(Eq. 12) |
Equations 11 and 12 are useful for predicting chip temperature (either package or die) when the heat-generating source is outside the package. One example could be a nearby high-current MOSFET that dissipates lots of heat.
When we know kA and θJA we can calculate the temperature at different times. Alternatively, if P is a complex function of time, we can use the above equations to evaluate temperature as a time-based simulation and use MATLAB® software to write a program that plots temperature as a function of time.
The θJA value is provided in data sheets. However, when a setup imposes conditions other than those of the JEDEC standard, that published θJA value for these calculations can cause errors. The JEDEC standard 51-3 states, "It should be emphasized that values measured with these test boards cannot be used to directly predict any particular system application performance, but are for the purposes of comparison between packages."2 Thus, to properly estimate temperature, you should either measure θJA for the prototype board or es贴片电感timate it directly as explained below.
Consider the system of Figure 3, in which a three-body system (similar to a chip) generates heat on the die and dissipates it through the epoxy and package to the environment. Body 1 is the die, Body 2 is the epoxy, and Body 3 is the chip package.
Figure 3. Compare this thermal three-body model with the Figure 2 model. Here the flow of heat generated on the die is more complicated.
To solve for θJA in this system, we must define the equations for all three bodies.
Body 1:
(Eq. 13)
Body 2:
(Eq. 14)
Body 3:
(Eq. 15)
Where:
TB1, TB2, TB3 are the instantaneous temperatures of Bodies 1, 2, and 3.
P12 is po绕行电感器wer in the form of heat transferred from Body 1 to Body 2.
P23 is power in the form of heat transferred from Body 2 to Body 3.
PG is the power generated on Body 1 or directly transferred to Body1.
Power generated by the die (PG) minus power absorbed by the die is:
(Eq. 16)
Power received by the epoxy minus power absorbed by the epoxy is:
(Eq. 17)
Substituting Equations 16 and 17 in Equations 13, 14, and 15:
(Eq. 18)
(Eq. 19)
(Eq. 20)
The solution of this three-body system in Equations 18, 19, and 20 can be complicated, but the use of Laplace transforms makes it easier. The form of the solution is:
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