In Fig. 10 we are therefore modifying the ordinate of Fig. trace cross-section is not correct. With Eq. (5) we give a
9 by a multiplier {P(w=0.2 mm; I=1 A)/P(w;I)}-0.07, each transformation law for other values of trace thickness.
being a constant for the board model. Experiments with the
exponent exhibit that for the pure FR4 model a value around -
0.07 gives the best correlation coefficient indeed. The data
points for the isotropic board model 1 are closer together
now, and the trend is very similar to the low conductivity
board from Fig. 7. For the other models the scatter cannot be
removed. We suspect that the already mentioned temperature
dependent influences and the 3D structure of the boards are
beyond the capacity of the simple theory presented in Sect.
4.1. For example boards 2,4,6 have the same copper content,
but significantly different thermal resistances of the trace. A
posteriori, this justifies our initial numerical approach and
rules out oversimplified usage of Eqs. (3), (4) and their
extrapolation to other scenarios. One should always bare in
mind, that for a trace thickness t other than 35 μm, Eq. (5) is
still valid.
Figure 10: Re-scaled thermal resistance of the trace in
scenarios 1 ( ), 2 (˝), 4 (x) and 6 ( ) from Table 1.
x We also test our numerical model successfully against
new experimental results which were undertaken for a
revision of IPC-2221, called IPC-2152.
x For more up-to-date 3D board structures, we calculate
new graphs for trace temperature rise as function of
electrical current and trace width. The better the heat
spreading, the lower of course the temperature, and the
higher the allowable electrical current. Not only the
copper content in the board influences the temperature
but also the isolation distance between trace and first
copper layer. To understand the underlying dependencies
on board parameters like conductivity, thickness and heat
exchange coefficient, we adopt a simple semi-analytic
heat transfer model: the trace is cooling like a plate and
the board around is cooling like a heat sink fin. Although
being far from an analytic 2D solution, Eqs. (11) and (14)
Figure 9: Uncorrected numerical thermal resistance of the are the principle scaling laws for the thermal resistance of
trace in scenarios 1 ( ), 2 (˝), 4 (x) and 6 ( ) from Table 1. a trace under conditions of constant material and heat
exchange properties.
5. Conclusions
x The numerical results for non-homogeneous boards and
The aim of this article is twofold: first, we want to
temperature dependent heating and cooling properties are
reproduce the graphs in design rule IPC-2221 by numerical
not easily put into an analytical framework. The fact that
model calculations and to review it critically, second, we want
boards with same copper content but different vertical
to calculate current-temperature correlations for more up-to-
position of layers have significantly different cooling
date board scenarios.
characteristics justify our initial numerical (CFD-)
x As for the graphs in IPC-2221, we find that electrical approach.
engineers should be warned against regarding the graphs Subject of future work are calculations with forced
as being universal, and taught that its usage is restricted convection cooling, metal core or metal laminated PCBs,
to certain board and trace geometries: a board with 35μm PCBs inside enclosures multiple heat sources and much more.
copper layer on the back and a long trace of thickness Some analytical work has already been done [10] and some
35μm. The simple dependence of trace temperature on numerical activities have already been started [11]. Another
Adam, New Correlations Between Electrical Current and … 20th IEEE SEMI-THERM Symposium
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