The old and obsolete understanding of R_θJC is shown in Equation 3.

Equation 3.

Here, the package thermal performance R_θJA is reported to be the sum of two resistances: R_θJC and R_θCA. R_θCA stands for the case-to-ambient thermal resistance, which was defined by this equation. This might have been a valid equation for packages with metal cans, which were relatively at a constant temperature and were not thermally coupled to the PCB. But, these conditions do not apply with today’s plastic or ceramic packages that are tightly coupled to the PCB. Large thermal gradients are common across modern packages, so the meaning of Equation 3 is questionable.

A traditional, but invalid, usage of R_θJC is to calculate the junction temperatures of chips operating in a system. Case temperatures of devices operating in the system are measured using thermocouples, IR cameras, or Fluoroptic® probes. Equation 4 is then mistakenly used to calculate the junction temperature: Equation 4:

Equation 4.

The fallacy here is that only a very small percentage of heat energy in a typical plastic package is convected and radiated off the top surface of the package. Many models have shown 60%-95% of thermal energy from a chip is actually convected and radiated off the PCB to which the package is attached. If one assumes the entire power is dissipated by the top surface, the junction temperature calculated by Equation 4 is higher than reality. In designs with thermal margin, this is a nuisance, but in designs without thermal margin, erroneous limitations might be imposed. This limitation of R_θJC is overcome by the new thermal metric, Ψ_JT, which is described below.

Equation 5 shows the proper application of R_θJC for those instances when a high-efficiency heat sink is applied to the top surface of a device for which R_θJC is small compared to R_θJA:

Equation 5.

Here, R_θ(SA) is the heat sink-to-ambient performance of the heat sink and R_θ(CS) is the case-to-heat sink thermal resistance of the thermal interface material (see Equation 7). The ambient temperature is at the location used for characterizing R_θ(SA), usually some distance away from the heat sink. This equation is the most accurate for packages where R_θJC is small compared to R_θJA, meaning that most of the heat can be dissipated through the top surface of the package when a sufficiently efficient heat sink is applied.

Equation 6 shows an approximation that is more accurate than Equation 5 for any combination of R_θJA, R_θJC, or R_θ(SA) if R_θJA is known for the system configuration:

Equation 6.