Development of a New Electro-thermal Simulation Tool for RF circuits

20 2.2. Chip thermal model - mathematical considerations
2.2.4. Thermal impedance
Figure 2.7: Thermal impedance as a response to a step application of power, logarithmic
time scale.
From the definition, thermal impedance Zth is a response to a step application of
a power. Final value of thermal impedance always reaches steady state value Rth, as
shown in Fig. 2.7.
Since an equivalence of electrical and thermal quantities exists, a popular way to
approximate the thermal impedance is by means of electrical thermal impedance, that
is by an infinite amount of RC pairs. In this way, by means of electrical equivalence,
Figure 2.8: Schematic pass from steady state to transient case.
thermal phenomena can be described using circuit simulation environment. However,
for computational reasons it is not possible to include infinite amount of RC pairs in a
circuit simulator. The less amount of RC pairs is used, the better for a simulation time
for a cost of accuracy. In these circumstances, a reasonable trade-off must be found.
A well known representation for thermal impedance is Foster (Fig. 2.9a) and Cauer
(Fig. 2.9b) RC series. Both networks can be easily transformed between each other
[13].