I measured a slab of copperclad FR4 as having a capacitance tempco around +900 PPM/degC. I wonder what would be the temperature coefficient of delay for a microstrip or stripline on FR4. Not only does the dielectric constant change, but a board will expand in x/y/z too.
I guess I could measure it, which could be a nuisance.
To leading order, the effective epsilon of microstrip is (1+eps_FR4)/2. Delay is approximately proportional to the square root of that (i.e. the refractive index n), so one expects that
n ~ sqrt((1+eps))/2
You can obviously do that out at length, but for SWAG purposes, it's easier to do it numerically, with eps = 4 and d/dT(eps) = 0.0036/K.
sqrt((1+4.0036)/2)/sqrt((1+4)/2)-1 = 0.00036, i.e. 360 ppm/K.
The in-plane thermal expansion coefficient is less than this, so at this accuracy level it can probably be ignored.
Cheers
Phil Hobbs
Yeah, I guess the dimensional changes will be small compared to Er.
We're designing a test board for a picosecond instrument. If we match trace lengths to, say, 200 ps, 360 PPM of that is pretty small.
I just measured one the other day. I got 75% of that value. Nice approximation.
Thanks, it's good to pass the sanity check at least occasionally. ;)
Cheers
Phil Hobbs
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