*4.5. Construction of the Macrocircuit*

The macrocircuit representing the ET behavior of the packaged DUT was constructed in the PSPICE environment as follows. The linear equivalent thermal network, provided in the form of a netlist, was enriched with *N* nonlinear voltage-controlled voltage sources to account for the Kirchhoff's transformation (18), and the thermal feedback block was thus obtained. It must be remarked that nonlinear thermal effects could in principle be *accurately* described by extracting a *fully nonlinear* equivalent thermal network with a variant of the FANTASTIC tool [11]. However, the complexity of the nonlinear network grows with the discretization *N* much more rapidly than that of the linear counterpart (used in this paper); for *N* = 79, such a network would be composed by about 32 × 10<sup>6</sup> elements, with insurmountable memory-storage problems. As a consequence, the adoption of a calibrated Kirchhoff's transformation represents the only viable strategy to ge<sup>t</sup> accurate enough results. The Δ*T* and *PD* nodes of the subcircuits (the individual transistor cells) were connected to the thermal feedback block. As shown in Figure 10c, all the gate terminals of the subcircuits were shorted together, as well as the drain and source ones, and it is possible to activate an electrical network to include the de-biasing over the source pad. A simplified scheme of the adopted strategy is shown in Figure 16.

**Figure 16.** Schematic representation of the proposed strategy to perform a fully coupled ET analysis in a circuit simulation tool: the feedback loop between the electrical circuit (**left**) and the thermal feedback block (TFB, **right**) relying on the DCTM-based equivalent network is highlighted.

After the circuit simulation run, the whole spatial-temporal temperature rise distribution can be reconstructed in a post-processing stage at negligible computational cost and memory storage using (41).
