# Incandescent Lamp

Model incandescent lamp, with resistance depending on temperature

Passive Devices

## Description

The Incandescent Lamp block models an incandescent lamp, the key characteristic of which is that the resistance increases as the filament warms up.

Under the simplifying assumption that the rate of heat loss from the filament is proportional to temperature difference to ambient, the temperature of the filament is governed by

$k{t}_{c}\frac{dT}{dt}={i}^{2}R-kT$

and the filament resistance is governed by the following equation

$R={R}_{0}\left(1+\alpha T\right)$

where:

• R0 is the initial resistance at turn-on (when filament is at ambient temperature).

• T is the filament temperature relative to ambient temperature.

• α is the resistance temperature coefficient.

• tc is the thermal time constant.

• k is the heat transfer coefficient.

• R is the filament resistance.

• i is the filament current.

There are two parameterization options:

• If you select ```Specify resistance values directly```, the block uses values that you provide for filament resistance when on and at turn-on to determine the value for the heat transfer coefficient.

• If you select `Specify currents`, the block uses values that you provide for filament current when on and at turn-on to determine the value for the heat transfer coefficient.

Optionally you can specify a simulation time at which the lamp fails by providing a finite value for the Time at which lamp goes open circuit parameter on the Faults tab. When in the open-circuit state, the lamp resistance is set to be the value of the Open-circuit resistance parameter.

## Dialog Box and Parameters

### Resistance Tab

Parameterization

Select one of the following methods for block parameterization:

• `Specify resistance values directly` — Provide the values for filament resistance at turn-on and when on in steady state. The block determines the value for the heat transfer coefficient based on these values. This is the default option.

• `Specify currents` — Provide the values for filament current at turn-on and when on in steady state. The block determines the value for the heat transfer coefficient based on these values.

Initial resistance at turn-on

The resistance seen by the external circuit when the lamp is initially turned on. This parameter is only visible when you select ```Specify resistance values directly``` for the Parameterization parameter. The default value is `0.15` Ω.

The resistance seen by the external circuit when the lamp is on and in steady state. This parameter is only visible when you select ```Specify resistance values directly``` for the Parameterization parameter. This resistance should be greater than the Initial resistance at turn-on. The default value is `1` Ω.

Inrush current at turn-on

The current through the lamp when it is initially turned on. This parameter is only visible when you select ```Specify currents``` for the Parameterization parameter. The default value is `70` A.

The current through the lamp when it is on and in steady state. This parameter is only visible when you select ```Specify currents``` for the Parameterization parameter. This current should be less than the Inrush current at turn-on. The default value is `10` A.

Rated voltage

The rated voltage for the lamp, and the voltage value for which the resistance or current values are provided in the on and turn-on states. The default value is `12` V.

Resistance temperature coefficient

The fractional increase in resistance per unit increase in temperature. The default value is `0.004` 1/K.

### Dynamics Tab

Thermal time constant

The first-order thermal time constant for filament temperature when the lamp is turned on or off. The default value is `25` ms.

Initial lamp state

Select between `On` and `Off`. The default is `Off`.

### Faults Tab

Time at which lamp goes open circuit

For simulation times greater than this parameter value the filament resistance becomes equal to the Open-circuit resistance. The default value is `inf` seconds. Specifying a finite value for this parameter lets you simulate the fault dynamics when the bulb burns out.

Open-circuit resistance

The value of the filament resistance used when the lamp goes open-circuit. The default value is `1e6` Ω.

## Ports

The block has the following ports:

`+`

Positive electrical port

`-`

Negative electrical port