Thermal Design

Thermal design does not usually appear in an electrical engineer's formal education. Circuit design classes may mention components' thermal resistance, but usually do not make a great impression on him. He may also encounter heat transfer in physics class and in applied math class where heat diffusion equations may be discussed and some partial differential equations with simplified boundary conditions may be solved, but connection to actual circuit design may not be apparent.

More likely, he first realizes the importance of thermal design when his fingers are burnt by an overheated component on a circuit board, or plastic case of a component melts, or a darken scorch mark is left on the circuit board, or sometime a formal thermal analysis is required. Knowledges in thermal design often come from IC manufacturers' application notes. Simple calculations can be made with thermal resistance numbers given in the data sheets, which usually include thermal resistances of junction to case and case to ambient. He is told that the thermal resistances can be treated as analog of electrical resistances, so can be simulated with circuit simulators.

Conductive thermal resistance is derived from Fourier's law of heat conduction, which states that heat flux is proportional to temperature gradient. The proportionality constant is the thermal conductivity. Thus the thermal resistance is distance divided by thermal conductivity multiplied by cross section area. So we can calculate that 1 sq inch of 2 oz copper has thermal resistance of 40 C/W in the lateral direction (copper thermal conductivity is 9 W/in C). A 20mil diameter via in a standard circuit board has thermal resistance of 67 C/W if plated with 1oz copper.

Convective heat transfer poses much greater challenge to analysis. In still air, we have natural convection, where heated air rises in the earth atmosphere. Note that when we design for satellites or spacecraft, natural convection does not exist. The Newton's law of cooling is a simplified theory to describe convection; it introduces a proportionality constant called convection heat-transfer coefficient or film coefficient. However, the film coefficient is hardly a constant, it is depended on many factors including temperature. Any sensible calculation would require computational fluid dynamics.

Radiation is another means of heat transfer. The heat flux is calculated from the Stefan-Boltzmann law. A square inch of a perfect blackbody emitter 50C above ambient room temperature radiates 1/4W. Circuit components may only radiate 1/3 as much depending on the emissivity.