A graph of allowable power versus temperature is very similar to the first approach, but instead of a simple number, you follow a graph of allowable power versus temperature (Figure 1). Again, this is a very conservative approach and should allow for a very reliable design, but it does not provide you with the most accurate results.
A more comprehensive method for performing thermal calculation is to use a thermal model. Thermal models have been created for some optocouplers containing multiple dice —including phototriacs — for the most simple and accurate calculations.
Multiple Dice Optocoupler Thermal Model
This article demonstrates a simplified resistive model. When used correctly, this model produces results that provide "engineering accuracy" for practical thermal calculations. Figure 2 provides the simplified electrical analogous model for any optocoupler.
θCA = Thermal resistance, case to ambient, external to the package.
θDC = Thermal resistance, detector to case
θEC = Thermal resistance, emitter to case
θDB = Thermal resistance, detector junction to board
θDE = Thermal resistance, detector to emitter die
θEB = Thermal resistance, emitter junction to board
θBA = Thermal resistance, board to ambient, external to the package
TJE = Emitter junction temperature
TJD = Detector junction temperature
TC = Case temperature (top center)
TA = Ambient temperature
TB = Board temperature
Thermal resistances and specified junction temperatures for a particular device are provided in select datasheets.
Thermal Energy Transfer
There are three mechanisms by which thermal energy (heat) is transported: conduction, radiation, and convection. Heat conduction is the transfer of heat from warm areas to cooler ones, and effectively occurs by diffusion. Heat radiation (as opposed to particle radiation) is the transfer of internal energy in the form of electromagnetic waves. Heat convection is the transfer of heat from a solid surface to a moving liquid or gas.
All three methods occur in optocouplers. However, for most products in most environments, the majority (~ 75 %)
of heat leaving the package exits through the lead frame and into the board. This occurs because θBA is a conductive phenomenon with a much lower thermal resistance than the convective and radiative phenomena associated with θCA (θCA is typically an order of magnitude larger than other thermal resistances). Because very little heat leaves through the top of the package (heat convection), junction-to-case temperatures (θDC and θEC) are negligible in most environments.
This phenomenon is shown graphically in Figures 3a-c by the package temperature profile and strong heat flux contours evident in the die, lead frame, and board via. Because very little heat leaves through the top of the package, the top case temperature is a poor indicator of junction temperature. This means that the majority of the heat is transferred to the board, and very little heat is transferred to the air via the case, which can be verified in the thermal network.
Therefore, θDC and θEC can be removed from the thermal model (Figure 2). In this situation, the critical package thermal resistances become θDE, θDB, and θEB. θBA is the thermal resistance from the board to the ambient, and is primarily driven by the geometry and composition of the board. The type of board design used defines this characteristic. Junction-to-case thermal resistances are removed based on the fact that very little heat is leaving through the top of the package (Figure 4).