Impedance formula for an edge coupled differential stripline in an asymmetrical stackup?

I've been searching and have not been able to find a formula for calculating the impedance of differential lines on inner layers where the dielectric above and below it is not symmetrical. I've seen plenty of examples of symmetrical stackups, but that would not help in my case. Does anyone know what the formula would be for this? Thanks!

Edited for more information: For those that don't know, a stackup consists of all the different layers of a PCB (Printed Circuit BOard). You can have, for example, a 4 layber PCB which has individual copper material & glass epoxy stacked on top of each other. This allows the board to have more layers for routing the nets of the circuits.

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For those of us who don't know, could you tell us what a stackup is? –  Greg P Jan 14 '11 at 16:27
(I am one of those people by the way) –  Greg P Jan 14 '11 at 16:28
A stackup consists of all the different layers of a PCB (Printed Circuit BOard). You can have, for example, a 4 layber PCB which has individual copper material & glass epoxy stacked on top of each other. This allows the board to have more layers for routing the nets of the circuits. –  Dan Jan 14 '11 at 17:09
that would be good information to edit into the question itself. Also, (to anyone) would this question also fall under the [condensed-matter] tag or something like that? –  David Z Jan 14 '11 at 21:01
This is a problem of theoretical electronics, often solved by physicists :=( –  Georg Jan 25 '11 at 15:58

Of course it doesn't matter what voltage the voltage planes are held at so assume both are at ground. Now, take advantage of symmetry: assume that the voltages on the two strips are opposite. Use the same logic as with the presence of a charge near a conducting plane implies the presence (for calculation purposes) of an image charge. Therefore the problem reduces to one of determining the impedance of a single strip in a trough. I'll draw something up in paint:

You may be able to look up the impedance of the above single asymmetric stripline. If not, you can calculate it. A reference I quickly found that seems useful is:
http://lss.fnal.gov/archive/tm/TM-1270.pdf
but I bet you can find better in your electrical engineering library.

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To go further, it would be nice to know if you're trying to achieve a particular impedance (i.e. by adjusting the width of the copper traces and their spacing), or you have given dimensions and want to know the impedance of them. –  Carl Brannen Feb 1 '11 at 0:14
After much searching around, I was able to find the formula for the single stripline (in an unbalanced stackup) as Carl suggested. With this, I can plug in the numbers for the differential to get the impedance. The formulas I found were from "High-Speed Digital Design - A Handbook of Black Magic". I don't know of an easy way to add formulas, so here is a link the author of the book has that describes the book. sigcon.com/books/bookHSDD.htm Thanks for everyone's help! –  Dan Feb 1 '11 at 20:03
So why didn't you mark my answer as useful, and the correct one? –  Carl Brannen Feb 2 '11 at 1:35
How do I mark it as answered? I don't see an option for that. I tried using the up arrow, but it said I didn't have enough reputation to do that. –  Dan Feb 2 '11 at 12:34