2.3.3.1 Conductor

The constitutive relations for a linear, temperature dependent conductor are

$$\vartheta$$ I = (2.29)

$$\vartheta \left(\vphantom{ 1 + \alpha \cdot (\vartheta - \vartheta_{\mathit{ref}}) }\right. \alpha \vartheta \vartheta_{\mathit{ref}}^{} \left.\vphantom{ 1 + \alpha \cdot (\vartheta - \vartheta_{\mathit{ref}}) }\right)$$ = (2.30)

P = V ^. I (2.31)

If $\alpha$$\ne$ 0, the conductor will be modeled temperature dependently. For thermal simulation the dissipated power P will result in self-heating of the conductor and the problem becomes non-linear. Otherwise the temperature dependent entries are ignored. The stamp is given as

yx, y	$\varphi_{1}^{}$	$\varphi_{2}^{}$	$\vartheta$	f
n1	G	- G	- V . $\alpha$ . G0	- I
n2	- G	G	V . $\alpha$ . G0	I
$\vartheta$	-2 . V . G	2 . V . G	- V2 . $\alpha$ . G0	P

Figure 2.5: Electro-thermal compound model for a heat dissipating resistor

The conductor acts as a heat source connected to the thermal circuit node $\vartheta$ and to thermal ground (reference temperature).