Hi all,


I'm reading a book called "Signal and Power Integrity - Simplified" by Eric Bogatin, and regarding line resistance, it is calculated as (Ch 6, section 6.16, pg 199),

R_DC = ρ/wt
R_AC = ρ/wδ

where ρ is resistivity, w is line width, t is line thickness, and δ is the skin depth.

In the book, there is also a figure showing the simulated current distribution of a cross-section of a line at three different frequencies. In the figure, at high frequency, it looks like most of the current is pushed to the side walls which makes sense to me since the line is much wider than it is thick. However, according to the above formulae, it seems that the calculation assumes that the current is pushed to the top and bottom surfaces of the metal. This is obvious since the formula for R_AC includes w but not t. Can anybody explain why this is the case? The formula only makes sense to me if there is a nearby ground plane, but then the current distribution would be entirely at the bottom surface of the conductor and not how it is in the figure (6-24 on pg 198 if you have the book).


thanks,
Aaron