Q: I want to make a PCB trace that fuses (opens, breaks, burns out) at this many Amps, how wide should it be in mils?
For copper traces to fuse in 1s with I current (Amps) your trace should probably be a bit thinner than…
WidthMils = ( CurrentAmps / 0.188 ) / ( 1.4 * CopperOz)
Where CopperOz is the copper weight on the PCB per square foot (typically 1oz or 2oz).
This is just a rough ballpark and you should determine experimentally yourself based on this approximation.
Example 1, you want to fuse 2A on 1oz copper PCB in 1s…
WidthMils = ( 2 / 0.188 ) / ( 1.4 * 1 )
WidthMils = 7.59 mils = probably possible with a 6 or 7 mil trace
Example 2, you want to fuse 5A on 2oz copper PCB in 1s….
WidthMils = ( 5 / 0.188 ) / ( 1.4 * 2)
WidthMils = 9.49 mils = probably possible with a 8 or 9 mil trace
Example 3, you want to fuse 1A on 1oz copper PCB in 1s…
WidthMils = ( 1 / 0.188 ) / ( 1.4 * 1)
WidthMils = 3.8 mils = good luck getting that manufactured
Example 4, I have a 1oz 6 mil trace, what sort of current might be required to fuse in 1s…
6 = ( CurrentAmps / 0.188 ) / 1.4
6 * 1.4 = CurrentAmps / 0.188
6 * 1.4 * 0.188 = CurrentAmps
CurrentAmps = 1.58 Amps
Q: How do these equations arise?
These are derivations of Onderdonk’s equation for fusing current of wires of certain thicknesses and over certain period of time in such case that there is no thermal transmission (an adiabatic situation the wire continues to heat up never losing heat to the environment). For very short periods of time, this seems a reasonable approximation.
Douglas Brooks wrote an article in Printed Circuit Design, 1998 (original source) where he explored these equations as they relate to fusing current of PCB traces and made some analysis.
Brooks’ reduction of Onderdonk’s equation (available in the PDF linked above) is:
I = 0.188 * (Area / Time0.5)
where Area is the cross sectional area measured in Square Mils
If we take a 1 second fusing time, then we can simplify to
I = 0.188 * Area
We can rearrange thusly to solve by area as follows
I = Area * 0.188
I / 0.188 = Area
“1oz” pcb copper layers are 1.4 mils thick (and 2oz is 2.8mils and so on), so if we assume a 1oz copper layer we can subsitute as…
Area = WidthMils * 1.4
I / 0.188 = WidthMils * 1.4
we can solve for the width as…
( I / 0.188 ) / 1.4 = WidthMils