[NLRS] looking for an equation

[JamesDuffey]

Barry - Here is an chapter from a book that treats coupling between transmission lines in general terms. Although edge-to-edge coupling is shown in one figure, the theory and math are general and apply to your broadside case as well. Sections 12.2 and 12.4 contain material pertinent to your question.

< https://www.ece.rutgers.edu/~orfanidi/ewa/ch12.pdf >

The math in the article is not overly advanced, but it is not trivial either. I suspect that this is not what you are looking for. 

These days most people solve these problems with a computational electromagnetic solver. In principle, you could model it in a NEC program such as 4NEC2. 

But I suspect that measuring it will be simplest. - Duffey

James Duffey KK6MC
Cedar Crest NM

> On Feb 7, 2020, at 18:26, Barry B <barry.w0iy at gmail.com> wrote:
> 
> I'm trying to find the formula for determining the coupling coefficient of
> Broadside coupled lines with different materials (e^r) for the line to
> ground and between the coupled lines.
> 
> For example, I have a 2 layer pcb with a z=50 trace. Taking an identical
> pcb and placing the traces to face each other, the traces would be
> "broadside" coupled (rather than "edge" coupled in most literature.  e^r
> for PCB=~4.  e^r for air (between lines)=1.
> 
> My objective is to make a graph of distance 'd' between the lines vs.
> coupling (db) with a curve for each band. To simplify this, the line length
> is arbitrarily 100mm (not really arbitrary for construction purposes). Some
> distance d will result in approx -20db of coupling.
> 
> I've been looking at lots of web pages with no luck. Will try my Dubus
> archives when I get home FROM SUNNY ORLANDO where the fest today was ONLY
> IN THE MID 60s. A far cry from the 93 we had at the BEACH on Wed. (not that
> I want to rub that in).
> 
> In a couple of weeks I'll have PCB and can experimentally determine the d
> vs. coupling, but it would be nice to have a reference which would also
> likely tell me the effect of coupling on the line Z.
> 
> I expect after this I'll be banned from the list and Tuesday night meetings.
> 
> Barry w0iy
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