# Thermocouple

Sensor that converts thermal potential difference into electrical potential difference

**Library:**Simscape / Electrical / Sensors & Transducers

## Description

The Thermocouple block represents a thermocouple using the standard polynomial parameterization defined in the NIST ITS-90 Thermocouple Database [1].

For thermocouples Type B, E, J, K (t<=0 degC), N, R, S or T, the voltage
*E* across the device in mV is

$$E(mV)={c}_{0}+{c}_{1}t+\mathrm{...}+{c}_{n}{t}^{n}$$

where:

*ci*is the*i*element of the^{th}**Coefficients [c0 c1 ... cn]**parameter value.*t*is the temperature difference in degrees Celsius between the temperature at the thermal port A and the**Reference temperature**parameter value.

**Note**

The equation for voltage across the device as a function of temperature difference is defined in mV. The units of the voltage across the actual device is V.

For thermocouples Type K (t>=0 degC), the equation contains an additional exponential term:

$$E(mV)={c}_{0}+{c}_{1}t+\mathrm{...}+{c}_{n}{t}^{n}+{a}_{0}{e}^{{a}_{1}{\left(t-{a}_{2}\right)}^{2}}$$

where *a*_{0},
*a*_{1}, and
*a*_{2} are additional coefficients, required
only by the Type K thermocouple, defined by the **Coefficients [a0 a1
a2]** parameter value.

The following equation describes the thermal behavior of the block:

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

where:

*T*is the temperature at port A.*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.

To model the thermocouple in free space:

Connect the thermocouple to the B port of a Simscape™ Convective Heat Transfer block.

Connect the A port of the Convective Heat Transfer block to a Simscape Ideal Temperature Source block whose temperature is set to the ambient temperature.

Set the

**Area**parameter of the Convective Heat Transfer block to an approximate area*A*_{nom}.Set the

**Heat transfer coefficient**parameter of the Convective Heat Transfer block to*K*_{d}/*A*_{nom}.

## Assumptions and Limitations

The high-order polynomials this block uses are very sensitive to the number of significant figures used for computation. Use all available significant figures when specifying the

**Coefficients [c0 c1 ... cn]**parameter.**Coefficients [c0 c1 ... cn]**are defined for use over a specified temperature range.The maximum supported value for

`n`

in the**Coefficients [c0 c1 ... cn]**parameter is 14, that is, the vector cannot have more than 15 elements.

## Ports

### Conserving

## Parameters

## References

[1] Dean C. Ripple, NIST ITS-90 Thermocouple Database, December 21, 1999 (https://srdata.nist.gov/its90/main/)

## Extended Capabilities

## Version History

**Introduced in R2008a**