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qvia = the via s thermal resistance ( C/W) k = the thermal conductivity of Cu (W/mm- C) diametervia = the via s drill diameter (mm) Tplating = the Cu plating thickness in the via (mm) lvia = the via s length between the thermal land and thermal spreading plane
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Substituting some typical values such as a drill diameter of 0.3 mm, a plating thickness of 0.025 mm, a via length of 0.38 mm, and a thermal conductivity of 0.389 W/mm- C, the typical thermal resistance of a thermal via is found to be 45 C/W. Since a thermal resistance is analogous to an electrical resistance, equations for calculating parallel resistance can be used to calculate the effective
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thermal resistance of a thermal via array. Using Eq. 17.4 below, a 4 4 array of vias is found to give a thermal resistance of 2.8 C/W. It is evident that the thermal performance of a component can be optimized with a relatively small number of thermal vias (see Eq. 17.4). 1 = Rtotal where
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(17.4)
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Rtotal = the total resistance of the via group Ri = the resistance of each individual via
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Evaluating the thermal via resistance as a function of trace plating variability, a 0.015 mm thick plated via with the same dimensions as the preceding will have a thermal resistance of 73 C/W. Thus, the thermal performance of a PCB is sensitive to variations in the plating thickness of its thermal vias. To ensure thermal via performance, the plating thickness in the via should be checked. This is usually performed by parallel polishing down from the surface of the PCB rather than through a cross-sectional polishing of the via. When cross-sectioning a via, if sectioning plane does not intersect the exact center of the via, an incorrect plating thickness will be measured; this problem does not occur when parallel polishing into the depth of the PCB.
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Component Spacing on the PCB There is a finite spreading thermal resistance to any PCB as a function of its thickness and the number of planes in the PCB. Eq. 17.5 is a simple equation to calculate the in-plane thermal conductivity of a PCB as a function of the spreading plane thicknesses versus the FR-4 material layers. For example, if a 1.57 mm thick FR-4 board has a single solid thermal spreading plane that is 0.036 mm thick, the effective in-plane thermal conductivity of the plane is 8.9 W/m- C. This is substantially lower than the thermal conductivity of pure Cu, which is 386 W/m- C. Therefore, thermal spreading through the PCB with a single plane will be worse than thermal spreading through a plate of Cu with the same thickness as the PCB. keffective = ki ti
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ti
(17.5)
where
keffective = the PCB s effective in-plane thermal conductivity ki = the thermal conductivity of the ith layer ti = the thickness of the ith layer
The net effect of the limited spreading resistance of a PCB is that component temperatures will rise as they are clustered more tightly on a PCB of a given size and construction. For example, Table 17.2 shows the maximum component temperature of four small devices on a
TABLE 17.2 Case Example of Component Temperature versus PCB Spacing Component spacing (mm) 50 25 12.5 8 Maximum temperature ( C) 81.6 84.4 92.9 98.4
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100 100 mm PCB containing two buried planes. As the components were moved closer to each other, the device temperatures increased from 81.6 C to 98.4 C, representing an increase of 30 percent compared to the ambient temperature of 25 C. To make the best use of a PCB as a heat sink spreader, the power of individual components should be distributed as evenly as possible on the PCB to minimize hot spots. The location of a component with respect to the air flow is also important. As air flows across power sources on a PCB, it picks up heat and increases in temperature. Components in the air flow downstream from high-power devices are heated by the warmer air. Air temperatures can easily rise 10 to 30 C just past a high-powered component such as a microprocessor, power amplifier, or power regulator block. If a component is running too hot, one possible solution is to move it as far upstream in the air flow as possible such that it receives the coolest air.
Thermal Saturation of the PCB When the power of individual components has been evenly distributed over the PCB surface such that further geometrical rearrangement of the components or further optimization of the trace and thermal plane design is ineffective in cooling the components, thermal saturation of the PCB is said to have occurred. At this point, the power dissipation capability of the PCB becomes the factor limiting the component temperatures. The maximum power dissipation of a PCB with good thermal planes and evenly distributed power sources is in turn limited by a number of geometrical and system-level factors. These include:
The air stream velocity Any air ducting or shrouding around the PCB The configuration of heated surfaces around the PCB The altitude at which the PCB is operating The orientation of the PCB with respect to gravity
Each of these parameters impacts either the convection or radiation from the PCB. Convection is the heat transfer mechanism whereby heat is removed from the PCB through conduction of thermal energy into the gas or fluid that surrounds the PCB. In a natural convection environment, the heating of the air around the PCB causes its density to decrease. In the presence of a gravitational field, the less dense air will rise, carrying away heat with it fresh, cool air moves in to replace the heated air. In a forced-air environment, the heated air is blown away from the surface by cooler air, which in turn becomes heated through the conduction of thermal energy from the PCB. The heat removed from a surface of area A due to convection, either natural or forced, can be represented by the simplified one-dimensional Eq. 17.6. q = hA(Tsurface Tambient) where q = heat h = convection coefficient A = surface area Tsurface = the average temperature of the surface Tambient = the temperature of the ambient air (17.6)
Equations to calculate the convection coefficient h are beyond the scope of this chapter. Convection is a function of (1) the PCB size, with smaller PCBs having higher convection efficiencies; (2) the PCB orientation, with vertical PCBs being more efficient; (3) altitude, with lower altitudes being more efficient than higher altitudes; and (4) air ducting, with ducting tending to make the PCB more efficient in forced air environments.4
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