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56 The PCB Design Magazine • September 2016 lations. Finally, the detailed model is modeled explicitly and is the most accurate model; how- ever, it also increases the simulation time and requirements for computing resources. For the PCB, four detailing levels from simple to complex also are used in simulation: lumped approximation, individual layers' rep- resentation, layers modeled with "patches," and copper tracks and areas modeled in detail. Using lumped approximation (Figure 2), the PCB is represented as a single block with ther- mal orthotropic thermal conductivity (different in all directions) applied in the x,y (in-plane) and z (through-plane) axes. This method has a fast modeling and solving time. However, the heat-spreading effect is lost for surface-mount devices with high-power losses. Using individual layers' representation (Fig- ure 3), each layer is modeled as a separate ob- ject with individual thermal conductivity. This method is better at capturing in-plane heat- spreading behavior of surface-mount devices and is still low in computational resource de- mands. It provides optimistic results for some IC that don't have cooling measures (copper areas, thermal vias) implemented. For state-of-the-art simulation, each indi- vidual layer of the PCB can be modeled. Each layer is subdivided into an array of "patches" (Figure 4). For each patch, orthotropic thermal conductivity is calculated from the copper and FR-4 composite distribution within that area. This method provides more accurate results, but takes a long time to model and solve and THE FUNDAMENTALS OF IMPROVING PCB THERMAL DESIGN Figure 1: Simulation models for a chip package, from the simplest to more complex.