the National Bureau of Standards (NBS) back in 1956 [3,4 T20=20 degC (for Eq. (3), t and w have to be in mm, L in m).
and references therein]. The original plots of the current vs. The electrical resistance increases with temperature
cross-section diagrams reproduced in [4] show a wide scatter approximately at a rate of D20=0.00395 K-1. The cross-section
of data points. This is due to a variety of printed boards with of the trace is A=tŸw. The CFD calculations solve consistently
different structure and coating. The nomographs (i.e. Figure the steady-state thermal equilibrium due to Joule heating and
1) represent the upper limit of the points. The lower limit is in cooling by conduction, convection and radiation together
close agreement with the so-called Design-News (“DN”) with the natural convection flow field around the board.
correlations brought to our notice by Brooks [2]. Brooks also Adjusting of any parameter is neither done nor required. The
gives the following fits: results for an ambient temperature of Ta=20 degC, a mean
the IPC-Data (A in sq.mils) I =0.065*'T 0.43*A0.68, (1) temperature rise of the trace of 'T=20 degC (i.e. T=40 degC)
the DN-Data I =0.040*'T 0.45*A0.69. (2) and a trace thickness of t=35 μm are compared in Fig. 3. The
The pertinent questions are now: is it possible to dashed lines are from equations (1) and (2), resp., the solid
reproduce the experimental curves by theoretical lines are results of our simulations. The trace length L is of
calculations? What can be learned? Can they be extrapolated minor importance, as both power and cooling area to the left
to other scenarios? and right increase with L.
To answer the first question, we perform numerical Our calculations (Fig. 3) show that we can reproduce the
studies on a simple 3D model of a board and a trace with a Design-News correlation (Eq. 2) by a bare epoxy board with
commercially available code [5]. The equations which are one heated trace on it, and the IPC-2221 correlation (Eq. 1)
solved in a discretized form are Fourier’s equation (heat by a board with a backward 35μm copper plane. Taking into
conduction), the Navier-Stokes equation together with the account the uncertainties in both methods, the results are in
conservation of mass (fluid dynamics), the Stefan-Boltzmann reasonable agreement. The reason for the difference between
law of radiation and some wall functions for momentum and IPC and DN correlations is of course the different kinds of
heat transfer. We restrict our investigations on the steady- heat spreading in the PCB. The board with 35μ copper back
state, discrete current and laminar natural convection. Without layer is a better heat spreader than the pure FR4 board and
knowledge of the exact NBS experimental arrangement, we therefore cooler, or, can carry a higher current, respectively.
are assuming a model with a PCB in Euro-Format (Lx=100
mm, Ly=160 mm, D=1.6 mm) made of pure FR4
(conductivity k=0.3 W/m-K, emissivity H=0.9), with one
copper trace of length L=100 mm and thickness t=35 μm (=1
oz) on the top face and with an optional copper layer on the
back plane (also of thickness 35 μm, conductivity k=395
W/m-K and with a solder resist with emissivity H=0.9) (Fig.
2).
Figure 3: Simulation results (solid lines) compared with Eqs.
(1) and (2) (dashed lines) on linear and log scales.
2.3. Criticism of IPC-2221
1. The close agreement between the numerical result and
the IPC correlation implies that the applicability of the IPC
correlations is limited to PCBs with little copper content.
Nowadays PCBs contain more copper, so that they can carry
more current, which is observed in practice.
2. Other calculations [6] also show that the 50% current
de-rating of internal traces found in IPC-2221 is not justified
Figure 2: Description of variables of our numerical models.
but must have been a matter of speculation at that time.
Internal conductors heat and cool almost like external
The trace is characterized by a local temperature T [deg C]
conductors (according to our calculations current de-rating is
and geometry-dependent electrical resistance Rel [Ohm]
about 5%)
L Ÿ 1( D (T T20))
U 20 20 . (3)
R Ÿ 3. The simple dependence on trace cross-section A cannot
el t w
be correct. Consider two traces of same cross-section, but
The power deposition P [W] due to current I [A] is according
different width w and thickness t (Fig.4). Assume the traces
to Joule’s law
have the same current, the heat spreading topology and hence
2
P R elŸI . (4) cooling will be different. The heat flow into the PCB is
U20=0.0175 Ohm mm˛/m is the specific electrical resistivity primarily dominated by the footprint of the trace, i.e. by the
of a copper wire of length 1 metre and cross-section 1 mm˛ at width. The horizontal trace (left) will provide better cooling
Adam, New Correlations Between Electrical Current and … 20th IEEE SEMI-THERM Symposium
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