microstrip line on lossy ground plan?

Any one knows how to calculate the impedance of a microstrip line on the lossy ground plan? Is there any fomula?

Thanks a lot.

If you make the ground and the strip out of the same metal, the strip contributes most of the loss, and the ground only a small portion. If memory serves me correctly, it is about 90/10 split. The reason the ground has such a small influence on loss is that there is no concetrated high edge current, as there is on the strip. It is the high edge current where all the loss occurs. The current on the ground is a nice smooth Gausian-like blob, very low loss.

To get a quick number, use any good planar EM simulator. If you don't already have one handy, download the free SonnetLite (www.sonnetsoftware.com, I work for Sonnet). Complex characterisitic impedance is a default output. Just analyze a through line of the desired dimensions. To see how much of the Zo is due to lossy ground, analyze with a lossy ground, and then with a lossless ground.

If high accuracy is important, be sure to run a convergence analysis, cutting the cell size in half and re-analyzing, and repeating.

Dear yzriver:

Your results may vary depending on the type of ground plane you are using. If you use a metal ground plane (with finite loss), there are several simulators to give you such a good result.

If you are using a high conductivity substrate (like heavily doped silicon) you should take care in how you simulate this. Not all field solvers do a really good job of this. I think that that Sonnet Lite that rautio talks about could do this, but you have to make sure to make the substrate big enough so that the simulation box walls don't make an alternative return current path. If you use a 3D field solver to do this, make sure you use a high enough mesh density to resolve the conduction current in the substrate accurately.

--Max