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When designing a PCB, do you need to worry about the inrush/surge current or just the continuous/RMS current on the board? Everything I have seen including IPC documentation is for continuous current. Is the assumption that if you are ok from a temperature/trace width stand point, you will be ok for an inrush current?

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It all depends on what the surge current could do to the other circuitry on the board. The continuous current analysis generally settles itself around the acceptable voltage drop in the traces and safe operation to prevent fires or fusing of overloaded traces. Surge current on the other hand could be huge, as addressed by @Huisman in another answer, and could very well overrate the traces. If the duration is long enough then the surge current value should actually replace the current value used in the continuous current analysis.

But there is another consideration as well which can occur even if the surge current is on the same order of magnitude as the continuous current. This comes into play when the rate of change in the current flow is really fast.

[story time]

Many years ago I was working on a prototype of a product that had a two layer circuit board and power and ground for the DIP packages on the board laid out as shown below:

enter image description here

Fingered power and ground like this was very common in DIP board days and made it fairly convenient to place bypass caps along on the bus fingers between each DIP IC.

Well every thing was going along really fine with the prototype development till the software got to the point of using the relay. Switching the relay turned out to cause the microprocessor program to crash about 15% of the time. A long debug session led to learning that if the relay on / off command was placed inline in the code things were much better but when the relay command was at the end of a utility subroutine followed by a RET (return) instruction the software would crash. This led to creating a small test software that did nothing but switch the relay on and off about 10 times per second. This program would run and not crash at all and also permitted using a scope to be able to probe repetitive waveforms and find out what was going on. It turned out that the current draw of the relay coil, which was about 40mA and of similar magnitude as the current requirement of the SRAM in its active mode, was causing a current surge in the ground bus. The fast rate caused a ground level ringing of around a volt that lasted long enough to corrupt what the MCU would be trying to read out of SRAM if the value had '0' bits in it.

In these olden days the MCU did not have onboard RAM for its stack and data storage and the ground bus corruption was causing the subroutine return address to be read wrong. The fix turned out to be adding a big capacitor to the supply bus right at the relay and then adding a wire to the design to interconnect the right ends of the ground bus fingers as shown in the picture above.

[/story time]

So the big lesson here is that surge current analysis is very important for every design due to effects like described in the story or for other effects where fast current changes can couple to adjacent traces.

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It depends how the surge current is related to the continuous current (is \$I_{surge} = 10*I_{cont}\$ or \$I_{surge} = 1000*I_{cont}\$ ?) and the duration of the inrush current. It's all about how much the temperature of the trace will rise.

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Surge Current can be important.More than 10 years ago I saw a simple PCB with some relays that operated some 230VAC pumps .The PCB traces were rated from an internet table for 10 Amps.Steady state trace temps were fine running 24/7 .The pumps were protected with a 7.5 amp fuse which did not nuisence blow .The origional 5 Amp fuse was not reliable.One day a short circuit fault occurred in the pump wiring assembly .The fuse did not blow but the tracks did which is not good .So the tracks had to be heavier than what was first thought.

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