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Radiation is the removal of heat from a surface by the emission, or radiation, of photons. These photons are generated when thermally excited atoms collide with each other, resulting in overlapping electron energy states. Since electrons are fermions, meaning no two electrons can occupy the same energy band, when the energy states of two electrons overlap during the collision, one electron is forced into a higher, empty energy state.This reduces the momentum of the colliding atoms, ensuring that energy is conserved. After collision, the displaced electron decays back to its initial energy state, giving up a photon of energy in the process. At the surface of the object, this photon is emitted, carrying away some of the thermal energy, while in the bulk of the material, this photon is reabsorbed by neighboring atoms.The simplified one-dimensional equation that describes the total energy loss from a surface due to radiation is shown in Eq. 17.7.This equation for radiation neglects heat that the PCB might reabsorb from heated objects such as power supplies around it, but does include an ambient temperature radiation reabsorption.
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4 4 q = A Tsurface Tambient
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(17.7)
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q = heat e = the emissivity of the surface s = the Stefan-Botzmann constant (5.67 10 8 W/m2- K4) Tsurface = the PCB surface temperature Tambient = the ambient temperature
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The emissivity of the object is a unitless number that describes how efficiently a surface radiates. It varies from 0, which is a surface with no radiation that is perfectly reflective, to 1, which is a perfectly radiative and absorptive black surface. The emissivity of the surface is a function of both the type of material that composes the surface as well as the roughness of the surface. Typical solder mask material has an emissivity ranging from 0.85 to 0.95. Typical exposed Cu trace has an emissivity ranging from 0.1 to 0.3 depending on the roughness and oxidation condition of the Cu. It is important to note that the area of the PCB plays a major role in both of these equations. This is intuitive; the larger the PCB, the more heat it can dissipate. In combination, the preceding equations can be used to estimate the power that a given PCB at a given temperature can dissipate. For example, Fig. 17.9 shows the best-case power that can be dissipated by a series of PCBs ranging in size from 10 10 cm to 20 20 cm. The PCBs were assumed to be oriented horizontally in an unobstructed natural convection environment of 25 C with no significant neighboring radiating surfaces. Convection was allowed to vary as a function of 90 temperature. Most importantly, the power 80 was assumed to be uniformly distributed 70 over the PCB such that there were no thermal gradients on the PCB. This is a major 60 assumption, meaning that the power dissipa50 tion figures in the chart are best-case, a con40 10 10 cm dition that no practical PCB will attain. The 30 chart indicates that 50 W can t realistically 15 15 cm 20 be dissipated in natural convection from a 20 20 cm 10 PCB that is 10 10 cm, but it can be dissi0 pated by the 15 15 and 20 20 cm PCB.The 0 50 100 15 15 cm PCB will rise 80 C above the ambient to dissipate 50 W, while the 20 20 Watts (W) cm PCB will rise only 50 C to dissipate the FIGURE 17.9 Temperature rise above 25 C of a horisame power. This graph has been formatted zontal PCB in natural convection as a function of PCB to look the same as typical heat sink curves size and power dissipation. Both convection and radiation that are available from many vendors. are dissipating the power.
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PCB temperature rise ( C)
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