The line loss increases because the eddy currents, induced by signal current on the line, dissipate into the conductive substrate. If the substrate were a perfect conductor then only the inductance of the line would be affected.

Essentially the line is magnetically coupled to the conductive substrate resulting in the eddy currents.

One interesting point is that the substrate needs to be conductive enough for the eddy currents to be appreciable before the losses due to eddy currents is noticeable. For conductivities lower than that needed for eddy currents to be significant, the loss in the substrate matters more for the capacitive coupling from the line to the lossy substrate.

I am not aware of a good reference that clearly delineates the transition from losses due to capacitive coupling to substrate versus eddy current induced into the substrate. It would be nice to see the transition as a function of the conductivity of the substrate and perhaps the line dimensions.

RFICDUDE wrote on Jun 28^th, 2010, 3:11am:



Hi rfdude,

Thanks or the reply.

I understand this now. the loss come from the magneticly induced current flowing in the lossy conducting substrate. If the substrate is totally insulating, or perfectly conducting, this loss is gone. although the perfect conducting substrate will greatly decrease the inductance of the line.

i also found a website on this.
http://bmf.ece.queensu.ca/mediawiki/index.php/Transmission_Line_Design_on_Silico...
it has a equation on this resistance, Rl. I doubt on this equation, and i calculated the value of this resistance at 10GHz, (and subsrate conductivity as 10S/m, line width of 10um), it is almost 20Mohm/m. It is so big comparing to the impedance of the inductance, which means the loss due to the substrate is omitable. I couldn't understand this.

Do you have some comments on this?

Cheers,
Jimiblues