Frequency dependent impedance calculation for microstrip

I need a hint. I'm stuck on outer layer impedance calculation for high speed design. Other PCB designers route high speed tracks on inner layers because of not controlled plating thickness on outer layers, which causes impedance variation. I went deeper and jumped into theory but can't find out if thickness at all matters (in case: skin depth < mictostrip thickness)?

Stackup:

• copper 36um
• substrate 100um
• copper 17um (plane)
• ...

For example at frequency of 2GHz the skin effect depth will be $\tilde{}1.41\mu m$

What copper thickness should be used for impedance calculations? $36\mu m$ or $1.41\mu m$?

The skin depth doesn't really have much, if anything, to do with impedance. It simply defines a loss mechanism. Note that with a thicker track, you will have marginally less skin effect losses due to a larger surface area for the track.

The impedance of microstrip is inversely proportional to the thickness of the signal track, but the difference for 0.5 oz copper and 1 oz copper is quite small, and definitely smaller than the 10% impedance variation most fabricators will guarantee.

I often use surface layers for some high speed signals as there is marginally less dielectric absorption loss as the velocity of the signal is a bit quicker (due to the effective dielectric constant being lower as half of the signal is in air, not FR-4).

Surface layers are normally plated up to 1 oz or sometimes 2 oz thicknesses. Talk to your PCB supplier to find out what they normally do.

Your stackup looks normal for 1 oz plating on the surface and 0.5 oz plane copper thickness.

36um. Impedance is SQRT(L/C). And with the thin substrate, the thickness plays a significant role for the capacitance as you can imagine.

If you want more accuracy, the characteristic impedance (see also Wikipedia) is defined as:

The L and C you understand (and you can see how that becomes frequency dependent through the jw multiplier). The R is given by DC-resistance plus skin-effect loss and is frequency dependent and G is given by dielectric loss (also frequency dependent).

Notice that skin-effect goes down with trace width and dielectric loss goes up with trace width.

When talking about skin-effect loss, also note that for higher frequencies skin-effect loss goes up also due to surface roughness... and this becomes very difficult to calculate... so your best bet may be to measure the effect. This is normally only an issue a bit above 2 GHz.

• but, SQRT(L/C) results depends on C value, capacity depends from conductor details, and conductor depends from skin depth, which depends from frequency. Sounds logic, or not? Commented Aug 10, 2015 at 12:59
• Edited the answer - did that help? Commented Aug 16, 2015 at 18:50