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Say I have a surface PCB trace, 4 oz, 50 mils. That trace should be able to carry around 15 amps continuous, according a calculator I'm using. (Obviously your trace ampacity estimates may vary with calculators, but that shouldn't matter for the purposes of this question.) So if a trace can carry 15A continuous, how much could it do for ten seconds? Two seconds? Half a second? Are there any rules for determining the pulse current rating of a trace as compared to its continuous rating?

Stephen Collings
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    comes down to how hot can the FR4 can get. You might be able to use the Onderdonk eq. to estimate the heat rise. it is meant to estimate the time for copper etch to rise to fusing temp. Have you looked at any of the stuff at ultracad.com? I think they have a freeware tool to calculate etch heat rise based on Onderdonk. Here is one of their papers: http://www.ultracad.com/articles/fusing.pdf – gsills Jun 13 '13 at 21:35
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    What kind of duty cycle are we considering? ie, does the trace have time to cool off completely between pulses? Are we concerned about how much current will destroy the board, or are we concerned about power loss? – Phil Frost Jun 14 '13 at 01:11
  • Assume the trace has time to cool off completely, and that we're worried only about destroying the board. – Stephen Collings Jun 14 '13 at 21:04
  • @gsills that would make a really good answer. Do you want to make it one? – Stephen Collings Jun 16 '13 at 13:17

1 Answers1

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Ultimately this is a question of when the FR4 will reach maximum specified temperature of 135 degrees C given an etch dimension and current.

The only analytical equation (that I've seen) that addresses time of heat rise of conductor given a current is the Onderdonk equation. The equation is meant to cover heat rise to fusing temp (copper is 1083C). You can find a write up about it here on the ultracad site.

I = \$\frac{A \sqrt{\frac{\log \left(\frac{T_m-T_a}{T_a+234}+1\right)}{t}}}{\sqrt{33}}\$

or turned around:

\$t_{\text{fuse}}\$ = \$\frac{A^2 \log \left(\frac{T_m-T_a}{T_a+234}+1\right)}{33 \text{ I}^2 }\$

where A is circular mils, temperatures are in degrees C, and time is seconds.

Be aware that the Onderdonk eq was written to estimate the time to fusing wire in air for a given current, not etch on a PCB. Looking at its structure, it appears to consider only thermal conduction through the cross sectional area of the conductor (I don't see any surface area). It is probably not accurate for times longer than 5 or 6 seconds, indeed for a long enough time zero current will reach \$T_m\$.

Using the second form of the equation, 20Amps through a 50mil by 5.6mil etch would reach fusing temp in about 7 seconds and would reach \$T_m\$ of 135C in about 1.5 seconds. These times seem shorter than expected.

It's a difficult problem and the thermal paths can have widely differing boundary conditions, limiting analytical solution region of usefulness. You may get the best estimates by building some test boards and measuring.

Note: In my comment I mentioned a freeware tool at ultracad to calculate heat rise, but now see that it is no longer freeware.

gsills
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