New Correlations Between Electrical Current and Temperature Rise in PCB Traces
Johannes Adam
Flomerics Ltd.
Raiffeisenstr. 16, D-70794 Filderstadt, Germany
johannes.adam@flomerics.de
higher currents can be put on a trace. Second, the IPC2221
Abstract
diagrams for so-called internal conductors (those inside the
The widely used design rule IPC-2221 (=MIL-STD-275)
PCB) are de-rated in current by a factor of exactly two with
for the ‘current carrying capacity’ of traces on printed circuit
respect to external conductors (those on the surface of the
boards is subject of a closer investigation. These historical
PCB). These suspicious facts make it necessary to ask for
studies on correlations between electrical current and
further theoretical and experimental investigations. There is
temperature rise of the trace can be reproduced by numerical
also need for new correlations because new materials and
heat transfer simulations only if the board has a back 35μm
geometries have emerged since the fifties.
copper layer and the thickness of the trace is 35 μm. As this
makes an extrapolation to other boards impossible, we will 2. The IPC-2221 design rule
present numerical studies for FR4-based board models with
2.1. The data
other copper planes and also for ceramic substrates. For a
The design rule IPC-2221 (=IPC-D-275=MIL-STD-275)
better understanding of the results, 2D heat conduction
(Fig.1) is widely used to estimate the temperature rise due to
calculations for traces on boards with constant internal and
an electrical current. The usage is according to the following
external conditions are performed. Quantitatively, they can be
two steps (dashed lines)):
interpreted as parallel thermal resistances of the trace and the
rest of the board, where we treat the board approximately as a Step 1: determine the cross-section A of the trace (in
heat sink fin. These semi-analytic limits give scaling laws for square mils) in the lower diagram from trace width (in inches)
the thermal resistance of the trace as function of board and the thickness (in ounces of copper per square foot, 1 oz is
conductivity, heat exchange coefficient, board thickness and about 35 μm, 2oz=70 μm).
trace width. For the more realistic board models this Step 2: Transform the cross-section to the upper diagram
simplified theory is not powerful enough as the thermal and read the data couple of current I and temperature rise 'T.
isolation between trace and first copper plane is not included.
Keywords
Joule heating, current, PCB cooling, CFD
1. Introduction
An electrical current flowing in a copper wire causes
deposition of thermal energy in that wire. To honour James
Joule [1], the discoverer of the effect, it is called “Joule
heating”. Joule heating also plays an eminent role for copper
traces on printed circuit boards (PCBs). The temperature of a
copper trace on a PCB is the result of thermal equilibrium
between Joule heating and convective and radiative cooling
by the heat flux from the board to the ambient environment.
However, there are technological limitations to the
temperature of a copper trace: the temperature of the trace
must not exceed certain limits, e.g. the glass transition
temperature of FR4 around 110 degC or a comparable limit
due to solder stability aspects. Joule heated traces on PCBs
are the ‘energy pipelines’ in automotive control units and
other power control devices.
In recent years the electrical power consumption in
automobiles rose and hence a reasonable prediction of trace
Figure 1: Nomograph from IPC-2221 for „external
and board temperatures is needed. For this purpose, the
conductors“ [2] with example of usage.
graphs in IPC-2221 (=MIL-STD-275) are widely used as a
‘design rule’ for trace geometry (i.e. trace cross-section) for a
2.2. Origin and reproducibility
given pair of current and temperature rise. They had been
While working on a revision of the design rule, called
published by the National Bureau of Standards back in 1956.
IPC-2152, the IPC Task Group 1-10b lead by Jouppi, found
There are well-founded doubts whether this ‘standard’ is
the roots of IPC-2221 as having been experimental work for
really useful and valid. First, layout experts tell, that usually
0-7803-8363-X/04/$20.00 ©2004 IEEE 20th IEEE SEMI-THERM Symposium
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