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q = the heat energy A = the area of the plate l = the thickness of the plate k = the thermal conductivity of the material T1, T2 = the applied temperatures on the plate s opposing faces

Table 17.1 lists typical thermal conductivity values important to PCB and electronic components.Where a range of material properties is given, multiple factors determine the exact thermal conductivity value. These factors can include the filler percentage and composition in a polymer, or in the case of silicon (Si), the doping type and level. Material property measurement or vendor data should be used to determine the thermal conductivity of the specific material of interest. One alloy of Cu is shown to demonstrate that the Cu alloy

FIGURE 17.2 Typical thermal conductivity test schematic showing a block of material with area A constrained by two different temperatures, T1 and T2, on opposing faces. Q indicates the heat flow direction when T2 is greater than T1.

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TABLE 17.1 Typical Thermal Conductivity Values2,3 Material Air Copper (pure) Copper EFTEC-64T FR-4 (in-plane) FR-4 (out-of-plane) Solder mask material IC encapsulant Silicon k (w/m- C) at 25 C 0.0026 386 301 0.6 0.85 0.25 0.3 0.15 0.5 0.6 1.0 110 149

Temperature rise above ambient ( C)

250 230 210 190 170 150

Trace length (mm)

The other index found in this expression, a , is a free index. If we elect to change the free index, it must be changed on both sides of the equation. Therefore it

FIGURE 17.3 Modeled temperature rise above ambient thermal performance of an 8-pin SOIC powered at 1 watt as a function of the trace length.

composition can play a role in the thermal conductivity of metals These material properties are valid at room temperature (~23 C) Due to the temperature-dependent nature of thermal conductivity, further references for these properties should be pursued when operation is expected at temperatures above 85 C or below 25 C It is critical to note that the thermal conductivity of Cu is three orders of magnitude greater than the conductivity of most polymers such as PCBs and solder mask materials This means the majority of the thermal energy will be conducted through the Cu, which implies that the layout of the Cu traces and power planes will be critical to the thermal performance of the PCB as a heat sink Figure 173 shows this graphically In this model, an eight-pin smalloutline integrated circuit (SOIC) package dissipating 1 watt was soldered to a single-layer FR4 PCB of 1.

57 mm thickness The temperature rise above ambient is plotted as a function of the trace length connected to the device pins As shown, the device temperature changes by ~40 percent for this variation in trace length The data show that to get the lowest possible temperatures, the longest possible traces should be used to spread heat away from components Equally important, the widest possible traces should be used These thermal design optimizations need to be made within the constraints of the electrical performance requirements such as the system time delay budget An important feature of thermal management is evident from this chartAfter a trace length of about 15 mm, there was little additional improvement as the trace lengthened further seeking thermal optimization by increasing the trace length had reached a point of diminishing return.

Often, once a specific parameter has been optimized, further changes in that parameter lead to little additional efficiency gain Intuitively, heat flow can be thought of by analogy to fluid flow through pipes of different diameters The pipe with the smallest diameter limits the fluid flow rate for a given fluid pressure If the diameter of this constriction is made larger, the next smallest pipe diameter becomes the next constriction Thermal resistance is analogous to the resistance to fluid flow in this pipe illustration Once a thermal resistance restriction has been minimized, the thermal conduction bottle neck moves to a different portion of the problem The PCB trace thickness is another important parameter that interacts with the trace length and width If the traces are thick, they offer less thermal resistance to heat transfer.