in ambient temperature occurs. The default value is

`5`

s.**Dissipation factor**The thermal power required to raise the thermistor temperature by one K. The default value is

`7.5e-4`

W/K.**Initial temperature**The temperature of the thermistor at the start of the simulation. The default value is

`298.15`

K.

The block has the following ports:

`A`

Thermal port

`+`

Positive electrical port

`-`

Negative electrical port

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